a national discipline-specific professional …

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2011

Final Report

A NATIONAL DISCIPLINE-SPECIFIC PROFESSIONAL DEVELOPMENT PROGRAM

IN THE MATHEMATICAL SCIENCES Project leader

Leigh Wood, Macquarie University Project team

Nalini Joshi, The University of Sydney Matt Bower, Tori Vu, Macquarie University

Walter Bloom, Murdoch University Birgit Loch, Swinburne University of Technology

Diane Donovan, The University of Queensland Natalie Brown, Jane Skalicky, University of Tasmania

Author Tori Vu, Macquarie University

Support for this project has been provided by the Australian Learning and Teaching Council Limited, an initiative of the Australian Government. The views expressed in this report do not necessarily reflect the views of the Australian Learning and Teaching Council.

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ISBN 978-1-921856-90-7

2011

Effective teaching and learning in the quantitative disciplines i

Contents

Executive summary ......................................................................................................... 1 1. About the project ......................................................................................................... 2 2. Project methodology ................................................................................................... 5 3. Professional development resources .......................................................................... 9 4. Dissemination and implementation ............................................................................ 22 5. Lessons learnt for future projects .............................................................................. 24 6. Evaluation ................................................................................................................. 26 7. Summary .................................................................................................................. 28 8. References ............................................................................................................... 29 Appendix A. Professional development unit outline ....................................................... 31 Appendix B. Module 1. Introduction to teaching mathematics ....................................... 46 Appendix C. Survey on teaching experience and professional development needs ...... 57 List of tables Table 1. Standards in the Higher Education Academy Framework (HEA, 2006, p. 3) .... 11 Table 2. Domains of pedagogy within the Higher Education Academy framework

(HEA, 2006, p. 4) ............................................................................................. 11 Table 3. Indicators for each level of operation for the core knowledge domain of the

professional development framework (Brown et al., 2010, p. 138) ................... 13 Table 4. Indicators for each level of operation for the areas of activity domain of the

professional development framework (Brown et al., 2010, p. 139) ................... 14 Table 5. Indicators for each level of operation for the core values domain of the

professional development framework (Brown et al., 2010, p. 140) ................... 15 Table 6. Unit learning outcomes .................................................................................... 18 Table 7. Module learning outcomes .............................................................................. 18

Effective teaching and learning in the quantitative disciplines 1

Executive summary Quality professional development is highly successful in improving the effectiveness of teaching and learning. Mathematics education is a specialised teaching pursuit with its own forms, functions, representations and concepts; as such, it requires its own discipline-specific approach to professional development. Secondary school research indicates that professional development of teachers is an essential driving factor for improving student achievement in mathematics. Our project, supported by the Australian Mathematical Society (AustMS), is a practical response to these challenges and makes a valuable contribution to professional development practice and principles. We have aimed to improve the learning of students based on the enhancement of effective teaching through discipline-specific professional development. We have produced an accessible, practical and evidence-based program that is designed specifically for tertiary mathematics teachers. These materials were tested and refined through multiple iterations. Our project has delivered the following outcomes: • A comprehensive data set and analysis of the teaching needs of tertiary

mathematics teachers and their future professional development requirements.

• A criterion-based professional standards framework, which explicitly identifies performance indicators for teaching in order to provide clearer guidance surrounding the different responsibilities of tertiary teachers. This can be used as a model for professional standards for teaching in other disciplines.

• A professional development unit designed specifically for tertiary mathematics teachers and offered online on the AustMS website at http://www.austms.org.au/Professional+Development+Unit.

• As part of the unit: assessment tasks and marking rubrics, which are constructively aligned to the unit learning outcomes; and an online learning community, which includes a discussion board.

• A professional development workshop series for tertiary teachers of mathematics.

• Significant professional development for over 60 mathematics tertiary teachers from over 20 universities, gained through participation in workshops and a trial of the unit.

• A refereed conference paper and presentation at the 33rd Higher Education Research and Development Society of Australasia (HERDSA) Annual International Conference on the professional standards framework (Brown et al., 2010) and a refereed paper on the professional development needs of tertiary mathematics teachers (Wood et al., 2011) published in International Journal of Mathematical Education in Science and Technology for the 8th Delta conference for learning and teaching in mathematics and statistics.

Through our multi-faceted dissemination activities, we have generated stronger and broader engagement with the benefits, challenges and methods of effective teaching and learning in tertiary mathematics education. The project will continue to have impact as the team disseminates outcomes through further academic publications, presentations and production of materials. Ongoing collaboration with AustMS and continuing iterations of revising and evaluating the unit and workshop series will extend project outcomes into the future.

http://www.austms.org.au/Professional+Development+Unit�


1. About the project 1.1 Project team Leigh Wood (Macquarie University [MQ]), project leader Nalini Joshi (The University of Sydney [USyd]), deputy project leader Walter Bloom (Murdoch University [Murdoch]) Matt Bower (MQ) Natalie Brown (University of Tasmania [UTas]) Diane Donovan (The University of Queensland [UQ]) Birgit Loch (Swinburne University of Technology [Swinburne]) Jane Skalicky (UTas) Tori Vu (MQ), project manager 1.2 Acknowledgements Reference group Peter Taylor, Australian Mathematical Society [AustMS] President Michael Mitchelmore, independent evaluator Katherine Seaton, LaTrobe University, consultant Matthew Parsons, research assistant Ross Moore, AustMS, web editor Glyn Mather, MQ, editor 1.3 Project rationale Around 18,000 undergraduate students in Australian universities study a subject in the mathematical sciences1

each year (Thomas et. al., 2009). We make the assumption that academics employed to teach in mathematics programs have sufficient mathematical knowledge for their teaching – but what of their knowledge of teaching and learning?

Quality professional development has been identified as being highly successful in improving the effectiveness of teaching and learning (Elmore, 2002; Elmore & Burney, 1997; Guskey & Huberman, 1995; Hawley & Valli, 1999). Many mathematics teaching staff receive some induction in teaching and learning run at a university level. A 2008 survey of 31 Australian universities indicated that over 70 per cent of institutions require staff to engage in such a program (Goody, 2008). These programs are predominantly delivered centrally through an academic development unit (Goody, 2007). However, the content of many of these courses is largely generic, dealing with pedagogical issues common to all subjects (Luzeckyj & Badger, 2009). The challenge in the Australian context is to contextualise existing training to be relevant and meaningful for tertiary teachers in the mathematical sciences. Mathematics education is a specialised teaching pursuit with its own forms, functions, representations and concepts (Wood, 2011); as such, it requires its own discipline-specific approach to professional development. From secondary school research, professional development of teachers is accepted to be an essential driving factor for improving student achievement in mathematics (American Federation of Teachers, 2002; Hawley & Valli, 1999; Sowder, 2007). 1 Our definition of the mathematical sciences is broad and inclusive of any quantitative discipline (such as finance, mathematics, statistics, operations research, psychology). For simplicity, we will refer to this collective group as mathematics.


Internationally, there is growing interest in discipline-specific professional development practices in higher education (see Healey, 2009; Webster, Mertova & Becker, 2005). In mathematics, Paterson et al. (2011) describe a professional development intervention they implemented at the University of Auckland, where eight academics (four mathematicians and four mathematics educators) used video recordings in lectures in order to improve practice. In the United Kingdom, the Mathematics, Statistics and Operational Research subject centre of the UK Higher Education Academy offers induction courses and support for lecturers and co-ordinators of mathematics departments (Cox & Mond, 2008). In the United States, the Mathematical Association of America offers a series of professional development workshops each year for new or recent PhDs in the mathematical sciences, in which teaching and learning are addressed. Our project was developed to improve the learning of students based on the enhancement of effective teaching through discipline-specific professional development. The project represents an opportunity to revitalise mathematics education by fostering enthusiasm, inspiration and innovation for teaching and learning amongst early- and mid-career academics. The project proceeded with the support of AustMS, the national society for mathematics in Australia, which was regarded as a crucial anchor for the project by providing professional oversight and acting as a host for the program. The team was led by Leigh Wood, the Chair of the AustMS Standing Committee on Mathematics Education, with Nalini Joshi, the President of AustMS at the time of project inception, as deputy leader. 1.4 Project objectives The broad objectives of our project were to: develop a professional development program for university lecturers and tutors teaching in the mathematical sciences. To this end, the project aimed to: • summarise the literature on learning and teaching in the mathematical

sciences • survey tertiary mathematics teachers about their teaching experience and

professional development needs • develop a national professional development unit designed specifically for

tertiary mathematics teachers. 1.5 Project outcomes In brief, the outcomes of the project are as follows: • A comprehensive data set and analysis based on an Australia-wide survey of

the teaching needs of tertiary mathematics teachers and their future professional development requirements.

• A criterion-based professional standards framework, which explicitly identifies performance indicators for teaching in order to provide clearer guidance surrounding the different responsibilities of tertiary teachers. In the framework, criteria for tertiary teaching are based on three domains of pedagogy: core knowledge, areas of activity and core values. Moreover, for each of the criteria, indicators of good practice are articulated at each of the three levels of operation: teaching classes, co-ordinating units and leading programs. This can be used as a model for professional standards for teaching in other disciplines.


• A professional development unit designed specifically for tertiary teachers of mathematics. The unit is hosted on the AustMS website (http://www.austms.org.au/Professional+Development+Unit) so that materials are publicly available. However, the unit will be administered in such a way that only participants enrolled in the unit through AustMS will be able to access and submit assessment tasks. The unit provides practical, discipline-specific teaching strategies based on good practice in mathematics education. The unit is comprised of 12 modules and is aligned to the professional standards framework to focus on teaching a small section of a unit, such as a class or lecture, and the more complex role of co-ordinating a unit and a teaching team.

• As part of the unit: assessment tasks and marking rubrics, which are constructively aligned to the unit learning outcomes; and an online learning community, which includes a discussion board.

• A professional development workshop series for tertiary teachers of mathematics.

• Significant professional development for over 60 mathematics tertiary teachers from over 20 universities, gained through participation in workshops and a trial of the unit.

• A refereed conference paper and presentation at the 33rd HERDSA Annual International Conference on the professional standards framework (Brown et al., 2010) and a refereed paper on the professional development needs of tertiary mathematics teachers (Wood et al., 2011, in press) published in International Journal of Mathematical Education in Science and Technology for the 8th Delta conference for learning and teaching in mathematics and statistics.



2. Project methodology 2.1 Research methodology Our project was underpinned by an action research methodology (Haggarty & Postlethwaite, 2003), which involved a cycle of deliberative activity: planning, acting, observing and reflecting. The participative techniques and shared reflective practice proved to be an effective way of approaching a process of renewal and change in learning and teaching. It was also appropriate to the staged nature of the project (see below). The project team received input from tertiary mathematics teachers and industry representatives throughout the whole process, which significantly shaped our approaches as well as the development of the professional development materials. At each stage, the team presented progress reports to AustMS during their periodic Steering Committee and Council meetings. We incorporated the feedback received through this avenue into further development of the project strategies and outcomes. 2.2 Approach Interdisciplinary team The team represents a rich mix of expertise and disciplines within tertiary mathematics education. This diversity underpinned our approach to producing a professional development approach which is founded in evidence-based pedagogy and its specific applications to the tertiary mathematics teaching in a contemporary environment. This approach allowed us to differentiate our offering as discipline-specific professional development, as compared to the generic offerings in Australian universities. The team was comprised of: • Leigh Wood (MQ) is the Associate Dean, Learning and Teaching, in the

Faculty of Business and Economics, and is the Chair of the Standing Committee on Mathematics Education of AustMS.

• Nalini Joshi (USyd) was the Head of School of Mathematics and Statistics, and is the immediate Past President of AustMS (2008-2010).

• Walter Bloom (Murdoch), for the duration of the project, was the Head of School of Chemical and Mathematical Sciences and a member of the Standing Committee for Mathematics Education of AustMS.

• Natalie Brown (UTas) is the Co-Head of the Centre for the Advancement of Learning and Teaching, and leads staff academic development; she has a background in mathematics and science education.

• Matt Bower (MQ) works in the School of Education, particularly in the area of information and communication technology, and has a background in actuarial and quantitative analysis.

• Diane Donovan (UQ) works in the School of Mathematics and Physics, and is also a member of the Standing Committee on Mathematics Education of AustMS.

• Birgit Loch (Swinburne) works in the School of Engineering and Industrial Sciences and has a strong focus on the use of technology for learning and teaching in mathematics.

• Jane Skalicky (UTas) also works at the Centre for the Advancement of Learning and Teaching, dealing with staff academic development, and has a


background in mathematics education. Project management A blended communications strategy was used to facilitate the changing needs and geographical diversity of the project team. Monthly team meetings via web- and teleconferencing and intensive face-to-face meetings over two or three days were held throughout the project. A team-based website was established for document sharing, collaborative authoring and, in the later stages of the project, functioned as a mock-up for the professional development unit. A significant amount of time was dedicated to clarifying critical project terms, objectives and strategies. An agreed understanding was essential for effective communication within the team and with external stakeholders. Throughout the project, tasks were divided and distributed amongst the team using the buddy system, in which team members work in pairs or trios on a specified task. With each iteration of the action research approach, progress against task was reviewed by alternate sets of buddies to maximise cross-fertilisation of ideas and expertise. 2.3 Project plan Stage 1A: July – December, 2009 • The project team met face-to-face and via teleconferences to define and

refine the detail of the project and its methodology. • We employed a project manager. • We initiated a literature search on professional development, both generic and

discipline specific, in higher education. • The project leadership briefed members of AustMS at their annual meeting

about the project. • Queensland-based team members began to organise a professional

development workshop attached to the 2010 AustMS annual meeting in Brisbane to trial and disseminate project materials.

Stage 1B: January – June, 2010 • We designed and distributed an online survey to university teachers of

mathematics and statistics from around Australia to identify their teaching experiences and professional development needs.

• We developed a criterion-based professional development framework to provide the structure for a professional development program.

• We designed an outline of a professional development unit for tertiary mathematics teachers, informed by the survey findings and structured by the professional development framework.

• We devised a distributed work package for developing the unit, based on the buddy system (in which team members worked in pairs or trios on a specified task).

• Planning for the workshop at the AustMS annual meeting continued in earnest.

• We contracted an independent evaluator, who began formative evaluation of


the project (see Section 6.1 for more detail). Stage 2A: July – December, 2010 • We held a two-day professional development workshop at The University of

Queensland in September, in conjunction with the 2010 AustMS Annual Meeting. We presented selections from the learning modules at workshop sessions and received valuable feedback from 65 participants from over 20 institutions and with a range of teaching responsibilities.

• We continued to refine the unit learning modules based on feedback from the workshop; and to develop the delivery aspects of the unit, such as assessment, privacy and the online learning community.

• We developed a mock-up of the online learning platform for the unit to experiment with functions such as embedding media, facilitating discussion boards and general layout for each module and the whole unit.

• We submitted a proposal to AustMS regarding a long-term model of delivery for offering the professional development program as part of a teaching accreditation.

Stage 2B: January – August, 2011 • We ran a pilot of the unit from February to May with eight participants from six

institutions around Australia. The unit was hosted and completed on the AustMS website www.austms.org.au/Professional+Development+Unit.

• We made our final revisions to the materials and delivery aspects, using comprehensive feedback from participants and with the assistance of a consultant.

• We continued to disseminate materials and strategies, finalise handover of the program to AustMS and plan another workshop at the 2011 AustMS Annual Meeting at the University of Wollongong, NSW, in September.

• We prepared the final report for distribution to the ALTC, AustMS, and other key stakeholders.

2.3 Reference group The reference group was made up of representatives from academic and industry associations across multiple disciplines. They were regularly consulted on project activities and outcomes, and gave us feedback on project materials, particularly the professional standards framework, learning modules, and proposed accreditation models. They also provided input on the needs of teaching staff in service disciplines and the importance of offering practical applications of pedagogy when teaching with quantitative methods. Their evaluation and guidance has assisted the team with refining the project materials and improving their utility and accessibility for a variety of stakeholders. The project reference group members were: • Judy Anderson, Australian Association of Mathematics Teachers • Jim Denier, The University of Adelaide • Mike Donnelly, Australian Business Deans Council • Peter Petocz, Statistics Society of Australia



• David Robinson, Engineers Australia • Jo Ward, Australian Science Deans Council • Alison Wolff, AustMS. 2.4 Independent evaluator An evaluator, Michael Mitchelmore, formerly the Director of the Centre for Research in Mathematics and Science Education at Macquarie University, was appointed in May 2010. He provided formative and summative appraisal throughout the project; attending project activities, such as the workshop, and regularly reviewing materials and strategies for dissemination and implementation.


3. Professional development resources 3.1 Needs analysis It was important to gain insight into the experience of academics teaching in the mathematical sciences in Australian universities in order to understand their perceptions of challenges and solutions. We undertook a comprehensive survey in February 2010 about their teaching needs and their future professional development requirements. The survey design was based on a review of the literature and incorporated a mixed methods approach in order to acquire both quantitative and qualitative data (see Appendix 1 for the questionnaire). It consisted primarily of closed questions, plus several open-ended questions that were designed to gauge respondents’ opinions without imposing our preconceptions on them. The first section of the questionnaire gathered demographic and situational information about the respondents’ current role/s (e.g. tutor, lecturer, unit co-ordinator, head of department); and about their teaching conditions, such as the level of students they taught, the size of classes and the technological tools available in teaching spaces. The second part of the survey related to the extent of prior professional development and their views on future professional development needs. Specific focus areas of these latter questions included what learning and teaching challenges they believe are faced by early-career teachers; and which topics they think should be covered in a professional development unit for tertiary mathematics teachers. For the full list of questions in the survey, see Appendix C. An invitation to all academics and PhD candidates in mathematics departments and schools in Australian universities was distributed via Heads of departments and schools at each university. The survey was completed online by 111 respondents in total. The respondents included lecturers, tutors, unit co-ordinators, heads of departments, PhD candidates and research fellows; however, because the responses were anonymous we do not know how many universities were represented. We categorised and analysed the responses according to respondents’ role/s. The results of this national survey highlight the diverse needs of different academic roles and enable a deeper understanding of the specific challenges confronting teachers at the coalface. The teaching and learning challenges most commonly cited by respondents included: online learning platforms and changing modes of student learning; large class sizes; engaging service students in mathematics; lack of teacher training and/or experience; balancing teaching responsibilities and research; diverse student populations; variation in student preparedness in mathematics; and lack of mentoring/support from supervisors or senior colleagues. In relation to their professional development needs in regards to technology, respondents specified they would like further training in using SMART boards, pen-enabled screens, tablet PCs, video and screen recording. The survey revealed that, for instance, tutors mainly teach first year students as opposed to honours or postgraduate students, and thus require support for teaching entry-level and service-course mathematics. The need for enhancing support for all academics was a persistent theme across the study and tutors in particular felt that they had limited access to human guidance (such as supervision, evaluation, peer support) to assist in dealing with specific teaching challenges.


A surprising result was that only a minority of the participants in the survey had completed any studies in tertiary teaching beyond their initial induction – in fact, for most tutors a short induction was the most they had received in terms of training – which indicates there is indeed a gap to fill within academics’ professional learning pathways. Where more formal programs had been completed, a majority indicated that it would have been beneficial if courses had been more focused on the mathematical sciences. Preferences for face-to-face or online delivery of a professional development program varied. The results of the survey also highlighted the importance of developing soft skills, such as communication and management capabilities, in order to be an effective teacher in the mathematical sciences; the major challenges identified included addressing the negative attitudes of students, balancing research and teaching time, and methods of managing large classes. The survey confirmed the need for more formal, discipline-specific professional training for mathematics educators to address the issues raised by respondents. It also confirmed the importance of the professional development of tutors, even where they are not permanent staff members, since they can have a significant impact on student learning. The findings from the survey were used to design the overall professional development framework and program described below. The identification of needs, as disaggregated by teaching role, was fundamental to tailoring our resources to early- and mid-career university teachers. A full discussion of our findings will be published in the International Journal of Mathematical Education in Science and Technology (Wood et al., 2011, in press). We intend to use this valuable data set in future initiatives on mathematics education and professional development. 3.2 Standards for professional development A critical step in developing evidence-based curricula for our professional development program was to clearly articulate good practice in teaching. We have developed a criterion-based framework which explicitly identifies performance indicators relating to the knowledge, practice and values that apply at different levels of operation. The framework is generic in terms of its overall design, but incorporates disciplinarity to enable application to a range of learning domains. A full discussion was presented by a team member at the HERDSA Conference in 2010 and published in Research and Development in Higher Education: Reshaping Higher Education (Brown et al., 2010). Our approach − to build from a generic model and adapt to a specific discipline − has been a deliberate one to acknowledge the considerable body of evidence already in existence about quality teaching in higher education. More specifically, our framework is based on the Professional Standards Framework for teaching and supporting learning in higher education, released by the Higher Education Academy (HEA) in the UK (HEA, 2006). This is a contemporary and internationally recognised framework that has been adapted by several institutions to inform professional development, guide teaching practice and facilitate annual reviews (e.g. Durham University, 2009; University of East London, 2008; University of Western Australia, 2009). The HEA professional standards framework is based on three standard descriptors to reflect the different roles and career stages of those working in learning and teaching in the higher education sector (see Table 1). The first is aimed at early-career, teaching academics; the second at those with substantial teaching roles; and the third at those experienced teaching academics who have moved into mentoring and leadership.


Table 1. Standards in the Higher Education Academy framework (HEA, 2006, p. 3)

STANDARD DESCRIPTOR EXAMPLES OF STAFF GROUPS 1. Demonstrates an understanding of the student learning experience through engagement with at least 2 of the 6 areas of activity, appropriate core knowledge and professional values; the ability to engage in practices related to those areas of activity; the ability to incorporate research, scholarship and/or professional practice into those activities

Postgraduate teaching assistants, staff new to higher education teaching with no prior qualification or experience, staff whose professional role includes a small range of teaching and learning support activity.

2. Demonstrates an understanding of the student learning experience through engagement with all areas of activity, core knowledge and professional values; the ability to engage in practices related to all areas of activity; the ability to incorporate research, scholarship and/or professional practice into those activities

Staff who have a substantive role in learning and teaching to enhance the student experience.

3. Supports and promotes student learning in all areas of activity, core knowledge and professional values through mentoring and leading individuals and/or teams; incorporates research, scholarship and/or professional practice into those activities.

Experienced staff who have an established track record in promoting and mentoring colleagues in learning and teaching to enhance the student learning experience.

Underpinning each of these standards are three domains of pedagogy: professional activity, core knowledge and professional values, each comprising individual elements. Table 2. Domains of pedagogy within the Higher Education Academy framework (HEA, 2006, p. 4)

CORE KNOWLEDGE AREAS OF ACTIVITY PROFESSIONAL VALUES

1. The subject material 1. Design and planning of learning activities and/or programs of study

1. Respect for individual learners

2. Appropriate methods for teaching and learning in the subject area and at the level of the academic program

2. Teaching and/or supporting student learning

2. Commitment to incorporating the process and outcomes of relevant research, scholarship and/or professional practice

3. How students learn, both generally and in the subject

3. Assessment and giving feedback to learners

3. Commitment to development of learning communities

4. The use of appropriate learning technologies

4. Developing effective environments and student support and guidance

4. Commitment to encouraging participation in higher education, acknowledging diversity and promoting equality of opportunity

5. Methods for evaluating the effectiveness of teaching

5. Integration of scholarship, research and professional activities with teaching and supporting learning

5. Commitment to continuing professional development and evaluation of practice

6. The implications of quality assurance and enhancement for professional practice

6. Evaluation of practice and continuing professional development

Our framework (Tables 3-5) is outlined below. Criteria for tertiary teaching are


based on three domains of pedagogy (core knowledge [Table 3], areas of activity [Table 4] and core values [Table 5]), reflecting those adopted by the HEA (2006). Each of the three domains specified in the framework are broken into criteria drawn from the work of the HEA (Tables 1-2). Our framework differs significantly from the HEA framework and its derivatives. Building on the examples of staff groups for each standard of the HEA framework, we have specifically identified three levels of operation: teaching classes, co-ordinating units and leading programs. Moreover, we have articulated indicators of good practice for each of the criteria at each of these three levels of operation (listed as bullet points in Tables 3-5). Our framework aims to provide clearer guidance surrounding the different responsibilities of tertiary educators. In this way, teachers of classes, co-ordinators of units and leaders of programs may more accurately interpret and apply the general domains and criteria of the professional standards framework. We have further developed the HEA framework by adding another core value (or HEA’s “professional value”), ‘advancement of the discipline’ (see Table 5), to the existing core values in the original HEA framework. This reflects the shared purpose (Elmore, 2002) and core responsibility of tertiary educators to promote a genuine passion for their field of study, relevant to the discipline. In mathematics, promoting the field can strengthen its reputation and potentially its utility. Moreover, ‘better and more inspirational teaching’ has been recognised as a way to achieve advancement of the mathematics discipline (Cox & Mond, 2008, p. 7). This core value can be broadly adopted by other disciplines. Core knowledge (see Table 3) and core values (Table 4) underpin areas of activity (Table 5), aligning with other professional development models that base practice upon understanding and belief systems. The framework provides an often direct correspondence between core knowledge and areas of activity to highlight the links between knowledge and practice. For instance, core knowledge area 1 ‘The subject material’ directly informs areas of activity 1 ‘Design and planning of learning activities and/programs of study’. Some core values are directly related to areas of activity, for example core value 3 ‘Commitment to incorporating the process and outcomes of relevant research, scholarship and/or professional practice’ directly underpins area of activity 5 ‘Integration of scholarship, research and professional activities with teaching and supporting learning’. However there are also core values that relate to more than one area of activity, an example being core value 5 ‘Respect for individual learners’ that directly informs area of activity 1, 2, 3, and 4. This highlights the influence of belief systems upon teaching practice. The framework has been designed to be generally applicable to teaching in a range of fields. However, the model still attends to discipline-specific learning constructs and teaching processes by identifying these for each of the different levels of operation. For instance, core knowledge area 2 for Teaching classes explicitly acknowledges that there will be different approaches to communication, depending on the discipline in question. In this way the framework can be adapted for use in a range of fields. Our framework emphasises a research-based approach to teaching by incorporating areas of scholarship and reflective practice in all three dimensions. For instance Trigwell’s (n.d.) knowledge of teaching and learning, reflection on teaching and learning, communication of ideas and activities, and conception of teaching and learning are all integrated in the framework to promote a research-driven approach to teacher development. With the inclusion of design, practice,


theory and attitude elements, the framework also attends to all four areas of professional development that Cox (2004) proposed as requirements for university teachers of mathematics. Table 3: Indicators for each level of operation for the core knowledge domain of the professional development framework (Brown et al., 2010, p. 138)

CORE KNOWLEDGE

Teaching classes Co-ordinating units Leading programs

1. The subject material

• Unit content • Prerequisite

knowledge • Applications of unit

content

• The purpose of the unit

• How concepts in the unit relate to other units across and within year levels

• History of concepts in the unit

• Applications of the concepts in the unit

• External content requirements for professional bodies, accreditation

• Connections between discipline and other areas in the university

• Currency with trends in discipline area

2. Appropriate methods for teaching and learning in the subject area and at the level of the academic program

• Ways of communicating in the discipline

• Different approaches to explaining concepts

• Different approaches and techniques for solving problems

• Structuring the unit • Designing and

developing teaching activities and resources to align with learning outcomes

• Adapting materials for different learners

• Strategies for teaching large and small classes

• Current teaching practices in the field

• Teaching approaches being used across the program to support course level outcomes

3. How students learn, both generally and in the subject

• Contemporary learning theory

• How to differentiate teaching depending on student background and context

• How to cater to different learning styles

• Engagement and scaffolding

• Providing opportunities for students to engage with the unit content in different ways

• Sequencing the curriculum content to support development of learning outcomes

• Implications of students’ discipline backgrounds

• Contemporary learning theory in the discipline area

• Methods of structuring and sequencing of content across a program to enable appropriate development of concepts over a degree program

• Cognitive maturity of students

4. The use of appropriate learning technologies

• Available teaching technologies and how to use them

• LMS unit development and design skills

• How technologies can be used to represent concepts and facilitate collaboration to effectively achieve

• Available technologies for application in the discipline

• Emerging technologies for learning and teaching

• Trends in


learning outcomes • Electronic

assignment submission and marking approaches

• Supporting technology use by teaching staff

technology usage in discipline-specific research

5. Methods for evaluating the effectiveness of teaching

• Different approaches to collecting and analysing evidence about teaching and student learning

• Different approaches to collecting evidence about unit level student outcomes

• Approaches to analysing effectiveness of the unit

• Approaches to program evaluation at institutional and national levels

6. The implications of quality assurance and enhancement for professional practice

• University policies relating to teaching

• Professional development to improve classroom practice

• Institutional requirements

• Professional development to improve unit development and implementation

• National trends and policies

• Communities of practice for benchmarking

Table 4: Indicators for each level of operation for the areas of activity domain of the professional development framework (Brown et al., 2010, p. 139)

AREAS OF ACTIVITY

Teaching classes Coordinating units Leading programs

1. Design and planning of learning activities and/or programs of study

• Designing and planning classes

• Structuring the class and the teaching activities

• Constructive alignment of unit

• Liaising with relevant stakeholders

• Writing unit outlines • Selecting texts and

resources • Including a range of

learning activities and resources

• Determining course level learning outcomes

• Mapping program curricula

• Mapping graduate attributes

• Differentiating curriculum depending on stage in program

• Determining appropriate division of content and student workload between units

2. Teaching and/or supporting student learning

• Effective communication

• Encouraging participation and interaction

• Considering student diversity

• Creating a culture of inquiry

• Incorporating a range of strategies for teaching in small

• Leading and managing small teaching teams

• Ensuring there are appropriate channels of feedback and support for students

• Incorporating a range of strategies for teaching large groups

• Providing support and guidance for teaching teams to support effective practice

• Providing appropriate structures to support students

• Encouraging and providing for professional development of staff to improve teaching


groups • Giving students

opportunities to engage with feedback and reflect on their work

and learning • Encouraging and

modelling appropriate use of learning technologies

3. Assessment and giving feedback to learners

• Using different types of assessment

• Providing effective and timely feedback to individuals

• Designing effective and aligned assessment tasks

• Employing a range of assessment tasks

• Providing clear instructions and marking criteria

• Moderating between markers

• Ensuring appropriate variety and balance of assessment tasks across the program

• Calibrating levels of difficulty between units

• Leading the implementation of current assessment practices

4. Developing effective environments and student support and guidance

• Creating a positive culture in the classroom

• Engaging students • Encouraging student

interaction

• Providing support and guidance to tutors

• Facilitating student interaction in the unit

• Implementing avenues of unit-wide student support

• Providing program level support for students

• Employing, training and supporting teaching staff (including sessionals)

5. Integration of scholarship, research and professional activities with teaching and supporting learning

• Using tertiary teaching literature to inform classroom practice

• Integrating own and others’ research into teaching

• Using current learning and teaching research to inform curriculum design

• Conducting and encouraging research-based approaches to learning and teaching

6. Evaluation of practice and continuing professional development

• Collecting evidence to evaluate teaching

• Analysing and reflecting on collected data

• Undertaking relevant professional development

• Collecting data from a variety of sources to enable critical reflection upon unit

• Reflecting upon performance based on analysis of unit data

• Engaging relevant professional development to improve unit

• Managing and monitoring programs based on feedback

• Supporting professional development of departmental staff

• Contributing to professional bodies and communities of practice

Table 5: Indicators for each level of operation for the core values domain of the professional development framework (Brown et al., 2010, p. 140)

CORE VALUES

Teaching classes Coordinating units Leading programs

1. Respect for individual learners

• Developing a supportive and inclusive learning environment

• Demonstrating inter-cultural competence

• Planning for students with differing backgrounds and future pathways

• Providing accessible resources

• Choosing inclusive texts and learning examples

• Identifying and nurturing high achieving students

• Leading by example - demonstrating inclusive practice with students and staff

• Providing opportunities and pathways for high achieving students

2. Advancement

• Instilling enthusiasm for the discipline

• Raising awareness of opportunities for

• Providing opportunities for


of the discipline

amongst students students to participate in discipline activities

students to participate in discipline activities such as seminars and summer programs

3. Commitment to incorporating the process and outcomes of relevant research, scholarship and/or professional practice

• Valuing the use of discipline-specific education theory in teaching practices

• Sourcing and sharing relevant discipline-specific knowledge and teaching and learning research with members of the teaching team

• Leading the integration of educational research into learning and teaching across the department

• Setting up conditions for learning and teaching research that could contribute to the literature

4. Commitment to development of learning communities

• Creating and participating in learning and teaching communities

• Collaborating with unit co-ordinator and colleagues

• Facilitating collaboration between teaching staff

• Facilitating and participating in peer observation and review

• Leading the implementation of policies that support learning and teaching collaborations

• Leading and encouraging participation in learning and teaching communities

5. Commitment to encouraging participation in higher education, acknowledging diversity and promoting equality of opportunity

• Directing students to support and resources

• Monitoring student progress

• Negotiating support or alternative pathways for students at risk

• Planning, implementing and raising awareness of study pathways and resources for students from a diversity of backgrounds

6. Commitment to continuing professional development and evaluation of practice

• Engaging in reflective practice

• Seeking opportunities for professional development

• Seeking opportunities for professional development for self and members of team

• Creating opportunities for professional development across the department

• Promoting a scholarly approach to learning and teaching

3.3 Professional development unit Our professional development unit www.austms.org.au/Professional+Development+Unit provides discipline-specific approaches and strategies for teaching mathematics. The modules contain a mixture of practical strategies for teaching mathematics founded in education theory, as well as short activities and multimedia resources. In terms of workload and learning outcomes, the 12-week unit is equivalent to a one unit of a Graduate Certificate/Diploma in Higher Education. The unit is hosted on the AustMS website so that materials are publicly available for use by other institutions and associations. However, only participants enrolled in the unit through AustMS will be able to access, submit and receive marks for assessment tasks. Following the argument of the Australian Science Teachers Association (2002) that ‘an effective professional development system needs clarity about the areas in which teachers should improve’ (p. 6), the design of our professional development unit was informed by the survey findings and centred on our criterion-based professional standards framework.



Recognising that tertiary teachers have different needs based on their roles (tutors and lecturers, unit co-ordinators), our unit follows a linear structure. The modules are intended to be completed in order, from 1 to 12. The first seven modules are targeted at teaching a small section of a unit, such as a class or lecture (Teaching classes: Modules 1-7), and the next five modules are directed to the more complex role of co-ordinating a unit and a teaching team (Co-ordinating units: Modules 8-12). The learning outcomes for the unit also reflect the differentiated responsibilities and knowledge required in various teaching roles. We have developed a glossary to help explain possibly unfamiliar terms, and the terms have been put in a mathematical context. The intended learning outcomes for the unit and each module are based on criteria in our professional standards framework (Tables 3-5 above). The criteria were mapped out across the curriculum to ensure that each criterion is addressed in at least one module. We have modelled good practice in constructive alignment by designing the unit so that assessment tasks are aligned with intended learning outcomes, and learning and teaching activities are designed to provide opportunities for students to meet these learning outcomes. A unit overview, comprising a full list of modules and learning outcomes, is represented in Table 6 below. We have attempted to address the teaching challenges identified by the survey respondents, such as technology and service teaching. For example, development of Module 5 ‘Teaching in service units’ was based on our findings as well as being recommended by the reference group; this module covers different ways of engaging service students through increasing students’ understanding of the relevance of mathematics to their degree and career, and by assessing their prior knowledge of mathematics. Another example of building directly on the survey findings is the design of Module 11 ‘Developing learning communities’, which emphasises the role of online learning tools and how they can be used to enhance instruction. The unit also addresses soft skills such as communication, especially with large classes, which were also identified as areas of need in the survey. For example, Module 4 ‘Conducting lessons’ addresses how to establish two-way respectful relationships in small to large lectures and tutorials, and how to engage students with different learning styles. Module 9 ‘Managing units’ further identifies ways of co-ordinating communication with students, tutors and other stakeholders in a unit. The issues of technology, service teaching and communication addressed in these discrete modules are also integrated throughout the unit. The unit includes three assessment tasks, which must be completed by those enrolled in the unit in order to receive recognition of their participation. The assessment tasks are constructively aligned to the unit learning outcomes. We designed these tasks so that they could be related directly to each participant’s teaching situation. That is, the assessment component has been designed in a way that allows participants to use the output in their current teaching load or teaching portfolio. Examples of such practical assessment tasks include writing an annotated teaching sequence, a unit outline and a summative assessment task. The three assessment tasks are to be submitted online by participants and assessed by the unit convenor according to the marking rubrics that we have developed. Based on their marks, participants will receive a graded pass for the unit. Each module takes approximately three hours to complete, with three assessment tasks staged throughout the unit. Participants are free to complete


the unit at their own pace, although they must comply with the assessment schedule. We have endeavoured to provide both the convenience of self-paced online engagement and the personal engagement of a peer learning environment. (Survey respondents indicated they preferred a mix of online and face-to-face delivery of a professional development unit.) Participants engage in an online learning community and are asked to contribute responses to tasks in each module on an online discussion board, which is moderated by the unit convenor. Participants are linked up with a ‘buddy’ (another participant in the unit) with whom they discuss their progress and any queries at least once a week during the unit. For more detail on the unit, see Appendix A. For a sample of the unit, Module 1 ‘Introduction to teaching mathematics’, see Appendix B. Table 6. Unit learning outcomes

Unit learning outcomes

Part 1: Teaching classes • Demonstrate an enthusiasm for the discipline of mathematics and a commitment to develop a student learning community that is respectful of the individual learner

• Use knowledge of the discipline and how students learn (both generally and in the discipline) to select appropriate teaching and learning activities for mathematics classes

• Develop a repertoire of strategies to create positive learning environments that are supportive and engaging, and that allows students to gain feedback to enhance their learning

• Evaluate and reflect on effectiveness of teaching through collection of evidence about student learning and student engagement.

Part 2: Coordinating units • Develop cohort-building strategies to manage units, to support and guide tutors in their role, and to encourage students to connect with the discipline

• Use knowledge of discipline and graduate attributes, how students learn, and students’ prior experience to design units where the learning outcomes, teaching activities and assessment are constructively aligned

• Evaluate units through the systematic collection of evidence, and analysis of this evidence from multiple perspectives.

Table 7. Module learning outcomes

Module learning outcomes

Part 1: Teaching classes

1. Introduction to teaching mathematics

• Explain perspectives of teaching mathematics at university • Describe the variety that may exist within the student body you

teach • Explain the importance of instilling a passion for mathematics

in students. 2. Models of mathematical

learning • Explain different learning theories as they relate to

mathematics • Describe different approaches to mathematics learning and

how they can inform your mathematics teaching • Outline different learning styles and describe ways in which

your teaching may be adjusted to cater to them. 3. Planning and designing

lessons • Explain the importance of consolidating background knowledge

as the foundation for generating new understanding of mathematical concepts, and to develop techniques for higher


order mathematical thinking. • Identify relevant mathematical skills and concepts in proposed

lesson content, and be able to signal and enhance these during learning activities.

• Place new mathematical knowledge in both a broader context and a student-meaningful real world context.

4. Conducting lessons • Encourage enquiring minds as opposed to delivering a suite of mathematical facts

• Effectively communicate with both large and small classes • Utilise a range of teaching strategies to help students achieve

learning outcomes • Implement a range of technological options for unit and session

facilitation, and describe how each of them can contribute to effective teaching.

5. Teaching in service units • Understand the importance of service teaching for mathematics and statistics

• Explain how the needs and expectations of service unit students differ from those enrolled in degree programs in the mathematical sciences

• Identify the main teaching strategies for service units in mathematics and statistics

• Apply these strategies to cater to and effectively engage students in service units

• Celebrate the opportunity to engage with cross-disciplinary ideas and methods in mathematics and statistics.

6. Assessing students in classes

• Design learning and formative assessment tasks to check whether the learning objectives of a class have been met

• Adjust learning activities on the basis of formative assessment results

• Design effective and efficient feedback to students in classes. 7. Collecting evidence about

teaching • Describe how critical reflection can be used to enhance

teaching and learning outcomes • Plan and implement activities to obtain feedback from the

students, yourself, peers and the literature in relation to your teaching and learning practice

• Critically reflect on your teaching and learning practice • Collate feedback as part of a professional teaching practice

portfolio

Part 2: Coordinating units 8. Planning and designing

units • Develop a unit that incorporates purposeful student learning

outcomes, learning activities and assessment tasks based on integration of information pertaining to student background, course curricula, and the broader learning context

• Write a unit outline that reflects the best practice in unit design. 9. Managing units • Effectively manage and communicate with students, tutors and

other stakeholders in a unit • Organise and utilise resources and conduct procedures to

facilitate effective learning and efficient implementation of your unit.

10. Assessing students in units

• Compare and contrast a range of assessment strategies and approaches

• Design and implement effective assessment strategies in mathematical units, including writing rubrics and marking guidelines

• Describe strategies to make mathematics assessment accessible, equitable, valid and reliable.

11. Developing learning communities

• Describe attributes of positive learning communities and outline strategies that can be used to create them

• Explain how different technologies can be used to facilitate interaction and collaboration between students.

12. Evaluating units • Explain why units should be evaluated and how this aligns with


your obligations for unit evaluation within the Quality Assurance framework at your university.

• Identify and collect evidence that can be used to evaluate a unit, and outline how this evidence may be used to enhance a unit.

• Apply the principles of Action Research to plan for a small-scale intervention aimed at enhancing teaching in your unit, or a unit into which you teach.

• Become familiar with sources of research into undergraduate teaching of mathematics and professional development that both informs your practice and gives you an opportunity to share your practice with your peers.

We ran a pilot of the unit between February and May 2011, with eight participants from six institutions around Australia. The participants ranged from PhD candidates to Associate Professors. This was an opportunity to trial not just the content of the unit, but aspects of delivery such as usage of the discussion board, grading assessments, general administration and maintenance, and the actual time commitment demanded by the unit. The participants completed the unit in full and gave comprehensive feedback throughout. After each module, participants were asked to evaluate the module’s content and delivery; in addition participants were asked to detail their initial expectations of the unit and their overall evaluation of the value and quality of the unit. We incorporated this constructive feedback into the final review and revision of modules, assessment, online learning community and unit outline. For example, we revised the assessment tasks to reflect the responsibilities of tutors, based on participants’ comments such as: “As a tutor the first part of the assessment task was challenging for me, maybe in future you could have two options for task 2, one designing our own material and the other critiquing existing material”. In response to participants’ comments such as: “Modules 1 [Introduction to teaching mathematics] and 2 [Models of mathematics learning] were fairly abstract in nature and were more about general teaching philosophy. I felt that they could have been applied a bit more directly to mathematics in particular”, we have added clear references throughout each module which identify the links between the educational theory explained in Modules 1 and 2 and practical mathematical teaching strategies and examples in later modules. This concluded the final iteration in our project’s action research methodology cycle. The feedback from the pilot indicates that the unit has provided excellent professional development to the participants. As can be expected from a group representing a diversity of teaching responsibilities, each of the participants found different aspects of the unit valuable; some indicated that the most useful modules were those that explored the theories and bigger picture of mathematics education; others highlighted the modules that focused on practical details and strategies of teaching. Participants commented: • It has helped me make concrete a lot of "theory", and to analyse what I do

and why I do it. It has confirmed for me what is good about good practice, and given me a few things to think about doing differently. Or a different way to understand things I already do.

• The unit has exposed me to different theories about how students learn and highlighted the importance of reflection on your teaching. Overall, I think it will result in me giving more consideration to how I go about my teaching.

• Definitely more aware of my teaching and learning of students. The realisation that other academics are teaching “because that's the way we've always done it", is really a poor excuse of not wanting to change as it would create more work for themselves. It goes back to personal development. To be a good


teacher, you do need to be flexible, adaptable and [have] an awareness of students' learning and expectations.

• If you do this unit, I think that one's teaching will improve … This is also excellent as it is discipline based [maths], where teaching and learning is very different from generic courses.

• The unit has exposed me to different theories about how students learn and highlighted the importance of reflection on your teaching. Overall, I think it will result in me giving more consideration to how I go about my teaching.

• While this course may not immediately affect what I do in the classroom it has given me much to think about. I intend to continue to follow up on the readings especially with respect [to] online tools … it has contributed to my development as a teacher.

• It's made me revisit my Grad. Dip. Ed. work (educational theories etc) which is good. It has also reminded me to think more about my planning and teaching.

• It made me read and think about educational theories which I hadn't studied for the best part of 20 years.

• I have been pleasantly surprised that the focus hasn't been entirely on lecture/tutorial format while at the same time acknowledging that this is still a dominant format. My expectations were to be challenged about my current approaches to teaching and especially with respect to online teaching this has occurred.

• Realise what students feel and definitely have more empathy in my marking. • I enjoyed all of the units … they talked about the big picture of "teaching" …

and areas [on learning communities and evaluating teaching] where I felt my knowledge is not at all up-to-date … I intend to be revisiting these modules for some time to come.


4. Dissemination and implementation 4.1 Workshops The direct participation of tertiary mathematics teachers in using the professional development resources has informed the design and refinement of learning modules and unit delivery. The team held a two-day workshop ‘Effective teaching and learning in the quantitative disciplines’ in September 2010 to engage teachers and invite their feedback on the project. The workshop was held in conjunction with the 54th Annual Meeting of AustMS at UQ, Brisbane, which enabled those who were attending the Annual Meeting to also attend the workshop. Sixty-five participants, including PhD students and senior academics, from around 20 universities attended. The workshop featured two plenaries as well as interactive sessions on lesson and unit planning, assessment, planning your career, evidence-based teaching, service teaching and educational technologies. The workshop was facilitated by team members who explained the project and presented sections of the learning modules, and then worked closely with participants to investigate the usability and applicability of materials. Staff from the host university, UQ, actively contributed to facilitating the workshop, by running several sessions and demonstrating their teaching spaces and programs, and a UQ graduate delivered a plenary. The 2010 workshop proceedings, including the timetable, session abstracts and presenter biographies can be found on the AustMS website: http://www.austms.org.au/ALTC+Workshop+2010. We are holding another workshop at the University of Wollongong, in conjunction with the 55th Annual Meeting of AustMS in September 2011. Sessions will cover first year experience, peer review, service teaching, educational technologies, threshold concepts and assessment. The workshop facilitators − from The University of Auckland, LaTrobe University, MQ, Murdoch, USyd and University of Newcastle − represent a sample of those interested in continuing to further quality teaching in the quantitative disciplines. We are in discussions with AustMS to ensure these workshops will become a regular event associated with each annual meeting. Staging the workshop each year is critical to building capability across the higher education sector as the AustMS meeting moves around Australia and different universities take ownership of the professional development process. Workshops such as these play a crucial role in developing a community of practice and fostering enthusiasm, inspiration and innovation, when they are linked to focused knowledge on best-practice teaching. Many participants said they were enthused by the opportunity to engage with similarly passionate colleagues committed to teaching and learning in mathematics and statistics. Participants indicated they would attend future events and would also recommend the workshop to their colleagues. Participant feedback after the workshop included: • The most valuable thing was discussing these issues within the discipline (so

much more common ground). • Such a variety of ways to engage students online! • You’re never too old to learn more. • I need to become familiar with more technology so I’m not left behind!!!

http://www.austms.org.au/ALTC+Workshop+2010�


• I will consider materials in different styles, rather than providing more. • I will challenge the way I do things more! I will look at the research literature

more closely to inform my practice because it is time to move forward.

4.2 Presentations and academic papers • Dr Brown presented a refereed conference paper (Brown et. al., 2010) on the

professional development framework at the HERDSA Conference in July 2010.

• A paper (Wood et. al., 2011, in press) on the findings of our survey has been accepted for a special edition of International Journal of Mathematical Education in Science and Technology for the 8th Delta conference for learning and teaching in mathematics and statistics, which will be held in December 2011 in New Zealand.

• Associate Professor Wood discussed the project in her keynote at the 7th Delta conference for learning and teaching in mathematics and statistics, which was held in December 2009 in South Africa.

• Associate Professor Wood described the professional development framework at the ALTC Sharing Maths and Stats Resources Symposium at the University of Wollongong in February 2010.

• Associate Professor Wood explained the project in her presentation to the Department of Mathematics and Applied Mathematics at the University of Pretoria in South Africa in April 2011.

• Professor Joshi, Professor Bloom and Associate Professor Wood have briefed the Steering Committee and Council of AustMS and Australian Council of Heads of Mathematical Sciences throughout 2009-2011.

• An article reporting on the project and workshop appeared in the May 15-16, 2010 edition of The Weekend Australian (Jones, 2010).

• Regular updates on the project, workshop reports and samples of the learning modules have been provided to the general mathematics community through the AustMS quarterly publication, the Gazette of the Australian Mathematical Society (Bloom et al., 2011; “Classroom notes”, 2011; “Communications”, 2011). A report on the 2010 workshop at UQ also appeared in the Community for Undergraduate Learning in the Mathematical Sciences newsletter (“Report”, 2010).

• We have been invited to contribute a case study on the need for professional development for early-career teachers and also about the project to a forthcoming Routledge publication, Effective part-time teaching in contemporary universities: new approaches to professional development.

4.3 Implementation We have developed a long-term model of delivery for the professional development unit that is hosted by AustMS on their website. We are currently in discussions with AustMS to award accreditation to teaching staff who complete the unit and submit a portfolio of teaching achievements plus a record of appropriate qualifications.


5. Lessons learnt for future projects 5.1 Critical success factors The interdisciplinary expertise of the team was critical to striking a balance between mathematical content and educational theory in our professional development unit. It is imperative that our unit is sufficiently differentiated from general induction programs offered by universities. The team worked hard to offer professional development which is both applicable to mathematics and founded in evidence-based pedagogy. The outcomes were undoubtedly enriched by the cross-fertilisation of ideas and approaches from the perspectives of both mathematicians and educators. The support of AustMS throughout the project has been vital. In terms of practical assistance, inclusion of the professional development workshop in conjunction with their annual meeting at The University of Queensland was invaluable to ensuring it was well attended by the target market (university mathematics teachers across Australia); and hosting the professional development unit on the AustMS website is crucial to facilitating a secure and credible trial. In the future, their support for continuing offerings of the unit and workshops is central to the revitalisation of tertiary mathematics education in Australia. Collaboration with AustMS was considerably strengthened as a result of the efforts of team members who are members of various AustMS committees and its executive. Team members have also submitted regular articles relating to excellence and innovation in teaching and learning in mathematics to the AustMS Gazette to raise the profile of the project amongst the AustMS community. The workshop was a valuable step for the team, as the keen interest of participants in developing their teaching skills gave the team confidence that the need for professional development is widely felt amongst early- and mid-career university teachers, and that draft materials from the learning modules resonated with the audience. The enthusiasm generated from this interactive approach continued to drive progress in the later stages. The buddy system, in which team members work in pairs on a specified task, was applied successfully throughout the project. With the continually busy schedules of team members, mutual encouragement and feedback was critical to maintaining momentum. This was also an efficient way to allocate tasks amongst a large group. 5.2 Challenges Securing support from the broader academic community for professional development to enhance teaching and learning is both a critical success factor and a challenge. While support for outcomes was demonstrated throughout the project, from within the mathematics discipline and externally in service disciplines, it remains difficult to change attitudes and culture within the academic community over only a two-year period. Differences between team members’ expertise (both mathematics and education) was both a critical success factor and a challenge. This diversity meant that more effort and time was invested in decision-making processes. However, the interdisciplinary approach ultimately ensured the accessibility and applicability of the outcomes.


5.3 General lessons learnt In the initial stages we underestimated the time it would take to build a sound foundation on which to base the professional development unit. The first year was spent undertaking a needs analysis through surveying academics across Australia, conducting a literature search, developing the professional standards framework and outlining the structure for the unit. However, these activities were fundamental to fleshing out a well-planned, evidence-based unit that meets identified needs and incorporates a range of fields and foci; this was developed in the second year of the project. With such an extended development process, a broad scope of content, and few opportunities to meet face-to-face, the team recognises the importance of reviewing each others’ work using blended communication platforms. Decentralising the task of completing modules to separate buddies has been effective in allowing smaller groups to work more quickly, but this increased the risk of replicating the same content across multiple modules. The roles, responsibilities and expectations of team members, the means and extent of communication, and the procedure for producing academic research based on project outcomes must be clearly defined from the outset, and revisited for clarification throughout any project. There is much that team members can learn from other institutions, partner or otherwise. The collaborative nature of the project was instructive for team members, in the sense that each observed a range of policy and practice specific to each institution. Rotating locations for face-to-face meetings across different team institutions promoted this process of mutual learning.


6. Evaluation 6.1 Independent evaluator An independent evaluation of this project was undertaken by Michael Mitchelmore and this has been forwarded to the ALTC. The evaluator was engaged in the first stages of the project and provided valuable formative appraisal throughout. He provided pertinent guidance on aspects such as internal and external evaluation mechanisms, progress against milestones, and strategies for dissemination and implementation. 6.2 Users We also conducted stakeholder reviews of specific project activities; in particular we regularly sought the feedback of tertiary mathematics teachers, AustMS, and other academic and professional associations through members of the reference group. These included surveys about learning modules and unit delivery; invited responses obtained from presentations; and reflections from participants about the professional development workshops. These internal and external evaluation processes were used to improve the delivery of project activities and progress against the objectives. More specifically, workshop participants completed a satisfaction survey about each session and the workshop as a whole to give feedback on materials and the organisation of proceedings. Participants were asked to rate the workshop sessions using a Likert scale, and to list the most valuable ideas they gleaned from the session and the changes they would make to their professional practice as a result. Respondents’ feedback about the workshop will shape future offerings. Participants in the pilot unit were asked to answer open-ended questions on each module with regards to satisfaction of learning outcomes, clarity of content and tasks, usefulness of teaching strategies or concepts, appropriateness of module length and workload, and the functionality of technical aspects. They were also asked to give a summative evaluation of the unit, identifying: the modules or aspects of modules that were most and least helpful; the fairness and relevance of assessment tasks; the degree of satisfaction between the unit learning outcomes and their own expectations; the appropriateness of workload; possible improvements; and how the unit contributed to their development as a teacher. We incorporated this constructive feedback into the final review and revision of modules, assessment, online learning community and unit outline. This comprised the final iteration in our project’s action research methodology cycle. We intend to revisit participants in the future and determine which aspects of the unit they have used in their teaching, and how the unit has assisted in their longer term development as teachers. 6.3 Reference group The input of the reference group has had a significant impact on the focus and content of the unit. They were regularly consulted on project activities and outcomes, and gave feedback on project materials. They provided particularly pertinent input with regards to the needs of teaching staff in service disciplines. As expected from a group drawn from the academic and industry associations for science, business and engineering, they recommended a greater and more


explicit applicability of materials to service disciplines. We subsequently added a module that discretely addresses service teaching (Module 5 ‘Teaching in service units’), in addition to references interwoven throughout the unit. The reference group’s evaluation has assisted the team in refining the project materials and improving their utility and accessibility for a variety of stakeholders.


7. Summary The professional development framework for teaching in higher education developed during the early stages of the project represents an original contribution to higher education more generally, as it can be used as a model for professional development in other disciplines. We have made an original contribution to tertiary mathematics education through the development of an online discipline-specific professional development unit. The unit materials were tested and refined with end users through multiple iterations. Participation in the unit and associated workshops has already provided significant professional development for tertiary mathematics educators, from PhD candidates to Associate Professors. We have generated stronger and broader engagement with the benefits, challenges and methods of effective teaching and learning in tertiary mathematics education. We expect the impact on the mathematics profession and the broader quantitative disciplines to be significant as the unit continues to be offered by AustMS and enriched by the usage and evaluation of future participants. Although the unit focuses on teaching in the Australian context, with numerous examples of teaching practice and resources, similar issues in teaching are common around the world. The team will work on capitalising on the potential for international reach through offering the unit on the AustMS website and disseminating outcomes through further academic publications and presentations. The team thanks the ALTC for the opportunity to work on this project.


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teaching: A selected bibliography. Retrieved 16 April, 2010, from http://resources.glos.ac.uk/shareddata/dms/7A5FF0F9BCD42A0396B0BA27AE5AA1C8.pdf.

Higher Education Academy (2006). The UK Professional Standards Framework for teaching and supporting learning in higher education. Retrieved February 4, 2010, from http://www.heacademy.ac.uk/assets/York/documents/ourwork/rewardandrecog/ProfessionalStandardsFramework.pdf

Jones, A. (2010, May 15-16). Maths needs better class of numbers. Weekend Australian, p. 7.

Luzeckyj, A. & Badger, L. (2009). Literature review for preparing academics to teach in higher Education (PATHE). Retrieved August 15 2011, from: www.flinders.edu.au/pathe/PATHE_Project_LitReview.pdf

Paterson, J., Thomas, M., Postlethwaite, C. & Taylor, S. (2011, February). The internal disciplinarian: Who is in control? Paper presented at the Conference of the Special Interest Group of the Mathematics Association of America: Research in Undergraduate Mathematics Education, Portland, Oregon, USA.

Report: AustMS teaching and learning workshop. (2010). Community for Undergraduate Learning in the Mathematical Sciences, 2, November, 16-18. Retrieved from: http://www.math.auckland.ac.nz/CULMS/wp-content/uploads/2010/08/CULMS-No2-Complete-v2.pdf

Sowder, J.T. (2007). The mathematical education and development of teachers. In F. K. Lester Jr. (Ed.) Second handbook of research on mathematics teaching and learning (pp. 157-223). Reston, Virginia: National Council of Teachers of Mathematics.

Thomas, J., Wood, L.N., and Muchatuta, M. (2009), Mathematical sciences in Australia. International Journal of Mathematics Education in Science and Technology, 40(1), 17–26.

Trigwell, K. (n.d.) The scholarship of teaching: an Australian perspective. Retrieved February 4, 2010, from http://www.hrd.qut.edu.au/staff/docs/TrigwellScholarshipofTeaching.pdf

University of East London (2008). UEL professional standards framework. Retrieved February 4, 2010, from http://www.uel.ac.uk/lta/professional/framework.htm

University of Western Australia (2009) Summary of consultation and development of the teaching criteria framework. Retrieved February 4, 2010 from http://www.osds.uwa.edu.au/__data/page/152251/0824335_Teaching_Criteria_Framework_16.12.pdf

Webster, L., P. Mertova, P., & Becker, J. (2005). Providing a discipline-based higher education qualification. Journal of University Teaching and Learning Practice 2(2), 75-83.

Wood, L.N. (2011) Practice and conceptions: Communicating mathematics in the workplace. Educational Studies in Mathematics

Wood, L.N., Vu, T., Bower, M., Brown, N., Skalicky, J., Donovan, D., Loch, B., Joshi, N. & Bloom, W. (2011, in press). Professional development for teaching in higher education. International Journal of Mathematical Education in Science and Technology.

. DOI 10.1007/s10649-011-9340-3

http://resources.glos.ac.uk/shareddata/dms/7A5FF0F9BCD42A0396B0BA27AE5AA1C8.pdf�

http://resources.glos.ac.uk/shareddata/dms/7A5FF0F9BCD42A0396B0BA27AE5AA1C8.pdf�

http://www.heacademy.ac.uk/assets/York/documents/ourwork/rewardandrecog/ProfessionalStandardsFramework.pdf�

http://www.heacademy.ac.uk/assets/York/documents/ourwork/rewardandrecog/ProfessionalStandardsFramework.pdf�

http://www.flinders.edu.au/pathe/PATHE_Project_LitReview.pdf�

http://www.math.auckland.ac.nz/CULMS/wp-content/uploads/2010/08/CULMS-No2-Complete-v2.pdf�

http://www.math.auckland.ac.nz/CULMS/wp-content/uploads/2010/08/CULMS-No2-Complete-v2.pdf�

http://www.hrd.qut.edu.au/staff/docs/TrigwellScholarshipofTeaching.pdf�

http://www.uel.ac.uk/lta/professional/framework.htm�

http://www.osds.uwa.edu.au/__data/page/152251/0824335_Teaching_Criteria_Framework_16.12.pdf�

http://www.osds.uwa.edu.au/__data/page/152251/0824335_Teaching_Criteria_Framework_16.12.pdf�


Appendix A. Professional development unit outline

Professional development

Unit outline

Contact Unit convenor TBC


Unit description

The aim of this unit is to introduce university lecturers and tutors teaching in the mathematical sciences to the theories, principles and practice of university learning and teaching in this area. Our definition of the mathematical sciences is broad and inclusive of any of the quantitative disciplines (such as finance, mathematics, statistics, operations research, psychology). For simplicity, we will refer to this collective group as mathematics.

This unit has been designed to provide practical, discipline-specific and best-practice strategies for teaching and assessment so as to enhance student engagement and learning in mathematics. The unit has been written by a team of your colleagues who have endeavoured to develop tasks in each module that allow you to reflect and draw upon your own day-to-day teaching practice and context. Through a series of sequential online modules we will examine how students learn in mathematics and how you can use this knowledge to plan your lessons and units; when and how you might utilise learning technologies; how you go about writing assessment tasks and giving feedback; and planning for your ongoing professional development. One module specifically concerns issues related to service teaching.

The modules in this unit have been designed to take you from a consideration of teaching of classes, to the more complex role of co-ordinating a unit and a teaching team.

Intended learning outcomes

Part 1: Teaching classes On completion of modules 1 – 7 you will be able to:

T1. Demonstrate an enthusiasm for the discipline of mathematics and a commitment to developing a student learning community that is respectful of the individual learner

T2. Use knowledge of the discipline and how students learn (both generally and in the discipline) to select appropriate teaching and learning activities for mathematics classes

T3 Develop a repertoire of strategies to create positive learning environments that are supportive and engaging, and that allow students to gain feedback to enhance their learning

T4. Evaluate and reflect on the effectiveness of your teaching through collection of evidence about student learning and student engagement.

Part 2: Co-ordinating units On completion of modules 8 – 12 you will be able to:

C1. Develop cohort-building strategies to manage units, to support and guide tutors in their role, and to encourage students to connect with the discipline

C2. Use knowledge of discipline and graduate attributes, how students learn, and students’ prior experience to design units where the learning outcomes, teaching activities and assessment are constructively aligned

C3. Evaluate units through the systematic collection of evidence, and analysis of this evidence from multiple perspectives.

Alterations to the unit as a result of participant feedback


Examples of alterations include revising the assessment tasks to reflect the responsibilities of tutors. We have added clearer references linking the educational theory and mathematical examples.

Alterations will continue throughout subsequent iterations of the unit. We would very much appreciate your input to make these modules more useful to lecturers and tutors in the quantitative disciplines. We will continue to refine the unit materials so they more accurately reflect your teaching needs. We ask that you complete the feedback forms before you commence the unit, at the end of each module, and after you finish the unit.

Please note any typographic errors, technical glitches or other difficulties in working through the unit in the feedback forms. The unit convenor can also assist you as issues arise.

Prior knowledge and/or skills

You should have completed an undergraduate degree in mathematics, statistics or a related quantitative discipline.

In addition you should have experience, or be currently teaching, in a university course in a quantitative discipline. If you are not currently teaching a class, you will need to have access to a class for some of the tasks in the modules.

Learning expectations and teaching strategies/approaches

Expectations High standards of professional conduct are expected in all activities. If you are undertaking this unit there is an expectation that you will participate actively and positively in the teaching/learning environment, comply with workload expectations, and submit required work on time.

Learning resources required

Requisite texts Nil

Recommended reading There are readings outlined in each individual module.

There is a glossary http://www.austms.org.au/glossary with terms that you may not be familiar with. These terms have been put in a mathematical context.

Computer hardware and software Access to the online unit through the Australian Mathematical Society (AustMS) website http://www.austms.org.au/Professional+Development+Unit is necessary. Other software is only as required in your teaching.

Details of teaching arrangements The unit has been designed to be delivered online. The twelve modules are designed to be completed sequentially and each should take approximately three hours to complete, plus time to complete the assessment tasks.

Each of the modules includes tasks for you to complete as part of the learning experience. Some of these tasks will also be preparation for the formal assessment tasks of the unit. We encourage you to

http://www.austms.org.au/glossary�



add to the discussion board provided on the unit website http://www.austms.org.au/Discussion+Board as you work through the modules. In some modules we will invite you to post responses to one task but feel free to add more as you wish. The discussion board is visible only to participants in the unit and the unit convenor.

We will also assign you a “buddy”. This is someone else who has signed up for the unit that you can chat with offline. We ask the buddies to contact each other once a week to check on progress and any issues. You are welcome to swap assessment tasks with your buddy for comment before submitting them.

The formal assessment tasks are listed below. These tasks relate directly to your teaching and will be assessed by the project team. You will receive a certificate from the AustMS upon successful completion of the unit and the assessment tasks. The learning outcomes and the required study and assessment are equivalent to a one semester unit of a Graduate Certificate/Diploma in Higher Education.

Assessment

Assessment schedule Assessment task Date due Percent

weighting Links to intended learning outcomes

Assessment task 1: Teaching philosophy TBC 20% T1, T3

Assessment task 2: Annotated teaching sequence TBC 30% T2, T3, T4

Assessment task 3: Choose ONE of the assessment tasks (design a unit; design a summative assessment task)

TBC 50% C1, C2, C3

Assessment details

Assessment task 1: Teaching philosophy Task description Write a one page teaching philosophy statement that will serve as an introduction to a Teaching Portfolio. You should convey to the reader your own personal enthusiasm for your mathematical discipline and outline your beliefs about learning and teaching in your discipline, or of your discipline to students who are studying in a service-taught unit. Your statement should also discuss how you enact your philosophy through the learning and teaching activities in your classes.

http://www.austms.org.au/Discussion+Board�


Task length 1-2 pages (maximum 750 words) Links to unit’s intended learning outcomes

Learning outcomes T1 and T3

Date due TBC

Assessment task 2: Annotated teaching sequence Task description Write a teaching sequence of 2 to 3 lectures or tutorials that you will be taking with a class. Your sequence should be annotated to indicate why the content was chosen and sequenced in the chosen way, as well as the reasons for the choice of the particular tasks that you selected to support this sequence. You should also indicate how students will be engaged in the activities and how the learning will be supported and feedback given. Once the sequence has been trialled, indicate what changes you may make in the future and provide a summary of any feedback you have received on the sequence from your students. If you do not have the opportunity to plan your own teaching sequence, select a sequence that you have taught and annotate this to indicate what worked well and why, and what changes you might make if you were able to do so. Task length Planning + 2 - 4 pages of annotations/summary of feedback Links to unit’s learning outcomes

Learning outcomes T2, T3 and T4.

Date due TBC

Assessment task 3: Choose ONE of the following assessment tasks Option 1: Design a unit Design a new unit that you would like to, or will, teach. You should complete a ‘unit outline’ that is consistent with the requirements of your university or use a template from links provided in Module 8. Your outline should include:

• an introduction to the unit and where it fits in the context of the course; • a list of the learning outcomes (making explicit how these contribute to course level goals and

graduate attributes as appropriate to your university) • the assessment tasks and how they link to the learning outcomes • a sequenced outline of the content of the course and the teaching activities that will be used

to develop these. Any additional opportunities for students to support their study should also be identified in the document, together with a plan for ensuring consistency of delivery across the teaching team. A short accompanying statement should be appended to the unit outline that indicates how ongoing evaluation of the unit will be conducted.

Option 2: Design a summative assessment task Design an assessment task such as a quiz or assignment.

• Give reasons for your choice of questions and question types. • Prepare a marking guide and feedback for students. • Describe how you prepare students to do the assignment and how you communicate your

expectations and standards to them. • If you are able to use the assessment with students, reflect on the results and student

responses.


Task length Task 1 – Unit Outline document + 1- 2 additional pages Task 2 – Assessment task, marking guide and feedback + 2 additional pages

Links to unit’s learning outcomes

Learning outcomes C1, C2 & C3.

Date due TBC

Linkage between learning outcomes and assessment criteria The following table is provided to support you in the completion of the assessment tasks.

Task-specific criteria have been developed that link the learning outcomes for the unit with each assessment task. These criteria will be used both to assess and to provide feedback for each of your submitted assessment tasks.

Assessment tasks 1 and 2 enable you to demonstrate the four intended learning outcomes (T1 to T4) for the Teaching Classes modules of the unit.

Assessment task 3 enables you to demonstrate all three intended learning outcomes (C1 to C3) for the Co-ordinating Units modules of the unit.

Part 1: Teaching classes

Learning outcome Assessment criteria

Task 1 Task 2 T1. Demonstrate an enthusiasm for the discipline of mathematics and a commitment to develop a student learning community that is respectful of the individual learner

Criterion 1. Create a short statement that outlines your enthusiasm for the discipline of mathematics and your beliefs about student learning. Criterion 2. Reflect on how your attitudes to mathematics and philosophy of learning and teaching mathematics influence your learning and teaching practices.

T2. Use knowledge of the discipline and how students learn (both generally and in the discipline) to select appropriate teaching and learning activities for mathematics classes

Criterion 1. Write a teaching sequence for two to three lectures or tutorials that is informed by both your knowledge of the discipline of mathematics and your understanding of student learning.

T3. Develop a repertoire of strategies to create positive learning environments that are supportive and engaging and allow students to gain feedback to enhance their learning

Criterion 3. Discuss how your teaching philosophy is enacted in the teaching and learning activities you use in the classroom.

Criterion 2. Explain how students will be engaged in the sequence of activities, how the learning will be supported and how feedback will be given.

T4. Evaluate and reflect on Criterion 3. Reflect upon the


the effectiveness of your teaching through the collection of evidence about student learning and student engagement

evidence collected and feedback given to recommend future changes for your teaching.

Part 2: Co-ordinating units

Learning outcome Assessment criteria

Option 1 Option 2 C1. To develop cohort-building strategies to manage units, to support and guide tutors in their role, and to encourage students to connect with the discipline

Criterion 1. Outline how you have given consideration to consistency of delivery across the teaching team

Criterion 1. Describe the strategies that tutors will use to mark and give feedback to students. Justify your answer.

C2. To use knowledge of discipline and graduate attributes, how students learn and students’ prior experience to design units where the learning outcomes, teaching activities and assessment are constructively aligned

Criterion 2. Formulate learning outcomes that reflect the intent of the unit and pay explicit attention to ensuring course-level and graduate attributes are taken into account. Criterion 3. Design a unit that constructively aligns the learning outcomes with assessment tasks and teaching and learning strategies.

Criterion 2. Justify the assessment task in terms of linkage to learning outcomes. Criterion 3. Explain how you have designed tasks that allow good students to be able to demonstrate high level outcomes and weak students to demonstrate their learning.

C3. To evaluate units through the systematic collection of evidence and analysis of this evidence from multiple perspectives

Criterion 4. Devise a plan for ongoing evaluation of the unit.

Criterion 4. Reflect on the task and the outcomes for the students and revise the task accordingly.


Marking rubrics

Assessment task 1: Teaching philosophy

Criterion High Distinction Distinction Credit Pass 1. Create a short statement that outlines your enthusiasm for the discipline of mathematics and your beliefs about student learning.

As for a Distinction, and your enthusiasm for mathematics is embedded throughout the statement and evidenced by compelling examples. There is clear flow and connection between your beliefs about student learning and your practice.

Your personal enthusiasm for mathematics is clearly articulated with examples of how you convey this to your students. Your beliefs about student learning in mathematics are student focused and multi-faceted.

Your enthusiasm for mathematics is articulated and you have conveyed several key beliefs about teaching and learning in mathematics.

There is some evidence of your enthusiasm for mathematics and you have outlined one key idea about student learning in mathematics.

2. Reflect on how your attitude to mathematics and your philosophy of learning and teaching mathematics influence your learning and teaching practices.

You have discussed how you approach/structure your teaching practice to take into account your beliefs about mathematics learning and teaching. There is persuasive evidence that this has involved your reflecting on your personal beliefs and experiences.

You have discussed how you approach your teaching practice and explicitly linked this to your beliefs about mathematics learning and teaching. There is clear evidence of personal reflection on your practice.

You have outlined how you approach your teaching practice and linked this to your beliefs about mathematics and student learning in mathematics. There is some evidence of personal reflection on your practice.

You have outlined how you approach your teaching practice.

3. Discuss how your teaching philosophy is enacted in the teaching and learning activities you use in the classroom.

A variety of specific teaching and learning activities have been discussed and justified according to your stated beliefs about mathematics and student learning.

A variety of teaching and learning activities has been outlined and links made to your stated beliefs about mathematics and student learning.

Specific teaching and learning activities have been outlined with some links to your stated beliefs about mathematics and student learning.

You have included examples of teaching and learning activities that you use in the classroom.


Assessment task 2: Annotated teaching sequence

Criterion High Distinction Distinction Credit Pass 1. Write a teaching sequence, for two to three lectures or tutorials, that is informed by both your knowledge of the discipline of mathematics and your understanding of student learning.

As for a Distinction, with consideration of areas of difficulty and potential misunderstanding and specific inclusion of examples, illustrations, and models to address these.

As for a Credit, and there is evidence that ideas and concepts are reinforced through the exercises and links made explicitly for students. Examples have been chosen to specifically illustrate points and these may include the use of multimedia or technology. As for Pass, with evidence of consideration of the prior understanding needed, and in what direction the mathematics will be taken in future classes.

As for a Pass, with explanations presented fully worked with no jumps between steps. Examples have been well chosen. There is evidence that the topic/problems are introduced with attention to applications.

The chosen sequence is well placed in the relevant unit/topic and the activities are structured in such a way as to scaffold students’ understanding.

The mathematics has been written with care and there is consistency of definitions and terminology throughout the planning.

The mathematics is correct, but there may be some changing of use of terminology/definitions that has the potential to confuse students.

2. Explain how students will be engaged in the sequence of activities, how the learning will be supported and how feedback will be given.

As for a Distinction, with consideration given to how student learning is facilitated through the different activities that have been planned. Feedback to students is given at multiple times and in several different ways.

Efforts have been made to engage the students through an understanding of applications of the concept/topic, the future use of the topic and through connections with other concepts where appropriate. Students have also been engaged though active learning that includes opportunities for discussion and for receiving feedback.

Student engagement has been facilitated in several ways through the sequence. Feedback to students is built into the plan.

There has been some effort made to promote student engagement in the plan, and at least one point of feedback has been identified.

3. Reflect upon the Systematic evidence, of more than More than one form of evidence There is evidence that There is evidence that


evidence collected and feedback given to recommend future changes for your teaching.

one type, has been collected from the students and this has been considered with a view to uncover students’ understanding (or misunderstanding). Suggestions to address these issues in future teaching have been made.

has been collected to gain insights into understanding, and these findings have been used to suggest future teaching activities.

feedback has been sought from the students with respect to their understanding leading to a suggestion or suggestions for future activities.

some feedback has been sought from the students leading to a suggestion or suggestions for future activities.


Assessment task 3: Option 1) Design a unit

Criterion High Distinction Distinction Credit Pass 1. Outline how you have given consideration to consistency of delivery across the teaching team

A clear process of induction of tutors, support throughout the unit and moderation at the point of assessment has been outlined. The process is achievable and respectful of members of the team.

A clear process of support and moderation of assessment has been outlined. There is attention to orientation to the unit. The process is achievable.

As for a Pass, but also providing opportunities for interaction with your teaching team.

There is a consideration of support given to address consistency and/or opportunities for comparison of assessment.

2. Formulate learning outcomes that reflect the intent of the unit and pay explicit attention to ensuring course level and graduate attributes are taken into account

As for a Distinction, and unit learning outcomes are manageable in number and extend to encouraging higher order thinking and skills.

As for a Credit, and links between unit learning outcomes, course level learning outcomes, and graduate attributes are made explicit.

Unit learning outcomes clearly set out with reference to generic attributes or course level outcomes.

Unit learning outcomes and graduate attributes are listed.

3. Design a unit that constructively aligns the learning outcomes with assessment tasks and teaching and learning strategies

Assessment tasks have been purposefully selected to address specific learning outcomes in the most appropriate manner. It has been made clear how the learning and teaching strategies have developed these learning outcomes.

As for a Credit, and assessment tasks have been selected to address specific learning outcomes with a focus mostly on content.

Clear links have been made in the unit outline between learning outcomes, teaching activities and assessments.

Learning outcomes are linked with assessment tasks.

4. Devise a plan for ongoing evaluation of the unit

As for a Distinction, with evidence collected across all four lenses of reflection (Brookfield, 1995)

The evaluation collected multiple forms of evidence at more than one point in the semester. The evidence is centred on student learning. An intent to deeply reflect and act upon evidence is clear.

Evaluation is collected from more than one source and a plan is included for how this will be acted upon.

Some evaluation is carried out to inform future unit delivery.


Assessment task 3: Option 2) Design a summative assessment task

Criterion High Distinction Distinction Credit Pass 1. Describe the strategies that tutors will use to mark and give feedback to students. Justify your answer

A clear process of induction of tutors and moderation at the point of assessment has been outlined. The process is achievable and respectful of members of the team.

A clear process of moderation has been outlined and there is attention to orientation to the task. The process is achievable.

A rubric or detailed marking scheme has been provided to support tutors.

There is a consideration of comparison of assessment and/or support given to address consistency.

2. Justify the assessment task in terms of linking to learning outcomes.

As for a Distinction, with a justification that draws on literature or knowledge of the development of conceptual understandings.

The assessment task has been designed to link with unit learning outcomes as well as generic attributes and/or course level outcomes and made explicit for the students.

As for a Pass, and the mode of the assessment task has been purposefully selected to link with learning outcome/s and made explicit to the students.

Learning outcomes are linked with the assessment task.

3. Explain how you have designed tasks that allow good students to be able to demonstrate high level outcomes and weak students to demonstrate their learning

As for a Distinction, and tasks are open-ended or allow some creativity in student responses that encourages students to pursue areas of interest through the task.

The design of the task scaffolds the students’ learning and incorporates increasing complexity for high achieving students. There is flexibility inherent in the task.

The assessment task design incorporates flexibility that allows students to meet the requirements of the task at different levels or in different ways.

There is opportunity for high achieving students to be extended through the assignment.

4. Reflect on the task and the outcomes for the students and revise the task accordingly

As for a Distinction, with evidence of reflection collected across all four lenses of reflection (Brookfield, 1995)

The evidence for reflection has been collected from multiple sources and more than once. The evidence is centred on student learning. An intent to deeply reflect and act upon evidence is clear.

Evidence to inform reflection is or has been collected from more than one source and a plan is included on how this has been or will be enacted.

Some evidence has been collected to inform reflection.

43 Effective teaching and learning in the quantitative disciplines

Submission of assignments

Assignments should be submitted electronically on the AustMS website http://www.austms.org.au/Assessment. Your assignments will be visible only to the marking team.

You should ensure that you keep a copy of your assignment for your records.

Requests for extensions

Any requests for extensions should be made in writing to the unit convenor prior to the due date for the assessment task.

Academic referencing

In your written work you will need to support your ideas by referring to scholarly literature, works of art and/or inventions. It is important that you understand how to correctly refer to the work of others and maintain academic integrity.

The appropriate referencing style for this unit is APA, a citation style created by the American Psychological Association. Links to APA referencing guides can be found through most university library sites. The most recent published guide is:

American Psychological Association. (2010). Publication Manual of the American Psychological Association (6th ed.). Washington DC: American Psychological Association.

Academic misconduct

Academic misconduct includes cheating, plagiarism, allowing another student to copy work for an assignment or an examination and any other conduct by which a student:

(a) seeks to gain, for themselves or for any other person, any academic advantage or advancement to which they or that other person are not entitled; or (b) improperly disadvantages any other student.

Plagiarism Plagiarism is a form of cheating. It is taking and using someone else's thoughts, writings or inventions and representing them as your own; for example, using an author's words without putting them in quotation marks and without citing the source; using an author's ideas without proper acknowledgment and citation and/or copying another student's work. If you have any doubts about how to refer to the work of others in your assignments, then consult the academic integrity webpage at your own university.

Further information and assistance

Please contact the unit convenor to assist you as issues arise. In addition, feel free to post your query to the discussion board to invite the input of other participants in the unit, or ask your buddy.

Unit schedule

http://www.austms.org.au/Assessment�


You may complete modules at your own pace; however, access to the site will be closed off after (date TBC).

The unit is composed of 12 modules, each designed to be completed in one week of semester. The learning outcomes for each module are summarised below.

Module Module learning outcomes

Part 1: Teaching classes (Weeks 1-7)

1. Introduction to teaching

mathematics • Explain perspectives of teaching mathematics at university • Describe the variety that may exist within the student body you teach • Explain the importance of instilling a passion for mathematics in

students.

2. Models of mathematics learning

• Explain different learning theories as they relate to mathematics • Describe different approaches to mathematics learning and how they

can inform your mathematics teaching • Outline different learning styles and describe ways in which your

teaching may be adjusted to cater to them.

3. Planning and designing lessons

• Explain the importance of consolidating background knowledge as the foundation for generating new understanding of mathematical concepts, and to develop techniques for higher order mathematical thinking

• Identify relevant mathematical skills and concepts in proposed lesson content, and be able to signal and enhance these during learning activities

• Place new mathematical knowledge in both a broader context and a student-meaningful real world context.

4. Conducting lessons • Encourage enquiring minds as opposed to delivering a suite of mathematical facts

• Effectively communicate with both large and small classes • Utilise a range of teaching strategies to help students achieve learning

outcomes • Implement a range of technological options for unit and session

facilitation, and describe how each of them can contribute to effective teaching.

5. Teaching in service units

• Understand the importance of service teaching for mathematics and statistics

• Explain how the needs and expectations of service unit students differ from those enrolled in degree programs in the mathematical sciences

• Identify the main teaching strategies for service units in mathematics and statistics

• Apply these strategies to cater to and effectively engage students in service units

• Celebrate the opportunity to engage with cross-disciplinary ideas and methods in mathematics and statistics.


6. Assessing students in classes

• Design learning and formative assessment tasks to check whether the learning objectives of a class have been met

• Adjust learning activities on the basis of formative assessment results • Design effective and efficient feedback to students in classes.

7. Collecting evidence about teaching

• Describe how critical reflection can be used to enhance teaching and learning outcomes

• Plan and implement activities to obtain feedback from the students, yourself, peers and the literature in relation to your teaching and learning practice

• Critically reflect on your teaching and learning practice • Collate feedback as part of a professional teaching practice portfolio.

Part 2: Co-ordinating units (Weeks 8-12)

8. Planning and designing units

• Develop a unit that incorporates purposeful student learning outcomes, learning activities and assessment tasks based on integration of information pertaining to student background, course curricula, and the broader learning context

• Write a unit outline that reflects the best practice in unit design.

9. Managing units • Effectively manage and communicate with students, tutors and other stakeholders in a unit

• Organise and utilise resources and conduct procedures to facilitate effective learning and efficient implementation of your unit.

10. Assessing students in units

• Compare and contrast a range of assessment strategies and approaches

• Design and implement effective assessment strategies in mathematical units, including writing rubrics and marking guidelines

• Describe strategies to make mathematics assessment accessible, equitable, valid and reliable.

11. Developing learning communities

• Describe attributes of positive learning communities and outline strategies that can be used to create them

• Explain how different technologies can be used to facilitate interaction and collaboration between students.

12. Evaluating units • Explain why units should be evaluated and how this aligns with your obligations for unit evaluation within the quality assurance framework at your university

• Identify and collect evidence that can be used to evaluate a unit, and outline how this evidence may be used to enhance a unit

• Apply the principles of Action Research to plan for a small-scale intervention aimed at enhancing teaching in your unit, or a unit into which you teach

• Become familiar with sources of research into undergraduate teaching of mathematics and professional development that both informs your practice and gives you an opportunity to share your practice with your peers.


Appendix B. Module 1. Introduction to teaching mathematics

Introduction In this first module we outline the background to teaching mathematics at university, with a particular emphasis on the role of the teacher, the nature and attributes of the students, and the importance of instilling a passion for mathematics in your students.

Our aim is for your teaching to become more: efficient, effective and enjoyable

Learning outcomes

At the end of this module, you will be able to:

• explain perspectives of teaching mathematics at university • describe the variety that may exist within the student body you teach • explain the importance of instilling a passion for mathematics in students.

Module structure

The module proceeds as follows:

• The context of teaching mathematics in Australia • What does good and poor teaching look like? • What do you believe about learning and teaching? • Seven principles of learning • What expert teachers know

The context of learning and teaching mathematics in Australia University education in Australia is changing. Many students are coming to university to improve their prospects of getting professional employment. The emphasis of learning has moved from content where a student gains knowledge to being where a student becomes a professional. All universities now state graduate/generic skills/attributes/capabilities as part of what a student will achieve in their university studies.

This change in emphasis has made the job of teaching more complex and interesting. You teach the discipline content and the graduate skills the student will require after university. We have always done this however it has been implicit rather than explicit. Now governments, industry, graduates and students are requiring that we demonstrate that students achieve both discipline-specific knowledge and graduate skills.

For those of us teaching in quantitative disciplines, this is a boon. Most graduate attribute statements include the quantitative and analytic skills that we are teaching!

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This unit of 12 modules will help equip you for this new teaching environment. The unit will enhance your teaching as well as show you how to prepare a portfolio for your teaching career.

Our aim is for your teaching to become more:

efficient, effective and enjoyable

What does good and poor teaching look like?

We can understand the elements of good teaching by examining examples of both good and poor teaching, deconstructing the interaction and the relationship between the teacher and the learner. The video below provides an example of poor teaching. Focus primarily on the teaching, rather than the content.

Task 1.1 Attributes of poor teaching

In the following five minute video extract from The Big Bang Theory, Sheldon (a physics researcher) is teaching Penny (a waitress and a physics novice) about the physics research that her boyfriend is undertaking. Penny has actively sought out help to learn.

Watch the video, then read the questions below and re-watch the video, pausing as necessary to answer the questions, being as specific as possible.


Extract from "The Big Bang Theory", Sheldon teaches Penny Physics, (SuperTbbt, 2009)

Questions:

1. What does the teacher believe about teaching and learning? How does that belief influence his teaching? How does he change his approach in response to feedback?

2. What was the student experience of the teacher's teaching? Specifically what was she feeling? How did the teacher's actions support or impact her motivation?

3. What was the teacher's expectation of the student performance? 4. How did the teacher check the developing understanding of the student, and how the

student was constructing knowledge? 5. What things does the teacher do which you would not want to do if you were in his

position?

Task 1.2 Attributes of good teaching in a mathematics / science context

Compare and contrast the teaching and learning interaction above with the thoughts and examples of Harvard University Professor Eric Mazur, in From Questions to Concepts.


(BokCentre, 2008)

Questions:

1. What does Professor Mazur believe about teaching, and how does that influence his teaching.

2. What is the student experience of learning led by Professor Mazur?

What do you believe about learning and teaching? Lecturers and tutors of university mathematics come from a wide range of backgrounds and experiences, both professionally within the discipline of mathematics and from their past experience as learners exposed to a wide diversity of teaching styles and approaches throughout their secondary and post-secondary education.

During that time, you will have developed some key mental models that shape your current approach as a lecturer or tutor - particularly in relation to fundamental concepts including your beliefs in relation to what mathematics is, what teaching is, and how learning occurs.

Task 1.3 Reflections on learning, teaching and mathematics

Answer each of the three questions below, writing between one and three sentences. It is important to realise there is no right or wrong answer. This activity is not directed towards what you think an examiner thinks, or what an educational psychologist might think; it is all about what you think and believe in relation to mathematics, teaching and learning.


Take 10-15 minutes to consider and write your answers. If it helps, you can also consider why you have formed these views, and what influenced your viewss.

1. What is mathematics? 2. What is teaching? 3. What is the goal in teaching mathematics? 4. What is learning: how do students learn mathematics?

Post your answer to the last question on the discussion board.

Common myths about teaching undergraduate mathematics

In an article based on a conference plenary address, Why the Professor Must be a Stimulating Teacher (2010), Alsina identifies a series of myths and practices in relation to the teaching of mathematics at an undergraduate level. From personal experience in Spanish universities, Alsina outlines myths in the teaching of mathematics at an undergraduate level, and makes suggestions as to changes going forward in teaching, assessment and technology. The myths are:

• The researchers-always-make-good-teachers myth • The self-made-teacher tradition (i.e. maths teachers do not need training to be

teachers) • Context-free universal content (a core curriculum is necessary irrespective of the

major being pursued) • Deductive organization (learners learn through representations of deductive

reasoning in general form with proofs) • The top-down approach (Maths taught in the most general form is the most useful,

and students will be able to apply it to specific contexts. Real world examples are not necessary.)

• The perfect-theory presentation (Maths is almost complete, and mathematics is a process of getting the right answer which is always possible. Exploration and difficulties are not presented.)

• The ‘master class'/formal lecture paradigm (teaching is about transmitting knowledge to the students)

• The mature students myth (students can be assumed to be motivated, prepared and aware of the need for maths in their training. Diversity of backgrounds is ignored)

• The routine individual-written assessment (the written end-of-unit exam is the ideal way of assessing whether students have mastered the content delivered in lectures)

The non-emotional audience (students enrolled in a maths course have a singular goal of learning maths, and come without any emotional, personal, or individual problems). You may recognise these myths, and even agree with some of them, to some extent. Bear them in mind, and your own responses to Task 1.3, as you proceed.

The influence of teacher beliefs on student performance

Although the research context was junior mathematics, Carter and Norwood (1997) found teacher beliefs in relation to mathematics had a significant influence on student beliefs about success factors in mathematics, specifically that working hard to solve problems and striving for understanding would lead to success.

Carlson (1999) investigated the mathematical behaviour, experiences and beliefs of successful graduate mathematics students. She found that consistent beliefs of the graduate students included:

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"mathematics involves a process that may include many incorrect attempts; problems that involve mathematical reasoning are enjoyable; individual effort is needed when confronting a difficulty; students should be expected to "sort out" information on their own; and persistence will eventually result in a solution to a problem." (p. 224)

Task 1.4 Reflections on the power of beliefs

1. How do you feel your beliefs impact the beliefs of your students in relation to mathematics?

2. What is your role in helping students establish these beliefs and how can this be achieved?

Task 1.5: Exploring paradigms of undergraduate education

The following article by Barr and Tagg (1995) examines the paradigms that pervade undergraduate education. Although written some time ago, this often cited piece provides a useful context to examine the role of teachers in an undergraduate setting, and the differences between the dominant Instruction Paradigm and a Learning Paradigm of undergraduate education. After reading the article, answer the questions below.

Questions:

1. Which paradigm of undergraduate education do you consider appropriate for your teaching? Why?

2. In the terms outlined in the article, how would you describe your current teaching practices?

3. How would your students describe your teaching paradigm? 4. How do you measure the success of your teaching? What are the goals you set or the

measures which you value?

Task 1.6: The variety of student knowledge, understanding and skills

In teaching undergraduate mathematics it is easy to overestimate the level of skills in the student body, and to erroneously assume that if students have certain mathematical understandings then they are readily transferrable by those students to other contexts. For example, Trigueros and Ursini (2003) found that first year mathematics undergraduates evidenced a wide range of misconceptions and approaches characteristic of algebra beginners in secondary school, and that students responses can often be characterised as reactions to symbols present in an expression (exponentials, the equals sign etc) rather than a considered mathematical response.

The Trigueros and Ursini article (2003) confronts teachers with the reality of the range of applied mathematical skills present in their class, and the challenge of applying known mathematical contexts in non-routine cases. Please read the Trigueros and Ursini article and answer the following questions.

1. Describe some of the problems that the undergraduate students evidenced in dealing with variables.

2. Provide examples where students possessed the mathematical "knowledge" to solve a problem, but were unable to apply that knowledge in the context of the question posed.

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3. What implications does this diversity in understanding have for the teaching of undergraduate mathematics? Did any of your responses in Task 1.3 allow for these?

4. Do you have any strategies (yet) as an undergraduate mathematics teacher to identify misconceptions and help students develop skills to apply mathematical knowledge in non routine contexts?

Seven principles of learning The body of research in the cognitive, learning and neurological sciences has yielded a range of insights into how people learn, how they organise and internally construct knowledge, how they differ in their preferences and learning styles, and how people develop expertise. In Evaluating and Improving Undergraduate Teaching in Science, Technology, Engineering and Mathematics (Fox & Hackerman, 2003), the US National Research Council identified seven principles of learning (p. 20):

1. Learning with understanding is facilitated when new and existing knowledge is structured around the major concepts and principles of the discipline In the context of mathematics, this requires identification and teaching of the big ideas and core concepts of the discipline rather than students learning a series of disconnected facts. Mathematical knowledge can be more readily transferred to new contexts when the big ideas and core concepts are understood rather than isolated, issue-specific problem-solving processes being mastered. Students must build knowledge structured around the major organising principles and core concepts of the discipline and understand how new knowledge is related to those major concepts.

2. Learners use what they already know to construct new understandings Students existing knowledge (both correct, and incorrect), beliefs and skills shape their approach to learning and their understanding of new knowledge. In the context of mathematics, this means teachers must determine what students already know about a subject, probe to identify and confront misconceptions, and plan ways to build the new knowledge on top of, and networked into, existing knowledge of the students. This student-specific construction of knowledge filtered through their existing knowledge and conceptions is the opposite of the transmissive model of teaching, which relies on a belief that teaching is telling and that students internalise the message as understood by the teacher who is transmitting that knowledge.

3. Learning is facilitated through the use of metacognitive strategies that identify, monitor, and regulate cognitive processes Metacognitive strategies - thinking about thinking, learning, and problem solving - are key skills in human learning, and especially significant in mathematical problem solving. These strategies include assessing current mastery levels, monitoring performance, consciously connecting new knowledge to existing knowledge, deliberate selection of thinking or problem-solving strategies, and thinking strategies of planning, monitoring and evaluating. In the context of mathematics, this requires explicit instruction focused on the development in students of a range of metacognitive skills for managing learning and problem solving, the modelling of thinking skills, the sharing of internal thought processes by "thinking out loud", and probing students' existing metacognitive strategies.

4. Learners have different strategies, approaches, patterns of abilities, and learning styles that are a function of the interaction between their heredity and their prior experiences As students have different skills, and learn at different rates in response to different learning activities and approaches (learning styles), there is no universal teaching strategy for the effective development of higher mathematical skills. It follows that a single mode of assessment task will advantage some learners and disadvantage others. Importantly, the different skills and learning preferences of the teacher will affect the range of teaching approaches with which the teacher is most comfortable,


and will influence the teacher's beliefs in what constitutes effective teaching - i.e, constrained by the view of what would be effective teaching if the teacher were the student. In the context of mathematics, this means that teachers needs to be aware of teaching assumptions influenced by their preferences and backgrounds, to be alert to the range of abilities and learning styles in the classroom, and to design and deliver a range of learning activities across different learning styles in both unit content and assessment processes.

5. Learners' motivation to learn and sense of self affect what is learned, how much is learned, and how much effort will be put into the learning process There is strong research evidence that learners' beliefs about their own abilities in a subject area are strongly connected with success in that subject. In the context of mathematics, building learners' self belief in relation to their ability to understand and engage with the core concepts and principles of the definition is a key component of increasing student performance. In any classroom, some students will believe that their mathematics ability is pre-determined, whilst others will believe their ability to learn is a function of effort expended. A belief in pre-determined skill level, which cannot be altered by effort, is a constraining self-fulfilling prophecy which will significantly impair learning, problem solving and performance.

6. The practices and activities in which people engage while learning shape what is learned The way in which knowledge is learned, and the range of uses to which that knowledge is put in the learning process, are important parts of the knowledge that is learned. Where knowledge is learned in a narrow, or artificial, context, students find difficulty abstracting that knowledge and transferring and applying it to other contexts. Whilst the knowledge can be applied again in the context in which it was taught, students are unable to see connections and applicability to other contexts, novel problems, or different disciplines. In the context of teaching mathematics, diverse real world applications of knowledge and problem solving can be used to support students in building these broader connections, especially with problem-based and case based learning and assessment.

7. Learning is enhanced through socially supported interactions Conceptual learning is enhanced where students have opportunities to interact and collaborate with others, both as part of the learning processes and tasks, and as part of assessment tasks. The process of students interacting with other students in sharing, challenging, and building understanding is particularly effective with conceptual learning, and can be used by teachers as a less teacher-centred teaching strategy. In the context of mathematics, activities include joint problem solving, peer explanation of concepts, solo problem solving followed by sharing and comparing strategies, and observed problem solving with students articulating their thought processes aloud. The sources of student learning are not limited to the teacher, and one of the roles and challenges for the teacher is how to leverage this additional learning source in the classroom.

Task 1.7: Considering your current teaching and experiences of teaching

1. How, and to what extent, does your current teaching address each of these seven principles of learning?

2. Consider the teaching of one of your best higher education mathematics teachers. How, and to what extent, did their teaching practice address each of these seven principles of learning?

What expert teachers know

Whilst the research on learning tells us about how students learn as individuals constructing knowledge, and how they learn from each other, the other major influence in the classroom


is the teacher: the knowledge and activities of the effective teacher.

Shulman (1987) identified the following specific knowledge that expert teachers know:

1. the academic subjects they teach 2. general teaching strategies independent of discipline (classroom management,

effective teaching, evaluation) 3. applicable curriculum materials and programs for their subject 4. subject specific knowledge for teaching: teaching different types of students, and

teaching particular concepts 5. the characteristics and cultural backgrounds of learners 6. the settings in which students learn: pairs, small groups, classes etc 7. the goals and purposes of teaching.

In the context of science, technology, engineering and mathematics (Fox & Hackerman, 2003) the following five criteria for teaching effectiveness were identified (p. 27):

1. knowledge of subject matter 2. skill, experience and creativity with a range of appropriate pedagogies and

technologies 3. understanding of, and skill in using, appropriate assessment practices 4. professional interactions with students within and beyond the classroom 5. involvement with and contributions to one's profession in enhancing teaching and

learning.

Task 1.8: Assessing your knowledge

Using a scale of 1-10 where 10 is very strong and 1 is very weak - rate your current level of knowledge and skills across each of the dimensions of knowledge and teaching effectiveness outlined above.

Is there one "correct" expert?

Although in our discpiline there is general agreement about correctness, when it comes to teaching approaches there are no such absolutes! For example, Dubinksy and Krantz have quite differing perspectives on the teaching of undergraduate mathematics. Many people find both views enriching and helpful for their teaching. Steven Krantz, Professor of Mathematics at Washington University, St. Louis invited Ed Dubinsky (then a Professor at Georgia State University) to write a reflection in his book How to Teach Mathematics (Krantz, 2000). Krantz's book was a bestseller, and included an appendix in which he sought contributions from those who agreed, and those who disagreed, with his views on the teaching of mathematics expressed in his book. Dubinksy's reflection is included within that appendix. In his reflection, Dubinsky (2000) provides a useful analysis and discussion of constructivism in the context of undergraduate mathematics education, and a commentary on "traditional" teaching of mathematics. Note that Krantz's is personal reflection and Dubinksy is using evidence-based research. Read this as a counterpoint and reflect on the implications of this debate on your teaching practice.

Review and conclusion Your ideas about mathematics and learning will influence how you teach.


For yourself, write down three ideas you have learnt in this module, and one way in which you will change your teaching or that has challenged your beliefs.

In the next module we will look at models of learning mathematics.

References • Alsina, C. (2010). Why the professor must be a stimulating teacher. In D. Holton

(Ed.), The Teaching and Learning of Mathematics at University Level: An ICMI Study (pp. 3-12). The Netherlands: Kluwer Academic Publishers.

• Artigue, M. (2010). What can we learn from educational research at the university level. In D. Holton (Ed.), The teaching and learning of mathematics at university level: An ICMI Study (pp. 207-220). The Netherlands: Kluwer Academic Publishers.

• Barr, R., & Tagg, J. (1995). From teaching to learning: A new paradigm for undergraduate education. Change, 27(6), pp. 12-25. Retrieved from http://www.athens.edu/visitors/QEP/Barr_and_Tagg_article.pdf

• BokCentre. (2008, January 20). From Questions to Concepts: Interactive Teaching in Physics Video file. Video posted to http://www.youtube.com/watch?v=lBYrKPoVFwg

• Carlson, M. P. (1999). The mathematical behavior of six successful mathematics graduate students: Influences leading to mathematical success, Educational Studies in Mathematics, 40(3), pp. 237-258.

• Dubinksy, E. (2000). Reflections on Krantz's How To Teach Mathematics: A different view. In S. Krantz, How to Teach Mathematics (2nd ed.) (pp. 197-214). Providence, Rhode Island: American Mathematical Society.

• Fox, M. A., & Hackerman, N. (Eds). Evaluating and improving undergraduate teaching in science, technology, engineering, and mathematics. Washington, DC: The National Academies Press.

• Holton, D. (Ed.). (2010). The teaching and learning of mathematics at university level: An ICMI study, The Netherlands: Kluwer Academic Publishers.

• Krantz, S. (2000). How to Teach Mathematics (2nd ed.) Providence, Rhode Island: American Mathematical Society.

• Norwood , K. S., & Carter, G. (1997). The relationship between teacher and student beliefs about mathematics, School Science and Mathematics, 97(2), pp. 62-67. Retrieved from http://www.merga.net.au/documents/MERJ_15_1_Handal.pdf

• Schoenfeld, A. H. (2010). Purposes and methods of research in mathematics education. In D. Holton (Ed.), The teaching and learning of mathematics at university level: An ICMI study (pp. 221-236). The Netherlands: Kluwer Academic Publishers.

• Selden, A., & Selden J. (2010). Tertiary mathematics education research and its future. In D. Holton (Ed.), The teaching and learning of mathematics at university level: An ICMI study (pp. 237-254). The Netherlands: Kluwer Academic Publishers.

• Shulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), pp. 1-22.

• SuperTbbt. (2009, December 28). The Big Bang Theory - Sheldon Teaches Penny Physics Video file. Video posted to http://www.youtube.com/watch?v=AEIn3T6nDAo.

• Trigueros, M., & Ursini, S. (2003). First year undergraduates' difficulties in working with different uses of variable. In A. Selden, E. Dubinsky, G. Harel, & F. Hitt (Eds.), Conference Board of the Mathematical Sciences Issues in Mathematics Education (Vol. 12), Research in Collegiate Mathematics Education (Vol. V, pp. 1-29). Providence, Rhode Island: American Mathematical Society.

Further Reading

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• Clark, M. and Lovric, M. (2009). Understanding secondary-tertiary transition in mathematics, International Journal of Mathematical Education in Science and Technology, 40(6), pp. 755-776

• Radloff, A. (2006). Applying principles for good teaching practice at CQU - Can we? Should we? Retrieved 28 February, 2011, from: http://iris.cqu.edu.au/FCWViewer/view.do?page=8827.

• Schoenfeld, A.H. (1989). Explorations of students' mathematical beliefs and behavior. Journal for Research in Mathematics Education. 20(4), pp. 338-355.

• Selden, A. (2005). New developments and trends in tertiary mathematics education: or, more of the same?, International Journal of Mathematical Education in Science and Technology, 36(2), pp. 131-147.

• Speer, N.M., Smith III, J.P., & Horvath, A. (2010). Collegiate mathematics teaching: An unexamined practice. The Journal of Mathematical Behavior. 29(2), pp. 99-114.

• Wood, L. N. (2010). Graduate capabilities: putting mathematics into context. International Journal of Mathematical Education in Science and Technology, 41(2), pp. 189-198.


Appendix C. Survey on teaching experience and professional development needs Name of project: A national discipline-specific professional development program for lecturers and tutors in the mathematical sciences You are invited to participate in a study that investigates the learning and teaching needs of lecturers and tutors teaching in the mathematical sciences in Australian universities. The purpose of the study is to establish what aspects should be included in a standard discipline-specific professional development programme for early and mid-career academics. Your feedback in this study will inform the design of resources which will transform the way that new lecturers and tutors engage with students in disciplines which are strongly based on quantitative analysis skills. This project is funded by the Australian Learning and Teaching Council. If you decide to participate, you will be asked to reflect on your teaching experiences and needs, with regards to the effectiveness of current practice and your perceptions of professional development for teachers in the mathematical sciences. The questionnaire will be online and should take no longer than fifteen minutes to complete. No personal details will be gathered or are required in the course of the study. No individual will be identified in any publication of the results, as the study is strictly anonymous. The information gathered will not be used as an individual staff performance evaluation tool. Participation in this study is entirely voluntary: you are not obliged to participate and if you decide to participate, you are free to withdraw at any time without having to give a reason and without consequence. However, it will not be possible to withdraw your participation after your response has been submitted. 1. What is your current role? (more than one role can be selected)

a. Tutor b. Lecturer c. Unit co-ordinator d. Head of department/school e. PhD candidate f. Other

2. Are you a casual staff member delivering lectures and/or tutorials? a. Yes b. No

3. How many years of experience do you have in tutoring? (open) 4. How many years of experience do you have in lecturing? (open) 5. What level of students do you teach?

a. First year b. Second year c. Third year d. Honours e. Postgraduate

6. What kind of students do you teach? (more than one category can be selected) a. Face to face b. Distance c. online

7. What technological tools are available to tutors in your teaching spaces? a. Document camera b. Screen recording c. Video recording d. Audio recording


e. Desktop computers f. Tablet PCs g. Remote control h. SMART board i. Pen-enabled screens j. Internet connection k. Overhead projector l. Fixed microphone m. Lapel microphone n. Data projector o. I don’t know

8. What technological tools are available to lecturers in your teaching spaces? a. Document camera b. Screen recording c. Video recording d. Audio recording e. Desktop computers f. Tablet PCs g. Remote control h. SMART board i. Pen-enabled screens j. Internet connection k. Overhead projector l. Fixed microphone m. Lapel microphone n. Data projector o. I don’t know

9. In which of these tools would you like training for teaching mathematics? a. Document camera b. Screen recording c. Video recording d. Audio recording e. Desktop computers f. Tablet PCs g. Remote control h. SMART board i. Pen-enabled screens j. Internet connection k. Overhead projector l. Fixed microphone m. Lapel microphone n. Data projector o. I don’t know

10. What would be the approximate class size for the largest lecture group in mathematical sciences at your university? (open)

11. What is the upper limit on the number of students in a tutorial group in the mathematical sciences at your university? (open)

12. What programs or resources does your department/school have in place to support lecturers and casual tutors in the mathematical sciences at your university?

a. Department-based supervision and evaluation by Heads Of Departments b. Buddy system c. Funded attendance at teaching conferences/seminars d. Money to support innovative teaching e. handbook of procedural matters relating to managing a lecture/course f. recognition and encouragement of research into teaching


g. enrolment in formal teaching programmes h. other (open)

13. In your opinion, what are the teaching and learning challenges faced by early career teachers in the mathematical sciences? (open)

14. How important is it for the following issues to be addressed in a training session for lecturers in the mathematical sciences?

a. Student learning styles b. Preparation of lecture material c. Lecture delivery modes (ie. black/whiteboard, OHP, visualiser, computer, laptop,

tablet PC) d. Methods of assessment e. Classroom management f. Course profile development g. Curriculum development

15. How important is it to address the following issues in a training session for tutors in the mathematical sciences?

a. Student learning styles b. Presentation of ideas c. tutorial delivery modes (ie. black/whiteboard, OHP, visualiser, computer, laptop,

tablet PC) d. method of assessment e. assessment feedback f. classroom management g. student collaboration

16. In addition to the above, what would you like to see covered in a training session for lecturers or tutors in the mathematical sciences? (open)

17. How would you like this unit to be delivered (eg. format and mode of delivery) (open) 18. What courses have you undertaken in tertiary teaching and learning?

a. Induction session b. Foundation unit c. Foundation program d. Graduate certificate e. Formal education qualification f. None g. Other (open)

19. Were there any areas that you would have liked to have been addressed, which were not included in the course? (open)

20. Any additional comments (open)

a national discipline-specific professional …

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