Mathematics Reform-based Instruction:Mathematics Reform-based Instruction:Hearing Teachers’ VoicesHearing Teachers’ Voices

Mary C. Enderson Azita ManouchehriMiddle Tennessee State University Central Michigan UniversityMathematical Sciences Mathematical Sciences

mcenders@mtsu.edu Azita.M@cmich.edu

Messages from research on implementation Messages from research on implementation

of reform in schoolsof reform in schools reform-minded teaching remains a novelty

in school settings (Ball & Cohen 1998).

many teachers are unaffected by the reform and continue to teach in a traditional manner (Tobin 2001).

Factors contributing to this problemFactors contributing to this problem

teachers’ lack of familiarity (and comfort) with a gradual development of the subject matter which prevents them maintaining instructional coherence

teachers’ inability to present mathematics as a chain of interpenetrating concepts rather than as isolated skills due to their narrow understanding of the subject

Factors (continued)Factors (continued)

teachers’ reluctance to conform to new methods of teaching due to a mismatch between their own beliefs about the nature of mathematics and the philosophies that guide the reform recommendations

teachers’ reliance on locally driven theories about practice rather than current research on learning and teaching

Critique of research on reform-based Critique of research on reform-based teaching and teachersteaching and teachers

The results of these studies represent the researchers’ (research team’s) perceptions of what ought to happen in classrooms, what teachers do not or can not do and the value they attach to the teachers’ choice of pedagogy or student learning.

CritiqueCritique (continued) (continued)

These studies evidence the absence of teachers’ voice in deepening our understanding of the complexities associated with instructional change and in shaping the direction of research within the discipline (Goodson 1996).

CritiqueCritique (continued again) (continued again)

Most studies have focused on elementary and middle levels. Studies that concentrate on high school mathematics teachers and their practices are rare.

Omission of teachers’ perspectives and views is problematic (Clark 1996).

Issues in need of attentionIssues in need of attention

What do mathematics teachers think about the recommendations of the reform for teaching and learning?

What value mathematics teachers attach to research in mathematics education?

Issues (continued)Issues (continued)

How do teachers characterize their needs and their expectations of research in helping them meet those needs?

Goals of current researchGoals of current research

document teachers’ views on the current recommendations for reform in curriculum and instruction.

elicit teachers’ assessment of the usefulness of current research in mathematics education in advancing their skills in implementing reform-based practice.

GoalsGoals (continued) (continued)

identify those elements, from the teachers’ perspectives, that facilitate instructional change.

Focus High School Mathematics Teachers

ProcessProcess

Survey-Design and pilot

Content:1. Biographical information 2. Teachers rated their confidence with innovative

instructional roles and techniques. 3. Teachers ranked their level of proficiency in

implementing aspects of reform minded practice.

ContentContent (continued)(continued)

4.   Teachers identified areas in which they felt they needed professional development.

5. Teachers rated their familiarity with current research in mathematics education, whether they found such research reports beneficial to their work, and to identify areas that they felt must gain research attention.

ProcessProcess (continued)(continued)

Interviews Classroom Observations

Data analysisData analysis

Factor analysis

Number of years of teaching, age, gender, post-graduate training, school district, types of professional development activities in which they were engaged within the last 5 years, courses they taught, and their level of knowledge about, and support of, reform based curriculum and instruction as well as research in mathematics education

SampleSample

500 surveys mailed in both states, 212 were returned

Mean teaching experience 21 years 32 teachers had less than 10 years of

teaching experience. 87 teachers taught in rural schools 66 in urban schools

Sample (continued)Sample (continued)

54 in suburban school districts 161 were white 39 teachers taught upper division

mathematics courses (Pre-calculus, calculus, and statistics).

Others’ taught courses ranging from fundamentals of mathematics, geometry, Algebra I and II.

SampleSample (continued)

62 teachers had participated in content specific professional development activities (technology in instruction, using new textbooks, and authentic assessment techniques.

108 teachers had completed at least one graduate course at the university within the last three years.

79 teachers had completed a master’s degree in curriculum and instruction within the last ten years.

  

GeneralGeneral resultsresults

143 teachers were familiar with PSSM. Nearly a half of this population was supportive of their agenda.

25 teachers were familiar with Professional Standards for Teaching Mathematics.

General results (continued)General results (continued)

There was a positive correlation between the level of mathematics preparation of the participants and their degree of support of the NCTM’s guidelines for practice. Those teachers with a more sophisticated mathematics background (more coursework in mathematics education) were more supportive of, and confident in their ability to implement innovative curriculum and instruction.

More resultsMore results

Female teachers were more supportive of recommendations of reform for learning and teaching mathematics.

Teachers in suburban school districts were more familiar with the standards and found them more applicable to their work.

126 of teachers who taught in rural and urban schools found the current guides for instructional change impractical for their settings.

Results (continued)Results (continued)

Age, number of hours of involvement in professional development activities, and years of teaching experience did NOT serve as significant factors on participants’ level of support of the reform based instruction.

No significant changes were detected according to geographic location (state).

Only three teachers in the entire sample found merit in current research findings for advancing their professional efforts.

Teachers’ reports of their level of comfort with Teachers’ reports of their level of comfort with fostering reform-based learner behaviorsfostering reform-based learner behaviors

Learner Actions VE E D VD NS

NR Problem solve 55 42 93 8 17

2

Develop conceptual understanding 6 55 106 17 21

2

Use technology to pose and solve problems 13 36 118 37 3

0

Pose mathematical questions in class 2 31 89 59 11

6

Express their thinking both verbally and in writing 38 69 57 23 16

5

Make mathematical conjectures 12 57 107 23 5 4 Approach problems in different ways 59 72 43 34 0

0

Work through ambiguous and challenging problems 23 33 89 21 37

5

Teachers’ reports…learner behaviors Teachers’ reports…learner behaviors (continued)(continued)

Learner Actions VE E D VD NS

NR Verify and test answers in collaboration with peers 25 57 61 27 24

14

Confident in their ability to learn mathematics 25 50 95 21 17

0

Learn where and how mathematics is useful in real life 18 27 101 37 15

0

Communicate mathematics effectively 10 32 112 41 13

0

Listen to peers’ mathematical arguments 14 26 82 47 31

8

Appreciate and enjoy mathematics 12 38 93 65 0

0

Debate accuracy of answers 10 25 121 11 18 23

Teachers’ reports of their level of comfort Teachers’ reports of their level of comfort with reform-based instructional behaviorswith reform-based instructional behaviors

Teaching Actions VE E D VD NS

NR Teaching for problem solving 27 59 72 17 23 10 Teaching for conceptual understanding 8 11 17 116 54 2 Teaching for connection making 2 25 83 56 42 0 Supporting classroom discourse 7 11 114 31 35 0 Inquiry based mathematics instruction 9 31 88 58 12 10 Technology-enhanced explorations 17 37 116 28 0 0

Teachers’ reports…instructional behaviors Teachers’ reports…instructional behaviors (continued)(continued)

Teaching Actions VE E D VD NS

NR Teaching reasoning 46 34 67 61 2 0 Utilizing multiple representations 11 35 87 44 25 3 Accommodating all students’ needs 13 10 132 45 0 8 Connecting children’s thinking to important mathematical structures 10 26 112 23 37 0

Some general areas of concern included:Some general areas of concern included:

State-wide testing: “How am I supposed to do innovative things with

my students when all teachers hear is – you must prepare your students to do well on the test!” [DAN]

“Testing has everything to do with me keeping my job! Why shouldn’t I feel pressure?” [SALLY]

Areas of concern (continued)Areas of concern (continued)

Support by school administration: “I am able to do the things I do because my

principal supports me in the process. This gives me a great deal of comfort knowing he is behind me.” [RUTH]

More areas of concernMore areas of concern

Mathematics preparation prior to High School taking

a closer look at the foundation students’ possess:

“How am I supposed to teach students if they don’t even have the basic skills needed for an Algebra II course? I don’t know what they are doing in the middle schools these days.” [TONY]

Areas of concern (continued)Areas of concern (continued)

School and classroom conditions – classroom environment, class size, availability of aids or assistants (to meet the needs of all students), materials/tools

Instructional preparation time – collaborating, mentoring, planning, assessing

Curricular issues – content and coverage of content

Areas of concern (continued)Areas of concern (continued)

Available resources to help with instruction– how do I go beyond what the textbook has?

How to motivate students Finding TIME to “do it all” How to keep “good” teachers in the

profession

Areas of concern (continued)Areas of concern (continued)

When (and how) to reflect on my own teaching?

“They keep telling us about this Japanese lesson study, but they don’t help us get there. When are we given time to really think about what happened in our lessons? When do we have time to go visit other teachers’ classrooms to see what they are doing? All these reports are good, but they don’t seem to work here in our situation!” [JERRY]

Assessment of past professional development Assessment of past professional development opportunitiesopportunities

165 teachers rated their professional development experiences as ineffective. 109 of these teachers claimed the content of the sessions they had attended was either too difficult, or too trivial.

63 teachers from this category expressed the content of their workshops either too narrow to have practical merit for long term instructional planning, or too general to have mathematical merit.

Assessment (continued)Assessment (continued)

32 teachers rated those workshops that focused on the use of technology in instruction as extremely helpful.

Areas in need of professional development:Areas in need of professional development:

Topics most frequently cited by teachers included: writing lessons that utilize applications of

mathematics (n=137), using calculators in lessons (n=201), using computers in lessons (n=182), implementing discovery learning activities

(n=173),

Areas in need of prof. development Areas in need of prof. development (continued)(continued)

ways to maintain productive discussions about mathematics among students (n=162),

ways to involve/engage all students in mathematics learning (n=195),

dealing with diverse abilities and background students’ bring to class (n=191),

convincing students that mathematics is important and useful (n=143),

Areas in need… (continued)Areas in need… (continued)

implementing open-ended exploratory activities (n=86),

establishing interest in mathematics and mathematics learning among students (n=191),

helping students take charge of their learning (n=94),

need for assistance in finding meaningful activities to use in instruction (n=73),

Areas in need…(continued)Areas in need…(continued)

organizing and monitoring cooperative group activities (n=88),

using students’ life experiences in my instruction (n=88),

using assessment techniques other than standard tests (n=59),

need for further training in how to facilitate learning rather than telling students what to do (n=23),

More Areas in Need…More Areas in Need…

do long term instructional planning (n=4), explaining “why” mathematical algorithms work

(n=44), deciding which mathematical conventions are

important for students to know (n=26), connecting mathematics to other subject areas

(n=57), making connections among various mathematical

topics (n=21).

Areas in need of prof. dev. (continued)Areas in need of prof. dev. (continued)

All teachers from urban schools: ESL and Absenteeism.

65% of the teachers in rural schools were concerned with learning about how to work with limited resources in classroom.

Views on research in mathematics education Views on research in mathematics education (3 questions)(3 questions)

First question asked teachers to rank their familiarity with findings of current research in mathematics education from very high (4) to very little (0).

M=3.1 = 0.4 ***See next slide for note***

Views on research… (continued)Views on research… (continued)

NOTE: It was determined through some interviews that many teachers interpreted documents and articles (like those in the MT) as mathematics education research rather than something specific from a research journal (like JRME)

Views on research… (continued)Views on research… (continued)

Second question asked teachers to rate the findings of current research along a continuum from very useful (4) to not useful at all (0). They were also asked to state the reasons for their rating.

M= 0.2 = 0.8

Explanations OfferedExplanations Offered

current research does not address the level of mathematics they taught (n=137).

research reports difficult to understand (n=121). failure to provide concrete guides for practice

(119). research studies did not focus on answering

questions that related to their particular settings (n=123). Nearly 95% of this population taught in rural and urban school districts.

Explanations (continued)Explanations (continued)

research reports did not make sense to them (n=86).

research settings artificial, thus, their findings not applicable to their own particular situation (n=74).

Twenty-five teachers made statements that indicated a lack of trust for those conducting research in mathematics education (i.e. University people like to tell us what to do).

Views on Research (continued)Views on Research (continued)

The third question asked the participants to identify areas in which they felt additional research was needed.

Responses: how to motivate all students in learning (n=181). methods to bridge informal explorations to formal

mathematics (n=139).

Other categories identified by teachers:Other categories identified by teachers:

Long term student outcomes of teaching concepts (n=51),

the influence of block scheduling on learning (n=37),

the impact of technology on mathematics learning (n=46).

Fourteen teachers stated that they did not know how to respond to the question.

Where do we go from here?Where do we go from here?

Need-driven research vs. curiosity-driven research: A balancing act

Authoritarian voice of research Making research reports useful and

meaningful: Ownership of results Early intervention: Teacher preparation Action research

Where do we go from here?Where do we go from here? (continued) (continued)

What do we do with reform in Urban and Rural school districts?

Components of effective professional development designs for HS teachers?

Closing comments: Pronouncing the Closing comments: Pronouncing the teachers’ voiceteachers’ voice

Here we deal with kids that have no vision of what is out there… they come from environments… tough environments… I mean, they go home and there is no one there… they work to support their families, school is not an important consideration for them. I have kids that can’t read. I have kids that don’t speak a word of English, and I have kids that come to school only to have a quiet place to sleep. These are tough, I mean, tough things to deal with. I don’t believe anyone has talked about what to do in these conditions. Good teaching in a place like this is hard-- it is really hard not to give up. (Amy)

Closing Comments (continued)Closing Comments (continued)

I really want to help all my students be successful. Finding the time to do this is a whole ‘nother thing. (Carolina)

I believe the reform movement is important, but when are administration and public officials going to place some value in what teachers think? My principal appears to be more concerned with state testing than if students really learn or retain the information. This makes it really difficult for me to change my instructional practices. (Kenny)