TEACHERS’ KNOWLEDGE AND PEDAGOGICAL CONTENT

KNOWLEDGE

LEARNING OUTCOMES:

•State teachers knowledge, and •Describe PCK orientation to mathematics teaching

“To teach is first to understand “ (Shulman, 1986)

“If the promise of the teaching profession is to achieve, we must attend to the processes by which its knowledge base is developed and transmitted” (Howsam et al. (1976)

What knowledge base? Is enough known about teaching to support

a knowledge base? Isn’t teaching little more than personal

style, artful communication, knowing some subject matter, and applying the results of recent research on teaching effectiveness?

Policymakers and Teacher Educators :

• Basic skills• Content knowledge• General pedagogical skills

Elbaz (1983) – 5 components:a) knowledge of selfb) knowledge of the milieu of teachingc) knowledge of subject matterd) knowledge of curriculum developmente) knowledge of instruction

Leinhardt & smith (1985)- 2 componentsa) knowledge of subject’s matterb) knowledge of lesson’s structure

Content knowledge General pedagogical knowledge Pedagogical contents knowledge (PCK) Curriculum knowledge Knowledge of learners and their characteristics Knowledge of educational context Knowledge of educational ends, purpose, and

value and their philosophical and historical grounds

Shulman (1986) – 7 categories of knowledge

Substantive structure: Knowledge of the major facts, concepts,

principles within a field and the relationships among them.

Syntactic structure: Knowledge regarding methods, rules of evidence

and proofs in that domain and into how knowledge is being evaluated by the discipline’s experts.

The amount and organisation of knowledge per se in the mind of the teacher.

Principle and strategy of classroom management as well as its organisation that arises in the delivery of the subject matter.

- Example: understand how students learn, theories of learning, child psychology, teaching strategies, classroom

management, assessment, etc....

Curriculum knowledge: -Particular grasp of the materials and programmes

that serve as ‘tool of the trade’ of teachers. - CDC provides Mathematics teachers with

syllabuses of the KBSM Mathematics and Additional Mathematics along with the curriculum specification.

Aims and Objectives: - Need to understand the aims and objectives of the

mathematics curriculum – the planned teaching activities are in tandem.

The needs of learning basic mathematical concepts Learners difficulties Learners misunderstanding Learners misconception

These knowledge involve conceptual and procedural knowledge, conceptual errors and level of understanding.

Need to know techniques in evaluating learners’ understanding and diagnosing misconception/appropriate learning strategies

Need to know students’ learning style (imaginative, analytical, practical and dynamic learner)

Knowledge of school, classrooms and all setting where learning takes place ( districts, school, communities and cultures).

Grossman (1990) – Contextual knowledge includes knowledge of the area where the teacher teaches like the area’s aspiration, expectations and limitations.

Educational ends Purposes of teaching and learning Values Philosophy of teaching mathematics Historical ground

Domain of knowledge that was different from both knowledge of the content and general knowledge of teaching (Shulman,1986).Knowledge formed through the synthesis of three knowledge bases: content knowledge, pedagogical knowledge and contextual knowledge – unique mixture of pedagogy and content.

Pedagogical knowledge

Content knowledge

PCK

Teacher’s deep understanding of a subject area she/he must also be able to foster understanding of subject or concepts for students

PCK also include: the most useful forms of representation of those ideas, the most powerful analogies, illustrations, examples, explanations, and demonstration.

PCK

Bridge that a teacher builds to link his or her understanding of the content to that of the students understanding of the same content (Grossman, et al. 1989)

The teachers organise the new knowledge related to the discipline into content that can be easily understood by the students during instructions

(Tamir, 1987)

A unique knowledge to the teacher and is the fundamental knowledge to have in enabling him or her to connect the pedagogical knowledge (how to teach) with the content knowledge (what to teach)

(Pesno, 2002)

The most regularly taught topics in one’s subject area, the most useful forms of representation of those ideas, the most powerful analogies, illustrations, examples, explanations, the ways of representation and formulating the subject that make it comprehensible to others

(Shulman, 1986)

COMPONENTS

OF PCK

• Knowledge related to teacher’s belief

• Comprehension of the concepts & misconceptions

• Knowledge about curriculum

• Knowledge about instructional strategies & methods of delivery of the topic.

(Shulman, 1986 & Grossman, 1990),

• Knowledge about content

• Knowledge about students

• Knowledge of instructional strategies

• Climate of T & L processes

• Purpose of the instruction

Fernandez-Balboa (1995)

• Subject matter for instructional purposes

• Students’ understanding of the subject matter

• The use of media to teach the subject

• The instructional process for the subject

(Marks, 1990)

Subject Matter Knowledge General Pedagogical Knowledge Specific Pedagogical Knowledge

(Mathematical Pedagogy Knowledge – MPK)

Contextual Knowledge

Knowledge of Subject Matter

Substantive Structure knowledge

- knowledge of facts, concepts, principles of the discipline

are organized to incorporate its facts Syntactic structures knowledge

- rules of evidence, generated and validate in the subject,

proofs, history of the discipline

• Knowledge of substantive and syntactic structures has implication for what teachers choose to teach, and how they teach.

• The amount of the degree of substantive & syntactic structures that a teacher possesses concerning his/her respective field would certainly influence the delivery of the subject content to the students

Practical experience is necessary for the development of classroom experience and can be usefully supplemented by analysis of cases that provide realistic, contextualized exemplars of research-based principles of effective teaching.

Current practice: School Orientation Programmes (2 weeks)

Micro and macro teaching sessions

Practicum in school (10 – 14 weeks)

This practice is insufficient in helping future mathematics teachers to build up their contextual and pedagogical knowledge.

Each micro and macro teaching sessions should be recorded

- critically analyse

- carry out reflection Macro teaching session should involve school pupils rather than the peers as what is being currently practiced. School-based concept for macro teaching sessions and make a presentation of the teaching report as a ‘problem-based learning’ outcome Writing journals and reflections after each instructional session in the classroom

Subject Matter Knowledge

General Pedagogical Knowledge

Pedagogical Content

Knowledge

Knowledge of Educational

Context

Syntactic structure, content,

substantive structure

Learners learning,

classroom management,

curriculum instruction, other

subjectsKnowledge of

students’ understanding, curricular,instructional strategies

Community, district, school

Developed teacher knowledge model based on Grossman (1990) – four components involved:

- The content knowledge- The general pedagogical knowledge- The specific pedagogical knowledge- The contextual knowledge.

Subject matter knowledge Substantive knowledge Syntactic knowledge Beliefs about the subject

Curriculum knowledge General pedagogical knowledge Knowledge/Models of Teaching Knowledge of learner, empirical and cognitive, knowledge of contexts Knowledge/Models of Teaching Knowledge of Self Knowledge of Educational Ends

Content knowledge General pedagogical knowledge Curriculum knowledge PCK Knowledge of learner, empirical and their

characteristics Knowledge of educational context Knowledge of educational ends, purpose,

values, and philosophical and historical grounds

Grossman (1990) and Shulman (1986)

Pedagogical knowledge

Content knowledge

PCK

Orientation to mathematics teaching