3 “To teach is first to understand “ (Shulman, 1986) TeacherS’ Knowledge“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)
4 Knowledge Base of Teaching 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 skillsContent knowledgeGeneral pedagogical skills
5 Models of Teacher Knowledge Elbaz (1983) – 5 components:a) knowledge of selfb) knowledge of the milieu of teachingc) knowledge of subject matterd) knowledge of curriculum developmente) knowledge of instructionLeinhardt & smith (1985)- 2 componentsa) knowledge of subject’s matterb) knowledge of lesson’s structure
6 Models of Teacher Knowledge Shulman (1986) – 7 categories of knowledgeContent knowledgeGeneral pedagogical knowledgePedagogical contents knowledge (PCK)Curriculum knowledgeKnowledge of learners and their characteristicsKnowledge of educational contextKnowledge of educational ends, purpose, and value and their philosophical and historical grounds
7 Content knowledge (Subject matter knowledge The amount and organisation of knowledge per se in the mind of the teacher.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.
8 General pedagogical knowledge 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....
9 Knowledge of Curriculum, aims and objectives 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.Erti kurikulumSatu program aktiviti yang disusunoleh guru untuk membolehkan pelajar mencapai objektif yang telah dirancangkannya.(Hirst, 1975)
10 Knowledge of learners and their characteristics The needs of learning basic mathematical conceptsLearners difficultiesLearners misunderstandingLearners misconceptionThese 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 strategiesNeed to know students’ learning style (imaginative, analytical, practical and dynamic learner)
11 Knowledge of Educational Context 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.
12 Knowledge of Educational ends, purposes, and values, and their philosophical and historical grounds. Purposes of teaching and learningValuesPhilosophy of teaching mathematicsHistorical ground
13 Pedagogical contents knowledge (PCK 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.
14 Pedagogical contents 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)Pedagogical knowledgeContent knowledgePCKPCK also include: the most useful forms of representation of those ideas, the most powerful analogies, illustrations, examples, explanations, and demonstration.
15 Pedagogical Content Knowledge (PCK) 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)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)PCKA 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 teachers organise the new knowledge related to the discipline into content that can be easily understood by the students during instructions(Tamir, 1987)
16 Components of Pedagogical Content Knowledge (PCK) Knowledge about contentKnowledge about studentsKnowledge of instructional strategiesClimate of T & L processesPurpose of the instructionFernandez-Balboa (1995)Knowledge related to teacher’s beliefComprehension of the concepts & misconceptionsKnowledge about curriculumKnowledge about instructional strategies & methods of delivery of the topic.(Shulman, 1986 & Grossman, 1990),COMPONENTSOF PCKSubject matter for instructional purposesStudents’ understanding of the subject matterThe use of media to teach the subjectThe instructional process for the subject(Marks, 1990)
17 Developing PCK in Mathematics of Pre-service Education Subject Matter KnowledgeGeneral Pedagogical KnowledgeSpecific Pedagogical Knowledge(Mathematical Pedagogy Knowledge – MPK)Contextual Knowledge
18 Knowledge of Subject Matter Substantive Structure knowledge- knowledge of facts, concepts, principles of the disciplineare organized to incorporate its factsSyntactic structures knowledge- rules of evidence, generated and validate in the subject,proofs, history of the disciplineKnowledge 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
19 PCK and Contextual Knowledge 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 sessionsPracticum in school (10 – 14 weeks)This practice is insufficient in helping future mathematics teachers to build up their contextual and pedagogical knowledge.
20 Each micro and macro teaching sessions should be recorded - critically analyse- carry out reflectionMacro 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’ outcomeWriting journals and reflections after each instructional session in the classroom
21 Model of Teacher Knowledge (Shulman, 1987) ComprehensionTransformation-Preparation-Representation-Selection-AdaptationInstructionEvaluationReflectionNew Comprehension
22 Model of Teacher Knowledge (Grossman 1990) Subject Matter KnowledgeGeneral Pedagogical KnowledgeSyntactic structure, content, substantive structureLearners learning, classroom management, curriculum instruction, other subjectsPedagogical Content KnowledgeKnowledge of students’ understanding, curricular,instructional strategiesKnowledge of Educational ContextCommunity, district, school
23 Model of Teacher Knowledge (Noor Shah, 2006) 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.
24 Model of Knowledge Base for Teaching (Turner-Bisset, 1997) Subject matter knowledgeSubstantive knowledgeSyntactic knowledgeBeliefs about the subjectCurriculum knowledgeGeneral pedagogical knowledgeKnowledge/Models of TeachingKnowledge of learner, empirical and cognitive,knowledge of contextsKnowledge of SelfKnowledge of Educational Ends
25 Model of Knowledge Base for Teaching (Shulman, 1987) Content knowledgeGeneral pedagogical knowledgeCurriculum knowledgePCKKnowledge of learner, empirical and their characteristicsKnowledge of educational contextKnowledge of educational ends, purpose, values, and philosophical and historical grounds
26 Understanding of purposes for teaching subject matter Components of PCKUnderstanding of purposes for teaching subject matterKnowledge of student understanding in a subjectCurricular KnowledgeKnowledge of instructional practicesGrossman (1990) and Shulman (1986)
27 RELATIONSHIP BETWEEN CONTENT KNOWLEDGE, CURRICULUM KNOWLEDGE, PEDAGOGICAL KNOWLEDGE, AND KNOWLEDGE ABOUT THE STUDENTS AND INSTRCUTIONAL STRATEGIESPedagogical knowledgeContent knowledgePCKOrientation tomathematics teaching)Mathematical content knowledgeSpecific mathematic curriculumGoal and outcomes of T & L mathematicsKnowledge about evaluationDimension of learning mathematicsMethods of mathematics learningKnowledge on how students understand mathematicsThe need of learning mathematicsDifficult topic to learnKnowledge about instructional strategiesSpecific teaching methodsSpecific strategies for topic