TEACHING AND LEARNING APPROACHES IN MATHEMATICS

There are two main approaches in teaching and learning mathematics based on the psychological theories in education:

 Behaviorist approach :

1. drill -practice (practice makes perfect)
2. mastery of skills (lower order thinking skills- knowledge, comprehension and application)
3. performance- based  (how to do) - suitable for routine/familiar problems
4. focus on algorithm (procedures/steps of calculation)
5. mistakes and errors should be avoided/minimized
6. teacher- centered (focus on teaching)

Cognitive approach :

1. construction of meaning (searching for meaning)
2. conceptual understanding (higher order thinking skills - analysis, synthesis and evaluation)
3. thinking- based (emphasis on why) - suitable for non- routine/ unfamiliar problems
4. focus on heuristic (general methods of solving problems) - Polya's Model
5. mistakes and errors is good indicators of misconceptions and difficulties
6. student- centered (focus on learning)

Discuss with suitable examples on how to use behaviorist and cognitive approaches in teaching and learning mathematics in the classroom. Why teachers need to master both approaches?




 

PERSPECTIVES OF MATHEMATICS ANT ITS RELATION TO TEACHING AND LEARNING

Perspectives of mathematics :

Mathematics as a dynamic and continually expanding field of human creation, involving the process of inquiry, thinking, reasoning (with its intellectual rigour), discovery and invention as well as a cultural product of various civilizations.

1. Mathematics is a practical and problem- driven and problem solving knowledge (ie mainly arise from practical or real- life situations).

2. Mathematics is a science of numbers, shape and space and relationships.

3. Mathematics as a language

4. Mathematics as a way of thinking


Assignment 1 :

Discuss in what ways do the perspectives of mathematics influence the curriculum design in mathematics at the secondary school level ?

Assignment 1

Assignment 1 (20%) with presentation

Problem solving is a fundamental process and an integral part of mathematics.
Critically discuss with suitable examples the epistemology (origin/sources/discovery/grows/development/potential/validity/limitation (if any) of one mathematical concept/topic/branch in the contexts of problem solving (refer to at least one mathematics textbook at the primary or secondary school).

Sinopsis MPS 1813

MPS 1813 -  PENYELESAIAN MASALAH DALAM PENDIDIKAN MATEMATIK
                      (PROBLEM SOLVING IN MATHEMATICS EDUCATION)

                      Key concepts/questions :

                      1. Mathematics - brief history and philosophy of mathematics related to problem 
                          identification, formulation and solution.

                     2.  Mathematics as problem solving - models (strategies, methods, heuristics
                          and techniques).

                     3.  Mathematics education (teaching, learning and assessment) from the perspective of
                          problem solving.

                     4.  Research on problem solving in mathematics education.

                     5.  Issues and trends of problem solving in mathematics education.

                     



                    

MATHEMATICS - THE SCIENCE OF PATTERNS AND ITS IMPLICATIONS TO TEACHING AND LEARNING

Mathematics is one way of understanding the world and universe.
Patterns are everywhere. Patterns occur in geometry (eg wallpaper/tiles patterns using various geometrical shapes/figures), in music,  in human behavior (eg voting patterns )

What the mathematician does is mainly looking for a  pattern or to examine abstract patterns which give rise to different branches of mathematics - numerical patterns/patterns of numbers and counting  (arithmetic and number theory), patterns of shape, symmetry and regularity (geometry; the mathematics of beauty- transformation), patterns of motion and change (mathematics in motion- calculus), patterns of reasoning and communicating (logic; logical arguments/connections), patterns of chance (probability theory - making prediction etc), patterns of closeness and position (topology), and so on.

Those patterns can either real or imagined, visual or mental, static or dynamic, qualitative or quantitative,
purely theoretical or utilitarian.

Those patterns can arise from the world or phenomena around us, from the depths of space and time
( geometry of the universe; three- dimensional physical universe etc), or from the inner workings of the human mind.

Discuss the implications of maths as a science of patterns to the teaching and learning of mathematics in secondary schools.

KAEDAH UMUM PENYELESAIAN MASALAH

Dalam kehidupan seharian, kita sering menghadapi pelbagai jenis masalah (persoalan) samada berbentuk peribadi, keluarga, masyarakat, ekonomi, politik dsb (kecil atau besar) yg memerlukan kemahiran kita menyelesaikan masalah masalah berkenaan dgn betul dan berkesan. Oleh yg demikian kemahiran menyelesaikan masalah merupakan satu perkara asas yg dapat membantu kita berfungsi dgn lebih berkesan dlm kehidupan ini.

Sesaorang itu dikatakan menghadapi masalah bilamana ia tidak mempunyai penyelesaian serta-merta/segara terhadap sesuatu soalan yg dikemukakan . Terdapat dua syarat utama yg menentukan kewujudan sesuatu masalah kpd sesaorang individu iaitu :

1. mesti terdapat tujuan/matlamat/objektif/perkara yg jelas untuk dicari/dicapai/diselesaikan.
2. mesti terdapat halangan(obstacles) terhadap jalan penyelesaian itu.

Namun demikian kita perlu maklum bahawa bergantung kpd pengalaman dan pengetahuan sedia ada
masing masing sesuatu masalah yg menjadi "masalah" kepada sesaorang individu tidak semestinya menjadi masalah kpd indidividu yg lain. Sebagai contoh selesaikan masalah berikut :

Ahmad mempunyai RM 60. Dia menggunakan 1/4 drp wangnya untuk membeli 2 kg udang.
Berapakah harga sekilogram udang itu?

Secara umumnya terdapat 4 langkah utama ( dlm pendidikan matematik ini dikenali sbg kaedah Polya) bagi menyelesaikan sesuatu masalah :

1. memahami masalah ( tentukan data/maklumat yg ada/diberi - lebih umum lagi apakah punca punca kpd
    masalah berkenaan?) - pemikiran kritis
2. merancang strategi penyelesaian (tentukan kaedah,langkah,formula, teknik, lukis gambarajah, bina jadual,
    bina graf, laksanakan ujikaji, cadangan penyelesaian dsb) - pemikiran kreatif
3. melaksanakan strategi penyelesaian   - pemikiran kreatif
4. menyemak semula jawapan (adakah jawapan yg diperolehi tepat, munasabah dan logik?
     kaedah alternatif ?) - pemikiran kritis 

Walaupun kaedah diatas sering digunakan untuk menyelesaikan pelbagai jenis dan bentuk masalah matematik
tetapi  ianya boleh digunakan sbg kaedah dan proses umum bagi menyelesaikan sebarang masalah dlm konteks yg luas dlm kehidupan seharian.

MANTIK, KBKK DAN PENYELESAIAN MASALAH

Pengenalan

Mantik (logik) dan peranannya :

             -  akar kata/berasal drp bahasa arab "mantiq" bererti percakapan/pertuturan dan fikiran yg benar
                 (ilmu kaedah/cara/teknik/strategi berfikir secara bersistem dan teratur untuk mencari kebenaran
                  dan mengelak drp kesilapan dan kesalahan berfikir)

             -  salah satu cabang bidang falsafah selain epistemologi, metafizik dan aksiologi  (etika dan
                 estetika).
          
            -  dianggap ilmu sepunya/sejagat/ilmu alat bagi seluruh disiplin ilmu, samada falsafah atau bukan
                falsafah
          
             -  melatih kekuatan hujah/kecekapan akal/ketajaman minda/ rasional dlm kehidupan seharian, dlm
                perbincangan, dialog, debat, penghujahan (yg sahih, benar dan tepat), pembuktian/evidens,          
                kemunasabahan, premis/dasar
                proposisi/pernyataan dsb.
           
             -  mendasari ilmu sains dan matematik, proses berfikir secara induktif (kes khusus kpd umum) dan  
                deduktif (kes umum kpd khusus)
          
             - mengembangkan kemahiran berfikir secara kritis dan kreatif, kemahiran aras tinggi (HOTs) serta
               kebolehan penyelesaian masalah dlm pelbagai konteks dan bidang.