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L1 introduction
1. PMC/PLG 561:
THEORIES OF TEACHING AND
LEARNING MATHEMATICS
Introduction and overview of
the theories of teaching and
learning mathematics
DR CHEW CHENG MENG PPIP
USM
2. Piaget’s theory of cognitive development
all people progress through four stages of
cognitive development:
sensorimotor stage (birth to 2 years)
preoperational stage (2 years to 7 years)
concrete operational stage (7 years to 11
years)
formal operational stage (11 years and above)
Overview of the theories of teaching
and learning mathematics
DR CHEW CHENG MENG PPIP
USM
3. four main factors that affect the four stages of
cognitive development:
I. maturation
II. experience
III. social interaction
IV. equilibration
Overview of the theories of teaching
and learning mathematics
DR CHEW CHENG MENG PPIP
USM
4. Bruner's stages of representation
Learning passes through three stages of
representation:
enactive stage
iconic stage
symbolic stage
Overview of the theories of teaching
and learning mathematics
DR CHEW CHENG MENG PPIP
USM
5. Dienes's theory of mathematics learning
four basic principles:
dynamic principle
perceptual variability principle
mathematical variability principle
constructivity principle
Overview of the theories of teaching
and learning mathematics
DR CHEW CHENG MENG PPIP
USM
6. Behaviorism
Pavlov’s Classical Conditioning
Thorndike’s Laws of Exercise and Effect
Skinner’s Operant Conditioning
Overview of the theories of teaching
and learning mathematics
DR CHEW CHENG MENG PPIP
USM
7. Information Processing Theory
focuses on how people attend to environmental
events, encode information to be learned and
relate it to knowledge in memory, store new
knowledge in memory, and retrieve it as needed
Overview of the theories of teaching
and learning mathematics
DR CHEW CHENG MENG PPIP
USM
8. Constructivism
Radical constructivism
Social constructivism
Overview of the theories of teaching
and learning mathematics
DR CHEW CHENG MENG PPIP
USM
9. Vygotsky’s (1978) theory of learning
Two levels of learning:
Zone of Proximal Development (ZPD)
Overview of the theories of teaching
and learning mathematics
DR CHEW CHENG MENG PPIP
USM
10. Van Hiele's Theory of Geometrical Thinking
students progress sequentially through five
hierarchical levels of thinking in the process of
learning geometry aided by appropriate instruction:
Level 1 (Recognition/Visualization)
Level 2 (Analysis)
Level 3 (Ordering/Abstraction)
Level 4 (Deduction)
Level 5 (Rigor)
Overview of the theories of teaching
and learning mathematics
DR CHEW CHENG MENG PPIP
USM
11. To help students progress from one level of geometric
thinking to the next, the theory suggests a sequence
of five phases of learning:
Phase 1 (Information)
Phase 2 (Guided orientation)
Phase 3 (Explicitation)
Phase 4 (Free orientation)
Phase 5 (Integration)
Overview of the theories of teaching
and learning mathematics
DR CHEW CHENG MENG PPIP
USM
12. Visualisation and representation in mathematics
Visualisation
Hanson et al. (1994)
Abraham Arcavi (2003)
Representation
Davis et al. (1982)
Overview of the theories of teaching
and learning mathematics
DR CHEW CHENG MENG PPIP
USM
13. Skemp's theory of learning mathematical
concepts
Instrumental understanding
Knowing rules without reasons
Relational understanding
Knowing both what to do and why
Overview of the theories of teaching
and learning mathematics
DR CHEW CHENG MENG PPIP
USM
14. Example: Robert Gagné’s learning hierarchy
Identifies eight hierarchical levels of learning:
Signal learning
Stimulus-response learning
Chaining
Verbal association
Multiple discrimination
Concept learning
Principle learning
Problem solving
Other theories of teaching and
learning mathematics
DR CHEW CHENG MENG PPIP
USM