L1 introduction

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

 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
USM

 four main factors that affect the four stages of
cognitive development:
I. maturation
II. experience
III. social interaction
IV. equilibration
USM

 Bruner's stages of representation
 Learning passes through three stages of
representation:
 enactive stage
 iconic stage
 symbolic stage
USM

 Dienes's theory of mathematics learning
 four basic principles:
 dynamic principle
 perceptual variability principle
 mathematical variability principle
 constructivity principle
USM

 Behaviorism
 Pavlov’s Classical Conditioning
 Thorndike’s Laws of Exercise and Effect
 Skinner’s Operant Conditioning
USM

 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
USM

 Constructivism
 Radical constructivism
 Social constructivism
USM

 Vygotsky’s (1978) theory of learning
 Two levels of learning:
 Zone of Proximal Development (ZPD)
USM

 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)
USM

 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)
USM

 Visualisation and representation in mathematics
 Visualisation
 Hanson et al. (1994)
 Abraham Arcavi (2003)
 Representation
 Davis et al. (1982)
USM

 Skemp's theory of learning mathematical
concepts
 Instrumental understanding
 Knowing rules without reasons
 Relational understanding
 Knowing both what to do and why
USM

 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
USM

L1 introduction

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L1 introduction