1. How Students Learn

2. Learning Theories Behaviorism Cognitivism Constructivism
Multiple Intelligences

3. – stresses teacher-centered approaches
Behaviorism
(Thorndike, Pavlov, Skinner) – early-mid 20th Century
Particularly interested in measurable changes in behavior
Behavior change indicates learning
Stimulus & Response
Critics claim behaviorists regard learners as empty vessels needed to be filled
– stresses teacher-centered approaches

4. Cognitivism (Gagne, (1950s to late 20th Century)
To complement behaviorism
Non observable mental constructs are also important
Non observable are hard to measure & analyzable
– stresses the mind: thinking, reflection, motivation, memory, student control, metacognition, etc.

5. Constructivism (late 20th Century till now)
Knowledge is actively constructed by learner
New knowledge is possible through reflection upon existing knowledge
Learning is a social process
stresses student-centered approaches, learning rather than teaching, contextual, cooperative, etc.

6. Multiple Intelligences
1 Linguistic
2 Logical-mathematical
3 Spatial
4 Bodily-kinesthetic
5 Musical
6 Naturalistic
7 Interpersonal
8 Intrapersonal
stresses individual-centered approaches

7. How Students Learn
Mathematics

8. How Students Learn Mathematics Generalization Discovery Investigation
Authentic
Motivation
Recognizing Patterns
Drill & Practice
Reflection
Mnemonics
Visualization
Connections
Competition
Social Interaction
In Isolation
Fun
Learn what they
like !

9. Investigation & Discovery
How Students Learn
Mathematics
- Pythagoras Theorem
Investigation & Discovery

10. Through Authentic Activities
How Students Learn
Mathematics
- Distances & Scales
Through Authentic Activities

11. How Students Learn Mathematics - Basic Operations & Beyond
Through Competition & Fun

12. Through Interests & Curiosity
Numbers - Division
If David Beckham gets $250 million in 5 years, what is his salary? Wage?
In a day? An hour? A second?
in Rupiah !!!!!!!!
Through Interests & Curiosity

13. Multiple Intelligences: Through Visualizations
How Students Learn
Mathematics
- Graphs
Multiple Intelligences: Through Visualizations

14. How Students Learn
Mathematics
- Formulas
Through Mnemonics

15. Through Mnemonics
sin x =
kos x =
tan x =

16. How Some Geniuses Learn
Mathematics

17. by Following Instructions
Found it

18. by Following Instructions
Found it

19. by Following the Rules

20. by Following the Rules

21. by Following the Rules

22. by Following More Rules

23. by Following More Rules

24. by Following More Rules

25. by Recognizing Patterns

26. by Recognizing Patterns

27. by Peter the Great