1. Applying Cognitive Psychology in the Mathematics Classroom
Lew Ludwig
Denison University –
2017 Mathfest - Encouraging Effective Teaching Innovation

2. Overview

3. Overview
testing to improve retention of knowledge

4. Overview testing to improve retention of knowledge
distributed practice and interleaving of material

5. Overview testing to improve retention of knowledge
distributed practice and interleaving of material
exploratory questioning

6. Based on
Inexpensive techniques to improve education:  Applying cognitive psychology to enhance educational practice
-- Roediger and Pye, 2012

7. Testing to improve retention of knowledge
Karpicke & Blunt (2011)

8. Testing to improve retention of knowledge
Karpicke & Blunt (2011)
The study – read a passage , then _____, then take a test a week later

9. Testing to improve retention of knowledge
Karpicke & Blunt (2011)
The study – read a passage , then _____, then take a test a week later
Read passage once for five minutes

10. Testing to improve retention of knowledge
Karpicke & Blunt (2011)
The study – read a passage , then _____, then take a test a week later
Read passage once for five minutes
Read passage in four consecutive five-minute sessions

11. Testing to improve retention of knowledge
Karpicke & Blunt (2011)
The study – read a passage , then _____, then take a test a week later
Read passage once for five minutes
Read passage in four consecutive five-minute sessions
Read passage and created a concept map during

12. Testing to improve retention of knowledge
Karpicke & Blunt (2011)
The study – read a passage , then _____, then take a test a week later
Read passage once for five minutes
Read passage in four consecutive five-minute sessions
Read passage and created a concept map during
Read passage, wrote free-form for 10 minutes, reread and took a test

13. Testing to improve retention of knowledge
Karpicke & Blunt (2011)
The study – read a passage , then _____, then take a test a week later
Read passage once for five minutes
Read passage in four consecutive five-minute sessions
Read passage and created a concept map during
Read passage, wrote free-form for 10 minutes, reread and took a test

14. Testing to improve retention of knowledge
Karpicke & Blunt (2011)
The study – read a passage , then _____, then take a test a week later
Read passage once for five minutes
Read passage in four consecutive five-minute sessions
Read passage and created a concept map during
Read passage, wrote free-form for 10 minutes, reread and took a test

15. Testing to improve retention of knowledge

16. Testing to improve retention of knowledge

17. Testing to improve retention of knowledge

18. How do I incorporate testing?
Test Tuesday
MTWF - every Tuesday
Page from an “old” test
Timed
Think-pair-share
10-15 minutes

19. Distributed practice and interleaving of material

20. Distributed practice and interleaving of material
Group 1
15 fast balls
15 curve balls
15 change ups

21. Distributed practice and interleaving of material
Group 1
15 fast balls
15 curve balls
15 change ups
Group 2
45 mixed balls, 15 of each

22. Distributed practice and interleaving of material
Group 1
15 fast balls
15 curve balls
15 change ups
Group 2
45 mixed balls, 15 of each

23. How do I incorporate distributed practice and interleaving?

24. How do I incorporate distributed practice and interleaving?
Five online questions per day,
Two old, three new

25. How do I incorporate distributed practice and interleaving?
Five online questions per day,
Two old, three new
Test Tuesday

26. Exploratory questioning

27. Exploratory questioning
Students monitor their learning by asking questions as they engage with the material:

28. Exploratory questioning
Students monitor their learning by asking questions as they engage with the material:
Does this passage make sense?

29. Exploratory questioning
Students monitor their learning by asking questions as they engage with the material:
Does this passage make sense?
How does this concept relate to what I already know?

30. Exploratory questioning
Students monitor their learning by asking questions as they engage with the material:
Does this passage make sense?
How does this concept relate to what I already know?
Why is this statement true?

31. How do I incorporate exploratory questioning?
Reading
Notes

32. How do I incorporate exploratory questioning?
Reading
Notes

33. Review testing to improve retention of knowledge
distributed practice and interleaving of material
exploratory questioning

34. References THANKS!! LUDWIGL@DENISON.EDU
Henry L Roediger III and Mary A. Pye (2012)
Inexpensive techniques to improve education:  Applying cognitive psychology to enhance educational practice, Journal of Applied Research in Memory and Cognition, Vol. 1, Issue 4 (December 2012):
Ludwig (2015)
Introduction to Proofs Over-Easy: A Low-Cost Alternative to the Flipped Classroom, Beyond Lecture: Techniques to Improve Student Proof-Writing Across the Curriculum, MAA Notes Series, 2015.
THANKS!!