OECD Conference Educating for Innovative Societies on 26 April 2012 - Session 3: STEM Education in Innovation-Driven Societies - Mathematics Education in Innovation-Driven Societies by Zemira Mevarech and Bracha Kramarski, Bar-Ilan University, Ramat-Gan

1. Metacognition and Math Education
in Innovation-Driven Societies:
What’s New?
Zemira R. Mevarech
Bracha Kramarski
Bar-Ilan University, Israel
OECD, Paris, 2012

2. Three Warm-up Questions
1. Why teach mathematics in innovation-driven
societies?
The answers are self-evident:
- To develop quantitatively literate citizens
- To enhance students’ ability to solve problems
- To encourage logical thinking
2. Does the standard school mathematics curriculum
advance these goals?
The answer is – Yes, to a partial extent:
- basic skills are necessary, though not sufficient
- It does not prepare students to solve complex, unfamiliar, non-
routine problems
- It is irrelevant for advancing math creativity, critical thinking, and
communications
- In no way does it train students to regulate problem-solving
processes
3. What types of problem solving are useful for
innovation-driven societies?

3. Problem Solving for Innovation-Driven Societies:
What Types of Problems are Useful?
• Standard, routine, textbook problems vs.
• Complex, Unfamiliar, Non-routine (CUN)
problems
• Authentic problems
Large variability in CUN problems:
What is complex to one student, is simple to another,
etc.

4. What Skills are useful
in Innovation-Driven Societies?
• Mathematical problem solving
• Mathematical reasoning
• Mathematical creativity and critical thinking
• Mathematical communications
• Meta-cognitive skills for regulating the solution of
CUN problems

5. Two Examples:
Which is the Cheapest Supermarket?
1. Before Christmas, several supermarkets advertised that they
were the cheapest supermarket in town.
• Your task is to decide which claim was correct.
• Please give your reasoning and findings.
• Please prepare a sixty-minute TV show to
present your findings.
2. Before Christmas, two supermarkets advertised that they
have sales. The prices in the two supermarkets were:
Supermarket A – 1kg of meat for $10 and 1kg of turkey for $8.
Supermarket B – 1kg of meat for $12 and 1kg of turkey for $6.
The Vincent family decided to buy 3kg of meat and 2kg of
turkey.
• Which supermarket is cheaper?

6. Is the Supermarket Problem (#1)
a CUN math problem?
• Is it authentic?
• Is it a mathematical task even though there are no
numbers in the task?
• Is it a complex task?
• Is it an unfamiliar task?
• Is it a non-routine task or is it based on ready made
algorithms?
• Can it advance mathematical reasoning, creativity,
critical thinking, or communications?
• How (if at all) can it create quantitative literate
citizens?
The progress from traditional to CUN problems requires the
application of meta-cognitive processes that regulate
cognitive processes

7. Meta-cognitive Processes for
Regulating Cognition
• What is meta-cognition all about?
• The nature of “meta”
• The “meta-cognitive engine”
• Does MC develop naturally and without
intervention?
• Teachers rarely emphasize the activation of
MC: Why is that?
• Is meta-cognition teachable? How?

8. Meta-cognitive Instruction:
When, How, and for Whom?
Research shows:
•Like cognitive strategies, MC needs to be explicitly
taught and intensively practice.
•MC instruction must be embedded in subject content.
•Learners must be informed of the usefulness of MC
activities.
•MC must be part of interactive learning environments,
like: cooperative learning or ICT.
•MC instruction is necessary at all grade levels: K-12,
HE, adults.
Veenman (2006); Mevarech and Kramarski (2012)

9. IMPROVE: MC Instructional Method
Theoretical Basis
Cooperative
Metacognitive Learning
IMPROVE
Guidance
Feedback-
correctives

10. IMPROVE:
MC Instructional Method
IMPROVE
Introduce new concepts to whole class
Meta-cognitive questioning practice in small groups
Practice using MCQ
Review use of MCQ
Obtain mastery over routine & CUN ps
Verification
Enrichment and remedial activities

11. IMPROVE:
MC Self-Directed Questioning
Comprehension: What is the problem about?
Connection: How is the problem similar to, or different from
problems I have already solved? Please explain your reasoning.
Strategies: What kinds of strategies are appropriate for solving
the problem and why? Please explain your reasoning.
Reflection: Does the solution make sense? Can the problem
be solved in a different way? Am I stuck? Why?

12. Findings

13. IMPROVE Effects Over One Year
Math Achievement & Reasoning
80
75
70
65
IMPROVE
60
Control
55
50
45
40
Pre-test Algebra Math Reasoning

14. IMPROVE & Long Lasting Effects:
Immediate & Delayed Post-tests

15. Which PIZZA is the best offer? Why?
Type Price Diameter Price for
of PIZZA per suppleme
PIZZA nts (NIS)
(NIS)
PIZZA BOOM
Personal 3.50 15 4.00
PIZZA
Small 6.50 23 7.75
Medium 9.50 30 11.00
Large 12.50 38 14.45
SUPPER PIZZA
Small 8.65 30 9.95
Medium 9.65 35 10.95
Large 11.65 40 12.95
MC PIZZA
Small 6.95 25 1.00
Large 9.95 35 1.25

16. IMPROVE for solving
Authentic Tasks &
Transferring to Routine Tasks Coop+IMP Coop
80
70
70
60
60
50
50
40 40
30 30
20 20
10 10
0 0
Authentic total Routine tasks

17. Online Mathematical Literacy Discourse
Motivation and Attitudes
towards Problem Solving, Reasoning, Communication
100 Online +IMP Online
90 6
80 5
70 4
3
60 2
50 1
0
40
30
20
10 • Motivation:
0 “Online learning aroused my interest
in mathematical problem solving”
• Reasoning:
“Online problem solving encouraged me
to explain my reasoning”
• Communication:
“ I look forward to my friends’ reactions
to my online solutions”

18. Development of Scientific Literacy
by Group and Time
ALN 6.98 10.55 before
ALN+meta 6.97 11.47
12
before after after
ALN+meta 5.47 10.36
F2F+meta 10 5.6 9.38
ALN 5.76 8.94
mean scores
F2F 8 5.47 8.02
0.770206 0.580645161
6
4 ‫מדידות‬ ‫מדידות‬ ‫הסקת מסקנוהסקת מסקנוהבנת מידע הבנת מידע תרשימים תרשימים‬
‫ת‬ ‫ת‬ ‫תכנון ניסוי‬
‫לפני‬ ‫אחרי‬ ‫לפני‬ ‫אחרי‬ ‫לפני‬ ‫אחרי‬ ‫לפני‬ ‫אחרי‬ ‫לפני‬
1 2 6.83 6.94 6.94 6.52 9.9 11.24 9.83 11.22 9.94
2 6.58 6.88 6.04 6.94 9.12 13.5 9.06 13.44 9.7
3 6.3 6.74 6.06 6.74 9.15 15.21 9.15 15.11 9.75
4
0 6 6.17 6.17 6.94 10.05 18.35 10.11 18.64 10.35
ALN+meta F2F+meta ALN F2F
ALN+Meta > F2F+Meta = ALN > F2F Range 0-15

19. Impact of IMPROVE at the College
4.1
4
3.9
76
3.8 IMPROVE
74 Control
72 3.7
70
3.6
68
66 3.5
IMPROVE Decla K Proc K Cond K
64
62 Control
60 IMPROVE
4.2
58 Control
56 4.1
Math Math 4
Knowledge Reasoning
3.9
3.8
3.7
3.6
3.5
Plan Info Monitor Debug Eval

20. Research shows:
• IMPROVE advances students’ CUN problem
solving without harming students’ abilities to
solve “standard” problems.
• Positive effects were found for K-12, HE, and
Professional Development, with or without ICT.
• Teaching strategies alone is not enough
• IMPROVE is suitable for all students: both lower
and higher achievers.
• IMPROVE showed similar positive effects in
science education.
• IMPROVE helps to increase motivation, self-
confidence, judgment of learning.

21. Challenges: What next?
Evidence-Based Policy Making
• International cooperation – don’t reinvent the
wheel
• To be effective teach MC directly and practice
it intensively – We know how to do this
• MC will be effective in the national curriculum
• Include CUN problems in textbooks, teacher
guides, and professional development
• Pre- and in-service professional development
followed by workshops and in-class mentoring

22. Challenges: What next?
Evidence-Based Policy Making (cont.)
• ICT: Students find it particularly difficult to
apply MC in ICT environments. It is therefore
essential to reconstruct these environments by
embedding MC in them.
• Assessment and evaluation – “You teach what
you assess”
• MC pedagogies in OECD countries
• Teaching for understanding can be achieved by
implementing evidence-based MC pedagogies

23. If you think education is
expensive, try ignorance!
Please contact us:
mevarz@mail.biu.ac.il;
Bracha.kramarski@biu.ac.il
Many Thanks!