1. Bar-Ilan University, Israel
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. Standard, routine, textbook problems vs.
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
Learning
Metacognitive
Guidance
IMPROVE
Feedback-correctives

10. IMPROVE: MC Instructional Method
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. MC Self-Directed Questioning
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

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

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

16. IMPROVE for solving Authentic Tasks & Transferring to Routine Tasks

17. Online Mathematical Literacy Discourse Motivation and Attitudes towards Problem Solving, Reasoning, Communication
Motivation:
“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
The greatest improvement in general scientific thinking and inquiry skills was among students who received metacognitive guidance in an ALN environment (Figures 1, 2). We found no difference among students in groups which did not receive metacognitive guidance in an ALN environment, and students in groups who received metacognitive guidance in a F2F environment. The least improvement was found among students who participated in a group that did not receive metacognitive guidance in a F2F environment.
ALN+Meta > F2F+Meta = ALN > F2F
Range 0-15

19. Impact of IMPROVE at the College

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:
Many Thanks!