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- 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 Questions1. Why teach mathematics in innovation-drivensocieties?The answers are self-evident: - To develop quantitatively literate citizens - To enhance students’ ability to solve problems - To encourage logical thinking2. Does the standard school mathematics curriculumadvance 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 processes3. What types of problem solving are useful forinnovation-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 theywere 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 theyhave 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 ofturkey.• 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 explicitlytaught and intensively practice.•MC instruction must be embedded in subject content.•Learners must be informed of the usefulness of MCactivities.•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 MethodIMPROVEIntroduce new concepts to whole classMeta-cognitive questioning practice in small groupsPractice using MCQReview use of MCQObtain mastery over routine & CUN psVerificationEnrichment and remedial activities
- 11. IMPROVE: MC Self-Directed QuestioningComprehension: What is the problem about?Connection: How is the problem similar to, or different fromproblems I have already solved? Please explain your reasoning.Strategies: What kinds of strategies are appropriate for solvingthe problem and why? Please explain your reasoning.Reflection: Does the solution make sense? Can the problembe solved in a different way? Am I stuck? Why?
- 12. Findings
- 13. IMPROVE Effects Over One Year Math Achievement & Reasoning80757065 IMPROVE60 Control55504540 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 8070 7060 6050 5040 4030 3020 2010 100 0 Authentic total Routine tasks
- 17. Online Mathematical Literacy Discourse Motivation and Attitudes towards Problem Solving, Reasoning, Communication100 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 TimeALN 6.98 10.55 beforeALN+meta 6.97 11.47 12 before after afterALN+meta 5.47 10.36F2F+meta 10 5.6 9.38ALN 5.76 8.94 mean scoresF2F 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 3.976 3.8 IMPROVE74 Control72 3.770 3.66866 3.5 IMPROVE Decla K Proc K Cond K6462 Control60 IMPROVE 4.258 Control56 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 isexpensive, try ignorance! Please contact us: mevarz@mail.biu.ac.il; Bracha.kramarski@biu.ac.il Many Thanks!

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