Metacognition and Math Education in Innovation-Driven Societies: What’s New?

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 problemsolvingare 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 taskeven 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 MethodTheoretical Basis Feedback-correctives Cooperative Learning Metacognitive Guidance IMPROVE

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

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

15. Which PIZZA is the best offer? Why?

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

17. Online Mathematical Literacy DiscourseMotivation and Attitudestowards 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 ofScientific Literacy by Group and Time 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: mevarz@mail.biu.ac.il; Bracha.kramarski@biu.ac.il Many Thanks!