Presentation on theme: "Bar-Ilan University, Israel"— Presentation transcript:
1 Bar-Ilan University, Israel Metacognition and Math Education in Innovation-Driven Societies: What’s New?Zemira R. MevarechBracha KramarskiBar-Ilan University, IsraelOECD, 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 thinking2. 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 processes3. 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) problemsAuthentic problemsLarge 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 solvingMathematical reasoningMathematical creativity and critical thinkingMathematical communicationsMeta-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 topresent 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 CooperativeLearningMetacognitiveGuidanceIMPROVEFeedback-correctives
10 IMPROVE: MC Instructional Method Introduce 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 MC Self-Directed Questioning IMPROVE:MC Self-Directed QuestioningComprehension: 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?
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)DiameterPriceper PIZZA(NIS)Typeof PIZZAPIZZA BOOM4.00153.50Personal PIZZA7.75236.50Small11.00309.50Medium14.453812.50LargeSUPPER PIZZA9.958.6510.95359.6512.954011.65MC PIZZA1.00256.951.25
16 IMPROVE for solving Authentic Tasks & Transferring to Routine Tasks
17 Online Mathematical Literacy Discourse Motivation and Attitudes towards Problem Solving, Reasoning, CommunicationMotivation:“Online learning aroused my interestin mathematical problem solving”Reasoning:“Online problem solving encouraged meto explain my reasoning”Communication:“ I look forward to my friends’ reactionsto my online solutions”
18 Development of Scientific Literacy by Group and TimeThe 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 > F2FRange 0-15
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 enoughIMPROVE 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 wheelTo be effective teach MC directly and practice it intensively – We know how to do thisMC will be effective in the national curriculumInclude CUN problems in textbooks, teacher guides, and professional developmentPre- 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 countriesTeaching for understanding can be achieved by implementing evidence-based MC pedagogies
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