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Immediate and delayed effects of meta-cognitive instruction on regulation of cognition and mathematics achievement. Z. R. Mevarech C. Amrany. Research questions.

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Immediate and delayed effects of meta-cognitive instruction on regulation of cognition and mathematics achievement

Z. R. Mevarech

C. Amrany

Research questions
Research questions on regulation of cognition and mathematics achievement

  • Are results obtained in previous studies involving the IMPROVE model reproducible with high school students studying for the matriculation exam?

  • Do students use procedural metacognitive processes in delayed, stressful situations (exams)?

Metacognition on regulation of cognition and mathematics achievement

  • Knowledge about cognition

    - awareness (statements about our own thinking)

    - evaluation (judgements regarding our own thinking)

  • Regulation of cognition (planning, setting goals, selecting strategies)

From research in math ed on metacognition and expert problem solvers we know
From research in Math Ed on metacognition and expert problem solvers we know…

  • Good problem-solving ability is associated with high levels of of metacognitive activity

  • Good problem solvers engage in metacognitive activity throughout various phases of problem-solving phases.

  • Poor problem-solvers show limited metacognitive activity, often limited to early stages of problem solving.

Can metacognitive skills be taught
Can metacognitive skills be taught? solvers we know…

  • A few studies based on IMPROVE model (Mevarech & Kramarski, 1997) successful in middle and high school settings: instruction in metacognitive strategies is combined with instruction in problem solving strategies similar to Polya’s model.

  • Other studies in elementary school settings

  • Other studies with computer-assisted instruction in middle school settings

  • Best results obtained in collaborative settings

The improve method
The IMPROVE method solvers we know…

Introducing new concepts

Metacognitive questioning


Reviewing and reducing difficulties

Obtaining mastery



Four self addressing questions
Four self-addressing questions solvers we know…

  • Comprehension questions: articulate the main ideas in the problem, “Describe …in your own words”,” This is a rate problem”, “the meaning of ….is….”

  • Strategic questions: justify the use of appropriate mathematical principle, use diagrams and tables

  • Connection questions: identify similarities and differences between the problem at hand and others previously solved

  • Reflection questions

Three basic principles
Three basic principles solvers we know…

(Veenman et al, 2006)

  • Embedding self-addressed questions in all activities (students’ work, instructor’s presentation)

  • Informing the learners about the usefulness of the meta-cognitive activities

  • Intensive practising by training students to apply the meta-cognitive self-addressing questioning in all their attempts to solve problems.

Method solvers we know…

  • N=61 high school students preparing for the matriculation exam (for entering university?)

  • 3 measurements

    - achievement test (pre/post, different tests)

    - questionnaire (pre/post) on meta-cognitive awareness

    - interviews (N= 7 from exp. N =8 from control) immediately after the exam

  • One semester of instruction

  • Matriculation exam took place 2 months after instruction

Results solvers we know…

Achievement tests

IMPROVE Control P-value

Pre-test M 16.90022.140 .001

(SD) (5.798) (6.370)

Post-test M 34.96032.000 .033

Adj M 35.776 31.152

(SD) (7.696) (7.744)

Questionnaire solvers we know…

24 items, 4 point likert scale (never to always)

Knowledge about cognition


Pre-test M 3.814 3.500 (SD .360 .327)

Post-test M 3.822 3.504

Adj. M 3.766 3.617 (SD .403 .372)

Regulation of cognition

Pre-test M 3.717 3.386 (SD .432 .433)

Post-test M 3.605 3.265

Adj. M 3.556 3.315 (SD .341 .50)

Interviews solvers we know…

Responses classified into 4 categories

  • Comprehending of problem (control did more often)

  • Constructing connections (exp. did more often)

  • Looking for appropriate strategies (exp. did more often)

  • Evaluating the solution (exp. did more often)

Take home message
Take-home message solvers we know…

  • Students in exp. condition did better on post test and elicited using strategies they were trained on.

  • Procedural meta-cognitive knowledge seems to help in high-stake situations (post-test)

  • Procedural meta-cognitive knowledge persists in delayed situation (matr. exam)

  • High school students may possess meta-cognitive knowledge about their learning, but ought to be trained to use this knowledge to regulate their learning