Immediate and delayed effects of
meta-cognitive instruction on
regulation of cognition and
mathematics achievement
Z. R. Mevarech
C. Amrany
Research questions
• 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
• 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…
• Good problem-solving ability is associated with
high levels of of metacognitive activity
• Good problem solvers engage in metacognitive
activity throughout various phases of problemsolving phases.
• Poor problem-solvers show limited metacognitive
activity, often limited to early stages of problem
solving.
Can metacognitive skills be taught?
• 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
Introducing new concepts
Metacognitive questioning
Practicing
Reviewing and reducing difficulties
Obtaining mastery
Verification
Enrichment
Four self-addressing questions
• 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
(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
• 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
Achievement tests
IMPROVE
P-value
Pre-test M 16.900
.001
(SD) (5.798)
Post-test M 34.960
.033
Adj M 35.776
Control
22.140
(6.370)
32.000
31.152
Questionnaire
24 items, 4 point likert scale (never to always)
Knowledge about cognition
IMPROVE Control
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
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
• 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