critical maths for innovative societies - the role of meta-cognitive pedagogies
DESCRIPTION
This presentation was given by Zemira Mevarech of Bar-Ilan University and the David Yellin Academic College of Education at the CERI Conference on Innovation, Governance and Reform in Education on 4 November 2014 during session 3.d: 21st Century Pedagogies: Making Change Happen.TRANSCRIPT
Zemira R. Mevarech Bar-Ilan University, Israel
President
David Yellin Academic College of Education
OECD, Paris, November 2014
Critical Maths for Innovative Societies: The Role of Meta-cognitive Pedagogies
The What and the How
What types of problems are embedded in the standard math curriculum?
“A teacher is one who teaches you how to solve problems you have never encountered, unless you have met the teacher”
What types of problems are useful for innovation-driven societies?
• Complex, Unfamiliar, Non-routine (CUN) problems
• Authentic problems • ‘Standard’ problems are useful, but insufficient
Large variability in CUN problems:
What is complex to one student, can be simple to another one
Unfamiliar problems to one student,
might be familiar to another student
Sometimes non-routine problems become routine tasks
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 were having 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?
What Solving Skills are useful in Innovation-Driven Societies?
• Mathematical skills for solving CUN problems include: Mathematical reasoning, creativity, critical thinking, communications • Basic skills are necessary, though not sufficient • • Meta-cognitive skills for regulating the solution of CUN problems: MC is
the ‘GPS’ of the cognitive process
• Training students to “think about their thinking” during learning is beneficial to large kinds of skills that will increasingly matter in innovative societies
• Metacognitive processes involving planning, monitoring, control and reflection prove superior to other pedagogies in a variety of contexts and for a variety of problems
• The progress from traditional to CUN problems requires the application of meta-cognitive processes that regulate cognitive (and emotional) processes.
IMPROVE Introduce new concepts to whole class
Meta-cognitive self-addressed questioning in small groups
Practice the use of MCQ
Review the use of MCQ
Obtain mastery over routine & CUN tasks
Verification
Enrichment and remedial activities
Research shows: Like cognitive strategies also MC needs to be explicitly taught and intensively practice at all grade levels, K-12, HE, PD
IMPROVE:
MC Instructional Method
IMPROVE:
MC Self-Directed Questioning
Comprehension: What is the problem/phenomenon all 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?
MC is more effective in interactive learning environments: CL, ICT
Findings
IMPROVE & Long Lasting Effects: Immediate & Delayed Post-tests
0
10
20
30
40
50
60
70
80
90
Biology literacy Physics literacy
IMPROVE Control
0
1
2
3
4
5
6
Motivation Self-efficacy
IMPROVE Control
Effects of IMPROVE on scientific literacy,
motivation and self-efficacy
ICT vs F2F: Development of Scientific Literacy
by Group and Time
ALN 6.98 10.55
ALN+meta 6.97 11.47
before after
ALN+meta 5.47 10.36
F2F+meta 5.6 9.38
ALN 5.76 8.94
F2F 5.47 8.02
0.770206 0.580645161
מדידות מדידות תרשימיםתרשימים הבנת מידע הסקת מסקנותהסקת מסקנותהבנת מידע תכנון ניסוי
לפני אחרי לפני אחרי לפני אחרי לפני אחרי לפני
1 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 6 6.17 6.17 6.94 10.05 18.35 10.11 18.64 10.350
2
4
6
8
10
12
ALN+meta F2F+meta ALN F2F
mean
scores
before
after
ALN+Meta > F2F+Meta = ALN > F2F Range 0-15
Research shows:
• MC is teachable; It does not develop ‘naturally’ without intervention • 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 shows positive effects in mathematics and science education.
• IMPROVE helps to increase motivation, self- confidence, and judgment
of learning.
• IMPROVE helps to reduce math anxiety
It’s not about what it is, It’s about what it can become
Conclusions: From the book cover
• Dramatic changes in our understanding of the nature of learning over the past century have resulted in a shift in focus from “what” to “how”, and in particular, how to enhance students’ abilities to solve complex, unfamiliar and non-routine tasks (CUN).
• While these CUN problems allow students to develop the skills needed in societies driven by innovation, most mathematics textbooks and teaching still focus on problems based on the application of ready-made algorithms.
• CUN problems should become more central to mathematics education and examines innovative instructional methods that enhance mathematics education, notably metacognitive and cooperative pedagogies.
Challenges: What next? Evidence Based Policy Making
• International cooperation – we don’t have to reinvent the wheel: We would like to share our experience
• 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.
• MC has to be explicitly taught and intensively practiced
• Embedding CUN problems and MC in the national curriculum, textbooks, teacher guides, and professional development courses is essential for enhancing quantitative literacy
If you think education is
expensive, try ignorance!
Please contact:
Many Thanks!