Critical maths for innovative societies - the role of meta-cognitive pedagogies

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:

[email protected];

Many Thanks!