MAKING THINKING VISIBLE FOR SECONDARY MATHEMATICS LESSONS USING THINKING ROUTINES

Service With Honour

FLOW OF PRESENTATION

At the end of the sharing, participants will be able to see how thinking routines are incorporated into lessons.

(1) Introduction of Thinking Routines

(2) See, Think, Wonder

- Written Assignment: Types on Numbers

- E-Learning: Probability

- Hands-on Activity for You!

(3) Claim, Support, Question

- Activity: Sieve of Eratosthenes

- Activity: Types of Numbers

- Activity: Geometric Properties of Circles

WHAT ARE THINKING ROUTINES?

• Examine the development of learning processes in children, adults, and organisations.

• Today, Project Zero’s work includes investigations into the nature of intelligence, understanding, thinking, creativity, ethics, and other essential aspects of human learning.

Learning from the experts..

HARVARDGRADUATE SCHOOL OF EDUCATION

TOOLS FOR FOR THE TEACHERS, HABITS FOR THE STUDENTS

• Thinking routines are simple structures that students can settle down to during lessons.

• Thinking routines can be applied across disciplines and grade levels.

Tools for the teachers, habits for the students

Visible Thinking emphasises several ways of making students' thinking visible to themselves and one another, so that they can improve it.

Learning from the experts..

EDUCATIONAL LEADERSHIP

Tools for the teachers, habits for the students

SEE, THINK, WONDER

SEE, THINK, WONDER

Purpose

Encourages students to make careful observations and thoughtful interpretations.

Stimulates curiosity and sets the stage for inquiry.

Application: When and Where Can It Be Used?

Use the routine

• at the beginning of a new unit to motivate student interest

• with an object that connects to a topic during the unit of study

• near the end of a unit to encourage students to further apply their new knowledge and ideas.

SEE, THINK, WONDER

ASSESSMENT

• “See”: the ability to notice details

• “Think”: how students support their interpretation and assertions

• “Wonder”: questions that are broad and adventurous rather than those that require specific factual responses

from Making Thinking Visible

SEE, THINK, WONDER

WRITTEN ASSIGNMENT: TYPES OF NUMBERS

JH1 MA100 Written Assignment 1: Questions

SEE, THINK, WONDER

E-LEARNING: PROBABILITY

JH2 MA203 E-learning (June Holiday)

SEE, THINK, WONDER

SEE, THINK, WONDER

SEE, THINK, WONDER

THE DESIGN: FACTORS TO CONSIDER

• The video or object must offer a rich context or content such that details or interpretations can emerge after examination or thinking.

• While addressing a particular topic, there should be a scope for linking up different areas or fields.

• A platform must be provided for students to engage in group activity where participants build on the responses offered by others.

SEE, THINK, WONDER

SAMPLE RESPONSES FROM STUDENTS

SEE, THINK, WONDER

SEE: NOTICING DETAILS

• Student C.C.Y.

The dots on a die are created by removing the material used to make the die.

Between the sides with numbers '1' and '2', the side with number '2' will have more material removed, thus the die will be biased to one of the sides.

Therefore, the outcomes will not be equally likely. 

SEE, THINK, WONDER

WONDER: DRAWING BROAD IDEAS

• Student L.K.Y.

Something else that I like to say about the video is that the terms brought out are very insightful. One thing that I have learnt is that in math or in anything actually, we should always look at the big picture rather than the individual jigsaw puzzle pieces.

SEE, THINK, WONDER

WONDER: DRAWING BROAD IDEAS

• Student M.E.Q.

The fact that the human brain favours specific numbers and patterns also fascinates me.

What causes the human brain to think that certain numbers and patterns are more random than others?

Is it an unconscious action ingrained into our brains or is it caused by something else...(Any answers?)

SEE, THINK, WONDER

IN RESPONSE...

• Student T.Y.F.  

I'm not exactly sure about a good answer, but humans have a cognitive bias towards certain patterns,

which is "a pattern of deviation in judgment, whereby inferences of other people and situations may be drawn in an illogical fashion." (quote Wikipedia)

If you wish to inquire further, a good place to start would be about pseudo-randomness, though I'm not too sure if it is related.

SEE, THINK, WONDER

THINK: UNSUPPORTED ASSERTIONS

• Student H.W.G.

Probability is basically based on a fair situation under fair conditions.

SEE, THINK, WONDER

IN RESPONSE...

• Teacher

When you read the papers and people talk about

odds and probability, are the events/outcomes

all fair?

SEE, THINK, WONDER

SEE, THINK, WONDER: HANDS-ON ACTIVITY

Materials:

• Scissors

• Paper

• Wondering mind

SEE, THINK, WONDER

CLAIM, SUPPORT, QUESTION

CLAIM, SUPPORT, QUESTION

Purpose

Helps students develop thoughtful interpretations by encouraging them to reason with evidence.

Learn to identify truth claims and explore strategies for uncovering truth.

Application: When and Where Can It Be Used?

Use the routine with topics in the curriculum that invite explanation or are open to interpretation.

The questions can challenge the plausibility of the claim, and often lead to a deeper understanding of the reasoning process.

CLAIM, SUPPORT, QUESTION

CLAIM, SUPPORT, QUESTION

OBJECTIVES

(1) Engage students to explore strategies for uncovering mathematical relationships.

(2) Help students support their claims through logical reasoning.

(3) Develop students’ self-directed learning capability through the raising of questions by students.

CLAIM, SUPPORT, QUESTION

ASSESSMENT

When making a claim, are students:

• looking for generalisations that get to the truth?

When supporting a claim, are students

• anchoring the claim with solid evidence?

• recognising special cases?

from Making Thinking Visible

CLAIM, SUPPORT, QUESTION

GEOMETRIC PROPERTIES OF CIRCLES

• Students are given a pseudo-real life scenario.

• They need to use their knowledge of geometrical properties of circles to solve the problem of dividing food equitably during a shipwreck.

• The Claim-Support-Question Strategy is used to engage students in making their thinking visible.

CLAIM, SUPPORT, QUESTION

CLAIM, SUPPORT, QUESTION

TYPES OF NUMBERSNATIONAL JUNIOR COLLEGE JUNIOR HIGH 1 MATHEMATICS 2013

Name : ____________________ ( ) Class : ________ Date : ________ MA100 On a Math Odyssey Topic 1 Types of Numbers

Mathematics is a language made up of carefully defined terms and symbols.

Mathematics is the study of patterns & relationships.

Given that a, b and c are all real numbers.

CLAIM

SUPPORT

QUESTION

1

If ba , then 22 ba .

2

If ba , then bcac .

3

If ba , then cbca .

CLAIM, SUPPORT, QUESTION

SAMPLE OF STUDENT’S WORK

CLAIM, SUPPORT, QUESTION

SIEVE OF ERATOSTHENES

• Claim

Your friend claims that the above steps just needs to be repeated as far as the number 7 for all primes smaller than 100 to be identified.

• Support

Can you support your friend’s claim? http://en.wikipedia.org/wiki/File:Sieve_of_Eratosthenes_animation.gif

• Question

How do we determine if a number is prime?

CLAIM, SUPPORT, QUESTION

Thank You

QUESTION AND ANSWER