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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