thinking and working mathematically - delene

Using the Multi-Modal Think Board

• Mathematical ideas are abstract mental constructs.

• Representing abstract ideas in more concrete ways will help many students grasp abstract ideas more easily

• It is essential to have multiple ways of representation for teaching concepts

• In mathematics there are six commonly used modes of representation – numbers, words, symbols, diagrams, stories and real things

Using Multi-Modal Think-Board to Teach Mathematics Khoon Yoong Wong Mathematics and Education Academic Group , National Institute of Education,Nanyang Technological University, Singapore, July 2004

Thinking/Working Mathematically:A Think-Board [Multi-Model] to Teach Mathematics

Using Multi-Modal Think-Board to Teach Mathematics Khoon Yoong Wong, Mathematics and Education Academic Group , National Institute of Education, Nanyang Technological University, Singapore, July 2004

e5

Number-calculate e5

Word- communicate

e5

Diagram- visualisee5

Symbol- manipulate [algebra]

e5

Real Thing- do

[eg: manipulative materials]

e5

Story- apply

Thinking/Working Mathematically

Working/Thinking MathematicallyUsing Think Boards

Division of a decimal by an integer0.4 ÷ 2 = [zero point four divided by two]

Task [a] and [c] – most students nodifficulty

Task [d] to [f] – more difficult

When the task is changed to 0.4 ÷ 0.2 = even [a] and [b] become difficultand most students would not beable to completeUsing Multi-Modal Think-Board to Teach Mathematics Khoon Yoong Wong

• [a] Read this aloud - word• [b] calculate its value [not with a

calculator] - number • [c] draw a diagram to illustrate

the operation - diagram• [d] demonstrate the operation

using real objects - real thing• [e] write a story or word problem

that can be solved using this operation – story

• [f] extend this operation to algebra – symbol - symbol

Think- Board

Use for:• planning• instruction• reflection• assessment

• closed • open• ways to write good questions• using open questions to differentiate tasks

•

Questions

• Peter Sullivan and Pat Lilburn– Working backwards– Adapt a standard question

What are ways to create good questions?

How to Create Good Questions

Peter Sullivan/Pat LilburnOpen-ended Maths Activities, Peter Sullivan, Pat Lilburn, Oxford University Press 1997

Method 1: Working Backwards:Step 1 Identify a topicStep 2 Think of a closed question and write down the answer.Step 3 Make up a question which includes [or addresses] the answer

eg:MoneyTotal cost $23.50I bought some items at the supermarket. What might I have boughtand what was the cost of each item?

How to Create Good Questions

Peter Sullivan/Pat LilburnOpen-ended Maths Activities, Peter Sullivan, Pat Lilburn, Oxford University Press 1997

Method 2: Adapting a standard question:

Step 1 Identify a topicStep 2 Think of a standard questionStep 3 Adapt it to make a ‘good’ question

eg:Subtraction731-256=Arrange the digits so that the difference is between 100 and 200

• The Question Creation Chart- Education Oasis 2006

What are ways to create good questions?

Is Did Can Would Will Might

Who

What

Where

When

How

Why

Question Creation Chart (Q-Chart)

Directions: Create questions by using one word from the left hand column and one word from the top row. The farther down and to the right you go, the more complex and high-level the questions.

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Topic Answer Make up a questions which includes the answer

$ $75.00 I bought some items at the supermarket and got $9.50 change. What might I have purchased and what did they cost?

Number

x

9 What 2 numbers below the number 100 might I have multiplied to get the answer 9?

Place Value 4 971 Represent the number 4 971 in as many ways as you can

Volume and Capacity

A cubic structure is made out of

27 smaller cubes

A cubic structure is made up of 27 smaller cubes. Two of the smaller cubes are removed from the larger structure. What might the structure look like?

Area 24cm2 Draw some rectangles to represent an area of 24cm2

Draw some regular shapes to represent and areaof 23cm2

Peter Sullivan

Working/Thinking MathematicallyUsing Multi-modal Think Boards Khoon Yoong Wong 2004

Story- ApplyLinking real worldmathematics to ‘textbook mathematicsreinforces concepts andskills and enhancesmotivation for learning

Story- Apply• traditional word problems related

to everyday situations• reports in the mass media• historical accounts of

mathematical ideas • examples from other disciplines

• students can and should generate their own

Working/Thinking MathematicallyUsing Multi-modal Think Boards Khoon Yoong Wong 2004

Using the multi–modal Think Board for Planning, Assessmentand Reflection– a series of lessons on a particular topic– a lesson

– consider carefully whether all or only some modes will be used in which sequence

– ie: determine the optimal combination

– perhaps begin with concrete manipulative materials and support/supplement with virtual [ICT]

– eg: students may be asked to explain why [a+b]² = a²+ b² using number, diagram and real thing

Working/Thinking MathematicallyUsing Multi-Modal Think Boards

A Suggested Sequence

Real Thing

Number Word

Diagram

Symbol

Story

Virtual Manipulative

Academic Group , Khoon Yoong Wong 2004National Institute of Education, Nanyang Technological University, Singapore, July 2004

Working/Thinking MathematicallyUsing Think Boards

Teachers:For planning – day to day, weekly, units of workFor embedding the e5

For reflection For assessment -encompassing a variety of approachesFor……Students:For reflectionFor ways of demonstrating understanding/new understanding[elaboration/explanation/reflection…]For problem solvingFor……..

Turn and talk.

Khoon Yoong Wong, Using Multi-Modal Think-Board to Teach Mathematics Khoon Yoong Wong,Mathematics and EducationAcademic Group , National Institute of Education, Nanyang Technological University, Singapore, July 2004 -paper

Peter Sullivan and Pat Lilburn, Open-ended Maths Activities OxfordUniversity Press 2000

Andrew Fuller Creating Resilient Learners- The Get It! Model of Learning 2003 –PaperJohn Hattie, Visisble Learning Routledge 2009

George Booker, Denise Bond, Len Sparrow and Paul Swan, TeachingPrimary Mathematics 3rd Edition Pearson Prentice Hall 2004