thinking and working mathematically - delene
TRANSCRIPT
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.
del
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