1. Real thing- Do Diagram – Visualise Word- Communicate
Physical activity in a variety of contexts; Key thinking- diagrams to ‘represent’
making, demonstrating. Illustrations Essential medium for thinking about
Using concrete ‘manipulative’ materials Pictures mathematical ideas and communicating
– eg: paper, centi-cubes, tiles, cubes, Diagrams these ideas to others
paper and pencil….. Charts
Graphs Includes mathematical terms, phrases and
Principle: learning by doing: I hear and I Figures sentences
forget; I see and I remember: I do and I Diagrams
understand helps students develop mental
models that provide meaning to the Varying degrees of abstraction eg: a Often words used in everyday situations
abstract symbols literal picture of apples versus dots to and mathematics cause confusion
represent apples
Alternatively for those students who have Teachers should say mathematical terms
been found to lack numerical sense of Convey mathematical ideas in vivid ways precisely and consistently eg: ‘x²’ should
measures about real objects and hence constitute a mode of processing be ‘x to the power of two’ and not ‘x
cannot determine whether there are two’
answers are reasonable or not in the real
world Colour may be important to some Students should also use proper
learners mathematical language eg: saying
To facilitate conceptual development ‘numerator’ rather than ‘the number on
manipulative materials need to be well the top’
designed, appropriate to the context
and used well Written and oral communication
Doing- role plays, physical activity in a
variety of contexts, making, Explanation , demonstration
demonstrating
Symbol- Manipulate Story- Apply Number- Calculate
Some examples
Commutative/Associative properties Linking real-world applications to Computation [methods of ‘working out’]
Distributive rule ‘textbook mathematics’ -includes
Formulae traditional worked problems, problems Strategies used
BODMAS related to everyday situations and reports
The concepts of - The part- whole, in the mass media, historical accounts of Systems [steps] used to calculate
comparison and change, remainder, place mathematical ideas and applications algorithms/ equations
holder, equality, excess value, repeated from other disciplines
variable, constant difference, constant Differentiation through different ways of
quantity, constant totals…. Problems generated by students working out the same problem
Algebraic concepts/rules/strategies
Syntactic skills- what do I need to know Problems generated by manipulating
to use a calculator to work this out? Eg: equations –‘milking an equation for all
3/4 of 868 = its worth’
Use the Multi-Modal Think Board model as a tool
• to plan a lesson [e5]
• to plan a series of lessons
• to reflect – students and teachers
• for assessment [of, as, for]
• to integrate electronic technologies
• to embed e5 in instructional and assessment and reflection practices
Using Multi-Modal Think-Board to Teach Mathematics Khoon Yoong Wong

2. Mathematics and Education Academic Group, National Institute of Education Nanayang
Technological University Singapore, July 2004