Modelling Math versus Usual Method

Marie had 20 m of cloth. She used 3/5 of it to make some dresses. How many meters of cloth did she use?

1. Model method:

【】【】【】〖〗〖〗

5 units = 20 m

1 unit = 20 / 5= 4 m

3 units= 3 x 4 = 12 m

2. Usual method:

3/5 x 20 = 12 m

The 2nd method is too abstract for 8 or 9 yr-old kids who will resort to learn fraction “x” or “/” formula by rote.

Models appear ‘silly’ to adults who prefer abstract concept ‘3/5 x 20’;

Note 1: Singapore Primary School Modelling Math

Adopted since 1990 from Polya’s “How to Solve It” (1945) 4-Step *Problem Solving Process*

1. Understand the problem in English Word Math.

2. Devise a plan: draw models

3. Carry out the plan: solve

4. Look back: verify

The *Concrete-Pictorial-Abstract* Math approach is developed by Dr. Kho Tek Hong (retired in 2007) & his MOE team @ 1980s.

Note 2: Models can also help visualize & ‘concretize’ Abstract Algebra (Set, Group, Coset, subgroup, kernel, isomorphism …Galois theory). Feynman invented ‘model’ (Feynman diagram) to visualize quantum theory.