Teaching Word Problems

Math Word Problems - Exercises in Math Modelling

One of the important skills to be learnt through word problems is that of "modelling real life events" using math.

After students lean algebra & calculus, they can model a real life event in terms of equations & variables and actually run what is called a math simulation where the behavior of a model can be studied over a period of time and with tweaking of variables.

Most students think that problems in math are "just" that and they have no relation to the reality of life. Research studies have found that students across the world display a strong tendency to disregard the realistic context of the problem.

Hence, while teaching word problems, teachers need to emphasize continuously that the problems and their solutions need to be rooted in the reality of our world.

Let us see some solutions that result from this attitude.

Number of cars problem

The problem give was - "A school is planning a field trip for 245 students & teachers using some school buses. If each bus can carry 70 passengers, how many buses would be needed for the trip."

Many students arrived at an answer of 3 1/2 buses. They never thought whether "half a bus" was possible in real life. They had given the math solution of dividing 245 by 70! The realistic answer should have been 4 buses.

Birthday presents problem

A teacher asked students to write a "put together" problem in addition using 3-digit numbers.

One student answered - "For my birthday party my father gave me 345 pencils and my mother gave me 528 pencils. How many pencils did I get on my birthday."

The student never considered whether this problem in any way modelled a birthday party in real-life!

A story about the number of students in two separate grades in a school would have been more realistic.

Cutting wooden planks

“Vasu bought 4 planks each 2.5 m long. How many planks of 1 m can he get out of these planks?”

Many students got an answer 10. Their logic was that the total length of 10 m (4 X 2.5) would yield 10 planks each of 1 m long.

They had never considered the limitation of the 10 m, being in 4 separate pieces!

Some Pedagogical Approaches

How can teachers ensure that students think about the reality of the situations in a math problem? Some suggestions.

1. Do not depend only on problems from the textbook. Use more realistic or “non-routine” tasks in comparison to traditional textbook word problems.

2. Promote a greater variety of teaching methods, including small group problem-solving and explicit instruction on what “mathematical modeling” truly is

3. Encourage students to write their own word problems based on their life experiences.