Teaching Word Problems

Math Word Problems - Exercises in Math Modelling

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

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.

Dangers of not relating world problems to real-life situations Students often do not realise that the answer to a word problem in mathematics should also be related to the reality of life. For example if a problem yields a result that 12.50 buses are needed for a trip, students should automatically round the number up to 13. “Steve has bought 4 planks that are each 2.5 m long. How many planks of 1 m can he get out of these planks?” The straightforward process of multiplying 4 by 2.5 and answering “10 pieces” fails to consider that there would be four pieces of 0.5 m left over. Here, eight pieces is what is termed a “realistic response” in the literature For example, “John's best time to run 100 m is 17 s. How long will it take John to run 1 km?” Here there is not enough information in the problem to get a definite answer, as it is unlikely that John could run at the same pace for a much longer distance. Also, 17 s was his best time for 100 m; is it likely he normally runs at that same pace? With both types of problematic problems, previous studies have found students across the world display a strong tendency to disregard the realistic context of the problem Some approaches ) all approached this goal in distinct ways, in general they shared three common characteristics: (a) using more realistic or “non-routine” tasks in comparison to traditional textbook word problems; (b) promoting a greater variety of teaching methods, including small group problem-solving and explicit instruction on what “mathematical modeling” truly is; and (3) revising the classroom culture of mathematics where the sociocultural norms of problem-solving better reflect true mathematical modeling