Word Problems (and why students avoid them)


Summary

Why do students get a knee-jerk reaction at seeing word problems. Almost instinctively, as if ingrained, most students’ thought processes are captioned by “I suck at word problems”, and it becomes an all uphill battle for the teacher. Some possible reasons for this discussed, and possible solutions as well.

Reason 1: intentional confusion by syntax and diction

Word problems are thought experiments. Thought experiments are elegant and succinct, leading to wonderful conclusions about mathematics or logic (or more), but this is nothing that common word problems are. Good word problems should not be stated in confusing or distracting language; it’s about the patterns and logic “underneath the hood”, not about poorly communicated ideas. If a word problem has to be confusing in its language in order to be a challenging question, a teacher must revisit the purpose of the exercise.

Reason 2: obviously forced relevance

Paul Lockhart, in A Mathematician’s Lament (pdf), states:

Attempts to present mathematics as relevant to daily life inevitably appear forced and contrived [...] Algebra is not about daily life, it’s about numbers and symmetry- and that is a valid pursuit in and of itself [...] We don’t need to bend over backwards to give mathematics relevance. It has the same relevance in the same way that any art does: that of being a meaningful human experience.

I wholeheartedly agree. The use of mathematics should be natural, not forced, no tortured into being used in some contrived application. However, there are in many instances, beautiful applications of math to real life which we should expose.

What is a teacher to do

An anxiety-ridden attitude for solving word problems is a learned reaction. Firstly, numeracy needs to be an important cultural goal. We should not be okay to have a second-rate math education. Secondly, mathematical questioning and problems should be emphasized and should be treated as an art (albeit a difficult one). Thirdly, word problems often need context, hopefully one that can be experienced by the students. Do an experiment in the classroom that will lead, not push, students to discover different solutions and avenues of thought. Creativity in mathematics will enable students to generate (and motivate) their own learning and solutions to problems they create. See this link for more information on word problems.

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