Research School Network: Why are students so bad at word problems? (And what we can do about it) Amarbeer Singh Gill considers Disciplinary Literacy in Maths and how teachers can help pupils process information.

One of the most common challenges in maths is supporting students to identify ​‘the maths’ when faced with word problems.

As I’m sure many of us have experienced in our classrooms, once the problem has been translated into maths, success rates dramatically increase.

So why is it that students can struggle with these problems while (often) not struggling with the maths behind them?

Why is it that (often) simply ​‘translating’ the problem from prose to maths is all that’s needed to trigger that lightbulb moment for our students?

And what can we do to support students to have those moments independently?

The ​‘Problem-Solving’ Approach

When I started my teacher training there was a significant push towards teaching students ​‘problem-solving skills’. 

This push came from a good place: we wanted students to be fluent with their subject knowledge and see problems in the same way that we as subject experts did.

The approach that I often took, having seen other colleagues, was to pick a word problem (or several), model how to solve them, and then give students a selection of worded problems to attempt for themselves.

There were usually two outcomes that would result from this:

1. Students would experience some early success within that topic, but as soon as the topic changed, the hands and requests for help would immediately start going up around the room.
2. If the questions were on even slightly different topics to the models, or the disguising was different, then even the early success would dissipate and requests for help were almost immediate.

In essence it appeared that, regardless of the approach I took, it didn’t seem to solve the issue: students still struggled with novel word problems.

So why did this keep happening?

The Problem of Transfer

Transfer is the phenomenon applying knowledge and skills¹ in a context different to the one in which it was first learnt, and offers us a helpful explanation as to why I kept experiencing the above.

The problem is that what we learn is highly context dependent. So when we’re being asked to apply knowledge in a new context, the new context is devoid of all the cues we would normally be able to access to make sense of the situation.

Consider the question below:

At its core, this is a substitution problem. However, it’s likely that when we’ve first taught students about substitution we’ve explicitly used the word ​‘substitute’ either in our explanation, or in the question itself.

It’s also likely that, instead of writing it in words, we’ve written it mathematically eg m = 30. In the problem above, none of those cues are present which means students are having to process the content of question alongside trying to identify what maths the question involves.

It’s also why just ​‘translating’ the question into mathematical language, or telling students ​‘use substitution’ is often enough to get them going, we’ve added in the contextual cues that were previously missing.

The frustration for me in my classroom however, was that before I understood transfer, I simply couldn’t understand why students were struggling – I was suffering from expertise-induced blindness², which meant I just couldn’t ​‘see’ the problem from the point of view of my students.

A different approach

As outlined, one of the challenges was helping students to see the problems the same way I did as a subject expert.

So part of the solution involved becoming aware of this and trying, as much as possible, to apprentice students in my ​‘expert’ ways of thinking, ​“learning as an apprenticeship introduces students to the reading, thinking, speaking, and writing of a field”³.

A key strategy to achieve this is incorporating ​‘Think Aloud’ into your teaching.

Using ​‘Think Aloud’

Think Aloud strategies not only provide a model or worked example in which the process is explained, they also demonstrate ​“how an ​‘expert’ learner approaches a problem, making these invisible processes visible and accessible to pupils”⁴.

This suggests that, alongside explicit teaching of the underpinning mathematical knowledge, we can support students’ mathematical literacy by also explicitly teaching how we make sense of problems.

Mulholland (2022) splits the strategy into three phases:

1. Plan, where we look at a problem and describe how we are approaching it:
   a. What are the key bits of information we’re attending to?
   b. What are we ignoring?
   c. What do we think the question is likely to be about?
   d. Why?
2. Monitor as we work our way through the problem, continually testing the predictions made in the planning stage:
   a. Are they still valid
   b. Do we need to update them in light of new information?
3. Evaluate after completing the solution by reflecting on the process as a whole:
   a. Was our prediction correct?
   b. Can we check the answer?

If we return to the question from earlier we could provide an explanation like,

“I can see I’ve got an equation that involves multiple unknowns, and that I’ve been given the values for some of these unknowns. So first, I’m just going to translate everything into a more mathematical format and put it in one place.”

Writes on board:

“This definitely makes the problem seem a lot simpler, it looks like all I’ll need to do now is substitute in my values. Let’s do that and see what happens”

Writes on board:

“This gives me an even better indication that we’re along the right lines, because now I’m only left with one unknown and if I carry out the calculation I’ll get a value for that too, so I get”

Writes on board:

Summary

Word problems present significant challenges to students. Students have to process the content of the question alongside trying to identify what maths the question involves, before even getting to executing the relevant procedure(s).

The identification of the underlying mathematical concepts is likely to be a failure of ​‘transfer’ – being able to take knowledge learnt in one context and apply it in another.

This is something all humans struggle with because the way in which we learn is heavily tied to the context at the time of learning, but one way teachers can support students with this particular challenge is through using the ​‘Think Aloud’ strategy.

If you’ve enjoyed this blog, we’ll be delving further into it and looking at more examples in our upcoming webinars. Join us for our series starting on Wed 29 January: Disciplinary Literacy – Communicating subjects through their own languages