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The Word Problem Predicament.

September 18, 2017

One of the most common questions asked of a maths subject leader is: "How do I get my pupils to solve word problems?" Another lament is: "They understand the maths but cannot apply it in a word problem!" 

 

Firstly, we need to be clear what we mean by word problems. Words are used in most problems, otherwise they would be calculations, so usually the questioner is referring to context problems, where no image is provided and pupils have to translate the words into calculations to be solved. It is worth noting here that the debate on the best way to solve word problems can become rather contentious. 

 

Some educators swear by the use of acronyms, such as RUCSAC. Others will instruct teachers to look for key words. Another school of thought is to group types of problems together depending on their structures. The idea is that pupils will be able to spot the type and then draw on the way to solve that particular class of problem. Others will be fans of acting out the problem in some way, which could involve using manipulatives rather than people. A further choice is to be aware of different approaches, such as using tables, looking for patterns or working backwards. 

 

As usual, there is often no single right way but I have found that combining a couple of these ideas can be effective while others have not produced the desired results for my pupils.

 

I have never had much success using the RUCSAC acronym: six letters means that pupils often forget what some of them mean and when the U suggests that significant words should be underlined, some pupils struggle to discern the significant words. Stationery fans then see this is a wonderful excuse to use their new highlighter pens to underline everything, rendering the text more difficult to read than when it was simply black text on a white page. Jumping from the U of underlining to the C, which stands for calculate, can be too large a leap for some pupils.

 

Only identifying key words can also present issues since words such as more than are often identified as falling under the category of addition but it can just as easily be used in a difference problem.

 

        Joshua has 8 pencils. Ria has 3 more than Joshua. How many pencils does Ria have?

     

This will indeed involve adding the 8 and 3 to find out that Ria has 11 pencils.

        

       Joshua has 8 pencils. He has three more than Ria. How many pencils does Ria have?

       

Here, pupils will need to find the difference between 8 and 3 in order to work out that Ria has 5 pencils this time. This can of course be solved by working out what needs to be added to 3 but if the pupil does not understand the situation, they may be attempted to add 8 and 3 (due to the presence of the words more than) and suggest that Ria still has 11 pencils. 

 

Alternative words can also be used that are not in the given lists which can also confuse pupils if they have only been encouraged to look for specific key words.

 

I like the idea of grouping problems together since it focuses on the structure of the problems and can be very effective as long as pupils have some way to identify the structure, such as acting out, using number lines or other manipulatives or drawing an image.

 

After lots of experimenting, I decided to focus on the areas that are common errors when it comes to solving word problems:

 

        Pupils picking numbers randomly from the given text and inserting them into calculations that do not represent the  

        given scenario or pupils struggling to work out what calculations are needed. 

 

        Pupils getting to the end of a question but not rechecking whether they have answered the actual question, despite

        carrying out the correct calculations. Examples include answering only one part of the question and not converting an

        answer into the stipulated units or other requirements.

 

        Pupils providing answers which simply do not make sense, such as being given the  price of a group of items and stating

        that the cost per item is greater than the overall cost of the group.

 

Now for those of you who have had enough of acronyms, here is another one to add to the detested list, although the ideas could be introduced without even mentioning it if preferred. 

 

S

Pupils write a sentence (before doing anything else) based on the given problem, which will contain the currently unknown answer(s) to the problem. Underlined spaces are left for the answers to be inserted at the end which means that there is less likelihood that the problem hasn't been answered since the sentence will be read when the answers are inserted. 

 

 P

Pupils create a picture or some sort of visual image, which could involve manipulatives through to bar models, to help make sense of the problem. Once pupils have a visual image of the situation being described, they are less likely to create calculations that do not fit the context.

 

O

Pupils now work out what operations are needed for the calculation(s) based on the visual image that they have created. It is important that pupils show their working clearly since it clarifies their thinking and assists them when checking their work or revisiting it when the solution they have produced does not make sense.

 

T 

Pupils test whether their solution makes sense and carry out checks such as comparing their solution to any estimates or working backwards when adding in order to check a subtraction calculation.

 

This has been used successfully with pupils from six to eleven years old but of course, it does not provide a panacea to the issue of tackling word problems. Pupils will still need to be exposed to a whole range of word problems and experience the modelling of the problem solving process (including starting down a route that you then realise is wrong and having to revisit your approach) before they are going to become confident.

 

Understanding the language used is also essential; providing pupils with specific words and inviting them to experiment by creating their own problems can be a productive way to develop this since pupils have to appreciate the meaning of the words before they can do this effectively. Getting pupils to try this in pairs or groups also allows the clarification of ideas during the discussions.

 

So the next time you are planning to teach a particular concept, have you built in time for pupils to apply what they have learnt through problems? You could even start with a problem in context and use this to develop the concept that you are focusing on. Either way, there is no quick solution but the time invested in exploring concepts through context should alleviate some of the angst displayed when word problems are mentioned. 

 

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