Unable to solve word problems, fluent in arithmetic

A colleague of mine, teaches math to 6th graders. Some of his students are completely fluent in arithmetic, but can't solve word problems.

1. What practical ways exist to help them?
2. Is there any detailed article of book dealing with this matter?

Thanks.

• See, e.g,. Chapin, S., & Johnson, A. (2006). Math matters: Grade K-8 understanding the math you teach. Sausalito: Math Solution Publications. In particular, Chapters 3 and 4, pp. 55-83, cover word problems with the four different operations (addition, subtraction, multiplication, division). There are also additional citations there to work by, e.g., Carpenter, Fennema, Franke, Levi, Empson. You can find a summary table concerning similar material here: math.niu.edu/courses/math402/packet/packet-2.pdf Nov 19, 2014 at 9:47
• @BenjaminDickman That looks like an answer. Why not post it like one? :) Nov 19, 2014 at 18:40
• @MarkFantini It's mostly a reference. To write up a full answer (i.e. getting at what is contained in those chapters) would take a fair bit of time, but I may do so at some point. Meanwhile, I hope others can mention article/books of which they are aware, or use their experience as practitioners to give suggestions! Nov 19, 2014 at 19:13
• My mother had this problem when she was a child: she came to Belgium from Germany, so she did not understand the Dutch language. As a result she had no problems dealing with math formulas, but when a question requested understanding of the Dutch language, she got into problems. I'm giving this example just to show you that this kind of issue can be caused by a linguistic issues. Hence I'd advise you to contact his/her language teacher(s). Oct 2, 2018 at 14:38

Does your colleague have any information about these students' reading comprehension? The reason I ask is that, in my opinion, difficulty with word problems is not always a matter of taking the content of the word problem and reformulating it as equations. Rather, it is often a matter of getting the content of the problem in the first place. In other words, the reason some people can't convert a word problem into a mathematical formulation is that they don't understand the word problem. In such cases, it is their reading skills rather than their mathematical skills that need to improve.

One of my colleagues introduced me to a strategy called "3 Reads" which he details in his blog Misteristhisright. This strategy has two major features:

1. You remove the question from the problem. The problem only gives the context. This can be done with Dan Meyer's 3 act problems as well.
2. You read the problem 3 different times in order to become familiar with it: first for understanding context, second for understanding quantities, and third to generate questions that you can ask about the context and quantities.

The goal of the strategy is to have students understand the context before they begin answering the question. In my experience students (as they are often taught) jump right to the question and then go back to understand which results primarily in students mashing numbers together hoping that they will result in something meaningful.

• +1 for 3 act tasks :) Dec 11, 2014 at 0:11
1. Maybe try to use progression? Don't give them the hardest word problems to start. (Or if some kids can handle the regular word problems, keep a mix of difficulties.) By hard, I don't mean math hard only, I mean amount of word translation needed.

For example:

9 - 5 =?

Nine minus five =?

What is left when you subtract five from nine?

Johnny has nine pencils and gives five away. How many does he have left?

How many good pencils does Johnny have at the end of the day, if he had nine at the beginning of the day and during the day, he broke five pencils?

1. Also consider to lower math difficulty while raising word difficulty. Think about learning bra ket notation in quantum mechanics. When I have to learn that new, strange looking, notation, I prefer to do so with a very easy QM problem I have already solved with conventional notation. Not a hard old one. And definitely not a new problem (combining new content with new notation for the first smack in the face).

2. Love the comment about money. Emphasize that a lot. It is tactical, students have experience, it makes it matter, and it helps them in daily life. Same exact problem with money is probably easier than with physical dimensions.

3. Agree with the 3 reads concept and with teaching a process of translation. You got to take the WP, translate it into an equation, solve equation, translate back. Just teach this (step by step). Not as a concept. But actual step by step practice. (And per 2, do this with a crushingly easy example.)

4. Drill, drill, drill.

I think that Benjamin Dickman made a useful comment. Also, you can talk with your pupils about their own experience. For example, you can ask them:

• You have 10 dollars. Then you buy ice cream with 4 dollars. How many dollars do you have left?

• You go to the market and buy 8 pencils for 50 cents each. How much did you pay in total?

You can build more examples that motivate your students to think and to solve the exercise.