Several special education teachers responded in a poll indicating that the most difficult math topic to teach in elementary school is solving multi-step word problems. This happens to be a topic that is massively important and the first of several dominoes that will fall all the way through high school and beyond. One and two-step word problems are cited in the Common Core domain of Operations and Algebraic Thinking (images below) and the CCSS Coherence Map shows how these two standards lead to future algebraic thinking and algebra topics.
There are two aspects of word problems in elementary school that are incredibly important building blocks in terms of math education. First, these problems establish math as a language used to represent real life situations. Second, the multiplication word problems develop the student understanding of rates, which is a major topic in middle school math and in algebra of all levels.
Before I get into what I call a conceptual approach to word problems, which I recommend, I will share that I am not in favor of the key word approach (image below). The major flaw, as I see it, involves how the brain stores or memorizes information. The key word approach is based on rote memorization. For many of the students with special needs, this is exactly what they do NOT need, more taxes on their working memory.
Here is the approach I use, with a focus on addition and subtraction first (followed by a forthcoming PART 2 blog post on multiplication and division). The handout used is from Math-aids.com.
- I train students to highlight the quantities cited, along with any verbs. In the top photo is a legend for the elements of the word problem I highlight.
- The yellow is used for quantities given in isolation. For example, Jason found 7 seashells but this was not presented after an preceding number.
- In contrast, Fred found 6 seashells, which was in addition to what Jason found. Hence, Fred added to the number found and the green highlighting indicates this. Also note that the “+” is highlighted to indicate the adding on context.
- Orange is used to indicate the quantity that is unknown. This helps focus their attention on the number they are looking for and is an ancestor to the eventually use of a variable.
- The blue will be addressed in the PART 2 blog post. (Note: I do not use the term rate but wrote it for emphasis for the blog posts.)
The two-step addition and subtraction problems follow the same structure and involve minimal additional processing.
Additional notes about the process I follow.
I use a chunking approach in which I present the students several problems and have them practice 1 step at a time.
- highlight just the unknowns (orange)
- highlight the given values (yellow)
- highlight the additional values (green)
- then have new problems where they highlight all 3
- then I would have them write the equation for the the previously highlighted problems
- finally, they would attempt all the steps on a 3rd set of problems
There are additional types of problems such as Billy and 5 more tokens than Joey. If Joey has 8 topics, how many does Billy have? I would address these after the students show fluency with the process and the concept of using an equation to model a word problem. They do not follow the same type of structure I present above.
Our students may need help developing a conceptual understanding of addition and subtraction as well as the concepts underlying word problems. In my work with students I often find this to be a major obstacle in student progress with word problems. Hammering out conceptual understanding is likely to be a highly effective investment with a long range effect. It is not as easy to implement as the keyword strategy but we get what we pay for.