Answered by Jeff Richardson, Special Education Teacher at Sagonaska Demonstration School- Provincial Schools Board - Seconded from Hastings Prince Edward District School Board

I believe there are a number of ideas to keep in mind that are useful for students with working memory difficulties. These instructional strategies are largely based on the belief that all math should be taught with conceptual understanding as a goal (making sure students build a deep understanding of the math they are working with) before developing procedural fluency (applying a formula, algorithm, or procedure to get an answer). For example, students need to explore fractions in a variety of ways, and should develop an understanding of why fractions need a common denominator instead of being shown an algorithm for determining common denominators. This involves teachers using manipulatives, pictorial representations and graphic organizers before moving to a symbolic procedure. Students with working memory issues may also forget to provide complete solutions to problems, and need to be taught a structured approach to solving problems. Finally, there are technological tools that can help students use their mental resources for critical thinking rather than arithmetic calculations.

## Teach Conceptual Understanding

One challenge that may arise for students is working with symbolic representations. Students with working memory difficulties continually have to make sense of symbols, and may forget where they are in a procedure. Using manipulatives, graphic organizers, or pictorial representations can reduce this strain on their working memory, as these tools may allow students to draw on their strengths to represent their thinking.

For example, when solving proportions, many students find it more effective to represent the proportions with tiles rather than setting up the proportion symbolically. Another example is two-digit multiplication. Rather than teaching the traditional memorized algorithm, developing a graphic organizer for a partial products approach (e.g. the box method, as shown below) will be easier for students to follow.

This leads to another important idea - procedures should be developed based on a conceptual understanding. In the above two-digit multiplication example, students should first use base ten blocks to develop the concept of partial products in a visual/hands-on way, and then transition to a pictorial/symbolic procedure using the box method, which looks similar, but is more efficient.

Another example would be to teach a conceptual approach to division, rather than the traditional long division approach (as shown below). Students could again start with base ten materials and then progress to a procedure using repeated subtraction of “friendly multiples” (e.g. groups of 1, 2, 5, and 10 of the divisor).

On a related note, it is helpful not to teach procedures that are ‘tricks’ to students. An example is cross-multiplying. Students will not understand the procedure, and will therefore not understand when to use it. Instead, it is advisable to show students that solving a proportion is like solving any equation so they can still use the “isolate the variable using opposite operations to both sides” concept they learned the first time they solved simple equations in Grade 7.

## Teach Problem-Solving Strategies

One other issue for students with working memory difficulties is simply remembering the process and steps required to solve a problem. At Sagonaska Demonstration School, we explicitly teach a couple of problem solving frameworks. The most common is for typical application (word) problems that do not require students to sequence a number of steps, but do require students to understand what is required, make an estimate, select an appropriate tool or strategy to solve the problem, represent their thinking, reflect on their answer, and communicate their solution. We have made a laminated checklist for students to use as they work through the problem to ensure they complete all steps.

## Use Technology

Finally, I would suggest that there are some great technological tools that can support students with working memory difficulties, for example, the Algebra Touch app. Students with working memory difficulties may mix up the application of steps in solving an algebraic equation, especially if they also have fine motor skill difficulties and struggle to organize work symbolically. With Algebra Touch, students still have to enter appropriate steps to solve the equation, but the app takes care of the grunt arithmetic (e.g. subtracting 3x from both sides of an equation). Other calculators that keep a record of calculations performed so students can refer back to them are also useful.

## Conclusion

So, as you can see, there is a lot we can do to help students with working memory difficulties be successful in math. The nice thing is that these strategies are good for all students and lead to better overall math instruction based on conceptual understanding.

## Related Resources on the LD@school Website

Click here to access the LD@school learning module Concrete, Representational, and Abstract Strategies for Mathematics Instruction.

Click here to access LDs in Mathematics: Evidence-Based Interventions, Strategies, and Resources.