Educators teaching math typically start with the “mathy” stuff first. For example, for finding the sales price teachers may start with showing students the steps to calculate (photo below).
I start with the concept, either with a pictorial representation or actual objects to represent the underlying concept. In the photo above, I show an object (related to the student’s interest – this student is into weight training) on sale. The $50 circled in yellow represent the original price. I explain the concept of being on sale and discount and show that 20% is $10 to take away (marked out). This leaves $40 (in green) which is the sales price. This allows for conceptual understanding before showing him the “mathy” way of doing the problem.
All too often math topics are introduced first with the skills and steps. This is backwards. The photo above shows how I introduced solving equations a high school student with autism using the concept as an entry point.
We discussed what was involved in buying a car, including payments (no interest) then I posed the problem seen at the top. I asked him to figure out the monthly payment. He worked out the problem, overlooking the down payment. With a minimal prompt he self corrected. I followed this by “showing him the mathy way of doing the problem.” (Seen in the bottom half of the photo). He conceptually understood why the -1,000 was the first step and x had meaning.
This is a version of CRA.
Math is an esoteric subject for most people. Good instruction makes information meaningful. One method for making information meaningful is to connect new information to prior experience.
In this situation the new information involves determining whether shapes are similar (see photo below). One example of student prior experience with this topic would be shrinking people down. In the photo above I use Mini Me and Dr. Evil and their respective (and fabricated) weights and shoe sizes as measures that will eventually give way to measures of sides of a polygon (below). When working on the problem below the students can be prompted by recalling the analogy of Mini Me and Dr. Evil.
Solving equations with a variable on both sides proves to be exceedingly tricky for many students. My approach is to focus on the individual expressions taken from both sides of the equation and to present them in the context of a relevant real life situation. The photo shows a snippet of the handout I use. The table is scaffolded to help students compute costs based on number of toppings. The pizza places charge the same at 3 toppings. Domino’s charges more for 0-2 toppings and Pizza Hut charges more for 4 or more toppings. The color coding fleshes this out.
Overall the kids are actively engaged and the variable, expressions and the overall equation has meaning.
One model for memory is called the Information Processing Model or Dual Storage Model.
Here’s the suggested process in this model in a class instruction context:
Most if not all educational strategies would address some aspect of this model.