Trick for subtracting integers

I have algebra students, in high school and college, who struggle with evaluating expressions like 2 – 5.  This is a ubiquitous problem.

I have tried several strategies and the one that is easily the most effective is shown below. When a student is stuck on 2 – 5 the following routine plays out like this consistently.

• Me: “What is 5 – 2?”
• Student pauses for a moment, “3”
• Me: “So what is 2 – 5?”
• Student pauses, “-3?”
• Me: Yes!

I implemented this approach because it ties into their prior knowledge of 5 – 2. It also prompts them to analyze the situation – do some thinking.

Shaping Behavior

Shaping is a term in special ed which basically means to train a student to incrementally follow through on a sequence of substeps to accomplish a task. B.F. Skinner coined a different name for this which he called operant conditioning. The top photo below shows “Skinner’s box.” The pigeon was placed in the box and when it pecked at the metal wall a pellet of food was presented to it. Eventually the reward was given as the pigeon pecked closer and closer to the disk in the wall where its beak is in the photo. Finally, it learned that by pecking this disk was the only means of getting the pellet.

In special education, this shaping is used to train a student to achieve specific outcomes. In the bottom photo below my son Gabriel is playing with his favorite all time toy, Legos. As is the case with many with autism, he would not look at people in the eye. His therapists trained him to make eye contact by first holding his Legos in the air until he requested them. Eventually the Legos were held incrementally closer to the therapist’s eyes. The second to last step was to hold them next to the eyes and finally he had to look into the therapist’s eyes before getting the Legos.

This same approach can be used to train students to attempt problems, think critically, follow classroom norms such as the appropriate steps for starting classs and any other desired behavior.