Randi was a student in my 8th grade math class. She was considered to have such high needs that she was assigned a paraprofessional person, who came with her to every math class.
Randi’s parents were both in prison, and she lived with an aunt. She wore jewelry that looked like razor blades. She was disrespectful to teachers on many occasions. Being staffed in math class added to the picture of a troubled girl with an uncertain future.
Pythagorus’ theorem was the topic of a two week unit, and as usual, Randi was not keeping up. (This is the theorem that connects the lengths of the sides and the hypotenuse of a right triangle, a2 + b2 = c2 ) I was able to spend some time working with Randi individually. We cut out several right triangles and squares to visualize the theorem. We drew pictures that illustrated the theorem. We used graph paper to better show the lengths of the sides of the triangles. Suddenly everything clicked for Randi. She got it.
In fact, she was able to figure out how to take the square root of a number from these experiences. For example, she could see that the square root of 64 must be 8 from one of the examples.
Randi is an example of an honest learner. When she understood something, she truly understood it. When she didn’t fully understand something, she just shut down.
Her positive experiences with Pythagorus’ theorem showed her that she could actually be good at math, and she came to expect to understand. The paraprofessional person assigned to Randi couldn’t keep up with her!