On Wednesday, I attended Donna Knoell‘s session: “Helping students with learning disabilities understand mathematics concepts and solve problems.” She suggested lots of different strategies to use in this difficult area. With all of her suggestions, she kept the basic goals in mind – teach the students to make sense of the problems and to persevere to the solution using reasoning. She emphasized the importance of developing the students’ number sense. As appropriate for the LD students, she showed us ways to move away from reliance on the presentation, interrogation, response, and evaluation model, and toward getting the students engaged in problem solving and active learning.
She commented that calculators have their place, but are not universally applicable in mathematics instruction. For instance, after learning the concepts, students can use calculators to lessen the burden of pencil-and-paper demonstrations. It is good to remember that doing a bunch of calculations is not an effective way to teach mathematics. I think it is pretty difficult to generalize the Pythagorean theorem out of noticing that 32+42 = 52, 52+122 = 132, and the other solutions.
The best quotation for the session, to be used while the students are working on problems: “I love to hear the sound of your brains thinking!”
This is the first time I’ve heard Donna speak, but if she’s giving a talk at a conference you’re attending, I suggest attending her talk.