The third learning experience is modeling new mathematical ideas. I want to emphasize that I’m not necessarily talking about the teacher modeling new mathematical ideas. We don’t want to impose our thinking on students. We allow students to model mathematical ideas by providing manipulatives and showing them how to use pictures to model their thinking. Teachers might demonstrate the use of manipulatives and/or drawings to illustrate children’s thinking as the children are explaining their thinking. Even if children are explaining incorrect thinking, modeling that thinking can help children see and understand their mistakes. Students who are not able to explain their thinking, may be able to use materials or drawings to show their thinking.
Modeling mathematical ideas also fits with one of the Guiding Principles of Bridges in Mathematics, “Visual models help us remember and construct important mathematics.”
Teaching students to use drawings to model their thinking will not only help build understanding but it will also give them a good strategy to use in testing situations