Has this ever happened to you? “My lecture went perfectly! I worked the sample problems. I could tell the students really understood the material.” The next day: “I don’t know what went wrong! I thought all my students understood what I went over yesterday.” If we’ve been there,
“Engaging students” might be in the top five of most common phrases in mathematics teaching discussions, journals, and professional learning. Strategies to engage students have included cooperative learning, questioning strategies, and classroom discussions. What do these ideas have in common? Each is a way to
As mathematics teachers we have a language all our own. First there is the mathematics vocabulary: pi, perimeter, area, table, mean, etc. Then there is the mathematics education/teaching vocabulary: manipulatives, representations, lesson launch, closure, equity, opportunity to learn, diversity, etc. A new term of importance
Elaine doesn’t like it when her students struggle. She wants to run over to them, pick up the pencil, and show them the way. Yet she knows this is not best for them because when students productively struggle to make sense of the mathematics, they
This is a shameless play on “six degrees of separation.” I assure you Kevin Bacon will make no appearance, nor can I find any relationship between the two of us. Instead, I share some observations about representations in mathematics classes. Some are my own missteps.
In our work, we help teachers support rich, inclusive mathematical discussions among all students. For these discussions to happen, a classroom culture must be developed based on what are often new norms for mathematics class: that students should listen to each other, not just the
It always feels good when we ask a question and we get a correct answer in response. It feels good when our students do well. But sometimes their “success” fools us. We might think of correct answers as an example of learning. But along the
I think it’s intuitive for teacher. We all know this: We are supposed to connect our content to students’ interests. I was a high school math teacher. Niggling in the back of my mind was how to really hook students into learning the content I
Close to ten years ago, while serving as President of the National Council of Teachers of Mathematics (NCTM) I wrote a President’s Message that was entitled “Go Ahead, Teach to the Test!” I had very deliberately chosen the title of my message to “grab” readers,
How do we give our students a present without telling them what it is before they open it? Often when we tell our students what they are going to learn at the beginning of the lesson, I feel that we are telling them what the present