If I had a magic wand as an educator, I would wave it and magically see a student’s thinking. Knowing what a student is thinking is an incredibly powerful tool because it helps us know how to create experiences that will help students notice, make connections among their experiences, and construct knowledge. If you are just joining us, you may want to check out my previous posts in this series. (Part One and Part Two)
The research I have recently been reading has impressed upon me the significance of the teacher paying attention to what a student “notices”. In his book Children’s Counting Types, Dr. Leslie P. Steffe shows how the words students say could all be the same, but each student sees the problem differently and sees the “unit” differently.
The shift to Common Core is asking us as educators to deepen students’ knowledge. The following task will ask students to make connections and see the relationship among doubles and doubles plus one, successfully deepening their knowledge.
Today I’m going to show you a powerful classroom task that will help your students to think strategically about addition and their own number knowledge. (This task also involves Mathematical Practice Standards 1 and 7.) Through this activity, students will see the relationship between doubles and doubles plus one. You will want students to notice how the numbers are similar and how they are different. Watch the following video clip to see how I created an experience that helped students notice the similarities and differences. (Click on the link to download the ten frames I used in the video.)
From an adult’s point of view, partitioning (decomposing) numbers seems quite obvious, but that isn’t the case for students. Bethany was able to see the sets of two within the ten frame and the relationship between the two numbers. Weston only saw the ten frame as the number of dots, the shape, and the number of open squares. As Weston begins to think about numbers more abstractly, he will see what Bethany sees. In order for ten frames to not be just “one more thing to memorize”, we need to put two ten frames next to each other and ask opened-questions that encourage students to notice.
“HOW ARE THESE THE SAME AND DIFFERENT?” “WHAT DO YOU SEE?”
Although these questions might not seem mathematical, they are critical to help students build number knowledge and see relationships among numbers.