From “Defective” Fractions to Infinite Equivalents
On a recent site visit, I was observing in a fourth grade classroom. The teacher started the lesson (Unit 6, Session 2.1) by writing “3/2″ on the board and asking students to name the fraction. Most said “three halves” although one or two said “two thirds.” The teacher then displayed two blank 4 x 6 rectangles. She established that one rectangle was the whole, and asked students to use their copy of the rectangles to draw a representation that showed 3/2. The math coach called me...read more
What Does It Mean To Be Smart?
“Wow, you’re so smart.” These words drew my attention to a pair of 5th grade girls in a class I was visiting, who I’ll call Cassie and Sophia. They were mid-way through a turn and talk, each sharing her strategy for solving 84 x 59. I casually moved closer, curious about what prompted the comment and trying hard to see each girl’s strategy, recorded in their math journals. Upon hearing Cassie’s comment, Sophia responded in an inviting tone, “No, no. Explain to me what you did.” She...read more
Watch, Notice, and Learn
Classroom video is a powerful tool for studying and reflecting on mathematics teaching and learning. Unlike in-the-moment interactions with students, watching video enables us to slow down and more closely examine student-to-student exchanges. This affords us a unique opportunity to learn about students’ mathematical thinking. Several months ago, I began watching and discussing video footage of elementary mathematics classrooms with a group of colleagues. We were using the footage to study...read more
Puzzling Through Making Fraction Sets
Last year I volunteered in a third grade class. The school mainly uses Investigations 3. During a visit last spring, the class was working on the second session of the fractions unit. I was excited to find out about the students’ beginning understandings of fractions. I sat with a group of four students who were working on making fraction sets. Their task was to fold each of 5 sheets of paper into two, three, four, five, and six equal parts and then to label each piece. The students made 4...read more