Making Sense of Fractions
As I became a more accomplished teacher by regularly using formative assessment strategies, I began to develop a pretty good sense of students’ misconceptions in math. By the time I reached my eighth year of teaching, I knew that students dreaded the fraction unit in math, and I wasn’t quite sure why. Who doesn’t love problems about pizza and brownie pans? What caused this dread and instant confusion when fractions were announced?
The following is a great case for using multiple formative assessment strategies and occurred in my fifth grade advanced math class. We are talking about the top math students in the whole grade level; I was sure they had the most fraction sense of all students!
I’d seen something unexpected on a little pre-assessment I’d given a few days before to gauge fraction sense in this class. This pre-assessment was a series of fraction sense questions that I didn’t even “grade” – I simply wrote feedback on each student’s paper. This particular pair of questions greatly troubled me when only two students answered correctly. Was it possible that my bright, eager mathematicians really lacked this fundamental understanding about fractions? Surely not. Before handing back the pre-assessments, I decided to use the questions as my warmup – my activating strategy. Take a look and see how you would answer.
Sure enough, all but the same two students thought that the answer to question two was one-third. Wow. To me, it’s glaringly obvious that both pictures represent one-fourth! I knew that if I just gave the answer and an explanation the concept would never stick and we’d yet again struggle through the fraction unit. I mentally moved that day’s lesson to the next and spent the next hour of math time in rich discussion about the meaning of fractions, comparing and contrasting the pictures above, and coming up with strong definitions of numerator, denominator, and equal parts. My students gained so much out of this impromptu lesson about such a fundamental fraction concept, and I was able to refer to it throughout the unit as we moved forward.
Had I not taken the time to give the pre-assessment and devote so much time to fraction sense, I am not sure we would have reached some of the understandings that the fifth grade curriculum required. My two favorite fraction resources I used to build my unit are Beyond Pizzas and Pies and Elementary and Middle School Mathematics: Teaching Developmentally. These resources provide examples and problems you can adapt for your own classroom and curriculum.
Do your students struggle each year with fractions? Have you used formative assessment tools to determine which fundamental fraction concepts are still fuzzy?