Moving Beyond Brownies and Pizza

Fractions are a hard concepts for students to understand. Students struggle with the idea that fractions are numbers in and of themselves, not a composition of two, distinct, whole numbers. It is also likely that students fail to recognize fractions as discrete numbers because many math classes focus on understanding fractions as parts of wholes or parts of sets. The Common Core State Standards for Mathematics expect students to understand arithmetic operations on fractions by the time they leave fourth grade. Students may not be well prepared to meet this expectation if they think about fractions exclusively in terms of brownies, pizzas, or other area models. Students need to have opportunities to develop and explore their understanding of fractions as measures, that is, understanding both the relative size of fractions and understanding how fractions measure specific intervals. The number line model is a logical context within which these explorations can take place. There are three goals when it comes to student comprehension of fractions. these include: building students’ understanding of fractions as numbers with a definite magnitude, increasing students’ understanding of measuring with fractions, and developing fraction number sense by avoiding early introduction of traditional fraction algorithms. Students are already familiar with the number line from earlier grades, so they understands it as a concept, a representation, and a tool. This is why teachers should use the number line as a way to help teach students fractions. Looking at a fourth grade classroom, for a period of five weeks, students completed many different groups of fraction problems. Students worked in pairs to compare the fractional quantities in each problem set. At first, many students used part-whole concepts and diagrams to aid them in their work. However, a number of students noticed the linear context of each problem and began shifting to linear representations. The teacher encouraged these efforts and asked students to share their work during our whole-group discussion. The teacher continued to use the number line exclusively during whole-group discussions. She displayed student-drawn number lines on the walls and used them as reference points during lessons. Within a few weeks, nearly all the students began to demonstrate an understanding of fractions as actual quantities on the number line. All students in this class made progress in relation to the three goals the teacher had set for them. Students began to build an understanding of fractions as numbers with a definite magnitude. They were beginning to understand how to use the number line as a tool for representing fractions. In particular, students were using ideas connected to the measure subconstruct as a way to reason about the size of fractions in comparison to other fractions and to one whole. Finally, students were developing fraction number sense as they determined the relative size of fractions without resorting to traditional methods of comparison. I believe that using the number line is a great approach and allows students to better visualize the number. I will definitely be using a number line in my classroom!

Freeman, D., & Jorgensen, T. (2015). Moving Beyond Brownies and Pizza. Teaching Children Mathematics, 21(7), 412-420. Retrieved June 28, 2015, from http://www.nctm.org/Publications/teaching-children-mathematics/2015/Vol21/Issue7/Moving-beyond-Brownies-and-Pizza/