The National Council of Teachers of Mathematics [NCTM] (2000) highlights the importance of estimation activities from pre-kindergarten through grade 12. The NCTM (2000) remarks that estimation serves as a crucial companion to computation and also estimation activities play an important role in developing number sense of students. However, making estimation is not an easy skill for many students because, in mathematics courses, students often compute to solve problems without making any estimation. Instructional programs should enable all students to make reasonable estimations in various mathematics topics. Fractions are one of the topics so that estimation activities may help students to strengthen their understanding of fractions (Van de Walle, 2007). Therefore, students should be encouraged to work on estimation activities with fractions in mathematics courses and to explain their estimation strategies.
This study attempted to determine how middle-grade students estimate the fractions from given models by using the activity called “About How Much?” (Van de Walle, 2007, p.303). This activity offers visual estimating in the area and number line models. The participants of this study were 38 7th grade students, from two public middle schools. In this activity, students were asked to write a fraction that they think as a good estimate of the amount shown on area models or the indicated mark on the number line. Furthermore, students were asked to explain their thinking about why they chose that fraction. The data was collected through students’ written responses to the activity. The qualitative data analyses were carried out to analyze students’ written responses. The findings revealed that many students could not use reasonable strategies to make a good estimation and they failed to make reasonable estimations. Furthermore, the data gave evidence that students’ difficulties and misconceptions with fractions have created obstacles for them to make good estimates.