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# Comparing and ordering fractions - a learning study

Konferensbidrag (offentliggjort, men ej förlagsutgivet)
Författare Kristina Drageryd Malin Erdtman Cecilia Kilhamn WALS, international Conference 2013 in Gothenburg, Sweden. Lesson and learning study as teacher research. September 6-9, 2013 111 2013 Institutionen för didaktik och pedagogisk profession 111 en issuu.com/monaholmqvistolander/docs... learning study, mathematics, fractions , Annan matematik

## Sammanfattning

How can we develop mathematic teaching to enhance student’s understanding of fractions? This became the starting point of our Learning Study dealing with the ability to compare and order fractions implemented in grades 6 – 7 (age 12-13 years). Two features that distinguishes a Learning Study from a Lesson Study is the use of variation theory when planning a lesson and the use of pre- and post-tests as a way of assessing student knowledge and the impact of a lesson. In our presentation we will describe how these features helped us design and develop a lesson about comparing and ordering fractions. Through our learning study we found that a variation of forms of representation, such as part of a whole, part of a set, and points on a number line, did not in itself increase students’ ability to compare and order fractions. The separate the roles of the numerator and the denominator in a fraction were found to be critical, but not sufficient, aspects for the students to discern. The most essential critical aspect for this object of learning turned out to be the relationship between the numerator and the denominator. In order to make that relationship stand out we designed a lesson where fractions were mainly represented as points on a number line and both the numerator and the denominator were varied simultaneously but systematically and compared to the benchmark numbers 0, ½ and 1. We will demonstrate how the critical aspects were linked to the object of learning and how the different designs of a lesson had different impact in students’ learning. Furthermore, we will describe the workflow in a Learning Study and discuss some practical issues in the process of developing the quality of a mathematics lesson through a Learning Study.