Developing Namibian Grade 8 Learners’ Conceptions of Fractions Using Visual Models

Abstract

Learning rational number concepts is acknowledged as an important task but many learners find it difficult to make sense of them. This paper reports on a case study of the learning in a short (nine-lesson) learning programme for Grade 8 learners in a Namibian school, which sought to use visual models (circle area, bar area and number line) to deepen learners’ understanding of fractions as a means to represent rational quantities. The initial benchmark test indicated a number of ways of working with fraction representations, many of which were inappropriate to the rational quantity presented. Although most learners were able to use a fraction to appropriately describe a part–whole area diagram with a single whole, few were able to appropriately label a similar diagram with multiple wholes, or a quantity greater than 1 on the number line. In the learning programme learners worked with visual models that incorporated multiple reference wholes, to explicitly identify the reference whole, to quantify the size of appropriately subdivided units using unit fraction names and to use these units in a measurement process to quantify the quantities these models indicated. A final test showed a sound conceptualisation of the use of fractions to represent rational quantities less than and greater than 1, in such models.

Keywords:

• rational number learning
• conceptual understanding
• fraction representations
• visual models