Symbol sense characteristics for designing mathematics tasks

Abstract

Symbol sense, an analogy of number sense in the symbolic world of mathematics, is an ability to give meaning to symbols, expressions, and formulas that involves many characteristics, including friendliness with symbols, an ability to examine symbol meanings, and skills to manipulate symbolic expressions. The characteristics of symbol sense are usually used, for instance, for designing symbolic algebra tasks, but are a bit rare for designing mathematics tasks in general. Therefore, this study aims to use symbol sense characteristics for designing mathematics tasks for secondary school students. To do this, using a design research method, we conducted a literature study to collect characteristics of symbol sense and to see possibilities of designing mathematics tasks in general. Next, we designed mathematics tasks according to the symbol sense characteristics. Finally, we provided possible responses of students for the designed tasks. The results of this study included six types of tasks according to the characteristics of symbol sense, including tasks on symbolic problems and word problems—which require translation into symbolic problems. In addition, we provided predicted responses to examples for each type of the tasks and suggestions for use in the learning and teaching process. For further investigation, we recommend to use the set of designed tasks for assessing student symbol sense ability.