Digitally Expressing Algebraic Thinking in Quantity Variation

Abstract

In this chapter, we describe and analyse a number of examples of 7th and 8th graders showing diverse ways of expressing their mathematical thinking in solving algebraic word problems with a spreadsheet. Different youngsters’ approaches to situations where quantity variation is involved are characterised. The problems require finding an unknown value under a set of conditions that frame a problem situation. The use of the spreadsheet is thoroughly examined with the aim of highlighting the nature of problem-solving and expressing in the digital tool context as compared to the formal algebraic method; moreover, the ways in which students take advantage of the tool (being guided by and also guiding the spreadsheet distinctive forms of organising and performing variation in columns and cells) are important indicators of their algebraic thinking within the problem-solving activity. Finally, we pay attention to indicators of “co-action” in students’ work on the spreadsheet as it tends to be more related to structuring solutions by means of creating variable-columns than with tentative ways of generating inputs in recipient cells.

Two data sources are used: the online competition collection of participants’ solutions and in-class observations of 8th graders working on the same problems. Our analytic approach is a parallel analysis of solutions from the two settings, assuming that both data sources illuminate each other’s differences and similarities. Our overall purpose is to acquire a view of youngsters solving and expressing algebraic problems concerning quantity variation in terms of their various uses of the spreadsheet.