The latest educational reforms in Canada (ex.: Quebec Ministry of Education, Leisure, and Sport, 2004) prioritize problem solving in mathematics curriculum, both in elementary and secondary schools. In elementary school, problems are solved using arithmetic i.e. concrete numbers and operations. In secondary school, they are solved using algebra i.e. equations, inequalities, functions, knowledge of structures and relationships (Kieran, 1989; Schmidt & Bednarz, 2002; Cai & Knuth, 2011). In middle school, problems become more mathematically complex and students who continue to rely on the concrete numerical data and sequential operations on them experience severe difficulties. As these students move on to secondary schools, their problem-solving difficulties are compounded with difficulties in algebra, working with letters among other things (Bednarz et al. 1996). Researchers who studied the transition from arithmetic to algebra (Kieran 2014; Radford 2012; Carraher & Martinez 2008; Malara & Navarra 2002) argue that the development of algebraic reasoning should start in early grades in parallel with or within the study of arithmetic. In my doctoral research (Polotskaia, 2015), I studied young students thinking development when they were learning to model mathematical relationships present in arithmetic word problems. To ensure the smooth arithmetic-algebra transition, I complemented the modeling activities with a computer task where numbers were coded with letters in the text of word problems. Students had possibility to create a solution using letters or numbers. The video-recorded data of students’ performance analysed using the theoretical model of problem-solving-cycle (Savard, 2008) revealed positive results. At the beginning, all students used numbers to solve computer task problems, but after training, majority opted to letters. Students were able to analyse and express relationships between quantities in a general form using letters, performing reasoning of algebraic type. The study demonstrated great potential of the teaching approach for the development of algebraic thinking in young students.

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