Making meaning in mathematics problem-solving using the Reciprocal Teaching approach

This paper examines the application of the Reciprocal Teaching instructional approach to mathematical word problems in the middle years. The Reciprocal Teaching process is extended from the four traditional strategies of predicting, clarifying, questioning and summarising, to include further cognitive reading comprehension strategies applied to the context of solving mathematical word problems. Introduction Reciprocal Teaching (RT) is an evidence-based, dialogic instructional approach that has been proven to improve reading comprehension in literacy (Palincsar, 1986; Palincsar & Brown, 1983, 1984). The four comprehension strategies that traditionally constitute RT include predicting, clarifying, questioning and summarising. These four cognitive reading comprehension strategies, through the RT approach, have also been applied to support students to comprehend and solve mathematical word problems (Collen, 2011; Wessman Huber, 2011; Lamb, 2004; Quirk, 2010; Reilly, Parsons & Bortolot, 2009; Rudy, 1990; van Garderen, 2004). Reilly et al. (2009) conducted an action research project applying RT in mathematics with two Year 7 classes in Victoria, which were streamed for ability, gender and behaviour. One class used the RT approach and the other used any problem-solving strategy of their choice. The authors had previously found that students at the same school in Victoria had experienced significant improvement in their reading ages when using the RT approach in literacy. The researchers innovated on the RT approach for problem-solving in mathematics by including predicting, clarifying, solving and summarising as their key strategies or stages. Students were encouraged to predict the type of mathematical questions being asked, the mathematical operations required and what the answer might look like, using their prior knowledge, the structure of the text, including headings, illustrations/diagrams and problem content. During the clarifying stage, students listed words they were unfamiliar with, facts that they knew and information they had yet to determine to successfully solve the problem. In the solving phase, students used a range of problem-solving strategies and demonstrated their working using pictures, diagrams, numbers or words. Finally, during the summarising stage, students engaged in self-reflection, including justifying their answer, reflecting on how they might refine their approach if presented with a similar problem, and evaluating how they contributed to the group problem-solving task. Students also recorded their thinking under each of the four headings: predicting, clarifying, solving and summarising. The outcomes included the observation that the RT group completed fewer problems in the allocated time period, compared to the non-RT group; however, fewer than one-third of the students in the non-RT group solved the problems correctly, whereas three-quarters of the RT group had correct solutions. The non-RT group also displayed minimal working out or checking of answers. 8 Literacy Learning: the Middle Years