Teaching and learning algebra word problems : a thesis presented in partial fulfilment of the requirements for the degree of Master of Educational Studies in Mathematics, Massey University, Palmerston North, New Zealand
This study reports on a classroom design experiment into the teaching and learning of algebra word problems. The study was set in the mathematics department of a coeducational secondary school, and involved two teachers and 30 Year 12 students. The teachers and the researcher worked collaboratively to design and implement an intervention that focused explicitly on translation between word problems and algebra. Two issues were considered: the impact of the intervention on students, and the impact of the study on teachers. Students' responses to classroom activities, supported by individual student interviews, were used to examine their approaches to solving algebra word problems. Video-stimulated focus group interviews explored students' responses to classroom activities, and informed the ongoing planning and implementation of classroom activities. Data about the impact on teachers' understandings, beliefs and practices was gathered through individual interviews and classroom observations as well as the ongoing dialogue of the research team. The most significant impact on students related to their understandings of algebra as a tool. Some students were able to combine their new-found translation skills with algebraic manipulation skills to solve word problems algebraically. However, other students had difficulties at various stages of the translation process. Factors identified as supporting student learning included explicit objectives and clarity around what was to be learnt, the opportunity for students to engage in conversations about their thinking and to practise translating between verbal and symbolic forms, structured progression of learning tasks, time to consolidate understandings, and, a heuristic for problem solving. Participation in the project impacted on teachers in two ways: firstly, with regards to the immediate intervention of teaching algebra; and secondly, with regards to teaching strategies for mathematics in general. Translation activities provided a tool for teachers to engage students in mathematical discussion, enabling them to elicit and build on student thinking. As teachers developed new understandings about how their students approached word problems they gained insight into the importance of selecting problems for which students needed to use algebra. However, teachers experienced difficulty designing quality instructional activities, including algebra word problems, that pressed for algebraic thinking. The focus on translation within the study encouraged a shift in teacher practice away from a skills-focus toward a problem-focus. Whilst it was apparent that instructional focus on translation shifted teachers and students away from an emphasis on procedure, it was equally clear that translation alone is insufficient as an intervention. Students need both procedural and relational understandings to develop an understanding of the use of algebra as a tool to solve word problems. Students also need to develop fluency with a range of strategies, including algebra, in order to be able to select appropriate strategies to solve particular problems. This study affirmed for teachers that teaching with a focus on understanding can provide an effective and efficient method for increasing students' motivation, interest and success.