The computation choices made by students in years 5 to 7

This study was designed to explore the computation choices made by 78 students in Years 5 to 7. The ability to choose and use a repertoire of computation methods is an important goal of mathematics education. While one might expect to find a great deal of research evidence outlining the computation choices students make and why they make them, this was not the case; and as such it was decided to explore what computation choices students make and why they make them. When examining the literature dealing with computation choice few studies were found that directly discussed the issue. There were many studies of computation and discussion of factors that might affect computation choice. The literature also outlined the need for the computation focus to change from purely the development of skills, particularly with paper-and-pencil, to enhance the ability of students to make considered computation choices. Several models of computation were reviewed along with literature dealing with metacomputation. This prompted the need for a fresh look at computation in terms of a non-linear computation model that better reflected the computation process students pass through when solving a computation problem. In particular the role of metacomputation as a means of choosing a computation method, then guiding and monitoring the computation was explored. Students in Years 5 to 7 were chosen to participate in the study as it was felt 10---12 year-old students would have had enough exposure to various forms of computation so as to be confident and competent in using all forms of computation. Students were asked to complete a series of computation items using their preferred computation approach. Clinical interviews were conducted to determine why students made particular computation choices. Observational data and field notes were used to collect data on what computation choices were made and how successful s.tudents were in executing their chosen method of computation. Data were analysed and it was found that students made appropriate computation choices in slightly over 50 percent of cases based on the success rate experienced when completing computation questions using their favoured method. In some cases computation choice was limited by a lack of competence in all forms of computation. In particular it was noted that many students were unable to make use of simple calculators. Interview data indicated that students make computation choices with little hesitation and based on a set of rudimentary criteria such as the magnitude of the numbers involved, or the operation required. There was little evidence to suggest that students looked beyond these simple criteria when making a decision about which form of computation to use. The implication of the research is that teachers may better understand how students make computation choices and what hampers the making of computation choices. As a result of understanding of the process students use for making such choices, teachers should be able to raise student awareness of the process of making a computation choice. The thesis concludes with a recommendation that in much the same way that teachers have been encouraged to focus on developing mental computation strategies, they should also encourage students to discuss their criteria for making particular computation choices. In doing so students will be encouraged to broaden their thinking about the computation process. A suggestion is also made that time spent in the classroom developing each of the computation alternatives, mental, written and calculator, needs to better reflect the usage patterns of adults. Students who have a better understanding of how to use all types of computation will be in a better position to make appropriate computation choices.