Title from first page of PDF document. Includes bibliographical references (p. 35-37).

In this multiple-case study, I developed cases describing three students‘ (Mary, Ryan and David) solution methods for algebra word problems and investigated the effect of technology on their solution methods by making inferences about their preferences for visual or nonvisual solutions. Furthermore, I examined the students‘ solution methods when presented with virtual physical representations of the situations described in the problems and attempted to explain the effect of those representations on students‘ thinking preferences. In this study, the use of technology referred to the use of the dynamic software program Geogebra. Suwarsono‘s (1982) Mathematical Processing Instrument (MPI) was administered to determine their preferences for visual and nonvisual thinking. During the interviews, students were presented with paper-andpencil-based tasks (PBTs), Geogebra-based tasks (GBTs) and Geogebra-based tasks with virtual physical representations (GBT-VPRs). Each category included 10 algebra word problems, with similar problems across categories. (i.e., PBT 9, GBT 9 and GBT-VPR 9 were similar). By investigating students‘ methods of solution and their use of representations in solving those tasks, I compared and contrasted their preferences for visual and nonvisual methods when solving problems with and without technology. The comparison between their solutions of PBTs and GBTs revealed how dynamic software influenced their method of solution. Regardless of students‘ preferences for visual and nonvisual solutions, with the use of dynamic software students employed more visual methods when presented with GBTs. When visual methods were as accessible and easy to use as nonvisual methods, students preferred to use them, thus demonstrating that they possessed a more complete knowledge of problem-solving with dynamic software than their work on the PBTs. iii Nowadays, we can construct virtual physical representations of the problems in technology environments that will help students explore the relationships and look for patterns that can be used to solve the problem. Unlike GBTs, GBT-VPRs did not influence students‘ preferences for visual or nonvisual methods. Students continued to rely on methods that they preferred since their preferences for visual or nonvisual solutions regarding GBT-PRs were similar to their solution preferences for the problems on MPI that was administered to them to determine their preferences for visual or nonvisual methods. Mary, whose MPI score suggested that she preferred to solve mathematics problems using nonvisual methods, solved GBT-VPRs with nonvisual methods. Ryan, whose MPI score suggested that he preferred to solve mathematics problems using visual methods, solved GBT-VPRs with visual methods. David, whose MPI score suggested that he preferred to solve mathematics problems using both visual and nonvisual methods, solved GBT-VPRs with both visual and nonvisual methods.

Thesis (doctoral)--University of Limburg, Maastricht, 1992. / Summary in Dutch. Includes bibliographical references (p. 109-119)

The study explored factors that affect academic achievements in Grade 6 mathematics classrooms in a case of solving word problems. It investigated empirically the causes and perceptions that lead to difficulties in solving word problems and eventually identified strategies for teaching them. The constructivist philosophy was adopted. The study used the mixed-method design with quantitative data complementing the qualitative information. In gathering data, a word problem task, questionnaires, a class observation schedule, face-to-face and focus group interviews were used, focusing on SFS (pseudo) school learners and their teachers as a convenient sample. Data analysis was done in an integrated fashion where concurrent triangulation was followed. The statistics results illustrate that factors such as English language proficiency adversely affect the academic achievements of Grade 6 learners when solving word problems. Reading instructions aloud repeatedly and explaining key mathematical concepts have emerged as key strategies in understanding and solving word problems in mathematics. / Inclusive Education / M. Ed. (Inclusive Education)

South African learners struggle to achieve in both international and national Mathematics assessments. This has inevitably become a serious concern to many South Africans and people in the education arena. An algebraic word problem holds high preference among the topics and determines success in Mathematics, yet it remains a challenge to learners. Previous studies show there is a connection between learners’ low performance in Mathematics and errors they commit. In addition, others relate this low performance to English language inproficiency. This has encouraged the researcher to investigate the errors Grade 11 learners make when they solve algebraic word problems. The researcher used a sequential explanatory mixed approach to investigate Grade 11 learners from Gauteng, South Africa when they solve algebraic word problems. Accordingly, a convenient sampling helped to select three schools, and purposive sampling to choose the learners. In this study, the researcher employed a quantitative analysis by conducting a test named MSWPT with 150 learners. In addition, the researcher used qualitative analyses by conducting the Newman (1977) interview format with 8 learners to find out areas where errors are made and what kind of errors they are. Findings discovered that 90 learners demonstrated unfitness due to poor linguistic proficiency, while the remaining 60 learners fall into three main categories, namely those who benefitted from researcher unpacking of meaning; those who lack transition skills from arithmetic to algebra; and those who lack comprehension and calculation knowledge. Conclusively, the researcher found linguistic, comprehension, semantic and calculation errors. The reasons learners make these errors are due to (i) a lack of sufficient proficiency in English and algebraic terminology (ii) the gap between arithmetic and algebra. / Institute for Science and Technology Education (ISTE) / M. Sc. (Mathematic Science Education)

The study explored factors that affect academic achievements in Grade 6 mathematics classrooms in a case of solving word problems. It investigated empirically the causes and perceptions that lead to difficulties in solving word problems and eventually identified strategies for teaching them. The constructivist philosophy was adopted. The study used the mixed-method design with quantitative data complementing the qualitative information. In gathering data, a word problem task, questionnaires, a class observation schedule, face-to-face and focus group interviews were used, focusing on SFS (pseudo) school learners and their teachers as a convenient sample. Data analysis was done in an integrated fashion where concurrent triangulation was followed. The statistics results illustrate that factors such as English language proficiency adversely affect the academic achievements of Grade 6 learners when solving word problems. Reading instructions aloud repeatedly and explaining key mathematical concepts have emerged as key strategies in understanding and solving word problems in mathematics. / Inclusive Education / M. Ed. (Inclusive Education)