Student Number : 0316775W - MSc research report - Faculty of Science / This qualitative research project investigated the ideas of a small group of learners in the first year physics course at the University of the Witwatersrand in the area of atmospheric (air) pressure. These ideas constitute the prior knowledge with which these learners enter physics education at tertiary level. Clinical interviews were conducted with an initial sample of three (3) respondents, and the main study consisted of seven (7) first-year physics students. Data obtained during the course of the interviews was audio-taped and transcribed, and from an analysis of the transcripts a picture was obtained of the content of the knowledge held, and of the epistemological and ontological views that respondents entertained. What renders this work important is the argument that teachers are unable to assist the learning process without engaging actively with what their learners already know and believe. The first step in setting up learning experiences which can assist learners to become fluent in the construction of sound scientific explanations for phenomena and to become competent at weighing evidence is to determine the state of learners’ prior knowledge. The findings of this limited case study may be summed up as follows: There is very little indication, in the sample investigated in this study, that any meaningful learning has occurred in the areas of pressure, atmospheric pressure and the kinetic theory. These concepts have little or no explanatory power for learners in attempting to account for natural phenomena and technological applications in which atmospheric pressure is at work.

Alignment of the expectations of engineering faculty and the preparation engineering students receive in first-year mathematics and physics mechanics courses provided the motivation for the work contained in this study. While a number of different aspects of student preparation including intangibles, such as motivation, time management skills, and study skills, affect their performance in the classroom, the goal of this study was to assess the alignment of the mathematics and physics mechanics knowledge and skills addressed in first-year courses with those needed for a sophomore-level statics and dynamics course. Objectives of this study included: (1) development of a set of metrics for measuring alignment appropriate for an engineering program by adapting and refining common notions of alignment used in K-12 studies; (2) study of the degree of alignment between the first-year mathematics and physics mechanics courses and the follow-on sophomore-level statics and dynamics course; (3) identification of first-year mathematics and physics mechanics skills needed for a sophomore-level statics and dynamics course through the development of mathematics and physics instruments based on the inputs from faculty teaching the statics and dynamics courses; (4) analysis of tasks given to the students (in the form of homework and exam problems) and the identification of the mathematics and physics skills required; (5) comparison of the required skills to the skills reported by faculty members to be necessary for a statics and dynamics course; and (6) the comparison of student preparation in the form of grades and credits received in prerequisite courses to performance in statics and dynamics. Differences were identified between the content/skills developed in first-year mathematics and physics mechanics courses and content/skills expected by engineering faculty members in the sophomore year. Furthermore, skills stated by engineering faculty members as being required were not necessarily utilized in homework and exam problems in a sophomore engineering mechanics course. Finally, success in first-year physics mechanics courses provided a better indicator of success in a sophomore-level statics and dynamics course than that of first-year mathematics. Processes used in the study could be applied to any course where proper alignment of material is desired.

Mathematics plays a pertinent role in physics. Students' understanding of this role has significant implications in their understanding of physics. Studies have shown that some students prefer the use of mathematics in learning physics. Other studies show mathematics as a barrier in students' learning of physics. In this study the role of mathematics in students' understanding of electricity problems was examined. The study undertakes a qualitative approach, and is based on an intepretivist research paradigm. A survey administered to students was used to establish students' expectations on the use of mathematics in physics. Focus group interviews were conducted with the students to further corroborate their views on the use of mathematics in physics. Copies of students' test scripts were made for analysis on students' actual work, applying mathematics as they were solving electricity problems. Analysis of the survey and interview data showed students' views being categorised into what they think it takes to learn physics, and what they think about the use of mathematics in physics. An emergent response was that students think that, problem solving in physics means finding the right equation to use. Students indicated that they sometimes get mathematical answers whose meaning they do not understand, while others maintained that they think that mathematics and physics are inseparable. Application of a tailor-made conceptual framework (MATHRICITY) on students work as they were solving electricity problems, showed activation of all the original four mathematical resources (intuitive knowledge, reasoning primitives, symbolic forms and interpretive devices). Two new mathematical resources were identified as retrieval cues and sense of instructional correctness. In general, students were found to be more inclined to activate formal mathematical rules, even when the use of basic or everyday day mathematics that require activation of intuitive knowledge elements and reasoning primitives, would be more efficient. Students' awareness of the domains of knowledge, which was a measure of their understanding, was done through the Extended Semantic Model. Students' awareness of the four domains (concrete, model, abstract, and symbolic) was evident as they were solving the electricity questions. The symbolic domain, which indicated students' awareness of the use of symbols to represent a problem, was the most prevalent. / Science and Technology Education / D. Phil. (Mathematics, Science and Technology Education (Physics Education)))

Mathematics plays a pertinent role in physics. Students' understanding of this role has significant implications in their understanding of physics. Studies have shown that some students prefer the use of mathematics in learning physics. Other studies show mathematics as a barrier in students' learning of physics. In this study the role of mathematics in students' understanding of electricity problems was examined. The study undertakes a qualitative approach, and is based on an intepretivist research paradigm. A survey administered to students was used to establish students' expectations on the use of mathematics in physics. Focus group interviews were conducted with the students to further corroborate their views on the use of mathematics in physics. Copies of students' test scripts were made for analysis on students' actual work, applying mathematics as they were solving electricity problems. Analysis of the survey and interview data showed students' views being categorised into what they think it takes to learn physics, and what they think about the use of mathematics in physics. An emergent response was that students think that, problem solving in physics means finding the right equation to use. Students indicated that they sometimes get mathematical answers whose meaning they do not understand, while others maintained that they think that mathematics and physics are inseparable. Application of a tailor-made conceptual framework (MATHRICITY) on students work as they were solving electricity problems, showed activation of all the original four mathematical resources (intuitive knowledge, reasoning primitives, symbolic forms and interpretive devices). Two new mathematical resources were identified as retrieval cues and sense of instructional correctness. In general, students were found to be more inclined to activate formal mathematical rules, even when the use of basic or everyday day mathematics that require activation of intuitive knowledge elements and reasoning primitives, would be more efficient. Students' awareness of the domains of knowledge, which was a measure of their understanding, was done through the Extended Semantic Model. Students' awareness of the four domains (concrete, model, abstract, and symbolic) was evident as they were solving the electricity questions. The symbolic domain, which indicated students' awareness of the use of symbols to represent a problem, was the most prevalent. / Science and Technology Education / D. Phil. (Mathematics, Science and Technology Education (Physics Education))