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)))

<p>Syftet med detta examensarbete är att undersöka undervisning och lärande under en matematiklektion som präglas av traditionell skolmatematik. Metoden för undersökningen var en deltagande observation av en matematiklektion i åk 3 på gymnasiet. Med hjälp av begreppen matematikens lärandeobjekt, matematiska resurser, eleven som lärande aktör och sociomatematiska normer har jag tolkat de resultat som genererats från observationen. Två slutsatser som kan dras av undersökningen är att eleverna stimuleras till att bli oberoende lärande aktörer i undervisningen av traditionell skolmatematik samt att det i första hand är läraren som synliggör potentiella matematiska resurser för eleverna. Medvetenheten om elevernas användande av matematiska resurser skulle kunna påverka elevernas lärande genom att läraren synliggör matematiska resurser på ett mer medvetet sätt.</p> / <p>The aim with this degree project is to examine teaching and learning during a mathlesson characterized by traditional school mathematics. The method of the study was aparticipant observation of a mathematics lesson in year 3 in upper secondary school. Using the concepts of mathematical learning objects, mathematical resources, and pupil as an active learner in combination with socio-mathematical norms, I have interpreted the results generated from the observation. Two main conclusions can be drawn from the study. Firstly, pupils are encouraged to become independent as active learners in the teaching of traditional school mathematics. Secondly, it is primarily the teacher who makes potential mathematical resources visible and available for the pupils. With an increasing awareness of pupils’ use of mathematical resources, teachers can affect pupils’ learning by making potential mathematical resources explicit in a more conscious way.</p>

Syftet med detta examensarbete är att undersöka undervisning och lärande under en matematiklektion som präglas av traditionell skolmatematik. Metoden för undersökningen var en deltagande observation av en matematiklektion i åk 3 på gymnasiet. Med hjälp av begreppen matematikens lärandeobjekt, matematiska resurser, eleven som lärande aktör och sociomatematiska normer har jag tolkat de resultat som genererats från observationen. Två slutsatser som kan dras av undersökningen är att eleverna stimuleras till att bli oberoende lärande aktörer i undervisningen av traditionell skolmatematik samt att det i första hand är läraren som synliggör potentiella matematiska resurser för eleverna. Medvetenheten om elevernas användande av matematiska resurser skulle kunna påverka elevernas lärande genom att läraren synliggör matematiska resurser på ett mer medvetet sätt. / The aim with this degree project is to examine teaching and learning during a mathlesson characterized by traditional school mathematics. The method of the study was aparticipant observation of a mathematics lesson in year 3 in upper secondary school. Using the concepts of mathematical learning objects, mathematical resources, and pupil as an active learner in combination with socio-mathematical norms, I have interpreted the results generated from the observation. Two main conclusions can be drawn from the study. Firstly, pupils are encouraged to become independent as active learners in the teaching of traditional school mathematics. Secondly, it is primarily the teacher who makes potential mathematical resources visible and available for the pupils. With an increasing awareness of pupils’ use of mathematical resources, teachers can affect pupils’ learning by making potential mathematical resources explicit in a more conscious way.

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))