Mid Sweden University

It is agreed that algebra has an important role in physics, particularly through handling symbols. A lot of previous research has focused on how mathematics is used in physics from perspectives where mathematics is taken for granted, and not addressing potential differences of mathematics in the physics classroom and in the mathematics classroom. Studies addressing differences between both subjects have been based on researchers’ own experiences of mathematics in both subjects. Thus, more focused empirical research is needed. The purpose of this study is to clarify similarities and differences between mathematics and physics concerning the use of algebraic symbols. Analyses were based on comparisons between upper secondary textbooks in mathematics and in physics from a discourse perspective. Statistical methods were used to decide if there were any significant differences between the subjects. Results showed an overlap in the algebra discourse in both subjects, but also several differences concerning core aspects of algebra. For example, a higher number of different algebraic symbols in equations in physics than in mathematics, and algebraic symbols are more seldom referred to by words in mathematics than in physics. This can make it difficult for students to identify similarities in the algebraic discourses in both subjects

Begrepspförståelse är en central del av elevers lärande i matematik, som innebör en djupare förståelse för bland annat begrepps egenskaper och hur olika matematiska begrepp hänger samman, och som hjälper dem lösa matematiska problem. Genom att arbeta med utmanande problem, som kräver kreativa lösningar, främjar elevernas förmåga att tänka kritiskt och reflektera över matematiska begrepp, vilket i sin tur stärker deras långsiktiga lärande.

One way to stimulate conceptual considerations is through mathematical problem solving, which requires students to construct new solution methods, potentially including new representations. Hence, this study focuses on students’ use of and shift between representations during problem solving, specifically regarding the fundamental and often challenging concept of rational numbers. Swedish elementary school students were observed when tackling mathematical problems in pairs. The findings revealed that the students’ considerations concerned several conceptual properties of rational numbers through the use of different representations. However, students tended to use the representations presented in the problem, favouring the most familiar representation rather than constructing their own. As a result, they may have overlooked opportunities to explore a wider range of representations which could have deepened their understanding of the concept. This suggests a potential opportunity to design problems that require students to transfer between representations and grapple with unfamiliar ones.

Användningen av olika uttrycksformer är en central del inom matematik. I denna artikel beskriver författarna hur kontraster mellan uttrycksformer kan bli ett verktyg för bättre matematiklärande.

Eftersom studenter på olika högskoleutbildningar förväntas skriva akademiskatexter, har många lärosäten initierat projekt för att stötta studenterna i derasutveckling av akademisk litteracitet. Studier har bland annat visat vikten av attskrivstödet är ämnesintegrerat. Det blir då extra intressant att reflektera kringförutsättningar för skrivstöd i program som innehåller flera olika ämnen. Genomvår beskrivning av ett ämnesövergripande programutvecklingsarbete på grundlärarprogrammet vid Mittuniversitetet inom projektet Skrivlyftet, framkommerkomplexiteten i att utveckla ett programgemensamt skrivstöd när programmetbestår av flera olika ämnen. Speciellt avgörande tycks vara att det finns ett återkommande systematiskt arbete med akademiskt skrivande i programmet, däralla lärare i de olika ämnena/kurserna är involverade. Vår slutsats är dock attstommen i ett sådant arbete med fördel förläggs hos lärarutbildningsinstitutionenoch de programgemensamma kurserna, för att sedan implementeras i de olikaämneskurserna.

Problemlösning är en fundamental del av matematisk verksamhet, men hur ska problem utformas om syftet är att utveckla elevers begreppsförståelse? Hör har flera olika problem testats och reviderats för att skapa begreppsliga utmaningar.

Research has identified several aspects that influence students’ transitionto mathematics studies at university, but these aspects haveoften been studied separately. Our study contributes to the field’sunderstanding of the transition between upper secondary and universitymathematics by taking a multifaceted perspective not previouslyexplored. We analyse experiences and attainment in mathematicsof 154 engineering students with respect to known aspectsof this transition, and our results show that it is important to considerseveral aspects together in order to understand the full complexity ofthe transition. It is revealed that students with previous experiencesof university studies, when compared with new first year undergraduates,perceive a larger difference between studying mathematics atthe upper secondary level and university. Our results also show thatthe engineering students enrolled in distance programmes experiencelarger differences between secondary and tertiary levels thanengineering students enrolled in campus programmes. Furthermore,our analyses show that students’ success in mathematics is relatedto their perceptions of the rift experienced in the transition. In all,our results highlight the importance of taking a student perspectivein the development of explanatory and useful models of students’transition between upper secondary and university mathematics.

This presentation focuses on mathematics tasks that challenge students, which have proven beneficial for learning. Tension (as an opposite to cohesion) between different modes (e.g., words, symbols) can create such challenge. By using cohesion and tension as concepts to analyse students’ work on multimodal tasks, this study aims to identify characteristics in the task design that makes tudents develop understanding of the mathematics concept in focus. Preliminary results show that a high degree of cohesion can direct the attention of students to the intended tension. Also, the tension in a task, although relevant, can be too challenging for students, thus ignored, and make students rely too much on previous knowledge.

Generalization is one of the core aspects of algebraic thinking, and research literature points to the importance of objectification when generalizing mathematical discourses. To increase the field’s understanding of the objectification process in various algebra discourses, our study analyses Grade 6 teachers’ use of words, symbols, routines and narratives when they introduce various algebraic concepts. Our results show that there exist instances of objectification in the teachers’ discourses, but these are all implicit, which can make them difficult for students to notice. Thus, teachers need to be made more aware of the importance of making the objectification process explicit. Furthermore, our results show that instances of objectification are tightly connected to the use of formal algebraic symbols. This highlights the importance of the transition from concrete/iconic to formal/arbitrary representations.