This paper provides some insights into the use of example-generating tasks in the design of a technology-rich learning environment to enhance students' mathematical thinking. The paper reports on an early stage of a design-based research project concerning the design of tasks and associated feedback utilising the affordances provided by a combined…

We examine a group (N = 88) of Swedish first-year engineering students, their motivation, self-efficacy, and beliefs about the nature of mathematics, and how these relate to their task performance in mathematics. In our data, engineering students who emphasized the exact reasoning in their view of mathematics performed significantly better in a…

Graphical representations are an important tool used to model abstract processes in fields such as chemistry. Successful interpretation of a graph involves a combination of mathematical expertise and discipline-specific content to reason about the relationship between the variables and to describe the phenomena represented. In this work, we…

Students' difficulties with proof, scholars' calls for proof to be a consistent part of K-12 mathematics, and the extensive use of textbooks in mathematics classrooms motivate investigations on how proof-related items are addressed in mathematics textbooks. We contribute to textbook research by focusing on opportunities to learn proof-related…

This study examined outcomes for AP® Calculus and AP Physics students on the 2015 Trends in International Math and Science Study (TIMSS) relative to other participating countries and other advanced math and science students in the United States. Compared to other countries in the study, AP Calculus BC and AP Physics C: EM students outperformed all…

The aim of this study is to analyse how mathematical problem solving is represented in mathematical textbooks for Swedish upper secondary school. The analysis comprises dominating Swedish textbook series, and relates to uncovering (a) the quantity of tasks that are actually mathematical problems, (b) their location in the chapter, (c) their…

Textbooks in applied mathematics often use graphs to explain the meaning of formulae, even though their benefit is still not fully explored. To test processes underlying this assumed multimedia effect we collected performance scores, eye movements, and think-aloud protocols from students solving problems in vector calculus with and without graphs.…

This study reports on an educational development initiative where peer instruction was used instead of traditional lectures in a calculus course for first-year engineering students. The aim of the study was to explore students' experiences of this method. Data were collected by means of an open-ended questionnaire on two occasions: early and late…

This correspondence reports on a case study conducted in the Master's-level Machine Learning (ML) course at Blekinge Institute of Technology, Sweden. The students participated in a self-assessment test and a diagnostic test of prerequisite subjects, and their results on these tests are correlated with their achievement of the course's learning…

The study explores the nature of students' conceptual understanding of calculus. Twenty students of engineering were asked to reflect in writing on the meaning of the concepts of limit and integral. A sub-sample of four students was selected for subsequent interviews, which explored in detail the students' understandings of the two concepts.…

Empirical research shows that students often use reasoning founded on copying algorithms or recalling facts (imitative reasoning) when solving mathematical tasks. Research also indicate that a focus on this type of reasoning might weaken the students' understanding of the underlying mathematical concepts. It is therefore important to study the…

We are studying two groups of preservice teachers' conceptions, progression and especially the concept of function in connection to y=x+5 when they are taking a course in algebra or one in calculus in their third and sixth term, respectively, in a teacher preparation program. There is a similar development in that they use to a higher degree a…

Explains the reasons for low U.S. score results on the Third International Mathematics and Science Study (TIMSS) and compares them with students from other nations. Swedish high schools scored highest on the science test, which is attributed to their curriculum. Suggests that the majority of students are taught science that is irrelevant for their…