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International literature is increasingly disclosing the relevance of cultural aspects within the processes of teaching and learning mathematics. Knowledge is inextricably linked to the activities in which the subjects engage, and must be considered in relation to the socio-cultural context wherein the activity takes place. Literature reveals the relationship between the background culture (e.g. language, nationality, etc.) of prospective elementary teachers and their beliefs about mathematics and its teaching. In this paper, we define culture with reference to the wider discussion from cross-cultural psychology literature about cultural values, and we investigate if and how differences in individuals' cultural values are related to prospective teachers' beliefs about being successful in mathematics and in its teaching. We adopt a questionnaire from the studies by Schwartz to measure participants' values. We assign each prospective teacher of our sample to a cluster of beliefs and we analyse how the beliefs of prospective teachers are related to their values. Results show that cultural values and beliefs about mathematics are related, while this is not the case for beliefs about the teaching of this subject. [ABSTRACT FROM AUTHOR]

Many approaches to make mathematics relevant to first-year engineering students have been described. These include teaching practical engineering applications, or a close collaboration between engineering and mathematics teaching staff on unit design and teaching. In this paper, we report on a novel approach where we gave higher year engineering and multimedia students the task to ‘make maths relevant’ for first-year students. This approach is novel as we moved away from the traditional thinking that staff should produce these resources to students producing the same. These students have more recently undertaken first-year mathematical study themselves and can also provide a more mature student perspective to the task than first-year students. Two final-year engineering students and three final-year multimedia students worked on this project over the Australian summer term and produced two animated videos showing where concepts taught in first-year mathematics are applied by professional engineers. It is this student perspective on how to make mathematics relevant to first-year students that we investigate in this paper. We analyse interviews with higher year students as well as focus groups with first-year students who had been shown the videos in class, with a focus on answering the following three research questions: (1) How would students demonstrate the relevance of mathematics in engineering? (2) What are first-year students' views on the resources produced for them? (3) Who should produce resources to demonstrate the relevance of mathematics? There seemed to be some disagreement between first- and final-year students as to how the importance of mathematics should be demonstrated in a video. We therefore argue that it should ideally be a collaboration between higher year students and first-year students, with advice from lecturers, to produce such resources. [ABSTRACT FROM PUBLISHER]

There is considerable variety in inquiry-oriented instruction, but what is common is that students assume roles in mathematical activity that in a traditional, lecture-based class are either assumed by the teacher (or text) or are not visible at all in traditional math classrooms. This paper is a case study of the teaching of an inquiry-based undergraduate abstract algebra course. In particular, gives a theoretical account of the defining and proving processes. The study examines the intellectual responsibility for the processes of defining and proving that the professor devolved to the students. While the professor wanted the students to engage in all aspects of defining and proving, he was only successful at devolving responsibility for certain aspects and much more successful at devolving responsibility for proving than conjecturing or defining. This study suggests that even a well-intentioned instructor may not be able to devolve responsibility to students for some aspects of mathematical practice without using a research-based curriculum or further professional development. [ABSTRACT FROM AUTHOR]

Universities invest significant resources in the provision of mathematics tuition to first year students, through both traditional and non-traditional means. Research has shown that a significant minority of students do not engage with these resources appropriately. This paper presents findings from a study of two groups of students at Maynooth University. Both groups had similar mathematical backgrounds on entry to university. The first group consisted of seven students who had failed first year mathematics and had very low levels of engagement with available supports. The second group consisted of nine students who had passed first year mathematics and had engaged with the supports to a significant extent. It emerged that while both groups initially displayed similar tactics and encountered similar difficulties, their levels of reaction to a number of critical events in their mathematical education were key to their engagement levels and their subsequent progression. Further analysis revealed aspects of the students' behaviour which caused them to approach or avoid difficulties. The reasons behind the different student behaviours were investigated, and the main categories of influence on student behaviour which emerged from the interview data were fear, social factors, and motivation. [ABSTRACT FROM PUBLISHER]

In order to teach on the basis of the genetic approach. one should undertake an analysis consisting of the following two stages: (I) a genetic elaboration of the subject matter and (2) an analysis of the arrangement of the material. including a consideration of various ways of representing it and its effect on students. The genetic elaboration of subject mailer consists of the analysis of the subject From tour points of view: historical, logical. psychological, and socio-cultural. Also important is the epistemological analysis of the subject. This paper describes the design of the system of study of the concepts of Euclidean ring and equivalence relation. [ABSTRACT FROM AUTHOR]

Flipped learning is gaining traction in K-12 for enhancing students’ problem-solving skills at an early age; however, there is relatively little large-scale research showing its effectiveness in promoting better learning outcomes in higher education, especially in mathematics classes. In this study, we examined the data compiled from both quantitative and qualitative measures such as item scores on a common final and attitude survey results between a flipped and a traditional Introductory Linear Algebra class taught by two individual instructors at a state university in California in Fall 2013. Students in the flipped class were asked to watch short video lectures made by the instructor and complete a short online quiz prior to each class attendance. The class time was completely devoted to problem solving in group settings where students were prompted to communicate their reasoning with proper mathematical terms and structured sentences verbally and in writing. Examination of the quality and depth of student responses from the common final exam showed that students in the flipped class produced more comprehensive and well-explained responses to the questions that required reasoning, creating examples, and more complex use of mathematical objects. Furthermore, students in the flipped class performed superiorly in the overall comprehension of the content with a 21% increase in the median final exam score. Overall, students felt more confident about their ability to learn mathematics independently, showed better retention of materials over time, and enjoyed the flipped experience. [ABSTRACT FROM PUBLISHER]

There are numerous theories that offer cognitive processes of students of mathematics, all documenting various ways to describe knowledge acquisition leading to successful transitions from one stage to another, be it characterized by Dubinsky's encapsulation, Sfard's reification or Piaget's equilibration. We however are interested in the following question. Who succeeds at making the leap and can we describe the attributes that set them apart from the ones that do not? In this article, we offer a framework to categorize students as learners based on their individual approaches towards learning concepts in differential equations and related concepts – as demonstrated by their efforts to resolve a conflict, conserve and rebuild their cognitive structures. [ABSTRACT FROM PUBLISHER]

This study reported the specific findings of a larger comparative study concerning Turkish and German mathematics teachers' values. The main focus was on the teaching experience of the mathematics teachers. Interactions related to nationality were also of interest. The research methodology employed in this study was a descriptive study. The teachers involved in the study were 27 German and 33 Turkish mathematics teachers. A five-point Likert-type questionnaire was used as the data collection instrument. The data were subjected to descriptive and inferential statistics for analysis. Effect size coefficients were also calculated. The results showed that: (a) the teaching experience between the countries has a significant effect on the values and (b) both Turkish and German math teachers' level of experience does not have a significant impact on their values. [ABSTRACT FROM AUTHOR]

Students often play a passive role in large-scale lectures in undergraduate mathematics courses: they observe the lecturer demonstrate mathematical procedures, but they rarely engage in authentic mathematical activity themselves. This study uses semi-structured interviews of undergraduate students to investigate the implicit and explicit social norms and expectations that influence students to maintain their passive roles during lectures. Students were aware that their passivity was influenced by social norms, but perceived these norms as necessary for allowing the lecturer to get through the content in the allotted lecture time, while enabling students to avoid being publicly embarrassed in the lecture. However, the students appreciated opportunities to work on examples in small groups during lectures. We argue that the success of small group interactions during large-scale lectures depends on students and lecturers establishing supportive social norms, and adjusting their lecture goals from ‘covering the content’ to ‘developing mathematical understanding’. [ABSTRACT FROM AUTHOR]

The purpose of this study is to clarify what kind of mathematical beliefs are conveyed to student teachers during their studies. We restrict ourselves to the following research question: 'What kinds of beliefs do mathematics professors have of teachers' views of mathematics and its improvement?' Seven mathematics professors from five Finnish universities were interviewed in May 1996. Each was responsible for mathematics teacher education in their departments. The interview form used was a theme interview. The central results can be summarized as follows: professors estimated that the teachers' basic knowledge was poor and old-fashioned, requiring improvement. Furthermore, they emphasized the influence of a teacher's personality and his/her own view of mathematics on his/her teaching. They considered the teachers' working environment to be very poor, and stressed that it should be improved. [ABSTRACT FROM AUTHOR]

Reports data on the role played by cognitive factors in mathematics learning. Testing of 54 Italian seventh-grade students to determine their cognitive characteristics, intellectual development and cognitive style; Finding that gender seemed to have a limited significance on the rational number operations.