High school students' emotional experiences in mathematics classes

The aim of this qualitative research is to identify Mexican high school students' emotional experiences in mathematics classes. In order to obtain the data, focus group interviews were carried out with 22 students. The data analysis is based on the theory of the cognitive structure of emotions, which specifies the eliciting conditions for each emotion and the variables that affect the intensity of each emotion. The participant students' emotional experiences in mathematics classes are composed of: (1) satisfaction and disappointment while solving a problem; (2) joy or distress when taking a test; (3) fear and relief during classes; (4) pride and self-reproach during classes; and (5) boredom and interest during classes. Finally, we discuss how the theory of the cognitive structure of emotions and our analysis contribute to emotion research in mathematics education.     

Indicators of middle school students' mathematics enjoyment and confidence

A study involving 916 students spanning grades 5–8 was conducted to investigate indicators that may contribute to enjoyment and confidence in mathematics. For this group of middle school students, mathematics enjoyment, mathematics confidence, and attitudes toward school were found to generally decline across grade levels. Mathematics enjoyment and confidence were also found to differ significantly based upon student preferences for future careers. Gender differences as well as similarities regarding predictors of mathematics enjoyment and confidence were identified. Specifically, the best predictor for end of year mathematics enjoyment for males was beginning of year attitude toward school, while the most significant predictor of end of year enjoyment for females was beginning of year dispositions toward mathematics (semantic perception). A strong relationship between mathematics enjoyment and confidence overall was found, with indications that activities that increase mathematics enjoyment contribute to increased confidence, and also that activities that increase mathematics confidence contribute to increased enjoyment.     

Mexican high school students' social representations of mathematics,its teaching and learning

This paper reports a qualitative research that identifies Mexican high school students’ social representations of mathematics. For this purpose, the social representations of ‘mathematics’, ‘learning mathematics’ and ‘teaching mathematics’ were identified in a group of 50 students. Focus group interviews were carried out in order to obtain the data. The constant comparative style was the strategy used for the data analysis because it allowed the categories to emerge from the data. The students’ social representations are: (A) Mathematics is…(1) important for daily life, (2) important for careers and for life, (3) important because it is in everything that surrounds us, (4) a way to solve problems of daily life, (5) calculations and operations with numbers, (6) complex and difficult, (7) exact and (6) a subject that develops thinking skills; (B) To learn mathematics is…(1) to possess knowledge to solve problems, (2) to be able to solve everyday problems, (3) to be able to make calculations and operations, and (4) to think logically to be able to solve problems; and (C) To teach mathematics is…(1) to transmit knowledge, (2) to know to share it, (3) to transmit the reasoning ability, and (4) to show how to solve problems.     

Examining prospective mathematics teachers' pedagogical content knowledge on fractions in terms of students' mistakes

The aim of the study is to examine prospective mathematics teachers’ pedagogical content knowledge in terms of knowledge of understanding students and knowledge of instructional strategies which are the subcomponents of pedagogical content knowledge. The participants of this research consist of 98 prospective teachers who are studying in two universities in Turkey. The participants were selected with the purposive sampling method which is one of the non-random sampling methods. Case study method, which is based on the qualitative research approach, was used. The answers given by secondary school students to fraction-related open-ended questions in the study of Soylu and Soylu were used as the data collection tool. The obtained data were analyzed via the content analysis technique. The analyses showed that the prospective mathematics teachers’ pedagogical content knowledge on fractions was not at an adequate level in identifying and correcting students’ errors. However, it was observed that the prospective teachers experienced more difficulty in the knowledge of instructional strategies compared to the knowledge of understanding students.     

Emotion and disaffection with school mathematics

This paper reports some initial findings from research designed to understand more deeply the motivational and emotional landscape of disaffection with school mathematics. A context is described in which there has been significant concern expressed about a number of aspects of mathematics education, but where affect is seen as salient to these problems, including levels of attainment. A case is made that a focus on the qualitative study of motivation and emotion may be more central to an understanding of the phenomenon of disaffection than that of a quantitative study of attitude. The study involved students at two Further Education Colleges who had performed poorly in national examinations, but were required to continue studying mathematics. It was expected that many of them would be disaffected with mathematics. A mixed method approach was adopted, in which students were asked to complete a simple questionnaire on their experience of emotion in mathematics classrooms, and were then interviewed using a range of procedures to elicit qualitative data about their experience of mathematics. Reversal Theory was used as a framework to inform the design of the methods used and analysis of the data. Results demonstrate the richness and volatility of their motivational and emotional experiences of mathematics.     

How do domains of knowledge integrate into mathematics teachers’ practice?

This study is a part of a research project that seeks to characterize the relationship between mathematics teachers’ knowledge and their practice. In this paper, we focus on identifying the characteristics of subject matter knowledge and pedagogical content knowledge that two teachers integrate in decisions they make about the introduction of specific mathematical content. Then, we examine the changes that arise in their classrooms as their plans are put in action. Data were obtained through audiotapes of several semi-structured interviews, through observations, and through videotapes. Although the two teachers in this study had similar backgrounds and experiences, our analysis shows differences in the characteristics of the domains of knowledge they integrated in their planning as well as differences in the adaptations that each made in the classroom. In this sense, this study contributes to better understanding the complexity of teachers’ professional practice.     

Introducing computer algebra to school teachers of mathematics

Since the last decade, the use of computer algebra systems atthe Hong Kong school level is still very limited. Among variousreasons behind, the lack of exposure of this kind of softwareto local school teachers should be taken into account. In thisarticle, we describe how to introduce MAPLE in a BEd moduleof a local teacher-training programme. Reflection on the effectivenessof the module and barriers faced by the school teachers at presentare discussed.     

Factors influencing first-year students' success in mathematics

Qualitative data from lecturers and students were used to identify factors which were perceived as making the most important contributions to students' academic success or failure in first-year mathematics courses. The study was conducted in three phases involving exploratory open-ended questionnaires, Likert-type questionnaires, and interviews. The results highlight both areas of similarities and areas of differences in lecturers' and students' perceptions about influences on student success and failure. While both students and lecturers acknowledged the importance of motivation, differences in perceptions suggest further research is needed in the areas of active learning, help-seeking, and student effort and workload.     

Why mechanics should be integral to secondary school mathematics

Mechanics has never been the most popular subject in A-levelmathematics, the UK’s public examination for 16–18-yearolds, either with students, teachers or educators. The attemptsto popularize mechanics have failed and it is conceivable thatthe subject will be dropped from the A-level syllabus in theforeseeable future. This article argues the importance of mechanicsand why it should be integral to secondary school mathematics:Mechanics is the exemplar of mathematical modelling, is thelogical point of entry for the enculturation into scientificthinking and provides the means to develop an understandingof the relationship between mathematics, the theoretical objectsof science and the way science and mathematics speak of theworld. It enables learners across the ‘ability range’to think in the abstract and as such should be taught priorto the 6th form, that is, prior to the UK’s post-compulsorylevel of education.     

Changing patterns of transition from school to university mathematics

There has been widespread concern over the lack of preparedness of students making the transition from school to university mathematics and the changing profile of entrants to mathematical subjects in higher education has been well documented. In this paper, using documentary analysis and data from an informal case study, we locate the antecedents of this changed profile in the general shift across all subjects to a more utilitarian higher education, alongside the more specific changes in A-level mathematics provision which have been largely market driven. Our conclusions suggest that, ironically, changes put in place to make mathematics more widely useful may result in it losing just those features that make it marketable.     

再谈应用数学的发展——对“试谈”的补充意见

本文采用校勘的格式对 [1]提出补充意见     

On high-school students' use of graphic calculators in mathematics

When students are working with hand held technology, such as graphic calculators, we usually only see the outcomes of their activities in the form of a contribution to a written solution of a mathematical problem. It is more difficult to capture their process of thinking or actions as they use the technology to solve the problem. In this paper we report on two case studies that follow the progress of students as they solve mathematical problems. We use software that works in the background of the graphic calculator capturing the students' keystrokes as they use the calculator. The aim of the research studies described in this paper was to provide insights into the working styles of these students. Through a detailed analysis of their graphic calculator keystrokes, interviews and associated written solutions we will discuss the effectiveness of their solution strategies and the efficiency of their use of the technology and identify some barriers to the use of graphic calculators in mathematical problem solving.     

Opportunity to learn problem solving in Dutch primary school mathematics textbooks

In the Netherlands, mathematics textbooks are a decisive influence on the enacted curriculum. About a decade ago, Dutch primary school mathematics textbooks provided hardly any opportunities to learn problem solving. In this study we investigated whether this provision has changed. In order to do so, we carried out a textbook analysis in which we established to what degree current textbooks provide non-routine problem-solving tasks for which students do not immediately have a particular solution strategy at their disposal. We also analyzed to what degree textbooks provide ‘gray-area’ tasks, which are not really non-routine problems, but are also not straightforwardly solvable. In addition, we inventoried other ways in which present textbooks facilitate the opportunity to learn problem solving. Finally, we researched how inclusive these textbooks are with respect to offering opportunities to learn problem solving for students with varying mathematical abilities. The results of our study show that the opportunities that the currently most widely used Dutch textbooks offer to learn problem solving are very limited, and these opportunities are mainly offered in materials meant for more able students. In this regard, Dutch mainstream textbooks have not changed compared to the situation a decade ago. A textbook that is the Dutch edition of a Singapore mathematics textbook stands out in offering the highest number of problem-solving tasks, and in offering these in the materials meant for all students. However, in the ways this textbook facilitates the opportunity to learn problem solving, sometimes a tension occurs concerning the creative character of genuine problem solving.     

Renewing textbooks to align with reformed curriculum in former colonies: Ugandan school mathematics textbooks

Several nations have reformed both their mathematics pedagogy and curriculum. The remaining challenge is to review teaching and learning resources to support the renewed pedagogy and curriculum. This paper responds to the following question: what pedagogy and curriculum are depicted in textbooks used in Uganda? Ugandan textbooks were analyzed in terms of mathematics content structure and genre, and presentation of written and non-written voice and looks (appearance). Whereas certain Ugandan mathematics textbooks used the narrative form and others chose to eliminate the use of extensive text, these textbooks include common characteristics such as spiral coverage of mathematics content. A few strides toward reform pedagogy, such as use of contexts familiar to learners in development of rules and concepts, were evinced among selected Uganda textbooks. More strides are needed in revising a majority of textbooks to align with the renewed curricula on certain aspects including integrating learning tools—digital and non-digital—within the textbook resources. A critical reflection on curriculum renewals adopted from other countries is needed when designing textbooks to match these renewals.     

Links between science and mathematics in school

There exist obvious links between the science and mathematics taught in schools. This paper discusses the responses of trainee teachers in science and mathematics to a number of questions relevant to both subjects and points to failures of understanding and of communication. It further seeks to highlight problems of liaison between subject teachers.     

The concept of invariance in school mathematics

In this paper, we highlight examples from school mathematics in which invariance did not receive the attention it deserves. We describe how problems related to invariance stimulated the interest of both teachers and students. In school mathematics, invariance is of particular relevance in teaching and learning geometry. When permitted change leaves some relationships or properties invariant, these properties prove to be inherently interesting to teachers and students.