Enlisting excel--again

In Volume 26, Number 2, we reported on a group case study runfor level 3 mathematics students at the University of Brighton.At the core of the study was a quadratic assignment problem,and we reported on attempts by students to use Excel to solvethe problem, and on the attendant difficulties. We providedan elegant solution. In this article, we report on another interestingcase study, this time developed for level 2 mathematics students.Again Excel is used to achieve a solution. We report on ourefforts—and on how student answers led to improvements.     

Collaborative Workshops and Student Academic Performance in Introductory College Mathematics Courses: A Study of a Treisman Model Math Excel Program

High failure rates in introductory college mathematics courses, particularly among underrepresented groups of students, have been of concern for many years. One approach to the problem experiencing some success has been Treisman's Emerging Scholars workshop model. The model involves supplemental workshops in which students solve problems in collaborative learning groups. This study reports on the effectiveness of Math Excel, an implementation of the Treisman model for introductory mathematics courses (college algebra, precalculus, differential calculus, and integral calculus) at Oregon State University over five academic terms. Regression analyses revealed a significant effect on achievement (.671 grade points on a 4‐point scale) favoring Math Excel students. Even after adjusting for prior mathematics achievement using linear regression with SAT‐M as predictor, Math Excel groups' grade averages were over half a grade point better than predicted (significant at the .001 level). This study provides supporting evidence that programs like Math Excel can help students in making a successful transition to college mathematics study.     

Mathematics teacher training at the State Technical University in Chile

During the fifties and sixties in Chile many mathematics graduates of Pedagogical Institutes became university instructors rather than high school teachers as intended. In the late sixties Masters level programmes began giving more advanced training for university mathematics instructors. A ‘modern’ mathematics curriculum including computer science was introduced in the high schools. The first significant attempt to adapt the training of Chilean high school mathematics teachers to the new academic and social realities was begun in 1976 at the State Technical University with the cooperation of Teachers College, Columbia University, and the support of the Organization of American States.

The four‐year programme leads to Licenciatura (Bachelors) in Mathematics and Computer Education. All courses are taught by faculty members of the Department of Mathematics and Computer Science. The three basic areas of instruction are mathematics, computer science, and mathematics education. Funds provided by the O.A.S. have helped to make possible the development of curricular materials in Spanish, and the acquisition of computing and video tape equipment.     

Applying an alternative mathematics pedagogy for students with weak mathematics: meta-analysis of alternative pedagogies

Student mathematics performance and the need for work-ready graduates to be mathematics-competent is a core issue for many universities. While both student and teacher are responsible for learning outcomes, there is a need to explicitly acknowledge the weak mathematics foundation of many university students. A systematic literature review was undertaken of identified innovations and/or interventions that may lead to improvement in student outcomes for university mathematics-based units of study. The review revealed the importance of understanding the foundations of student performance in higher education mathematics learning, especially in first year. Pre-university mathematics skills were identified as significant in student retention and mathematics success at university, and a specific focus on student pre-university mathematics skill level was found to be more effective in providing help, rather than simply focusing on a particular at-risk group. Diagnostics tools were found to be important in identifying (1) student background and (2) appropriate intervention. The studies highlighted the importance of appropriate and validated interventions in mathematics teaching and learning, and the need to improve the learning model for mathematics-based subjects, communication and technology innovations.     

Investigations and explorations in the mathematics classroom

In Portugal, since the beginning of the 1990s, problem solving became increasingly identified with mathematical explorations and investigations. A number of research studies have been conducted, focusing on students’ learning, teachers’ classroom practices and teacher education. Currently, this line of work involves studies from primary school to university mathematics. This perspective impacted the mathematics curriculum documents that explicitly recommend teachers to propose mathematics investigations in their classrooms. On national meetings, many teachers report experiences involving students’ doing investigations and indicate to use regularly such tasks in their practice. However, this still appears to be a marginal activity in most mathematics classes, especially when there is pressure for preparation for external examinations (at grades 9 and 12). International assessments such as PISA and national assessments (at grades 4 and 6) emphasize tasks with realistic contexts. They reinforce the view that mathematics tasks must be varied beyond simple computational exercises or intricate abstract problems but they do not support the notion of extended explorations. Future developments will show what paths will emerge from these contradictions between promising research and classroom reports, curriculum orientations, professional experience, and assessment frameworks and instruments.     

Extracting factors for students’ motivation in studying mathematics

The purpose of this article is to identify factors that statistically explain the variation and the measures on the level of motivation of a sample of mathematics students in a university. Specifically, this analysis will identify groups of similar items and reduce the number of variables used in a study. This article explains the use of exploratory factor analysis in extracting factors of personal belief and motivational factors among students in learning mathematics. The adaptation of these factors can be used for assessing academic performance in relation to motivation level. By identifying these factors, the mathematics educators or researchers will be able to find ways to improve the condition of the factors and also to further investigate the factors based on confirmatory approaches.     

A case study of pedagogy of mathematics support tutors without a background in mathematics education

This study investigates the pedagogical skills and knowledge of three tertiary-level mathematics support tutors in a large group classroom setting. This is achieved through the use of video analysis and a theoretical framework comprising Rowland's Knowledge Quartet and general pedagogical knowledge. The study reports on the findings in relation to these tutors’ provision of mathematics support to first and second year undergraduate engineering students and second year undergraduate science students. It was found that tutors are lacking in various pedagogical skills which are needed for high-quality learning amongst service mathematics students (e.g. engineering/science/technology students), a demographic which have low levels of mathematics upon entering university. Tutors teach their support classes in a very fast didactic way with minimal opportunities for students to ask questions or to attempt problems. It was also found that this teaching method is even more so exaggerated in mandatory departmental mathematics tutorials that students take as part of their mathematics studies at tertiary level. The implications of the findings on mathematics tutor training at tertiary level are also discussed.     

Argumentation and participation in the primary mathematics classroom: Two episodes and related theoretical abductions

The main assumption of this article is that learning mathematics depends on the student's participation in processes of collective argumentation. On the empirical level, such processes will be analyzed with Toulmin's theory of argumentation and Goffman's idea of decomposition of the speaker's role. On the theoretical level, different statuses of participation in processes of argumentation will be considered. By means of the method of comparative analysis, different grades of autonomy according to the interactional contribution of a student can be reconstructed. The paper finishes with remarks about consequences for improving mathematics teaching in schools and mathematics teacher education at university level.     

基于SPSS和Excel的三峡库区经济主成份分析方法研究

介绍了主成份分析的数学模型,并用于三峡库区区域经济指标分析,介绍基于统计分析软件SPSS和Excel进行经济分析的方法和步骤,为三峡库区区域经济分析提供一种具体的可行的计算机辅助决策分析方法.     

Mathematics for computer scientists: problems and solutions

The results of a survey of the mathematics provision within UK university computer science departments are presented. In particular it is found that many academics are dissatisfied with the level of ‘mathematical preparedness’ of their students. A number of recommendations and resources are suggested to address this.     

Using E-Exercise Bases in Mathematics: Case Studies at University

E-Exercise Bases (EEB) are now used in the teaching of mathematics, especially at university. We discuss here the consequences of their use on the students’ activity during computer lab sessions. Results stem from observations of several teaching designs organised in different French universities with three e-exercise bases. The analysis focuses on new tasks and on specific solving strategies, which appear using these resources. Moreover, specific didactic contract clauses are studied.     

Materialization and organization

This summary of six articles which have been written in the past fifteen years focus on the question of the social relevance of mathematics on a principal level. The main theses are: Mathematics provides materializations of abstract issues, thereby it supports mass communication. the principles of mathematics are basic for our social organization. The limits of mathematics are limits of organization. But they can be overcome by emphasizing the reflexive potential of mathematics.     

Prior decisions and experiences about mathematics of students in bridging courses

We report on the survey responses of 51 students attending mathematics bridging courses at a major Australian university, investigating what mathematics, if any, these students had studied in the senior years of schooling and what factors affected their decisions about the level of mathematics chosen. Quantitative findings are augmented by qualitative responses to open-ended questions in the survey as well as excerpts from follow-up emails. The findings show that the major reasons for students taking lower levels of mathematics in senior year(s), or dropping mathematics, include finding enough time for non-mathematics subjects, confidence in mathematical capability, advice and maximizing potential ranking for university admission.     

The development of reasoning skills during compulsory 16 to 18 mathematics education

The belief that studying mathematics improves reasoning skills, known as the Theory of Formal Discipline (TFD), has been held since the time of Plato. Research evidence supports this idea, at least in the context of students who had chosen to study post-compulsory mathematics. Here we examined the development of reasoning skills in 16- to 18-year-old Cypriot students, who are required to study mathematics until age 18. One hundred and eighty-eight students, studying high- or low-intensity mathematics, completed the abstract Conditional Inference Task and the contextual Belief Bias Syllogisms task at ages 16, 17 and 18. While the high-intensity group improved on the conditional inference task and showed a reduction in belief bias, the low-intensity group did not change on either measure. This is promising for the TFD, but suggests that a certain level of mathematical study may be necessary for students' general reasoning skills to develop.     

The functions of function discourse – university mathematics teaching from a commognitive standpoint

This paper addresses a topic within university mathematics education which has been somewhat underexplored: the teaching practices actually used by university mathematics teachers when giving lectures. The study investigates the teaching practices of seven Swedish university teachers on the topic of functions using a discursive approach, the commognitive framework of Sfard. In the paper a categorization of the construction and substantiation routines used by the teachers is presented, for instance various routines for constructing definitions and examples, and for verifying whether an example satisfies a given definition. The findings show that although the overall form of the lectures is similar, with teachers using ‘chalk talk’, and overt student participation limited to asking and answering questions, there are in fact significant differences in the way the teachers present and do mathematics in their lectures. These differences present themselves both on the level of discursive routines and on a more general level in how the process of doing mathematics is made visible in the teachers’ teaching practices. Moreover, I believe that many of the results of the study could be relevant for investigating the teaching of other mathematical topics.     

Developing mathematical modelling skills: The role of CAS

Mathematical modelling as one component of problem solving is an important part of the mathematics curriculum and problem solving skills are often the most quoted generic skills that should be developed as an outcome of a programme of mathematics in school, college and university. Often there is a tension between mathematics seen at all levels as ‘a body of knowledge’ to be delivered at all costs and mathematics seen as a set of critical thinking and questioning skills. In this era of powerful software on hand-held and computer technologies there is an opportunity to review the procedures and rules that form the ‘body of knowledge’ that have been the central focus of the mathematics curriculum for over one hundred years. With technology we can spend less time on the traditional skills and create time for problem solving skills. We propose that mathematics software in general and CAS in particular provides opportunities for students to focus on the formulation and interpretation phases of the mathematical modelling process. Exploring the effect of parameters in a mathematical model is an important skill in mathematics and students often have difficulties in identifying the different role of variables and parameters This is an important part of validating a mathematical model formulated to describe, a real world situation. We illustrate how learning these skills can be enhanced by presenting and analysing the solution of two optimisation problems.     

The student experience of mathematical proof at university level

While proofs are central to university level mathematics courses, research indicates that some students may complete their degrees with an incomplete picture of what constitutes a proof and how proofs are developed. The paper sets out to review what is known of the student experience of mathematical proof at university level. In particular, some evidence is presented of the conceptions of mathematical proof that recent mathematics graduates bring to their postgraduate course to teach high school mathematics. Such evidence suggests that while the least well-qualified graduates may have the poorest grasp of mathematical proof, the most highly qualified may not necessarily have the richest form of subject matter knowledge needed for the most effective teaching. Some indication of the likely causes of this incomplete student perspective on proof are presented.     

Conceptualizations of slope in Mexican intended curriculum

Slope is a fundamental mathematics concept in middle and high school that transcends to the university level. An understanding of slope is needed at the university level since slope plays an important role in understanding problems involving variation and change. In this study Mexican curricula documents were examined to determine which conceptualizations of slope are addressed in the intended mathematics curriculum. To explain the results, we use conceptualizations of slope identified in previous research. Our findings reveal that, to a certain extent, the conceptualizations proposed in the Mexican intended mathematics curriculum differ slightly in terms of the emphasis and timing of instruction from what others have identified in the U.S., with slope as a geometric ratio receiving less emphasis in the Mexican curriculum. There was also noted discontinuity within the Mexican curriculum in introducing slope in grade 9 and subsequently introducing of linear functions in grade 10 without explicit mention of slope. Suggestions are made for future studies, both to consider the conceptualizations of slope promoted in the Mexican textbooks and the impact they have in classroom instruction and student learning of slope.