Search

Summarizes the construction of paper folding. Method for approximating rational subdivisions or arbitrary angles and line segments; Angle-folding algorithm; Approximating angles, regular polygons and star polygons; Dissection of angles into equal parts.

The article offers information on dynamical systems and irrational angle construction by paper-folding. Construction of rational angle to any desired accuracy by folding a strip of paper requires approximating method. The construction uses a periodic sequence composed of two types of folding moves, guided by number-theoretic properties of the angle's fractional representation. The number-theoretic scheme must be replaced by something new, the Folds and Switchfold prescription, in the construction of irrational angles.

Discusses which shapes are possible and impossible to construct using origami. Algebraic characterization of origami; Construction process; Possibility to construct a line parallel to a given line through any given point; Construction of a cube with twice the volume of a given cube.

In the article, by virtue of Maclaurin's expansions of the arcsine function and its square and cubic, the authors (1) give a short proof of a sum formula of a Maclaurin's series with coefficients containing reciprocals of the Catalan numbers; (2) establish four sum formulas for finite sums containing the ratio or product of two central binomial coefficients or the Catalan numbers. The instant proof simplifies discussions in the journal papers: College Math. J. 43 (2012), no. 2, 141-146; Amer. Math. Monthly 121 (2014), no. 3, 267-267; Amer. Math. Monthly 123 (2016), no. 4, 405-406; Elem. Math. 71 (2016), no. 3, 109-121; and Mathematics 5 (2017), no. 3, Article 40, 31 pages. [ABSTRACT FROM AUTHOR]

Provides a mathematical explanation on paperfolding. Some observations from paperfolding experiments; Theorems that explain the observations.

The article presents an appendix note on a statistical question raised in the preceding paper.

This paper aims to investigate the reasons some female mathematicians give to justify their choice to not work in academia after finishing their doctoral studies. Nine female mathematicians who finished a PhD in Sweden answered a written questionnaire. Through collective narrative analysis, two main tracks were identified. One narrative described the struggle with self-identity in a gendered structure which included implicit power, while the other was more positive about exposure to discrimination, and highlighted the desire to work with applied mathematics. Through deductive thematic analysis, the results show that the main obstacle raised was the difficulty of getting a job in academia after their doctoral studies, especially permanent positions, without support. Compared to previous research, the lack of family-oriented political policies was not considered a main problem. Instead, the reasons provided by the respondents are structural problems, such as access to post-doc positions, and the stress of having to get research grants, as well as cultural aspects within the structure, including implicit and explicit use of power. [ABSTRACT FROM AUTHOR]

Classroom management is an emotionally demanding task for mathematics teachers, especially if students exhibit frequent discipline problems. Intense classroom conflicts can result in persistent latent emotional dispositions, such as fear or anger, that teachers are not directly aware of but that have a strong influence on their classroom management. However, little is known about the relationship between mathematics teachers' latent emotions and their classroom management strategies. This paper reports on findings from an exploratory, video-based single case study in an urban secondary school in Germany. One mathematics double lesson (95 minutes in total) was videotaped to conduct a depth-hermeneutical analysis of identified classroom management strategies and the corresponding latent teacher emotions. The results suggest that mathematics teachers use classroom management strategies not only to establish orderly lessons but also to regulate intense latent emotions that arise during classroom teaching. [ABSTRACT FROM AUTHOR]

Motivated by earlier research highlighting Swedish teachers' beliefs that the setting of homework compromises deep-seated principles of educational equity, this paper presents an exploratory study of Swedish parents' perspectives on homework in their year-one children's learning. Twenty-five parents, drawn from three demographically different schools in the Stockholm region, participated in semi-structured interviews. The interviews, broadly focused on how parents support their children's learning and including questions about homework in general and mathematics homework in particular, were transcribed and data subjected to a constant comparison analytical process. This yielded four broad themes, highlighting considerable variation in how parents perceive the relationship between homework and educational equity. First, all parents spoke appreciatively of their children receiving reading homework and, in so doing, indicated a collective construal that reading homework is neither homework nor a threat to equity. Second, four parents, despite their enthusiasm for reading homework, opposed the setting of any homework due to its potential compromise of family life. Third, seven parents indicated that they would appreciate mathematics homework where it were not a threat to equity. Finally, fourteen parents, despite acknowledging homework's potential compromise to equity, were unequivocally in favour of mathematics homework being set to their children. [ABSTRACT FROM AUTHOR]

Several letters to the editor are presented in addition and response to articles in previous issues including "Gauss's Lemma for Number Fields," by Arturo Magidin in the May 2005 issue and "Almost Every Number Has a Continuum of ß-Expansions," by Nikita Sidorov in the November 2005 issue.

The article discusses the importance of the paper "Musical Scales and the Generalized Circle of Fifths," by J. Clough and G. Myerson in the mathematical music theory literature. The paper deals with the way the white keys in the piano, called the diatonic set, are embedded in the chromatic scale and studies the different-sounding progressions with the same structure. The use of chromatic length in defining equivalence relations on the set of note lines is also offered. It corrects the theorem and the corollary stated in the paper.

Living in complex knowledge societies requires citizens who master multiple literacies involving both cognitive and social skills. Thus, all individuals should be offered relevant educational opportunities and teachers capable of integrating subject expertise with relational aspects. This paper demonstrates a teaching design for mathematics that student teachers have indicated integrates both these dimensions. Drawing on theoretical perspectives that conceptualize academic literacy as a socially situated discourse practice, we investigate one teacher educator’s teaching design for mathematics. The evidence indicates that the teaching approaches in this design are highly student centered and process oriented. Student teachers report that the approach supports both individual and collective learning of the discipline of mathematics while also modeling how to teach mathematics as a school subject. The teaching design comprises varied and exploratory approaches to teaching mathematics and represents an alternative to more traditional mathematics pedagogy. In this way, the study contributes to an empirically informed understanding of how the goal of learning to master academic literacy may be facilitated by a varied repertoire of writing, reading, and oral activities. The study indicates challenges for traditional teaching and teacher education more broadly. [ABSTRACT FROM AUTHOR]

Background: The emergence of a participatory culture, brought about mainly by the use of Web2.0 technology, is challenging us to reconsider aspects of teaching and learning. Adapting the learning-as-digital-game-building approach, this paper explores how new educational practices can help students build skills for the 21st century. Purpose: This paper examines elementary students' learning experiences through digital game building and playing. The following research questions guided the study: (1) What emotions do students experience during the process of building digital games for others to use?; (2) What traits do students display when they learn through digital game-building?; and (3) What do students learn from the digital game-building experience? Sample: The participants were 21 elementary students (19 boys and two girls), aged between seven and 11, who were on a summer camp at a university in Canada. Design and methods: This small-scale study made use of enactivism (Li, Clark, and Winchester, Instructional design and technology grounded in enactivism: A paradigm shift?, British Journal of Educational Technology 41, no. 3: 403-419, 2010), a new theoretical framework, as a basis for analysing the students' experiences and responses as they created computer games to teach others the concept of Issac Newton's Three Laws of Motion. Quantitative and qualitative data collected included student and parent surveys, teacher and student interviews, field observations and the digital games created by the students. Data were subjected to quantitative and thematic analyses. Results: The results indicated that only a small minority of students reported never feeling the positive emotions excited/happy or smart/proud during the process of building digital games. In addition, analysis suggested that creativity, engagement and new identity were the three salient traits displayed by the students when learning by digital game-building. There was also evidence that students increased their understanding of the subject matter in question (mathematics, science and technology) and enhanced their general problem-solving abilities through the process. Conclusions: This small-scale study suggests that student engagement in the game-building experience can enhance not just the learning of the game design process but also subject matter and generic skills. Thus, the learning-as-building approach can empower students to 'take over the technology' and become creators rather than passive consumers. [ABSTRACT FROM AUTHOR]

This paper analyzes the impact of a Course Transformation process based on a Flipped Classroom strategy on Chilean Engineering students' attitudes toward university-level mathematics. The Attitudes Toward Mathematics Inventory (ATMI) questionnaire was applied as both pre- and post-test to 76 students in three mathematic courses (Calculus I, Calculus II and Elements of Algebra for Computing) at Universidad Católica de Temuco's Faculty of Engineering which adopted a flipped classroom method. The results showed a significant positive change in the perceived value of mathematics in the four ATMI categories (P < 0.05) with different effect sizes after the implementation of the flipped classroom and active learning strategies. The results suggest that the implementation of transformed courses using a Flipped Classroom method has a positive effect on students' attitudes toward Mathematics, especially in those who come from families with lower economical income. [ABSTRACT FROM AUTHOR]

The article reports on the flaw in Leonhard Euler's theory of polyhedra. It examines the proof laid down by Euler for his polyhedral formula and discusses the questions raised about his proof. It cites the papers "Elementa doctrinae solidorum" and the "Demonstratio nonnullarum insignium proprietatum quibus solida hedris planis inclusa sunt praedita" which Euler wrote to discuss his theory. It includes discussions on the proof of the angle sum formula and presents analysis an commentary on Euler's paper.

The article profiles the Russian mathematician Andrei Andreevich Markov Jr. It includes information on Markov's personal and educational background, as well as his early interest in abstract mathematics indicated by his series of papers on geometry, algebra, topology and analysis. Markov, however, is most well-known for founding the Russian school of constructive mathematics during the late 1940s and early 1950s. His constructive mathematics is considered as one of the 20th century's most important and coherent constructivist trends.

The article focuses on the a theorem about an infinite series which was communicated by Christian Goldbach to Leonhard Euler and is one of the theorems mentioned in Euler's paper "Variae observationes circa series infinitas." Goldbach and Euler's proof is a common example of what some historians consider a misuse of divergent series because it begins by assigning a value to the harmonic series Σ1/n and is then manipulated by subtractions and replacement of other series until the desired result is attained. The proof of the theorem is hereby reviewed in order to vindicate Goldbach and Euler's work. It is shown how the deficiency in the proof can be amended. However, other results obtained in said Euler's paper are not as easily amended.

The article explores the theory of dynamical systems in mathematics, examining the papers of A. N. Sharkovsky and T.-Y. Li and J. A. Yorke on interval dynamics, among others. It should be noted that neither Sharkovsky's theorem nor Li-Yorke's definition of chaos have a significant role in the core of modern one-dimensional dynamics. Meanwhile, J. Guckenheimer's paper established the foundations for the almost everywhere approach to dynamics, which states that if a map is sufficiently smooth, there may be a fair chance of offering an effective description of the asymptotic behavior of almost every point of the interval.

This paper has two goals. First, it seeks to show a logical inconsistency in Sraffian theory. The theory, it is argued, is conceived as a long-period approach but is unable to identify a long-period position. Second, the paper tries to show that even if we drop some of the building blocks of Sraffian theory, it is still possible to build a coherent alternative to neoclassical theory using (some of) the ideas of the classical economists. It suggests that we put the indefensible long-period method to one side, and build short-period equilibrium models with probabilistic prices. [ABSTRACT FROM AUTHOR]

The article presents information on various aspects on which perspectives were provided in the periodical "Journal of Quality Technology." Topics discussed include real time applications faced by practitioners in daily routine; future prospects of quality technology; and concepts discussed in mathematics.

In this article, we consider how to make data more meaningful to students through the choice of data and the activities we use them in drawing upon students lived experiences more in the teaching of statistics and data science courses. In translating scholarship around culturally relevant pedagogy from the fields of education and mathematics education we develop the idea of culturally relevant data. We see this development as a key ingredient to implementing culturally relevant pedagogy in teaching data-intensive courses leveraging the centrality of context through data in both statistics and data science to engage students particularly from historically marginalized groups in STEM. We provide suggestions as to ways of finding or creating culturally relevant data and using them in implementing culturally relevant pedagogy to support the learning and flourishing of students in statistics and data science courses. We also present findings from pilot work we have done in implementing these data in statistics courses. Finally, we discuss lingering questions and possible next steps for research in this area. for this article are available online. [ABSTRACT FROM AUTHOR]

The article reports that the Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to Mathematics for 2006 has been given to Hyman Bass of the University of Michigan in Ann Arbor for his having served on numerous boards and committees in the area of mathematics. His career started in Princeton and was inspired by Irving Kaplansky's lectures on homological methods in commutative algebra when he went to Graduate School at the University of Chicago in Illinois. He has been to 16 universities in 10 countries and he has published 86 papers in mathematics. One of his concerns is to develop an agenda on how mathematics can be taught and learned at the school level.

BackgroundThis paper is a qualitative evaluation of a small-scale pilot study that attempted to generate parental involvement in children’s learning. It used problem-solving mathematics homework in order to raise the children’s self-efficacy, or, put another way, the child’s belief that success lies in their own hands. PurposeHomework is often seen as a common sense practice which is conducive to the development of the attributes of an effective learner. The pilot investigated whether situating homework tasks in everyday mathematical contexts enhanced parent–child interaction. If so, the child was then more likely to commit to learning, recognise the usefulness of mathematics as a life skill, and the value of sharing ideas and accepting feedback. Design and methodsThe pilot took place between April and July 2015 in a primary school in the Northwest of England. Participants were a class of nine- and ten-year-old children (n = 27), their two class teachers and a self-selecting sample of parents. Children were asked to work on open-ended problem-solving activities designed to connect with everyday use of mathematics. The parental role was to model, encourage and reinforce rather than instruct. Data was collected from focus groups, from parent feedback sheets and from a self-efficacy questionnaire. The data was analysed thematically. Findings and conclusionsDespite limitations of time and scale, evaluation of the pilot suggests that the homework strategy does justify further research. The qualitative analysis of the data indicates that greater involvement of parents in learning was generated, the homework was well received by children and self-efficacy levels remained stable. The next step should be to run an extended version of the pilot. [ABSTRACT FROM PUBLISHER]

The article offers information on the life and works of mathematician Srinivasa Aiyangar Ramanujan in India. Mathematician V. Ramaswamy Aiyer, founder of the Indian Mathematical Society, not just acknowledged the creative spirits that produced the content of Ramanujan's notebook, but contact other mathematician to take the mathematics of Ramanujan for support. The big mathematical community that has flourished on the discoveries of Ramanujan for almost a century owes a big debt to Ramaswamy.

The article discusses the theorem on convergence of the iterated product of orthogonal projections in Hilbert space. The theorem which resulted from I. Halperin's proof for an arbitrary finite number of projections is presented. Proofs for this theorem, including that of H. H. Bauschke, et. al., I. Amemiya and T. Ando, K. T. Smith, et. al., and N. Nakano, are mentioned. S. Kakutani's lemma and proof of the theorem are presented. Another theorem about nonexpansive, nonnegative operator on the Hilbert space is also proven.

In his response to my original paper "The (Confused) State of Equilibrium Analysis in Modern Economics: An Explanation," Weintraub sets forth a competing account of the nature of equilibrium theorizing in economics. Weintraub supposes (1) his account is better because (2) his approach to understanding economics is more historical than my own. I suggest that neither of these claims is correct. [ABSTRACT FROM AUTHOR]

The following three articles are the results of papers presented and discussed at a symposium entitled "Improving the Workforce of the Future: Opportunities in Undergraduate Education," held August 12-13, 2000, in Indianapolis, IN. This symposium was sponsored by the American Statistical Association through its Undergraduate Statistics Education Initiative. The first article was the keynote address at the symposium. The latter two articles are position papers that were developed in part through discussions among representatives from liberal arts colleges, research universities, industry, and government at a May 1999 meeting at the ASA Headquarters and a subsequent April 2000 workshop in Alexandria, VA. This workshop was partially supported by the National Science Foundation. Other position papers based on symposium discussions are being developed and are scheduled to appear in the Journal of Statistical Education. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a generating function for a new generalization of Laguerre-based Apostol-Bernoulli polynomials, Apostol-Euler and Apostol-Genocchi polynomials. By making use of the generating function method and some functional equations mentioned in the paper, we conduct a further investigation in order to obtain symmetric identities of these polynomials. [ABSTRACT FROM AUTHOR]

The total irregularity of a simple undirected graph G is denoted by irrt(G) and is defined as irrt(G) = 1/2 ... |d(u) - d(v)|. In this paper, we introduce the notion of edge-transformation in relation to total irregularity of simple graphs with at least one cut edge as well as an edge-joint between two graphs. We also introduce the notion of total irregularity with respect to in-degree and out-degree in directed graphs. We also introduce the concept of total irregularity in respect of in-degree and out-degree in simple directed graphs. These invariants are called total in-irregularity and total out-irregularity, respectively. In this paper, we initiate a study on these parameters of given simple undirected graphs and simple digraphs. [ABSTRACT FROM AUTHOR]

Offers information on the contributions that mathematician Paul Erdos made to mathematics. Suggestion that every human activity, good or bad, except mathematics must come to an end; Background information on Erdos life; Career achievements of Erdos; Role that the Journal of Mathematics and Physics for High Schools played in the development of Erdos's interest in mathematics.

Self-efficacy is associated with a range of educational outcomes, including science and math degree attainment. Project-based statistics courses have the potential to increase students' math self-efficacy because projects may represent a mastery experience, but students enter courses with preexisting math self-efficacy. This study explored associations between pre-course math confidence and coding confidence with post-course statistical intentions and perceived achievement among students in a project-based statistics course at 28 private and public colleges and universities between fall 2018 and winter 2020 (n = 801) using multilevel mixed-effects multivariate linear regression within multiply imputed data with a cross-validation approach (testing n = 508 at 20 colleges/universities). We found that pre-course coding confidence was associated with, respectively, 9 points greater post-course statistical intentions and 10 points greater perceived achievement on a scale 0–100 (0.09, 95% confidence interval (0.02, 0.17), p = 0.02; 0.10, 95% CI (0.01, 0.19), p = 0.04), and that minoritized students have greater post-course statistical intentions than nonminoritized students. These results concur with past research showing the potential effectiveness of the project-based approach for increasing the interest of minoritized students in statistics. Pre-course interventions to increase coding confidence such as pre-college coding experiences may improve students' post-course motivations and perceived achievement in a project-based course. for this article are available online. [ABSTRACT FROM AUTHOR]

The Moving Maths study was conducted to increase third grade pupils' physical activity and support their learning in Finland. Altogether 397 children (mean age 9.3 years) and 22 teachers took part in an intervention with two types of physically active maths lessons for five months. One group carried out lessons in which PA was integrated into maths learning goals, while another group implemented PA as short breaks. A control group was also allocated. The aim of the current study was to qualitatively examine classroom teachers' (n = 12) experiences and perceptions of student engagement during the intervention. The results indicated that pupils showed positive emotional and social engagement in both intervention groups. Positive cognitive engagement was indicated by concentration on seated work after the activities, but some teachers reported uncertainty about the learning results. It is concluded that in addition to reducing children's harmful sedentary behaviour, physically active lessons can positively affect student engagement and may thus enhance learning. [ABSTRACT FROM AUTHOR]

Meeting the challenges of teaching to all individuals requires a multifaceted approach, especially from the Swedish standpoint of inclusive education for all pupils. In the context of applied standards for receiving special educational provision, the present paper strives to shed light on the scope of novel indicators which can accommodate pupils' different needs. Founded on three established and robust psycho-educational concepts working memory, test anxiety and self-regulation all of which are important for educational, social, emotional and behavioural development, the present study examines those concepts in terms of profiles and their relations to mathematical achievement. A battery of tests was completed by 624 children between the ages of 8 and 10 to assess their working memory, test anxiety, self-regulation, and mathematical achievement. Person-centred analyses confirmed the negative academic outcomes associated with the aforementioned variables but also revealed individual variations that warrant attention. Further, pupils labelled with an 'At-risk' profile were more likely to achieve low Maths scores, compared to pupils with an 'In-vigour' profile. An implication for special educational provision is discussed, and practical suggestions are provided. [ABSTRACT FROM AUTHOR]

Feedback does not always engage students. To better understand why this happens, the present study analysed Grade 2 (7- to 8-year-old) students' experiences of formative feedback in mathematics to identify aspects with potential importance for student engagement. The researcher processed the students' experiences with the help of stimulated recall and semi-structured interviews. Most of the students appreciated feedback that focused on the process, instead of simply offering solution methods. However, due to a conflict between teachers and students regarding the social and socio-mathematical norms, some of the students did not understand the purpose while others wanted the teacher to state the solution method. This shows that it is important not only which norms are established, but also that this is done at an early stage. Thus, both teachers and students need to understand and accept the norms, and potentially establish new norms, if the current ones are counterproductive. [ABSTRACT FROM AUTHOR]

Recently Tracy and Chen presented a parametric DEA model (PDEA) to assess relative efficiency in the presence of a generalized form of linear weight restrictions. This paper proposes a modification to the PDEA model that avoids the need to resort to searching algorithms to estimate efficiency, and assures that the correct efficiency scores are obtained in a single stage using mathematical programming solvers. The results of this model and the results of Tracy and Chen's PDEA model are compared using the examples reported in their paper. The results confirm the superiority of the model proposed in this paper. [ABSTRACT FROM AUTHOR]

The article explores the mechanics of the television game show "The Weakest Link." Contestants of the game answer general knowledge questions, with each correct answer raising the amount held in a temporary pot. The game involves several mathematical issues such as strategy optimization, existence of Nash equilibria, and voting considerations. The payoff vector as being the amount in the pot after a chain of correct answers was introduced to describe various versions of the game around the world.

This paper reports the mathematical generalizations of two groups of algebra students, one which focused primarily on quantitative relationships, and one which focused primarily on number patterns disconnected from quantities. Results indicate that instruction encouraging a focus on number patterns supported generalizations about patterns, procedures, and rules, while instruction encouraging a focus on quantities supported generalizations about relationships, connections between situations, and dynamic phenomena, such as the nature of constant speed. An examination of the similarities and differences in students' generalizations revealed that the type of quantitative reasoning in which students engaged ultimately proved more important in influencing their generalizing than a mere focus on quantities versus numbers. In order to develop powerful, global generalizations about relationships, students had to construct ratios as emergent quantities relating two initial quantities. The role of emergent-ratio quantities is discussed as it relates to pedagogical practices that can support students' abilities to correctly generalize. [ABSTRACT FROM AUTHOR]

The article discusses the life, works and contribution of Alexander Grothendieck in mathematics. Grothendieck is a man who changed mathematics within 20 years of work in functional analysis and algebraic geometry. He was born in Berlin, Germany in 1928 and became a political activist in all major European revolutions. He worked in functional analysis between 1950 and 1955, and posed many questions on the structure of topological linear locally convex spaces. Among his contributions to functional analysis include nuclear spaces, topological tensor products and Grothendieck inequality.

The National Numeracy Strategy was introduced in England in 1998 to reform mathematics teaching in all primary schools. The strategy has been widely implemented and this paper investigates some of the changes that are evident after the first five years. Reporting a comparison between studies in 1998 and 2003 of pupils’ calculating strategies for division, this study shows a small improvement overall but lack of the uniformity that may be expected from a national Strategy. Structured written recording, progressively developed from more intuitive understanding, was not evident in much of the pupils’ work. In some schools there was success with the new ‘chunking’ written method, identified in the Framework as ‘informal’, while in less successful schools, pupils continued to use various informal and inefficient strategies. While in 1998 success of boys and girls was not significantly different, in 2003 the boys were more successful. The boys made more use of informal working and mental strategies, while the girls relied on more structured written methods and in the schools where girls did better they used mostly the chunking algorithm. [ABSTRACT FROM AUTHOR]

The article explores the so-called λ-permutations shown by Steven Krantz and Jeffery McNeal in their paper "Creating more convergent series." They specified that a permutation σ of the positive integers is a λ-permutation if it has two characteristics. The first property is that for every convergent series, the summation of ak from k =1 to infinity, the summation of aσ(k) from k =1 to infinity also converges. The second property is that there is at least one divergent series which is the summation of ak from k =1 to infinity such that the summation of aσ(k) from k =1 to infinity converges.

The article provides two short and direct proofs of J. S. Pym's result in his 1969 paper "The linking of sets in graphs," regarding the Cantor-Bernstein theorem for paths in graphs. Both proofs are elementary, and they can be examined independently. The first proof employs transfinite induction. This proof starts from the first set of paths which is then transformed step by step into the wanted bijective set by integrating path segments from the second set. The choices made during this inductive process have been made arbitrary. For the second proof, these choices are made explicitly.

The article describes a method for allowing students to manipulate mathematical objects. It involves computer activities that can draw a student's attention to the big picture in a way that paper pencil textbook exercises cannot. The main feature is a window that displays the graph of a function. The expression that defines the function appears in a text box. Throughout the activity, student interaction with the computer consists mainly of clicking push buttons and watching the results. There is a bit of typing when a new function is to be defined. It is significant that the interaction is completely orchestrated. Teachers should sympathize with this perspective, because most of us have had the experience many times of completely losing the thread of meaning while listening to a lecture or colloquium. The carefully prepared explanations of the speaker cease to have any meaning, because they describe interconnections between mathematical constructs that has not been internalized. Students should be able to conduct experiments to answer questions.

In this paper I address the question: How is it that people come to choose mathematics and in what ways is this process gendered? I draw on the findings of a qualitative research study involving interviews with 43 young people all studying mathematics in post-compulsory education in England. Working within a post-structuralist framework, I argue that gender is a project and one that is achieved in interaction with others. Through a detailed reading of Toni and Claudia's stories I explore the tensions for young women who are engaging in mathematics, something that is discursively inscribed as masculine, while (understandably) being invested in producing themselves as female. I conclude by arguing that seeing 'doing mathematics' as 'doing masculinity' is a productive way of understanding why mathematics is so male dominated and by looking at the implications of this understanding for gender and mathematics reform work. [ABSTRACT FROM AUTHOR]

The Smith Report has generated central questions about the mathematics education of UK adolescents. This paper highlights the close match between the goals of school mathematics, adolescence and exploratory pedagogy. This is contrasted with the prescriptive nature of current regimes. In particular, without careful attention to pedagogy it is possible that the introduction of different pathways may lead to a failure to achieve the outcomes desired by employers and universities, and to inequity in provision for students. [ABSTRACT FROM AUTHOR]

The article presents a discussion about dialectic materialism and modern science. It discusses the conditions in which dialectic materialism creates for scientists and for scientific pursuits. Dialectic materialism holds that internal contradiction are inherent in all things and phenomena of nature, and treats reality being in constant flux and change. The relationship and the contributions of dialectic materialism in physics, theory of relativity, mathematics, and quantum theory are also discussed.

This paper suggests that mathematics may have become so important in economics for four reasons: (1) to make use of existing human capital, (ii) to attain scientific respectability, (3) to help assure security with respect to claims of truth, and (4) because economics was created primarily by Western economists to understand Western economic behavior. [ABSTRACT FROM AUTHOR]