International Journal of Mathematical Education (Int J Math Educ Sci Tech )

Publisher: Taylor & Francis

Description

Mathematical education is a key criterion for successful economic development and currently forms the basis of several government initiatives throughout the world. The International Journal of Mathematical Education in Science and Technology provides a medium by which a wide range of experience in mathematical education can be presented, assimilated and eventually adapted to everyday needs in schools, colleges, universities, industry and commerce. Contributions are welcomed from teachers and users of mathematics at all levels on the contents of syllabuses and methods of presentation. Mathematical models arising from real situations, the use of computers, new teaching aids and techniques also form an important part of the journal.

  • Impact factor
    0.00
  • 5-year impact
    0.00
  • Cited half-life
    0.00
  • Immediacy index
    0.00
  • Eigenfactor
    0.00
  • Article influence
    0.00
  • Website
    International Journal of Mathematical Education in Science & Technology website
  • Other titles
    International journal of mathematical education in science and technology, Mathematical education in science and technology
  • ISSN
    0020-739X
  • OCLC
    1605999
  • Material type
    Periodical, Internet resource
  • Document type
    Journal / Magazine / Newspaper, Internet Resource

Publisher details

Taylor & Francis

  • Pre-print
    • Author can archive a pre-print version
  • Post-print
    • Author cannot archive a post-print version
  • Restrictions
    • 12 month embargo for STM, Behavioural Science and Public Health Journals
    • 18 month embargo for SSH journals
  • Conditions
    • Some individual journals may have policies prohibiting pre-print archiving
    • Pre-print on authors own website, Institutional or Subject Repository
    • Post-print on authors own website, Institutional or Subject Repository
    • Publisher's version/PDF cannot be used
    • On a non-profit server
    • Published source must be acknowledged
    • Must link to publisher version
    • Set statements to accompany deposits (see policy)
    • Publisher will deposit to PMC on behalf of NIH authors.
    • STM: Science, Technology and Medicine
    • SSH: Social Science and Humanities
    • 'Taylor & Francis (Psychology Press)' is an imprint of 'Taylor & Francis'
  • Classification
    ​ yellow

Publications in this journal

  • [Show abstract] [Hide abstract]
    ABSTRACT: Linear algebra is a basic mathematical subject taught in mathematics and science depar-tments of universities. The teaching and learning of this course has always been difficult. This study aims to contribute to the research in linear algebra education, focusing on linear dependence and independence concepts. This was done by introducing student-generated examples regarding the concepts. With the help of these examples, we have analysed students’ understanding of linear dependence/independence and determined the effect of the example-generation process on student understanding of linear algebra. In addition, we identified some difficulties that were experienced by students learning the concepts of linear dependence/independence. In this study, APOS (action-process-object-schema) theory is the main tool utilized to explain students’ written responses. It was also used with regard to the interview questions that were posed to students with the purpose of identifying possible difficulties with linear dependence/independence and observing the adequacy of the relations that students might form between different elements of the genetic decomposition of linear dependence/independence concepts. The findings of this study confirmed that many students do not have appropriate mental structures at object and schema levels. Moreover, in order to ensure the success of such exercises, students must be encouraged to review and validate their responses to the example requests.
    International Journal of Mathematical Education 08/2014; 45(6).
  • [Show abstract] [Hide abstract]
    ABSTRACT: This paper presents a new twist on a familiar paradox, linking seemingly disparate ideas under one roof. Hilbert's Grand Hotel, a paradox which addresses infinite set comparisons is adapted and extended to incorporate ideas from calculus – namely infinite series. We present and resolve several variations, and invite the reader to explore his or her own variations.
    International Journal of Mathematical Education 08/2014; 45(6).
  • [Show abstract] [Hide abstract]
    ABSTRACT: This note provides asymptotic formulas for approximating the sequence factorial of members of a finite arithmetic progression by using Stirling, Burnside and other more accurate asymptotic formulas for large factorials that have appeared in the literature.
    International Journal of Mathematical Education 08/2014; 45(6).
  • [Show abstract] [Hide abstract]
    ABSTRACT: The changes in academic identity a teacher may undergo, as they modify their teaching practice, will vary depending on their experiences and the support they receive. In this paper, we describe the shifts in academic identity of two lecturers, a mathematician and a mathematics educator, as they both made changes to their teaching practice by implementing new questioning techniques in a large undergraduate mathematics course. Both the lecturers were members of the research group, which became their community of practice. Our findings recommend that lecturers endeavouring to step out and try changes to their teaching practice, particularly with large groups of students, belong to a community of practice. The community of practice provides a place for shared reflection, new learning, and opportunities to negotiate new identities.
    International Journal of Mathematical Education 08/2014; 45(6).
  • [Show abstract] [Hide abstract]
    ABSTRACT: Research suggests that there are two major reasons for the low numbers taking Higher Levelmathematics in Ireland: namely, ineffective teaching and a subsequent lack of student interest in the subject. Traditional styles of teaching make it difficult for students to take an interest in a confusing topic in which they can see no immediate relevance. This is particularly true regarding the topic of algebra and its teaching in school. This paper describes a pedagogical framework designed by the authors for the effective teaching of algebra at lower secondary level in Irish schools that engages students, and promotes interest in the domain. This framework has provided the basis for the design and development of a teaching intervention that has been piloted in Irish schools. In this paper the authors focus on the design of the pedagogical framework and its use to develop classroom materials for a school-based intervention.
    International Journal of Mathematical Education 08/2014; 45(6).
  • [Show abstract] [Hide abstract]
    ABSTRACT: Debates about how undergraduate mathematics should be taught are informed by different views of what it is to learn and to do mathematics. In this qualitative study 10 students enrolled in an advanced undergraduate course in mathematics shared their views about how they best learn mathematics. After participating in a semester-long course in combinatorics, taught using a non-traditional, formal group work approach, the 10 students shared their views about how such an approach fitted in with their experience of learning mathematics. A descriptive thematic analysis of the students’ responses revealed that despite being very comfortable with the traditional approach to learning new mathematics, most students were open to a formal group work approach and could see benefits from it after their participation. The students’ prior conceptions of the goal of undergraduate mathematics learning and their view of themselves as ‘mathematicians’ framed their experience of learning mathematics in a non-traditional class.
    International Journal of Mathematical Education 08/2014; 45(6).
  • [Show abstract] [Hide abstract]
    ABSTRACT: Understanding graphical representations of algebraic equations, particularly graphical representations of absolute value equations, significantly improves students’ mathematical comprehension and ignites within them an appreciation of the beauty and aesthetics of mathematics. In this paper, we focus on absolute value equations of linear and quadratic expressions, by examining various cases, presenting different methods of solving them by graphical representation, exhibiting the advantage of using dynamic software such as GeoGebra in solving them, and illustrating some examples of interesting graphical solutions. We recommend that teachers take advantage of the rapid development in technology to help learners tangibly visualize the solutions of absolute value equations before proceeding to the analytical solutions.
    International Journal of Mathematical Education 08/2014; 45(6).
  • [Show abstract] [Hide abstract]
    ABSTRACT: Given a composite function of the form h(x) = f(g(x)), difficulties are often encountered in calculating the value of the nth derivative at some point x = x 0 when one attempts to determine whether its nth derivative becomes zero at this point, or attempts to find the sign of the nth derivative by differentiating it n times and substituting x 0.This present paper offers an alternative method that allows the investigation of the nth derivative of function h(x) based on the investigation of functions f (x) and g(x) only.Several examples are given, which implement the conclusions on the properties of the relation.
    International Journal of Mathematical Education 08/2014; 45(6).
  • [Show abstract] [Hide abstract]
    ABSTRACT: In this note, we provide basic asymptotic formulas for approximating large g-gonal sequence factorials by using Stirling and Burnside asymptotic approximation formulas for large factorials. More accurate asymptotic approximation formulas for large g-gonal sequence factorials resulting from some recent, more accurate asymptotic formulas for large factorials that have appeared in the literature are presented.
    International Journal of Mathematical Education 08/2014; 45(6).
  • [Show abstract] [Hide abstract]
    ABSTRACT: This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students’ problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate this blended instruction as a local representative of the US calculus reform movements that helped foster it. These reform movements tended to emphasize problem-solving as well as multiple mathematical registers and quantitative modelling. Our statistical analysis reveals the influence of the blended traditional/reform calculus instruction on students’ ability to solve calculus-related, non-routine problems through repeated measures over the semester. The calculus instruction in this study significantly improved students’ performance on non-routine problems, though performance improved more regarding strategies and accuracy than it did for drawing conclusions and providing justifications. We identified problem-solving behaviours that characterized top performance or attrition in the course. Top-performing students displayed greater algebraic proficiency, calculus skills, and more general heuristics than their peers, but overused algebraic techniques even when they proved cumbersome or inappropriate. Students who subsequently withdrew from calculus often lacked algebraic fluency and understanding of the graphical register. The majority of participants, when given a choice, relied upon less sophisticated trial-and-error approaches in the numerical register and rarely used the graphical register, contrary to the goals of US calculus reform. We provide explanations for these patterns in students’ problem-solving performance in view of both their preparation for university calculus and the courses’ assessment structure, which preferentially rewarded algebraic reasoning. While instruction improved students’ problem-solving performance, we observe that current instruction requires ongoing refinement to help students develop multi-register fluency and the ability to model quantitatively, as is called for in current US standards for mathematical instruction.
    International Journal of Mathematical Education 08/2014; 45(6).
  • [Show abstract] [Hide abstract]
    ABSTRACT: A square of side length 2a, a > 0 is selected in the Euclidean plane. For each a > 0, two types of hexagons are constructed using the selected square. They are labelled type-1 hexagon and type-2 hexagon. For each a > 0, there are two type-1 hexagons and two type-2 hexagons. In relation to the selected square, they appear to be horizontal and vertical. The VKS ellipses circumscribe type-1 hexagons and type-2 hexagons. The construction of these two types of hexagons and the determination of the Cartesian equations of the circumscribing VKS type-1 and VKS type-2 ellipses form the main themes for this paper. The eccentricities of these VKS type-1 ellipses and VKS type-2 ellipses are also discussed. The author hopes that the construction of the hexagons and the ellipses will be useful to students in high schools and colleges.
    International Journal of Mathematical Education 08/2014; 45(6).
  • [Show abstract] [Hide abstract]
    ABSTRACT: We use freshman calculus to prove that for  ∈ (0, π) and n = 0, 1, 2, … ; in particular, we obtain a simple unified method for evaluating the following infinite series:
    International Journal of Mathematical Education 08/2014; 45(6).
  • [Show abstract] [Hide abstract]
    ABSTRACT: A Pascal-like triangle is constructed so that power sums can be conveniently obtained by college (or high school) students with no need for memorizing complicated formulas or performing difficult calculations.
    International Journal of Mathematical Education 08/2014; 45(6).
  • [Show abstract] [Hide abstract]
    ABSTRACT: The image of mathematics held by Irish post-primary students was examined and a model for the image found was constructed. Initially, a definition for ‘image of mathematics’ was adopted with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. Research focused on students studying ordinary level mathematics for the Irish Leaving Certificate examination – the final examination for students in second-level or post-primary education. Students were aged between 15 and 18 years. A questionnaire was constructed with both quantitative and qualitative aspects. The questionnaire survey was completed by 356 post-primary students. Responses were analysed quantitatively using Statistical Package for the Social Sciences (SPSS) and qualitatively using the constant comparative method of analysis and by reviewing individual responses. Findings provide an insight into Irish post-primary students’ images of mathematics and offer a means for constructing a theoretical model of image of mathematics which could be beneficial for future research.
    International Journal of Mathematical Education 08/2014; 45(6).
  • [Show abstract] [Hide abstract]
    ABSTRACT: The card game 24 is a mathematical game that traditionally engages elementary students to practice their mental computational skills. In this paper, we use probability to formulate and explore the game. We create score of difficulty level for solvable card combination set under various setup of game rules. Based on our findings, we create new playing rules and provide suggestions for different levels of players. Our results may serve as guidelines on introducing the game 24 into the practice of math education.
    International Journal of Mathematical Education 05/2014; 45(4).
  • [Show abstract] [Hide abstract]
    ABSTRACT: We report the implementation and evaluation of a ‘peer assisted learning’ (PAL) scheme designed to reduce the so-called ‘cooling off’ phenomenon in undergraduate mathematics. ‘Cooling off’ occurs when mathematics undergraduates lose motivation and interest in their studies, despite having previously actively chosen to study it at higher levels. We found that, despite concerns about the novel didactic contract inherent in PAL schemes, a majority of students chose to engage with the scheme, and that the student leaders of the PAL sessions were generally capable of implementing a student-centred pedagogy. Furthermore, we found that students who attended the PAL sessions had higher achievement in their final examinations, even after controlling for their lecture attendance and prior attainment. We conclude by arguing that PAL may provide a useful mechanism for reducing the prevalence of the ‘cooling off’ phenomenon in some – but not all – groups of mathematics students.
    International Journal of Mathematical Education 05/2014; 45(4).
  • [Show abstract] [Hide abstract]
    ABSTRACT: The aim of this study was to examine prospective mathematics teachers’ proof processes for algebraic concepts. The study was conducted with 10 prospective teachers who were studying at the department of secondary mathematics teaching and who volunteered to participate in the study. The data were obtained via task-based clinical interviews that were conducted with the prospective teachers. The data obtained were analysed in accordance with the content analysis by focusing on the difficulties highlighted in the literature. It was observed that the difficulties prospective teachers experience in proof processes were in parallel with the difficulties highlighted in the literature.
    International Journal of Mathematical Education 05/2014; 45(4).
  • [Show abstract] [Hide abstract]
    ABSTRACT: The aim of the present study is to determine the influence of concept definitions of cylinder and cone on primary mathematics student teachers’ construction of relevant concept images. The study had a relational survey design and the participants were 238 primary mathematics student teachers. Statistical analyses implied the following: mathematics student teachers did not have sufficient level of knowledge about the concepts of cylinder and cone; concept definitions were insufficient in constructing concept images; providing student teachers with formal definitions of the concepts increased performance in choosing the right models of cylinder and cone from a given set of models but decreased performance in constructing a new cylinder; formal definitions did not affect the selection of models which were not cylinder and cone and the construction of a new cone model.
    International Journal of Mathematical Education 05/2014; 45(4).
  • [Show abstract] [Hide abstract]
    ABSTRACT: This paper proves that the ratios of consecutive terms of the m-bonacci sequence converge to a limit φm m → ∞, these φm converge to 2. Further, it is shown that the generating functions for the m-bonacci sequences converge pointwise to the geometric series.
    International Journal of Mathematical Education 05/2014; 45(4).
  • [Show abstract] [Hide abstract]
    ABSTRACT: Asymptotic expansions are derived for the reciprocal of the gamma function. We show that the coefficients of the expansion are the same, up to a sign change, as the asymptotic expansions for the gamma function obtained by exponentiating the expansions of its logarithm due to Stirling and de Moivre. Expressions for the coefficients are given in terms of Bell polynomials.
    International Journal of Mathematical Education 05/2014; 45(4).

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