Showing papers in "International Journal of Mathematical Education in Science and Technology in 2008"
TL;DR: In this article, a first year calculus for non-majors course was paired with SI and the results showed that SI participation was statistically and practically significant, a 1.8 letter grade improvement after correction for selection bias.
Abstract: Supplemental Instruction (SI) incorporates collaborative learning in small, peer-led, group settings in order to integrate instruction in learning and reasoning skills with course content. Several meta-analyses speak to the efficacy of SI but fail to address selection bias due to ability/motivation and gender. In this study, SI was paired with a first year calculus for non-majors course. An ANCOVA indicated that: ability/motivation, as measured by prior grade point average, was a useful predictor of course letter grade; gender differences were statistically significant but trivial; and, SI participation was statistically and practically significant, a 1.8 letter grade improvement after correction for selection bias. For the pass/fail analysis, a sequential binary logistic regression indicated there was a sizable statistically significant improvement with SI participation after accounting for gender and ability/motivation selection biases. The odds of success were 2.7 times greater for the SI participants....
80 citations
TL;DR: In this article, the authors investigated pre-service mathematics teachers' concept images of radians and possible sources of such images and found that participants' concept image of radian was dominated by their concept image image of degree.
Abstract: This study investigates pre-service mathematics teachers' concept images of radian and possible sources of such images. A multiple-case study was conducted for this study. Forty-two pre-service mathematics teachers completed a questionnaire, which aims to assess their understanding of radian. Six of them were selected for individual interviews on the basis of theoretical sampling. The data indicated that participants' concept images of radian were dominated by their concept images of degree. As the data in this study suggested, pre-service mathematics teachers were reluctant to accept trigonometric functions with the inputs of real numbers but rather they use value in degrees. More interestingly, they have two distinct images of p : p as an angle in radian and p as an irrational number.
64 citations
TL;DR: In this article, the effects of self and cooperative-instructional strategies on senior secondary school students' attitude towards mathematics were investigated and the moderating effects of locus of control and gender were also investigated.
Abstract: This study investigated the effects of self and cooperative-instructional strategies on senior secondary school students’ attitude towards Mathematics. The moderating effects of locus of control and gender were also investigated. The study adopted pre-test and post-test, control group quasi-experimental design using a 3 × 2 × 2 factorial matrix with two experimental groups and one control group. Three hundred and fifty SSS II students from six purposively selected secondary schools in Ijebu-North Local Government Area of Ogun State were the subjects. Three instruments were developed, validated and used for data collection. Analysis of Covariance (ANCOVA) and Scheffe post hoc analysis were the statistics used for data analysis. Findings showed that the treatments had significant main effect on students’ attitude towards Mathematics. The participants exposed to self-instructional strategy had the highest post-test mean attitude score. The study found no significant main effects of locus of control and gen...
58 citations
TL;DR: The use of tablet PCs in teaching is a relatively new phenomenon and two of the most important features of the tablet PC are annotation and wireless communication.
Abstract: The use of tablet PCs in teaching is a relatively new phenomenon. A cross between a notebook computer and a personal digital assistant (PDA), the tablet PC has all of the features of a notebook with the additional capability that the screen can also be used for input. Tablet PCs are usually equipped with a stylus that allows the user to write on the screen. Handwriting recognition software converts this input into text for use with software such as internet browsers and email programs. As an educational tool, two of the most important features of the tablet PC are annotation and wireless communication. The annotation feature allows the user to write on almost any document much as one would annotate a printout of the same document. The wireless communication feature allows tablet PCs to share information with one another. The advantages of these features and their impact on the Murray State University (MSU) classroom will be discussed in the evaluation section.
53 citations
TL;DR: A review of the state of the art in mathematical e-learning and some personal experiences on this area developed during the last eleven years at the Open University of Catalonia (UOC), a completely online university located in Spain.
Abstract: In this article we present a review of the state of the art in mathematical e-learning and some personal experiences on this area developed during the last eleven years at the Open University of Catalonia (UOC), a completely online university located in Spain. The article discusses important aspects related to online mathematics courses offered in higher education programs, including: benefits and challenges, universities offering this type of education, methodological considerations, emergent technologies, learning projects and environments, etc. Also, key aspects of the UOC mathematical e-learning model and its historical evolution are described and analysed. Special attention is paid to mathematical curricula in computer sciences degrees, where a lot of work needs to be done in order to adapt mathematics courses to the continuously changing educational necessities of students. A curricula design proposal, based on a top-down approach, is presented as a best practice. Finally, some trends and future perspectives on the subject are suggested.
43 citations
TL;DR: In this article, the authors analyse upper secondary students' task-solving reasoning with a focus on grounds for different strategy choices and implementations, and conclude that mathematically well-founded cons...
Abstract: Upper secondary students’ task solving reasoning was analysed, with a focus on grounds for different strategy choices and implementations. The results indicate that mathematically well-founded cons ...
42 citations
TL;DR: In this article, the authors extended the debate concerning the mathematical skills deficit of bioscience undergraduates towards a deeper understanding of their mathematics learning, since only through the latter can appropriate and effective explicit teaching be implemented.
Abstract: This study extends the debate concerning the mathematical skills deficit of bioscience undergraduates towards a deeper understanding of their mathematics learning, since only through the latter can appropriate and effective explicit teaching be implemented. Three hundred and twenty-six first-year bioscience undergraduates, from three pre- and four post-1992 UK universities completed a basic mathematics test, comprising 10 pure abstract mathematical calculations and 10 brief word problems set within biological contexts. In addition to participants' overall performance in the test, the students' performances on individual test items were analysed and students' test scripts examined for the methods of calculation adopted as well as the types of errors and misconceptions students exhibited. The test proved challenging for many participants, with 60% of students achieving scores of =40% and only 6% of students scoring 70-90%; the mean score was 38.5%. Although students' scores on the abstract items correlated positively with their scores on the word problems, scores were significantly higher on the pure abstract mathematics questions (mean score 55%) than on the contextualized word problems (mean score 23%). A high proportion (52-95%) of students encountered difficulties with individual questions involving the calculation of volume or surface area, the conversion of units of measurement, working with ratios, proportions and powers of 10, and determining magnification or magnitude. Students also exhibited a greater reluctance to attempt the contextualized word problems (11-75% did not attempt individual items) than the pure abstract mathematics calculations (2-12% did not attempt individual questions). Many of the errors and misconceptions students exhibited were similar to those reported previously as made commonly by 13-14-year-old children. Factors potentially influencing the students' performance and the educational implications of the findings are discussed, with particular reference to contextualized mathematics learning and learning transfer in bioscience.
40 citations
TL;DR: In this paper, a framework that makes explicit the inherent dynamic structure of certain mathematical definitions by means of the four facets of context-entity-process-object is developed, and their interrelations are then used to capture and interpret specific aspects of student constructions of the concept of solution to first order differential equations.
Abstract: In this note we develop a framework that makes explicit the inherent dynamic structure of certain mathematical definitions by means of the four facets of context-entity-process-object. These facets and their interrelations are then used to capture and interpret specific aspects of student constructions of the concept of solution to first order differential equations.
35 citations
TL;DR: This paper explored the nature of students' conceptual understanding of calculus and found that the students were expressing their understanding of limit and integral within an algorithmic context, in which the very operations of these concepts were seen as crucial.
Abstract: The study explores the nature of students’ conceptual understanding of calculus. Twenty students of engineering were asked to reflect in writing on the meaning of the concepts of limit and integral. A sub-sample of four students was selected for subsequent interviews, which explored in detail the students’ understandings of the two concepts. Intentional analysis of the students’ written and oral accounts revealed that the students were expressing their understanding of limit and integral within an algorithmic context, in which the very ‘operations’ of these concepts were seen as crucial. The students also displayed great confidence in their ability to deal with these concepts. Implications for the development of a conceptual understanding of calculus are discussed, and it is argued that developing understanding within an algorithmic context can be seen as a stepping stone towards a more complete conceptual understanding of calculus.
30 citations
TL;DR: In this article, a method of converting a rhotrix to a special form of matrix termed a "coupled matrix" is proposed, which can be used to solve various problems involving n×× n and n×n and (n×n)×1)
Abstract: In this note, a method of converting a rhotrix to a special form of matrix termed a ‘coupled matrix’ is proposed. The special matrix can be used to solve various problems involving n × n and (n – 1) × (n – 1) matrices simultaneously.
26 citations
TL;DR: In this article, the logarithmic concavity of the function for a ∈ ∈ ℝ and t ∈ 0, ∞ is verified.
Abstract: The function for x > 0 is proved to be strictly decreasing. As an application of this monotonicity, the logarithmic concavity of the function for a ∈ ℝ and t ∈ (0, ∞) is verified. The possible origin and background of the function (*) are revealed to be related to the remainder of Binet's formula. Some applications of above results to the difference of θ(x) are noted.
TL;DR: It is revealed that the ROC analysis allows us to identify the better university entrance factor for each subject in predicting students’ academic success, and to establish cut-off scores for admissions and counselling purposes.
Abstract: This article attempts to present a novel application of a method of measuring accuracy for academic success predictors that could be used as a standard. This procedure is known as the receiver operating characteristic (ROC) curve, which comes from statistical decision techniques. The statistical prediction techniques provide predictor models and their goodness-of-fit; in addition, ROC analysis allows to assess the accuracy of the ability to discriminate from success and failures cases of a classifier or predictive model, and so it could be considered complementary to others more commonly used. Thus, the ROC curve is used to compare and interpret the relative contribution of each university entrance factor in the correct classification as success or failure of the academic performance, as well as to establish cut-off scores for admissions and counselling purposes. It is revealed that the ROC analysis allows us to identify the better university entrance factor for each subject in predicting students' academic success.
TL;DR: In this article, the authors investigated the relationship between the final secondary school qualifications in Mathematics with calculus of incoming students and their results in the core first-year mathematics papers at Canterbury since 2005, when students entered the University of Canterbury with these new reformed school qualifications for the first time.
Abstract: Given the recent radical overhaul of secondary school qualifications in New Zealand, similar in style to those in the UK, there has been a distinct change in the tertiary entrant profile. In order to gain insight into this new situation that university institutions are faced with, we investigate some of the ways in which these recent changes have impacted upon tertiary level mathematics in New Zealand. To this end, we analyse the relationship between the final secondary school qualifications in Mathematics with calculus of incoming students and their results in the core first-year mathematics papers at Canterbury since 2005, when students entered the University of Canterbury with these new reformed school qualifications for the first time. These findings are used to investigate the suitability of this new qualification as a preparation for tertiary mathematics and to revise and update entrance recommendations for students wishing to succeed in their first-year mathematics study.
TL;DR: Hazzan and Zazkis as discussed by the authors used reducing abstraction as a theoretical framework for explaining students' thought process in areas of advance mathematical topics in collegiate mathematics and analyzed two tenth-grade algebra students' ways of thinking on quadratic functions.
Abstract: One possible approach students can cope with abstract algebra concepts is reducing abstraction. This notion occurs when learners are unable to adopt mental strategies as they deal with abstraction level of a given task. To make these concepts mentally accessible for themselves, learners unconsciously reduce the level of the abstraction of the concepts (O. Hazzan and R. Zazkis, Reducing abstraction: the case of school mathematics, Educ. Stud. Math. 58 (2005), pp. 101–119). Reducing abstraction as a theoretical framework has been used for explaining students’ thought process in areas of advance mathematical topics in collegiate mathematics. By analysing two tenth-grade algebra honour students’ ways of thinking on quadratic functions, this article shows how the notion of reducing abstraction can be used for analysing students’ mental processes in secondary school mathematics and provides insights into students learning about graphs as well as reports two different strategies on translation tasks as an act of...
TL;DR: In this paper, the effects of webquest-based applications on pre-service elementary school teachers' motivation in mathematics were examined, and it was found that there was a statistically significant difference in participants' motivation between treatment and control groups favouring the treatment group.
Abstract: The purpose of this study was to examine the effects of webquest-based applications on the pre-service elementary school teachers’ motivation in mathematics. There were a total of 202 pre-service elementary school teachers, 125 in a treatment group and 77 in a control group. The researcher used a Likert-type questionnaire consisting of 34 negative and positive statements. This questionnaire was designed to evaluate a situational measure of the pre-service teachers’ motivation. This questionnaire was used as pre- and post-tests in the study that took place in two semesters. It was administered to the participants by the researcher before and after the instruction during a single class period. The paired-samples t-test, the independent-samples t-test and analysis of covariance with α = 0.05 were used to analyse the quantitative data. The study showed that there was a statistically significant difference found in participants’ motivation between treatment and control groups favouring the treatment group. In ...
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TL;DR: In this paper, an instructional approach to constructing discovery-oriented activities is presented, where the cornerstone of the approach is a systematically asked question "If a mathematical statement under consideration is plausible, but wrong anyway, how can one fix it?" or, in brief, "If not, what yes?" The approach is illustrated with examples from calculus and geometry.
Abstract: This article presents an instructional approach to constructing discovery-oriented activities. The cornerstone of the approach is a systematically asked question 'If a mathematical statement under consideration is plausible, but wrong anyway, how can one fix it?' or, in brief, 'If not, what yes?' The approach is illustrated with examples from calculus and geometry. It is argued that the 'If not, what yes?' approach facilitates conjecturing and proving, constructing meaningful examples and counterexamples and has a potential for creating learning situations, in which responsibility for achieving desirable mathematical results is devolved from an instructor to the learners.
TL;DR: This article presents a simple and systematic way of implementing the boundary element method for solving the Laplace's equation using MATLAB, a numerical software package commonly used in undergraduate courses and demonstrates that a package such as MATLAB serves well in introducing as well as implementing the boundaries element method.
Abstract: The boundary element method provides an excellent platform for learning and teaching a computational method for solving problems in physical and engineering science. However, it is often left out in many undergraduate courses as its implementation is deemed to be difficult. This is partly due to the perception that coding the method requires complex programming skills beyond the ability of a typical undergraduate. In this article, we present a simple and systematic way of implementing the boundary element method for solving the Laplace's equation using MATLAB, a numerical software package commonly used in undergraduate courses. The examples will demonstrate that a package such as MATLAB serves well in introducing as well as implementing the boundary element method.
TL;DR: Lesson study is a process by which a team of instructors works collaboratively to plan, teach, observe and revise one particular lesson as discussed by the authors, which will not only result in a student-focused lesson plan that maximizes student understanding, but will also encourage teaching-centered collaboration among colleagues and increase the participants' understanding of student learning.
Abstract: Lesson Study is a process by which a team of instructors works collaboratively to plan, teach, observe and revise one particular lesson. A successful lesson study will not only result in a student-focused lesson plan that maximizes student understanding, but will also encourage teaching-centered collaboration among colleagues and increase the participants’ understanding of student learning. A group of four instructors from the University of Wisconsin-Stout participated in a lesson study for Rolle's Theorem and the Mean Value Theorem beginning in the spring of 2007. This article summarizes the process of lesson study, the lesson itself, observations from the first round of teaching and possible revisions to the lesson. Included as an appendix are all of the materials of the preliminary lesson plan, as well as materials for the lesson study itself.
TL;DR: In this paper, a written test involving geometrical problems, which is based on an original experimental setting, was presented to put in question students' spontaneous and uncritical application of the simple and neat mathematical formula of linearity.
Abstract: In this study, we attempt to put in question students’ spontaneous and uncritical application of the simple and neat mathematical formula of linearity. This is impelled with the help of a written test involving geometrical problems, which is based on an original experimental setting. In this setting, grade 9 and 10 students were instructed first to solve all the geometrical problems and then to select only one problem as the appropriate for a given numerical answer. The difficulty of this choice lied in fact that a superficial handling of each problem would resolve to the same numerical answer as the one given. The results show that students’ choices are systematic and based on the solutions given to the tasks. However, the experimental setting has managed to help students question in some degree the applicability of the linear model in situations that appear to be linear but are not. †Part of the paper was presented at the 30th Conference of the International Group for the Psychology of Mathematics Educa...
TL;DR: In this article, the use of MapleTA® in the assessment of engineering mathematics at Liverpool John Moores University (JMU) is discussed with particular reference to the design of questions.
Abstract: The use of MapleTA® in the assessment of engineering mathematics at Liverpool John Moores University (JMU) is discussed with particular reference to the design of questions. Key aspects in the formulation and coding of questions are considered. Problems associated with the submission of symbolic answers, the use of randomly generated numbers in questions and the strategy of setting policies are all discussed. Some examples of questions are then given for illustration purposes. Discussion of peripheral aspects of the implementation of MapleTA® in assessment is also presented.
TL;DR: In this paper, the results of a qualitative research project on the effect of motion analysis activities in a Video-Based Laboratory (VBL) on students' understanding of position, velocity and frames of reference were presented.
Abstract: In this article, we present the results of a qualitative research project on the effect of motion analysis activities in a Video-Based Laboratory (VBL) on students’ understanding of position, velocity and frames of reference The participants in our research were 48 pre-service teachers enrolled in Education Departments with no previous strong science or mathematics background VBLs are presented in the context of a category of technology tools that allow the analysis of motion events for educational purposes followed by a review of literature regarding the use of VBL in science education The qualitative methodology that we undertook is presented and justified and the results of our study are stated, escorted by selected and detailed dialogue extracts from our interviews with the participating students The outcomes of our research are discussed and found to be positive and some implications for further research are stated
TL;DR: In this article, the authors compared the effects of technological environments with that of the paper-and-pencil environment on reasoning about the concept of derivatives in the context of maximum and minimum problems.
Abstract: The current study compared the effects of technological environments with that of the paper-and-pencil environment on reasoning about the concept of derivatives in the context of maximum and minimum problems. The data consisted of clinical interviews conducted with three pre-service secondary mathematics teachers and a newly registered graduate student all of whom had quite a lot of mathematics courses in their repertoire. The study revealed that participants mostly depended on and were limited to analytical reasoning within paper-and-pencil environments, whereas they were able to refer to practical and creative reasoning with the help of the facilities technology environments provided. On the other hand, although participants made progress and used different reasoning types within technology environments, there were cases where they could not move beyond analytical reasoning even within the presence of technological tools. The reason for such a limitation seemed to be because of the way they treated tech...
TL;DR: In this paper, a case study reveals how mathematization of the straight line concept in Euclidean and non-Euclidean geometry emerges through the use of analogy, imagination and motion, moving the student from an extrinsic view to an intrinsic view, thus providing a psychological account of how students learn a new geometry.
Abstract: The focus of the article is on the complex cognitive process involved in learning the concept of 'straightness' in Non-Euclidean geometry. Learning new material is viewed through a conflict resolution framework, as a student questions familiar assumptions understood in Euclidean geometry. A case study reveals how mathematization of the straight line concept in Euclidean and Non-Euclidean geometry emerges through the use of analogy, imagination and motion, moving the student from an extrinsic view to an intrinsic view, thus providing a psychological account of how students learn a new geometry. Practical implications for mathematics education are provided.
TL;DR: In this paper, the authors present detailed Flash tutorials that were developed and taught by the author to a group of mathematics professors in a summer course in 2005, which was followed by a 2-year study to assess the acceptance of the technology by the teachers and to gauge its effectiveness in improving the quality of mathematics education.
Abstract: Macromedia's FLASH development system can be a great tool for mathematics education. This article presents detailed Flash tutorials that were developed and taught by the author to a group of mathematics professors in a summer course in 2005. The objective was to educate the teachers in the techniques of animating equations and mathematical concepts in Flash. The course was followed by a 2-year study to assess the acceptance of the technology by the teachers and to gauge its effectiveness in improving the quality of mathematics education. The results of that 2-year study are also reported here.
TL;DR: In this article, changes in Mathematics for Informatics at the Faculty of Organisation and Information Sciences in the University of Zagreb are described, and correlated with students pass rates.
Abstract: In this article, changes in Mathematics for Informatics at the Faculty of Organisation and Informatics in the University of Zagreb are described, and correlated with students pass rates. Students at the Faculty work in an interdisciplinary field, studying Informatics within a business context. The main reason for introducing the changes in the curriculum and its delivery, reflecting internal pressures, was the very low student pass rate in Mathematics. The second reason, reflecting external pressure, was to address the requirements of the Bologna declaration in higher education in Croatia. The innovations were introduced in the following areas: content, methodology of teaching and learning, examination methods and support for students. The changes resulted in a significant increase in student pass rates and levels of student satisfaction.
TL;DR: In this article, two summation formulas for sequences with M-bonacci property were derived and applied to the arithmetic series, mth g − gonal numbers and the Fibonacci series.
Abstract: The note introduces sequences having M-bonacci property. Two summation formulas for sequences with M-bonacci property are derived. The formulas are generalizations of corresponding summation formulas for both M-bonacci numbers and Fibonacci numbers that have appeared previously in the literature. Applications to the Arithmetic series, mth g − gonal numbers and the Fibonacci series are demonstrated.
TL;DR: In this paper, the authors assembled the ideas about mathematics and about its teaching which were expressed by mathematicians and mathematics educators into two pairs of 'official' (collective) conceptions: mathematics is either static or dynamic, and mathematics teaching is either closed or open.
Abstract: We assembled the ideas about mathematics and about its teaching which were expressed by mathematicians and mathematics educators into two pairs of 'official' (collective) conceptions: mathematics is either static or dynamic, and mathematics teaching is either closed or open. These polar conceptions produce a 4-pair relationship between the conceptions of mathematics and its teaching. The adherence to official conceptions was tapped by a questionnaire encompassing 176 Israeli high school mathematics teachers, aimed at examining the relationship between their conceptions of mathematics and its teaching. The majority of these teachers either hold a single conception in one of the domains or do not adhere to any conception, and a quarter of them hold either the static-closed or dynamic-open pairs of conceptions that prevail among teachers in other countries. Consequently, we define a conception of an entity as a comprehensive and homogenous set of ideas about a particular characteristic or feature of that entity. Reality is that teachers practice their profession without adhering to any official conception, and perhaps are (/to be?/) praised for their reluctance to blindly adopt the clear-cut rigid official conceptions of mathematics and its teaching while maintaining their individual and independent blends of ideas.
TL;DR: In this article, a two-parametric generalization of the second-order difference equation has been explored using computer algebra software and a spreadsheet, together with the use of calculus, matrix theory and continued fractions.
Abstract: This article demonstrates how within an educational context, supported by the notion of hidden mathematics curriculum and enhanced by the use of technology, new mathematical knowledge can be discovered. More specifically, proceeding from the well-known representation of Fibonacci numbers through a second-order difference equation, this article explores its two-parametric generalization using computer algebra software and a spreadsheet. Combined with the use of calculus, matrix theory and continued fractions, this technology-motivated approach allows for the comprehensive investigation of the qualitative behaviour of the orbits produced by the so generalized difference equation. In particular, loci in the plane of parameters where different types of behaviour of the cycles of arbitrary integer period formed by generalized Golden Ratios realize have been constructed. Unexpected connections among the analytical properties of the loci, Fibonacci numbers and binomial coefficients have been revealed. Pedagogica...
TL;DR: In this paper, the authors present a study in which applications were integrated in the Multivariable Calculus course at the Technion in the framework of supplementary tutorials and find that significant positive effect of the tutorials on the students' beliefs.
Abstract: This article presents a study in which applications were integrated in the Multivariable Calculus course at the Technion in the framework of supplementary tutorials. The purpose of the study was to test the opportunity of extending the conventional curriculum by optional applied problem-solving activities and get initial evidence on the possible impact of the tutorials on students' beliefs about the value of learning mathematics with applications. The study lasted three semesters and consisted of three experiments in which supplementary tutorials were offered in different forms: a weekly evening meeting for interested students, a weekly extra hour added to the conventional calculus class, and a workshop which introduces mathematics concepts from the application perspective. The study reveals: (1) significant positive effect of the tutorials on the students' beliefs (in all three experiments); (2) statistically significant advantage of the group involved in the tutorials in relation to the group that learned in the conventional way (second experiment); (3) students' positive evaluation of the workshops for better understanding the course lectures (third experiment). Grounding on the study experience, we propose for further discussion a stage model of the applied problem solving cycle.
TL;DR: This paper employed the Excel function to design dynamic visual activities for factors and multiples word problem learning, and found that after using multiple-linked representations activities, students made greater progress in understanding target concepts.
Abstract: This study employs the Excel function to design dynamic visual activities for factors and multiples word problem learning. A teaching experiment was carried out eight times in 4 weeks on three fifth grade students. The result showed that after using multiple-linked representations activities, students made greater progress in understanding target concepts. The participants also mastered the relations in various external representations. For students, understanding word problem transformation becomes an internal representation, whereby they can solve the problems successfully.