Open Science Research Excellence

Open Science Index

Commenced in January 2007 Frequency: Monthly Edition: International Paper Count: 44

44
10010543
Limits Problem Solving in Engineering Careers: Competences and Errors
Abstract:

In this article, the performance and errors are featured and analysed in the limit problems solving of a real-valued function, in correspondence to competency-based education in engineering careers, in the south of Chile. The methodological component is contextualised in a qualitative research, with a descriptive and explorative design, with elaboration, content validation and application of quantitative instruments, consisting of two parallel forms of open answer tests, based on limit application problems. The mathematical competences and errors made by students from five engineering careers from a public University are identified and characterized. Results show better performance only to solve routine-context problem-solving competence, thus they are oriented towards a rational solution or they use a suitable problem-solving method, achieving the correct solution. Regarding errors, most of them are related to techniques and the incorrect use of theorems and definitions of real-valued function limits of real variable.

43
10010340
Developing Proof Demonstration Skills in Teaching Mathematics in the Secondary School
Abstract:

The article describes the theoretical concept of teaching secondary school students proof demonstration skills in mathematics. It describes in detail different levels of mastery of the concept of proof-which correspond to Piaget’s idea of there being three distinct and progressively more complex stages in the development of human reflection. Lessons for each level contain a specific combination of the visual-figurative components and deductive reasoning. It is vital at the transition point between levels to carefully and rigorously recalibrate teaching to reflect the development of more complex reflective understanding. This can apply even within the same age range, since students will develop at different speeds and to different potential. The authors argue that this requires an aware and adaptive approach to lessons to reflect this complexity and variation. The authors also contend that effective teaching which enables students to properly understand the implementation of proof arguments must develop specific competences. These are: understanding of the importance of completeness and generality in making a valid argument; being task focused; having an internalised locus of control and being flexible in approach and evaluation. These criteria must be correlated with the systematic application of corresponding methodologies which are best likely to achieve success. The particular pedagogical decisions which are made to deliver this objective are illustrated by concrete examples from the existing secondary school mathematics courses. The proposed theoretical concept formed the basis of the development of methodological materials which have been tested in 47 secondary schools.

42
10010359
The Use of Different Methodological Approaches to Teaching Mathematics at Secondary Level
Abstract:

The article describes methods of preparation of future teachers that includes the entire diversity of traditional and computer-oriented methodological approaches. The authors reveal how, in the specific educational environment, a teacher can choose the most effective combination of educational technologies based on the nature of the learning task. The key conditions that determine such a choice are that the methodological approach corresponds to the specificity of the problem being solved and that it is also responsive to the individual characteristics of the students. The article refers to the training of students in the proper use of mathematical electronic tools for educational purposes. The preparation of future mathematics teachers should be a step-by-step process, building on specific examples. At the first stage, students optimally solve problems aided by electronic means of teaching. At the second stage, the main emphasis is on modeling lessons. At the third stage, students develop and implement strategies in the study of one of the topics within a school mathematics curriculum. The article also recommended the implementation of this strategy in preparation of future teachers and stated the possible benefits.

41
10010360
Motivational Orientation of the Methodical System of Teaching Mathematics in Secondary Schools
Abstract:

The article analyses the composition and structure of the motivationally oriented methodological system of teaching mathematics (purpose, content, methods, forms, and means of teaching), viewed through the prism of the student as the subject of the learning process. Particular attention is paid to the problem of methods of teaching mathematics, which are represented in the form of an ordered triad of attributes corresponding to the selected characteristics. A systematic analysis of possible options and their methodological interpretation enriched existing ideas about known methods and technologies of training, and significantly expanded their nomenclature by including previously unstudied combinations of characteristics. In addition, examples outlined in this article illustrate the possibilities of enhancing the motivational capacity of a particular method or technology in the real learning practice of teaching mathematics through more free goal-setting and varying the conditions of the problem situations. The authors recommend the implementation of different strategies according to their characteristics in teaching and learning mathematics in secondary schools.

40
10009915
A Mixed Method Investigation of the Impact of Practicum Experience on Mathematics Female Pre-Service Teachers’ Sense of Preparedness
Abstract:

The practicum experience is a critical component of any initial teacher education (ITE) course. As well as providing a near authentic setting for pre-service teachers (PSTs) to practice in, it also plays a key role in shaping their perceptions and sense of preparedness. Nevertheless, merely including a practicum period as a compulsory part of ITE may not in itself be enough to induce feelings of preparedness and efficacy; the quality of the classroom experience must also be considered. Drawing on findings of a larger study of secondary and intermediate level mathematics PSTs’ sense of preparedness to teach, this paper examines the influence of the practicum experience in particular. The study sample comprised female mathematics PSTs who had almost completed their teaching methods course in their fourth year of ITE across 16 teacher education programs in Saudi Arabia. The impact of the practicum experience on PSTs’ sense of preparedness was investigated via a mixed-methods approach combining a survey (N = 105) and in-depth interviews with survey volunteers (N = 16). Statistical analysis in SPSS was used to explore the quantitative data, and thematic analysis was applied to the qualitative interviews data. The results revealed that the PSTs perceived the practicum experience to have played a dominant role in shaping their feelings of preparedness and efficacy. However, despite the generally positive influence of practicum, the PSTs also reported numerous challenges that lessened their feelings of preparedness. These challenges were often related to the classroom environment and the school culture. For example, about half of the PSTs indicated that the practicum schools did not have the resources available or the support necessary to help them learn the work of teaching. In particular, the PSTs expressed concerns about translating the theoretical knowledge learned at the university into practice in authentic classrooms. These challenges engendered PSTs feeling less prepared and suggest that more support from both the university and the school is needed to help PSTs develop a stronger sense of preparedness. The area in which PSTs felt least prepared was that of classroom and behavior management, although the results also indicated that PSTs only felt a moderate level of general teaching efficacy and were less confident about how to support students as learners. Again, feelings of lower efficacy were related to the dissonance between the theory presented at university and real-world classroom practice. In order to close this gap between theory and practice, PSTs expressed the wish to have more time in the practicum, and more accountability for support from school-based mentors. In highlighting the challenges of the practicum in shaping PSTs’ sense of preparedness and efficacy, the study argues that better communication between the ITE providers and the practicum schools is necessary in order to maximize the benefit of the practicum experience.

39
10009902
Multivariate Assessment of Mathematics Test Scores of Students in Qatar
Abstract:

Data on various aspects of education are collected at the institutional and government level regularly. In Australia, for example, students at various levels of schooling undertake examinations in numeracy and literacy as part of NAPLAN testing, enabling longitudinal assessment of such data as well as comparisons between schools and states within Australia. Another source of educational data collected internationally is via the PISA study which collects data from several countries when students are approximately 15 years of age and enables comparisons in the performance of science, mathematics and English between countries as well as ranking of countries based on performance in these standardised tests. As well as student and school outcomes based on the tests taken as part of the PISA study, there is a wealth of other data collected in the study including parental demographics data and data related to teaching strategies used by educators. Overall, an abundance of educational data is available which has the potential to be used to help improve educational attainment and teaching of content in order to improve learning outcomes. A multivariate assessment of such data enables multiple variables to be considered simultaneously and will be used in the present study to help develop profiles of students based on performance in mathematics using data obtained from the PISA study.

38
10009904
The Competence of Solving Mathematical Problems in the Formation of Ethical Values
Abstract:

A study and its preliminary results are presented. The research is descriptive and exploratory and it is still in process. Its objective is to develop an assessment method in the field of fostering values using competence mathematics problem solving. This is part of a more extensive research that aims at contributing to educational integration in Latin America, particularly to the development of proposals to link education for citizenship and the mathematics lessons. This is being carried out by research teams of University of Barcelona-España; University Nacional of Costa Rica; University Autónoma of Querétaro-México; Pontificia University Católica of Perú, University Nacional of Villa María- Argentina and University of Los Lagos-Chile, in the context of Andrés Bello Chair for the Association of Latin American Universities. This research was developed and implemented in Chile in 2016, using mixed research methods. It included interviews and a problem-solving math test with ethical values that was administered to students of the secondary education of the regions of Los Ríos and of the Lakes of Chile. The results show the lack of integration between the teaching of values and science discipline.

37
10009625
Evaluating the Perception of Roma in Europe through Social Network Analysis
Abstract:

The Roma people are a nomadic ethnic group native to India, and they are one of the most prevalent minorities in Europe. In the past, Roma were enslaved and they were imprisoned in concentration camps during the Holocaust; today, Roma are subject to hate crimes and are denied access to healthcare, education, and proper housing. The aim of this project is to analyze how the public perception of the Roma people may be influenced by antiziganist and pro-Roma institutions in Europe. In order to carry out this project, we used social network analysis to build two large social networks: The antiziganist network, which is composed of institutions that oppress and racialize Roma, and the pro-Roma network, which is composed of institutions that advocate for and protect Roma rights. Measures of centrality, density, and modularity were obtained to determine which of the two social networks is exerting the greatest influence on the public’s perception of Roma in European societies. Furthermore, data on hate crimes on Roma were gathered from the Organization for Security and Cooperation in Europe (OSCE). We analyzed the trends in hate crimes on Roma for several European countries for 2009-2015 in order to see whether or not there have been changes in the public’s perception of Roma, thus helping us evaluate which of the two social networks has been more influential. Overall, the results suggest that there is a greater and faster exchange of information in the pro-Roma network. However, when taking the hate crimes into account, the impact of the pro-Roma institutions is ambiguous, due to differing patterns among European countries, suggesting that the impact of the pro-Roma network is inconsistent. Despite antiziganist institutions having a slower flow of information, the hate crime patterns also suggest that the antiziganist network has a higher impact on certain countries, which may be due to institutions outside the political sphere boosting the spread of antiziganist ideas and information to the European public.

36
10009152
Leveraging Reasoning through Discourse: A Case Study in Secondary Mathematics Classrooms
Abstract:
Teaching and learning through the use of discourse support students’ conceptual understanding by attending to key concepts and relationships. One discourse structure used in primary classrooms is number talks wherein students mentally calculate, discuss, and reason about the appropriateness and efficiency of their strategies. In the secondary mathematics classroom, the mathematics understudy does not often lend itself to mental calculations yet learning to reason, and articulate reasoning, is central to learning mathematics. This qualitative case study discusses how one secondary school in the Middle East adapted the number talk protocol for secondary mathematics classrooms. Several challenges in implementing ‘reasoning talks’ became apparent including shifting current discourse protocols and practices to a more student-centric model, accurately recording and probing student thinking, and specifically attending to reasoning rather than computations.
35
10008590
Development of Active Learning Calculus Course for Biomedical Program
Abstract:

The paper reviews design and implementation of a Calculus Course required for the Biomedical Competency Based Program developed as a joint project between The University of Texas Rio Grande Valley, and the University of Texas’ Institute for Transformational Learning, from the theoretical perspective as presented in scholarly work on active learning, formative assessment, and on-line teaching. Following a four stage curriculum development process (objective, content, delivery, and assessment), and theoretical recommendations that guarantee effectiveness and efficiency of assessment in active learning, we discuss the practical recommendations on how to incorporate a strong formative assessment component to address disciplines’ needs, and students’ major needs. In design and implementation of this project, we used Constructivism and Stage-by-Stage Development of Mental Actions Theory recommendations.

34
10008138
Students Perceptions on the Relevance of High School Mathematics in University Education in South Africa
Abstract:
In this study we investigated the relevance of high school mathematics in university education. The paper particularly focused on whether the concepts taught in high school are enough for engineering courses at diploma level. The study identified particular concepts that are required in engineering courses whether they were adequately covered in high school. A questionnaire was used to investigate whether relevant topics were covered in high school. The respondents were 228 first year students at the Central University of Technology in the Faculty of Engineering and Information Technology. The study indicates that there are some topics such as integration, complex numbers and matrices that are not done at high schools and are required in engineering courses at university. It is further observed that some students did not cover the topics that are in the current syllabus. Female students enter the university less prepared than their male counterparts. More than 30% of the respondents in this study felt that high school mathematics was not useful for them to be able to do engineering courses.
33
10008184
Sfard’s Commognitive Framework as a Method of Discourse Analysis in Mathematics
Abstract:

This paper discusses Sfard’s commognitive approach and provides an empirical study as an example to illustrate the theory as method. Traditionally, research in mathematics education focused on the acquisition of mathematical knowledge and the didactic process of knowledge transfer. Through attending to a distinctive form of language in mathematics, as well as mathematics as a discursive subject, alternative views of making meaning in mathematics have emerged; these views are therefore “critical,” as in critical discourse analysis. The commognitive discourse analysis method has the potential to bring more clarity to our understanding of students’ mathematical thinking and the process through which students are socialized into school mathematics.

32
10008026
Practical Problems as Tools for the Development of Secondary School Students’ Motivation to Learn Mathematics
Abstract:

This article discusses plausible reasoning use for solution to practical problems. Such reasoning is the major driver of motivation and implementation of mathematical, scientific and educational research activity. A general, practical problem solving algorithm is presented which includes an analysis of specific problem content to build, solve and interpret the underlying mathematical model. The author explores the role of practical problems such as the stimulation of students' interest, the development of their world outlook and their orientation in the modern world at the different stages of learning mathematics in secondary school. Particular attention is paid to the characteristics of those problems which were systematized and presented in the conclusions.

31
10006370
Electoral Mathematics and Asymmetrical Treatment to Political Parties: The Mexican Case
Abstract:

The Mexican Chamber of Deputies is composed of 500 representatives: 300 of them elected by relative majority and another 200 ones elected through proportional representation in five electoral clusters (constituencies) with 40 representatives each. In this mixed-member electoral system, the seats distribution of proportional representation is not independent of the election by relative majority, as it attempts to correct representation imbalances produced in single-member districts. This two-fold structure has been maintained in the successive electoral reforms carried out along the last three decades (eight from 1986 to 2014). In all of them, the election process of 200 seats becomes complex: Formulas in the Law are difficult to understand and to be interpreted. This paper analyzes the Mexican electoral system after the electoral reform of 2014, which was applied for the first time in 2015. The research focuses on contradictions and issues of applicability, in particular situations where seats allocation is affected by ambiguity in the law and where asymmetrical treatment of political parties arises. Due to these facts, a proposal of electoral reform will be presented. It is intended to be simpler, clearer, and more enduring than the current system. Furthermore, this model is more suitable for producing electoral outcomes free of contradictions and paradoxes. This approach would allow a fair treatment of political parties and as a result an improved opportunity to exercise democracy.

30
10006208
Students’ Views on Mathematics Learning: A Cross-Sectional Survey of Senior Secondary Schools Students in Katsina State of Nigeria
Abstract:
The aim of this paper is to study students’ view on mathematics learning in Katsina State Senior Secondary Schools of Nigeria, such as their conceptions of mathematics, attitudes toward mathematics learning, etc. A questionnaire was administered to a random sample of 1,225 senior secondary two (SS II) students of Katsina State in Nigeria. The data collected showed a clear picture of the hurdles that affect the teaching and learning of mathematics in our schools. Problems such as logistics and operational which include shortage of mathematics teachers, non–availability of a mathematics laboratory, etc. were identified. It also depicted the substantial trends of changing views and attitudes toward mathematics across secondary schools. Students’ responses to the conception of mathematics were consistent and they demonstrated some specific characteristics of their views in learning mathematics. This survey has provided useful information regarding students’ needs and aspirations in mathematics learning for curriculum planners and frontline teachers for future curriculum reform and implementation.
29
10003332
Enhancing Teaching of Engineering Mathematics
Abstract:

Teaching of mathematics to engineering students is an open ended problem in education. The main goal of mathematics learning for engineering students is the ability of applying a wide range of mathematical techniques and skills in their engineering classes and later in their professional work. Most of the undergraduate engineering students and faculties feels that no efforts and attempts are made to demonstrate the applicability of various topics of mathematics that are taught thus making mathematics unavoidable for some engineering faculty and their students. The lack of understanding of concepts in engineering mathematics may hinder the understanding of other concepts or even subjects. However, for most undergraduate engineering students, mathematics is one of the most difficult courses in their field of study. Most of the engineering students never understood mathematics or they never liked it because it was too abstract for them and they could never relate to it. A right balance of application and concept based teaching can only fulfill the objectives of teaching mathematics to engineering students. It will surely improve and enhance their problem solving and creative thinking skills. In this paper, some practical (informal) ways of making mathematics-teaching application based for the engineering students is discussed. An attempt is made to understand the present state of teaching mathematics in engineering colleges. The weaknesses and strengths of the current teaching approach are elaborated. Some of the causes of unpopularity of mathematics subject are analyzed and a few pragmatic suggestions have been made. Faculty in mathematics courses should spend more time discussing the applications as well as the conceptual underpinnings rather than focus solely on strategies and techniques to solve problems. They should also introduce more ‘word’ problems as these problems are commonly encountered in engineering courses. Overspecialization in engineering education should not occur at the expense of (or by diluting) mathematics and basic sciences. The role of engineering education is to provide the fundamental (basic) knowledge and to teach the students simple methodology of self-learning and self-development. All these issues would be better addressed if mathematics and engineering faculty join hands together to plan and design the learning experiences for the students who take their classes. When faculties stop competing against each other and start competing against the situation, they will perform better. Without creating any administrative hassles these suggestions can be used by any young inexperienced faculty of mathematics to inspire engineering students to learn engineering mathematics effectively.

28
10002311
The Development of Student Core Competencies through the STEM Education Opportunities in Classroom
Abstract:
The goal of the modern education system is to prepare students to be able to adapt to ever-changing life situations. They must be able to acquire required knowledge independently; apply such knowledge in practice to solve various problems by using modern technologies; think critically and creatively; competently use information; be communicative, work in a team; and develop their own moral values, intellect and cultural awareness. As a result, the status of education significantly increases; new requirements to its quality have been formed. In recent years the competency-based approach in education has become of significant interest. This approach is a strengthening of applied and practical characteristics of a school education and leads to the forming of the key students’ competencies which define their success in future life. In this article, the authors’ attention focuses on a range of key competencies, educational, informational and communicative and on the possibility to develop such competencies via STEM education. This research shows the change in students’ attitude towards scientific disciplines such as mathematics, general science, technology and engineering as a result of STEM education. Two staged analyzed questionnaires completed by students of forms II to IV in the republic of Trinidad and Tobago allowed the authors to categorize students between two levels that represent students’ attitude to various disciplines. The significance of differences between selected levels was confirmed with the use of Pearson’s chi-squared test. In summary, the analysis of obtained data makes it possible to conclude that STEM education has a great potential for development of core students’ competencies and encourage the development of positive student attitude towards the above mentioned above scientific disciplines.
27
10002557
Academic Motivation Maintenance for Students While Solving Mathematical Problems in the Middle School
Abstract:
The level and type of student academic motivation are the key factors in their development and determine the effectiveness of their education. Improving motivation is very important with regard to courses on middle school mathematics. This article examines the general position regarding the practice of academic motivation. It also examines the particular features of mathematical problem solving in a school setting.
26
10002139
Mathematics Anxiety among Male and Female Students
Abstract:
The purpose of this study is to determine the relationship of anxiety level between male and female undergraduates at a private university in Malaysia. Convenient sampling method used in this study in which the students were selected based on the grouping assigned by the faculty. There were 214 undergraduates who registered the probability courses had participated in this study. Mathematics Anxiety Rating Scale (MARS) was the instrument used in study which used to determine students’ anxiety level towards probability. Reliability and validity of instrument was done before the major study was conducted. In the major study, students were given briefing about the study conducted. Participation of this study was voluntary. Students were given consent form to determine whether they agree to participate in the study. Duration of two weeks was given for students to complete the given online questionnaire. The data collected will be analyzed using Statistical Package for the Social Sciences (SPSS) to determine the level of anxiety. There were three anxiety level, i.e., low, average and high. Students’ anxiety level was determined based on their scores obtained compared with the mean and standard deviation. If the scores obtained were below mean and standard deviation, the anxiety level was low. If the scores were at below and above the mean and between one standard deviation, the anxiety level was average. If the scores were above the mean and greater than one standard deviation, the anxiety level was high. Results showed that both of genders were having average anxiety level. Among low, average and high anxiety level, frequency of males were found to be higher as compared to females. Hence, the mean values obtained for males (M = 3.62) was higher than females (M = 3.42). In order to be significant of anxiety level among the gender, the p-value should be less than .05. The p-value obtained in this study was .117. However, this value was greater than .05. Thus, there was no significant difference of anxiety level among the gender. In other words, there was no relationship of anxiety level with the gender.
25
10001215
Development of Researcher Knowledge in Mathematics Education: Towards a Confluence Framework
Abstract:

We present a framework of researcher knowledge development in conducting a study in mathematics education. The key components of the framework are: knowledge germane to conducting a particular study, processes of knowledge accumulation, and catalyzing filters that influence a researcher decision making. The components of the framework originated from a confluence between constructs and theories in Mathematics Education, Higher Education and Sociology. Drawing on a self-reflective interview with a leading researcher in mathematics education, Professor Michèle Artigue, we illustrate how the framework can be utilized in data analysis. Criteria for framework evaluation are discussed.

24
10001022
The Formation of Motivational Sphere for Learning Activity under Conditions of Change of One of Its Leading Components
Abstract:

This article discusses ways to implement a differentiated approach to developing academic motivation for mathematical studies which relies on defining the primary structural characteristics of motivation. The following characteristics are considered: features of realization of cognitive activity, meaningmaking characteristics, level of generalization and consistency of knowledge acquired by personal experience. The assessment of the present level of individual student understanding of each component of academic motivation is the basis for defining the relevant educational strategy for its further development.

23
5249
Increase Success by Decreasing Admission for Maths– Fairytale or Reality?
Abstract:
South Africa is facing a crisis with not being able to produce enough graduates in the scarce skills areas to sustain economic growth. The crisis is fuelled by a school system that does not produce enough potential students with Mathematics, Accounting and Science. Since the introduction of the new school curriculum in 2008, there is no longer an option to take pure maths on a standard grade level. Instead, only two mathematical subjects are offered: pure maths (which is on par with higher grade maths) and mathematical literacy. It is compulsory to take one or the other. As a result, lees student finishes Grade 12 with pure mathematics every year. This national problem needs urgent attention if South Africa is to make any headway in critical skills development as mathematics is a gateway to scarce skills professions. Higher education institutions initiated several initiatives in an attempt to address the above, including preparatory courses, bridging programmes and extended curricula with foundation provisions. In view of the above, and government policy directives to broaden access in the scarce skills areas to increase student throughput, foundation provision was introduced for Commerce and Information Technology programmes at the Vaal Triangle Campus (VTC) of North-West University (NWU) in 2010. Students enrolling for extended programmes do not comply with the minimum prerequisites for the normal programmes. The question then arises as to whether these programmes have the intended impact? This paper reports the results of a two year longitudinal study, tracking the first year academic achievement of the two cohorts of enrolments since 2010. The results provide valuable insight into the structuring of an extended programme and its potential impact.
22
17081
Constructive Proof of Tychonoff’s Fixed Point Theorem for Sequentially Locally Non-Constant Functions
Abstract:

We present a constructive proof of Tychonoff’s fixed point theorem in a locally convex space for uniformly continuous and sequentially locally non-constant functions.

21
2053
Investigating Transformations in the Cartesian Plane Using Spreadsheets
Abstract:

The link between coordinate transformations in the plane and their effects on the graph of a function can be difficult for students studying college level mathematics to comprehend. To solidify this conceptual link in the mind of a student Microsoft Excel can serve as a convenient graphing tool and pedagogical aid. The authors of this paper describe how various transformations and their related functional symmetry properties can be graphically displayed with an Excel spreadsheet.

20
15168
Optimized Multiplier Based upon 6-Input Luts and Vedic Mathematics
Abstract:

A new approach has been used for optimized design of multipliers based upon the concepts of Vedic mathematics. The design has been targeted to state-of-the art field-programmable gate arrays (FPGAs). The multiplier generates partial products using Vedic mathematics method by employing basic 4x4 multipliers designed by exploiting 6-input LUTs and multiplexers in the same slices resulting in drastic reduction in area. The multiplier is realized on Xilinx FPGAs using devices Virtex-5 and Virtex-6.Carry Chain Adder was employed to obtain final products. The performance of the proposed multiplier was examined and compared to well-known multipliers such as Booth, Carry Save, Carry ripple, and array multipliers. It is demonstrated that the proposed multiplier is superior in terms of speed as well as power consumption.

19
2188
Learning Undergraduate Mathematics in a Discovery-Enriched Approach
Abstract:
Students often adopt routine practicing as learning strategy for mathematics. The reason is they are often bound and trained to solving conventional-typed questions in Mathematics in high school. This will be problematic if students further consolidate this practice in university. Therefore, the Department of Mathematics emphasized and integrated the Discovery-enriched approach in the undergraduate curriculum. This paper presents the details of implementing the Discovery-enriched Curriculum by providing adequate platform for project-learning, expertise for guidance and internship opportunities for students majoring in Mathematics. The Department also provided project-learning opportunities to mathematics courses targeted for students majoring in other science or engineering disciplines. The outcome is promising: the research ability and problem solving skills of students are enhanced.
18
6070
Constructive Proof of the Existence of an Equilibrium in a Competitive Economy with Sequentially Locally Non-Constant Excess Demand Functions
Abstract:
In this paper we will constructively prove the existence of an equilibrium in a competitive economy with sequentially locally non-constant excess demand functions. And we will show that the existence of such an equilibrium in a competitive economy implies Sperner-s lemma. We follow the Bishop style constructive mathematics.
17
1483
On the Maximum Theorem: A Constructive Analysis
Abstract:
We examine the maximum theorem by Berge from the point of view of Bishop style constructive mathematics. We will show an approximate version of the maximum theorem and the maximum theorem for functions with sequentially locally at most one maximum.
16
13846
Math Curriculum Adaptation for Disadvantaged Students in an Inclusive Classroom
Abstract:
This study was a part of the three-year longitudinal research on setting up an math learning model for the disadvantaged students in Taiwan. A target 2nd grade class with 10 regular students and 6 disadvantaged students at a disadvantaged area in Taipei participated in this study. Two units of a market basal math textbook concerning fractions, three-dimensional figures, weight and capacity were adapted to enhance their math learning motivations, confidences and effects. The findings were (1) curriculum adaptation was effective on enhancing students- learning motivations, confidences and effects; (2) story-type problems and illustrations decreased difficulties on understanding math language for students from new immigrant families and students with special needs; (3) “concrete – semiconcrete – abstract" teaching strategies and hands-on activities were essential to raise students learning interests and effects; and (4) curriculum adaptation knowledge and skills needed to be included in the pre- and in-service teacher training programs.
15
9119
Emotion Classification for Students with Autism in Mathematics E-learning using Physiological and Facial Expression Measures
Abstract:

Avoiding learning failures in mathematics e-learning environments caused by emotional problems in students with autism has become an important topic for combining of special education with information and communications technology. This study presents an adaptive emotional adjustment model in mathematics e-learning for students with autism, emphasizing the lack of emotional perception in mathematics e-learning systems. In addition, an emotion classification for students with autism was developed by inducing emotions in mathematical learning environments to record changes in the physiological signals and facial expressions of students. Using these methods, 58 emotional features were obtained. These features were then processed using one-way ANOVA and information gain (IG). After reducing the feature dimension, methods of support vector machines (SVM), k-nearest neighbors (KNN), and classification and regression trees (CART) were used to classify four emotional categories: baseline, happy, angry, and anxious. After testing and comparisons, in a situation without feature selection, the accuracy rate of the SVM classification can reach as high as 79.3-%. After using IG to reduce the feature dimension, with only 28 features remaining, SVM still has a classification accuracy of 78.2-%. The results of this research could enhance the effectiveness of eLearning in special education.

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Vol:2 No:12 2008Vol:2 No:11 2008Vol:2 No:10 2008Vol:2 No:09 2008Vol:2 No:08 2008Vol:2 No:07 2008Vol:2 No:06 2008Vol:2 No:05 2008Vol:2 No:04 2008Vol:2 No:03 2008Vol:2 No:02 2008Vol:2 No:01 2008
Vol:1 No:12 2007Vol:1 No:11 2007Vol:1 No:10 2007Vol:1 No:09 2007Vol:1 No:08 2007Vol:1 No:07 2007Vol:1 No:06 2007Vol:1 No:05 2007Vol:1 No:04 2007Vol:1 No:03 2007Vol:1 No:02 2007Vol:1 No:01 2007