**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**156

# Search results for: Mathematics

##### 156 The Influence of Interest, Beliefs, and Identity with Mathematics on Achievement

**Authors:**
Asma Alzahrani,
Elizabeth Stojanovski

**Abstract:**

**Keywords:**
Mathematics achievement,
math efficacy,
mathematics interest,
identity.

##### 155 Classifications of Neuroscientific-Radiological Findings on “Practicing” in Mathematics Learning

**Authors:**
Felicitas Pielsticker,
Christoph Pielsticker,
Ingo Witzke

**Abstract:**

Many people know ‘Mathematics needs practice!’ statement or similar ones from their mathematics lessons. It seems important to practice when learning mathematics. At the same time, it also seems important to practice how to learn mathematics. This paper places neuroscientific-radiological findings on “practicing” while learning mathematics in a context of mathematics education. To accomplish this, we use a literature-based discussion of our case study on practice. We want to describe neuroscientific-radiological findings in the context of mathematics education and point out stimulating connections between both perspectives. From a connective perspective we expect incentives that lead discussions in future research in the field of mathematics education.

**Keywords:**
fMRI,
education,
mathematics learning,
practicing.

##### 154 Prospective Mathematics Teachers' Views about Using Flash Animations in Mathematics Lessons

**Authors:**
Esra Bukova-Güzel,
Berna Cantürk-Günhan

**Abstract:**

The purpose of the study is to determine secondary prospective mathematics teachers- views related to using flash animations in mathematics lessons and to reveal how the sample presentations towards different mathematical concepts altered their views. This is a case study involving three secondary prospective mathematics teachers from a state university in Turkey. The data gathered from two semi-structural interviews. Findings revealed that these animations help understand mathematics meaningfully, relate mathematics and real world, visualization, and comprehend the importance of mathematics. The analysis of the data indicated that the sample presentations enhanced participants- views about using flash animations in mathematics lessons.

**Keywords:**
Instructional technology,
animations,
prospective mathematics teachers.

##### 153 Gender Differences of Elementary Prospective Teachers in Mathematical Beliefs and Mathematics Teaching Anxiety

**Authors:**
Ersen Yazıcı,
Erhan Ertekin

**Abstract:**

In this study, any possible differences between mathematics beliefs and anxiety of prospective elementary mathematics teachers have been investigated according to their gender. In this purpose, 1st, 2nd, 3rd and 4th grade students from a Government University in Turkey were selected as a sample. Mathematics Teaching Anxiety Scale (MATAS) and Beliefs About Mathematics Survey (BAMS) has been used as data collection tools. As a result of the study, it has been observed that prospective male teachers have more instrumentalist approach in learning mathematics than females according to their mathematical beliefs. On the other hand, females have more mathematics teaching anxiety than males especially, for subject knowledge in mathematics and selfconfidence.

**Keywords:**
Mathematical beliefs,
mathematics teaching anxiety,
gender,
prospective elementary mathematics teachers.

##### 152 Students’ Views on Mathematics Learning: A Cross-Sectional Survey of Senior Secondary Schools Students in Katsina State of Nigeria

**Authors:**
Fahad Suleiman

**Abstract:**

**Keywords:**
Attitude,
education,
mathematics,
students.

##### 151 Sfard’s Commognitive Framework as a Method of Discourse Analysis in Mathematics

**Authors:**
Dong-Joong Kim,
Sangho Choi,
Woong Lim

**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.

**Keywords:**
Commognitive framework,
discourse analysis,
mathematical discourse,
mathematics education.

##### 150 Measuring Teachers- Beliefs about Mathematics: A Fuzzy Set Approach

**Authors:**
M.A. Lazim,
M.T.Abu Osman

**Abstract:**

**Keywords:**
belief,
membership function,
degree of similarity,
conjoint analysis

##### 149 Learning Undergraduate Mathematics in a Discovery-Enriched Approach

**Authors:**
Kam-moon Liu,
Kwok-chi Chim,
Kwok-wai Chung,
Daniel Wing-cheong Ho

**Abstract:**

**Keywords:**
Discovery-enriched curriculum,
higher education,
mathematics education,
project learning.

##### 148 Use of Technology to Improve Students’ Attitude in Learning Mathematics of Non-Mathematics Undergraduate Students

**Authors:**
Asia Majeed

**Abstract:**

This paper will investigate a form of learning mathematics by integrating technology in mathematics specifically for the university first-year calculus class to support students’ engagement in learning which influences students' conceptual and procedural understanding of the calculus content in a better way. The students with good grades in high school calculus generally struggle in first-year university calculus classes in learning mathematical analysis concepts. This problem has to be addressed. If this problem is not resolved, then most likely students with less ability to do mathematics might not able to complete their degrees. In this work, MATLAB is used to help students in learning and in improving calculus concepts.

**Keywords:**
Calculus,
first-year university students,
teaching strategies,
MATLAB.

##### 147 Development of Researcher Knowledge in Mathematics Education: Towards a Confluence Framework

**Authors:**
I. Kontorovich,
R. Zazkis

**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.

**Keywords:**
Community of practice,
knowledge development,
mathematics education research,
researcher knowledge.

##### 146 Integrating Computer Games with Mathematics Instruction in Elementary School- An Analysis of Motivation, Achievement, and Pupil-Teacher Interactions

**Authors:**
Kuo Hung Huang,
Chong-Ji Ke

**Abstract:**

**Keywords:**
computer games,
mathematics instruction,
pupil-teacher interaction,
technology-enhanced learning

##### 145 The Cooperative Learning Management in the Course of Principles of Mathematics for Graduate Level

**Authors:**
Komon Paisal

**Abstract:**

The aim of this research was to create collaborative learning activities in the course of Principles of Mathematics for graduate level by investigating the students’ ability in proving the mathematics principles as well as their attitudes towards the activities. The samples composed of 2 main group; lecturers and students. The lecturers consisted of 3 teachers who taught the course of Principles of Mathematics at Rajabhat Suan Sunandha Unicersity in the academic year 2012. The students consisted of 32 students joining the cooperative learning activities in the subject of Principles of Mathematics in the academic year 2012. The research tools included activity plan for cooperative learning, testing on mathematics with the reliability of 0.8067 and the attitude questionnaires reported by the students. The results showed that: 1) the efficiency of the developed cooperative learning activities was 69.76/ 68.57 which was lower than the set criteria at 70/70. 2) The students joining the cooperative learning activities were able to prove the principles of mathematics at the average of 70%. 3) The students joining the cooperative learning activities reported moderate attitude towards the activities.

**Keywords:**
Instructional Design,
Pedagogical,
Teaching/ Learning Strategies.

##### 144 The Views of Elementary Mathematics Education Preservice Teachers on Proving

**Authors:**
Belma Turker,
Cigdem Alkas,
Ebru Aylar,
Ramazan Gurel,
Oylum Akkus Ispir

**Abstract:**

This study has been prepared with the purpose to get the views of senior class Elementary Education Mathematics preservice teachers on proving. Data have been obtained via surveys and interviews carried out with 104 preservice teachers. According to the findings, although preservice teachers have positive views about using proving in mathematics teaching, it is seen that their experiences related to proving is limited to courses and they think proving is a work done only for the exams. Furthermore, they have expressed in the interviews that proving is difficult for them, and because of this reason they prefer memorizing instead of learning.

**Keywords:**
Belief on Proving,
Mathematics Education,
Proof.

##### 143 Leveraging Reasoning through Discourse: A Case Study in Secondary Mathematics Classrooms

**Authors:**
Cory A. Bennett

**Abstract:**

**Keywords:**
Discourse,
reasoning,
secondary mathematics,
teacher development.

##### 142 Enhancing Teaching of Engineering Mathematics

**Authors:**
Tajinder Pal Singh

**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.

**Keywords:**
Application based learning,
conceptual learning,
engineering mathematics,
word problem.

##### 141 Motivational Orientation of the Methodical System of Teaching Mathematics in Secondary Schools

**Authors:**
M. Rodionov,
Z. Dedovets

**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.

**Keywords:**
Education,
methodological system,
teaching of mathematics,
teachers,
lesson,
students motivation,
secondary school.

##### 140 Effective Factors Increasing the Students’ Interest in Mathematics in the Opinion of Mathematic Teachers of Zahedan

**Authors:**
Safiyeh Khayati,
Ali Payan

**Abstract:**

The main objective of this study was to identify factors and conditions that motivated and encouraged students towards the math class and the factors that made this class an attractive and lovely one. To do this end, questionnaires consisting of 15 questions were distributed among 85 math teachers working in schools of Zahedan. Having collected and reviewed these questionnaires, it was shown that doing activity in math class (activity of students while teaching) and previous math teachers' behaviors have had much impact on encouraging the students towards mathematics. Separation of educational classroom of mathematics from the main classroom (which is decorated with crafts created by students themselves with regard to math book including article, wall newspaper, figures and formulas), peers, size and appearance of math book, first grade teachers in each educational level, among whom the Elementary first grade teachers had more importance and impact, were among the most influential and important factors in this regard. Then, school environment, family, conducting research related to mathematics, its application in daily life and other courses and studying the history of mathematics were categorized as important factors that would increase the students’ interest in mathematics.

**Keywords:**
Interest,
motivation,
mathematical learning.

##### 139 Integrating Technology into Mathematics Education: A Case Study from Primary Mathematics Students Teachers

**Authors:**
Berna Cantürk-Günhan,
Esra Bukova-Güzel

**Abstract:**

The purpose of the study is to determine the primary mathematics student teachers- views related to use instructional technology tools in course of the learning process and to reveal how the sample presentations towards different mathematical concepts affect their views. This is a qualitative study involving twelve mathematics students from a public university. The data gathered from two semi-structural interviews. The first one was realized in the beginning of the study. After that the representations prepared by the researchers were showed to the participants. These representations contain animations, Geometer-s Sketchpad activities, video-clips, spreadsheets, and power-point presentations. The last interview was realized at the end of these representations. The data from the interviews and content analyses were transcribed and read and reread to explore the major themes. Findings revealed that the views of the students changed in this process and they believed that the instructional technology tools should be used in their classroom.

**Keywords:**
Integrating Technology,
Mathematics Education,
Primary Education,
Teacher Education.

##### 138 Optimized Multiplier Based upon 6-Input Luts and Vedic Mathematics

**Authors:**
Zulhelmi Zakaria,
Shuja A. Abbasi

**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.

**Keywords:**
Multiplier,
Vedic Mathematics,
LUTs,
FPGAs.

##### 137 Students Perceptions on the Relevance of High School Mathematics in University Education in South Africa

**Authors:**
Gilbert Makanda,
Roelf Sypkens

**Abstract:**

**Keywords:**
High school mathematics,
university education,
SPSS
package,
students’ perceptions.

##### 136 Emotion Classification for Students with Autism in Mathematics E-learning using Physiological and Facial Expression Measures

**Authors:**
Hui-Chuan Chu,
Min-Ju Liao,
Wei-Kai Cheng,
William Wei-Jen Tsai,
Yuh-Min Chen

**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.

**Keywords:**
Emotion classification,
Physiological and facial Expression measures,
Students with autism,
Mathematics e-learning.

##### 135 Practical Problems as Tools for the Development of Secondary School Students’ Motivation to Learn Mathematics

**Authors:**
M. Rodionov,
Z. Dedovets

**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.

**Keywords:**
Mathematics,
motivation,
secondary school,
student,
practical problem.

##### 134 Effects of Video Games and Online Chat on Mathematics Performance in High School: An Approach of Multivariate Data Analysis

**Authors:**
Lina Wu,
Wenyi Lu,
Ye Li

**Abstract:**

Regarding heavy video game players for boys and super online chat lovers for girls as a symbolic phrase in the current adolescent culture, this project of data analysis verifies the displacement effect on deteriorating mathematics performance. To evaluate correlation or regression coefficients between a factor of playing video games or chatting online and mathematics performance compared with other factors, we use multivariate analysis technique and take gender difference into account. We find the most important reason for the negative sign of the displacement effect on mathematics performance due to students’ poor academic background. Statistical analysis methods in this project could be applied to study internet users’ academic performance from the high school education to the college education.

**Keywords:**
Correlation coefficients,
displacement effect,
gender difference,
multivariate analysis technique,
regression coefficients.

##### 133 On the Maximum Theorem: A Constructive Analysis

**Authors:**
Yasuhito Tanaka

**Abstract:**

**Keywords:**
Maximum theorem,
Constructive mathematics,
Sequentially
locally at most one maximum.

##### 132 Further Investigations on Higher Mathematics Scores for Chinese University Students

**Authors:**
Xun Ge

**Abstract:**

Recently, X. Ge and J. Qian investigated some relations between higher mathematics scores and calculus scores (resp. linear algebra scores, probability statistics scores) for Chinese university students. Based on rough-set theory, they established an information system S = (U,CuD,V, f). In this information system, higher mathematics score was taken as a decision attribute and calculus score, linear algebra score, probability statistics score were taken as condition attributes. They investigated importance of each condition attribute with respective to decision attribute and strength of each condition attribute supporting decision attribute. In this paper, we give further investigations for this issue. Based on the above information system S = (U, CU D, V, f), we analyze the decision rules between condition and decision granules. For each x E U, we obtain support (resp. strength, certainty factor, coverage factor) of the decision rule C —>x D, where C —>x D is the decision rule induced by x in S = (U, CU D, V, f). Results of this paper gives new analysis of on higher mathematics scores for Chinese university students, which can further lead Chinese university students to raise higher mathematics scores in Chinese graduate student entrance examination.

**Keywords:**
Rough set,
support,
strength,
certainty factor,
coverage factor.

##### 131 The Use of Different Methodological Approaches to Teaching Mathematics at Secondary Level

**Authors:**
M. Rodionov,
N. Sharapova,
Z. Dedovets

**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.

**Keywords:**
Computer-oriented approach,
traditional approach,
future teachers,
mathematics,
lesson,
students,
education.

##### 130 Some Investigations on Higher Mathematics Scores for Chinese University Student

**Authors:**
Xun Ge,
Jingju Qian

**Abstract:**

To investigate some relations between higher mathe¬matics scores in Chinese graduate student entrance examination and calculus (resp. linear algebra, probability statistics) scores in subject's completion examination of Chinese university, we select 20 students as a sample, take higher mathematics score as a decision attribute and take calculus score, linear algebra score, probability statistics score as condition attributes. In this paper, we are based on rough-set theory (Rough-set theory is a logic-mathematical method proposed by Z. Pawlak. In recent years, this theory has been widely implemented in the many fields of natural science and societal science.) to investigate importance of condition attributes with respective to decision attribute and strength of condition attributes supporting decision attribute. Results of this investigation will be helpful for university students to raise higher mathematics scores in Chinese graduate student entrance examination.

**Keywords:**
Rough set,
higher mathematics scores,
decision attribute,
condition attribute.

##### 129 Investigating Transformations in the Cartesian Plane Using Spreadsheets

**Authors:**
D. Allison,
A. Didenko,
G. Miller

**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.

**Keywords:**
Mathematics education,
Microsoft Excel
spreadsheet,
technology.

##### 128 Academic Motivation Maintenance for Students While Solving Mathematical Problems in the Middle School

**Authors:**
M. Rodionov,
Z. Dedovets

**Abstract:**

**Keywords:**
Teaching strategy,
mathematics,
motivation,
student.

##### 127 Multivariate Assessment of Mathematics Test Scores of Students in Qatar

**Authors:**
Ali Rashash Alzahrani,
Elizabeth Stojanovski

**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.

**Keywords:**
Cluster analysis,
education,
mathematics,
profiles.