 Wan Fatimah Wan Ahmad
Development of a Mathematics courseware: Fractions
 Nor A'idah Johari, Lee Ooi Chan, Rohaiza Ramli, and Noorliah Ahmat 
The Effect of GSP on Students' Understanding in The Graphs of Trigonometric Functions
 Wan Mei Amanda Soon
Using MATLAB to Implement a ComplementarityConstrained Pricing Model
 Chieko Fukuda, Kyoko Kakihana
Solving Wasan Problems with an Inversion Method  Development of teaching materials for approaching complex geometry
 Andrzej Sokolowski
Scientific Inquiry in Mathematics: A Case of Implementing Scientific Simulations for Analyzing Problems on
Motion
 Jack Carter Beverly Ferrucci
Prospective Mathematics Teachers' TechnologyBased Presentations on Proportional Reasoning
 Afza Shafie, Wan Fatimah Wan Ahmad
Designing RolePlaying Games to learn Numbers
 QiuXia Li
The perfect conversion between "Number" and "form", "see" mathematics with HP graphics calculator
 Chengyang Liu
Mathematical Simulation Experiment by Using Graphing Calculator
 Yoichi Maeda
Construction of common perpendicular in hyperbolic space
 Pumadevi Sivasubramaniam
Socratic Method: Understanding Equations of Circles with the Use of a Graphing Calculator
 JeanJacques Dahan
The richness of a multi software approach: solving trigonometric equations with Cabri, TI NSpire and Autograph and therefore modelling refraction
 Lijun Ye
Integration of Graphing Calculators in Mathematics Teaching in China
 Ian Thomson
Acquiring Declarative and Procedural Knowledge with the Aid of the ClassPad Calculator
 Yapin Tian 
The Influence of Graphing Calculator on Students' Mathematical Capability of Selfexploration under the New Curriculum
 Shunji Ouchi, Setsuo Takato
HighQuality Statistical Plots in LATEX for Mathematics Education Using an RBased KETpic PlugIn
 Ling Yiguo 
Three Teaching Modes for Algorithms with a Graphing Calculator
 Zuraini Hanim Zaini , Wan Fatimah Wan Ahmad
The Use of Blended Learning in Development of Multimedia Courseware: Loci in Two Dimension
 Norashiqin Mohd Idrus, Nor Haniza Sarmin
The Nonabelian Tensor Square of a Centerless Bieberbach Group With the Dihedral Point Group of Order Eight: Theory and Calculation
 Hsiu Ju Chang
Factorization of Quadratic Polynomial with FaultTolerance and Practice Oriented Learning
 Betty Voon Wan Niu, Wong Ling Shing
Implementing Problem Based Learning in Mathematical Studies using Graphing Calculator and Real Time Data Streamer
 Shihong Jiang
The Graphing Calculator (HP39GS) Based Numerical Experiment
 Shaobing Wu
Graphing Calculator and Black Box Phenomenon and Strategies of Consolidation into Math Courses in China
 JeanBaptiste Lagrange, Tran Kiem Minh
Learning about Functions with a Geometrical and Symbolic Software Environment: a Study of Students' Instrumental Genesis along Two Years
 Kaoru Oka, Ryoji Fukuda
Reducing Points In a Handwritten Curve (Improvement in a Notetaking Tool)
 Tasos Barkatsas
Learning mathematics with Computer Algebra Systems  Middle and senior secondary students' achievement, CAS experience and gender differences
 Yeo Kai Kow Joseph
Beyond Computation: Calculators Can Enhance Problem Solving Process
 Maria Flavia Mammana, Mario Pennisi
Dragging quadrilaterals into tetrahedra
 HeeChan Lew, KyeongSik Choi, SeoYoung Jeong 
How do students act with Dynamic Mathematics Software in Classroom?
 Kumaresan N. and Kuru Ratnavelu
Optimal control for Linear Singular Fuzzy System Using Simulink
 Barry Kissane, Marian Kemp
Teaching and Learning Probability in an Age of Technology
 Lew Hee Chan, Yoon Okyo
Study on Instruction of elementary functions through geometric construction activity with dynamic geometry environment
 Guangming Wang, Guanghui Li, Nan Zhang
Graphing Calculator and the Algorithmic Questions in the 2010 China College Entrance Examination
 Hideyo Makishita
Solving Problems from Sangaku with Technology  For Good Mathematics in Education
 Hajar Sulaiman
Teaching Teachers With Mathematical Activities Using the Graphics Calculator
18223
Development of a Mathematics courseware: Fractions
Wan Fatimah Wan Ahmad  Nurul Hidayah Abd Latih
fatimhd@petronas.com.my
Universiti Teknologi PETRONAS; Universiti Teknologi PETRONAS
Misconceptions associated with numbers can be found along the way since mathematics exists. Students find it difficult to understand fractions when the mathematics curriculum is taught in English especially in Malaysia. Students have difficulties to tally with what they had learned in English when their native language is Bahasa Malaysia. Meanwhile teachers find it difficult to treat students’ misconceptions in the classrooms. A multimedia courseware has been developed on the topic of fractions in order to assist students in understanding fractions. The objective of this paper is to report on the development of a multimedia courseware for primary school students on the topic of fractions. The development has also adopted a gamebased learning method. The ADDIE Instructional Design Model is used in the development and tools used are VB.Net, Game Maker, Adobe Photoshop and Windows XP. An evaluation has been conducted. The evaluation was based on the usability criterion that is screen design, satisfaction and learnability. The result shows that students are satisfied with the design and find that the courseware is easy to learn. It is hoped that the courseware can improve learning by providing fun and outofclassroom environment to the students at their own time and pace.
The Effect of GSP on Students’ Understanding in The Graphs of Trigonometric Functions
NORAIDAH JOHARI  HAJAH ROHAIZA RAMLI  NOORLIAH AHMAT  et al.
hjhnoraidah@yahoo.com
SEK MEN VOKASIONAL SETAPAK; KUALA LUMPUR; MALAYSIA; SEK MEN SAINS ALAM SHAH CHERAS; KUALA LUMPUR; MALAYSIA; SEK MEN TEKNIK KUALA LUMPUR; CHERAS; KUALA LUMPUR; MALAYSIA; SEK MEN KEBANGSAAN ZON R1 WANGSA MAJU; KUALA LUMPUR; MALAYSIA
The Effect of GSP on Students’ Understanding in The Graphs of Trigonometric Functions The present study examined the effectiveness of the use of GSP in classroom teaching and learning process. It investigated whether GSP has any contribution in students’ understanding in sketching the Graphs of Trigonometric Functions. Further it investigated whether GSP is able to develop appropriate concept images of the Graphs of Trigonometric Functions. Experimental design was used in this study. Informationgathering exercises were carried out for one week with 120 form five students from four schools in Kuala Lumpur, a Science Residential School, a Technical, a Vocational School and a normal school. The students enrolled in two classes, 15 in the experimental group and 15 in the controlled group in each school. In addition, 20 students had participated in one–on–one interview with the researchers. The students in the experimental group were taught using GSP presentation resources while the students in the control group were taught by using the textbook. Both groups took the same pretest and post test, which was designed by the researchers. Statistical Packages for Social Studies ( SPSS ) was used in data analysis. Categorical Data Analysis performed on two of the respective dimensions lead to three objectives of this study. The method of analysis and the result generated are offered as a mean to tackle the effectiveness of Geometers’ Sketchpad into teaching and learning. The results indicated that there was more gain in the scores from the pretest to the post test. The results of the study also indicated that there was a statistical significant difference between the statistics descriptive of the students scores with favour to the experimental group.
USING MATLAB TO IMPLEMENT A COMPLEMENTARITYCONSTRAINTED PRICING MODEL
Wan Mei Amanda Soon  Keng Cheng Ang  Kok Ming Teo
wanmei.soon@nie.edu.sg
National Institute of Education; Singapore; National Institute of Education; Singapore
The demandprice relation in the real market can be approximated by a demand function (DF). A DF can be derived from the firstorder conditions of the maximization of a utility function, or estimated using data observed from the markets. In an earlier work, a piecewise nonlinear DF which remain nonnegative at all high prices was proposed, and was called a ComplementarityConstrained Demand Function (CCDF). In this work, we use MATLAB to test a new complementarityconstrained (CC) pricing model. The novel feature of this model is attributed to the CCDF incorporated within it. An algorithm to compare the revenues obtained from a generic pricing model and a CC pricing model was implemented on MATLAB. Results from these computational experiments indicate that the use of a CC pricing model is favourable, for certain ranges of parameters defining the demand function. This demonstrates the important use of computational tools such as MATLAB in pricing modeling studies, and provides justifications for further investigations of the CC pricing model.
Solving Wasan Problems with an Inversion Method  Development of teaching materials for approaching complex geometry
Chieko Fukuda  Kyoko Kakihana
pxm03664@nifty.ne.jp
Teikyo University; JAPAN; Tsukuba Gakuin University; JAPAN
Inversion is an interesting topic for students because they get unexpected results by this transformation. This method is useful for some intractable problems, as inversion transforms them to tractable problems. Moreover, it becomes easy to visually understand inversion using dynamic geometry software (DGS). We can simply express inversion by using complex numbers. Even though complex geometry is related to complex analysis which is an important subject for students majoring in engineering, there are few easily understood educational materials. We planned a teaching method using inversion as an approach to complex geometry. In this study, we tried to teach an inversion method by solving some Wasan problems. The Wasan problems are in Japanese ancient mathematics books and we can show how inversion is powerful to solve some of them and how students approach to complex geometry. In the first step of problem solving, students search for the center of the inversion and the circle using mathematics software Geogebra. Then, they understand what kinds of problems can be effectively solved using an inversion method. Using inversion as an approach to complex geometry, this material allows students to logically progress to an understanding of Mobius transformation.
Scientific Inquiry in Mathematics
Andrzej Sokolowski
andrzejsoko@yahoo.com
Texas A&M University; Magnolia West High School
This study examines the current methods on solving problems on motion presented in some mathematics textbooks used currently in the USA. We concluded that a wide diversity in the methods as well as the methods’ lack of coherence to scientific inquiry process results in students’ weak understanding of solving these problems. This conclusion is supported by findings of a pretest conducted on a sample of 80 college algebra students enrolled in one of the schools in Texas. It is hypothesized that if the interpretation of these problems is supported by physics methods as well as by extensive graphical representations, the strategies of solving motion problems will be better understood by students. The proposed method addresses one of the most fundamental mathematics objectives stated in the newly developed Texas EndofCourse Algebra Assessments (Texas Education Agency [TEA], 2009), which requires students to analyze situations involving linear relationships and formulate linear functions. The suggested strategy is also aligned with the calculus interpretation of kinematics quantities (College Board, 2009). An approximately 83 percent gain of students’ scores on posttest instruction proves that the hypothesis of the research is correct. Consequently, it is implied that students learn science application problems in mathematics classes successfully if presented methods integrate science contents and if they are parallel with students’ prior knowledge.
Prospective Mathematics Teachers'' TechnologyBased Presentations on Proportional Reasoning
Jack Carter, Beverly Ferrucci
jack.carter@csueastbay.edu
California State University; East Bay; Keene State College
This study investigated future teachers’ use of technology in teaching proportional reasoning lessons in a seniorlevel college seminar. Seminar participants were preparing to teach mathematics at an elementary, middle, or secondary school, and the technologybased lesson was a capstone experience wherein they were to demonstrate proportional reasoning concepts or principles that were appropriate for students in the grade levels that they were preparing to teach. Presentations were videotaped, graded, and analyzed for mathematical and technological content. Analysis showed presentations differed with respect to topics covered, prior knowledge required by learners, technological activities and extensions, and reported advantages or disadvantages of the technologies as applied within these lessons. Results also illustrated differences in the presentations based on the grade levels that the future teachers planned to teach. However, regardless of grade level, all the preservice teachers used a common technology as well as a variety of particular technologies in presenting their lessons.
Designing RolePlaying Games to learn Numbers
Afza Shafie, Wan Fatimah Wan Ahmad
afzashafie@gmail.com
Universiti Teknologi PETRONAS
This paper discusses on the design of a role playing game that could be used as a tool to learn numbers and basic mathematic operations. A simple prototype consisting of 3 mini games is being developed for10 year old children. Each of the mini games is grouped according to subtopics of numbers and has three levels of difficulty, basic, intermediate and advanced. This prototype is built with a storyline, challenges and a reward system just like any other ordinary games. Positive feedback on the appeal of the game is obtained from the evaluation.
The perfect conversion between
QiuXia Li
yinyuhui@bjbroadwin.com.cn
XI'AN Senior High School NO.85 DongTingMen XI'AN China
This article is based on the students’ interest in learning mathematics and analysis of problems encountered, and the study found out that the abstract symbols of language in mathematics, making mathematics learning becomes boring and difficult. Through the study of using APLET function a function in graphics calculator; we can use Mapping function of the calculator with function graph of function mosaic to make out some Common graphics such as smiling faces, the moon, fivepointed star, etc. This can also enable students to experience the 'form' to 'several' process in turn. We can also use HP calculators learn function to convert abstract sign to 'graphics' language use MCL to study and search the phenomena in life, to make mathematics as a tool to complete the final quantification of qualitative research. HP graphic calculator is very useful for the conversion between sign language and image languages, it provides students an effective tool with which to anylised the abstract image it provide teachers a platform to develop students ability of abstract as well.
Mathematical Simulation Experiment by Using Graphing Calculator
Chengyang Liu  Jianyi Yang
yinyuhui@bjbroadwin.com.cn
Quanzhou No.7 High School
Mathematical experiment is an experiment by using a combination method between thinking and operating. Graphing calculator brings possibility to do nathematical experiment. In practice, students could construct mathematics concept and solve mathematics problems by operating, observing, experimenting and argumentation independently and positively as teamwork. Breaking subject’s boundary in order to come up with multisubject knowledge point integrative creation and innovation so as to accomplish independent learning and researching indeed. In this paper, the author will discuss on simulation mathematical experiment by using HP39gs, also combine faircointossing experiment and normal distribution experiment to give an explanation. Key words: simulation mathematical experiment, normal distribution, faircointossing experiment, clock and time zone, HP39gs
Construction of common perpendicular in hyperbolic space
yoichi maeda
maeda@keyaki.cc.utokai.ac.jp
Tokai University
Construction problem is a good exercise for us to understand geometry deeply. Using dynamic geometry software, we can easily check whether our conjecture is right or not. In this paper, we introduce a construction of common perpendicular line to two lines in threedimensional hyperbolic space. Inversion is the most essential operation for this procedure. In addition, we show that the angle of a pair of skew lines is simply measured with this construction.
Socratic Method: Understanding Equations of Circles with the Use of a Graphing Calculator
Pumadevi Sivasubramaniam
puma_devi58@hotmail.com
Raja Melewar Treacher Training Institute; Seremban;Negeri Sembilan; Malaysia
The modern Socratic Method is a process that employs inductive questioning to lead a person to construct new knowledge through small steps. This knowledge can be a specific concept, training in approaches to apply a process such as the process of problem solving, or leading one to embrace a specific belief. The type of knowledge is not as important with the Modern Socratic Method compared to the fact that the knowledge gained is specifically anticipated by the Socratic questioner. Literature pertinent to oral questioning confirms the many benefits of the Socratic Method. This paper describes a case study of the use of the Socratic Method to develop understanding of the relationship between the standard form and the general algebraic form of the equation of a circle. The study was mediated with the use of the graphing calculator as the primary feedback tool to aid students to arrive at appropriate answers for the questions posed by their lecturer. Twentyone first year Bachelor of Education, Mathematics major students from a Malaysian teacher training institute participated in this study. The main source of data to describe the effects of the Socratic Method was from the traditional ethnographic technique of “participant observer”. The study also revealed the process of thinking of the students, the realization of the importance of a systematic record of data to aid the construction of new knowledge from prior knowledge and the need of an efficient feedback tool to explore students’ conjectures which lend to progress in the learning process.
The richness of a multi software approach: solving trigonometric equations with Cabri TI N’Spire and Autograph and therefore modelling refraction
JeanJacques Dahan
jjdahan46@yahoo.fr
IREM of Toulouse
Usually, teachers use software chosen by their school or the department of their college. Sometimes they have been trained on the use of this software, and are convinced that they can enrich their teaching in using it. I will show that even an expert can miss a lot of opportunities to change the points of view for a given problem. We will start with the equation sinx=siny and conjecture its solutions with the technique of soft loci in Cabri. We will also look at the possibility of locking variables using TI Nspire. Another point of view will be presented by using Autograph to display the intersection between the surface z = sin(x)sin(y) and the plane z = 0. We will extend this study to the family of equations “sinx = k.siny” in order to present an existing geometric model of refraction together with an analytic model I have created by using the power of the CAS embedded in Autograph and TI N’Spire.
Integration of Graphing Calculator in Mathematics Teaching in China
Lijun Ye
yeatsylj@126.com
Hangzhou Normal University; China
This study investigated the benefits of using the graphic calculators in mathematics teaching and examined the effects of the graphing in secondary mathematics classroom. In addition, this study discussed the advantages of using the graphic calculators in mathematics education programs in higher education instructions and in professional development.
Acquiring Declarative and Procedural Knowledge with the Aid of the ClassPad
Ian Thomson
ian.thomson@postgrad.curtin.edu.au
Curtin University
Abstract: In this paper, some findings from the use of the ClassPad calculator in the classroom are reported. Observations were made of Year 8 students who were introduced to ClassPad calculators in a classroom equipped with a tablet computer connected to a digital projector. The observations related to the use of an algebra error locator which was installed in the calculator and to the use of the interactive geometry application of the calculator. The advantages of using the technology were considered with reference to two main types of knowledge known as declarative knowledge and procedural knowledge as described in the Dimensions of Learning framework. The paper focuses on the benefits that the use of technology can bring to the shaping phase of acquiring procedural knowledge and the organizing phase of acquiring declarative knowledge.
The Influence of Graphing Calculator on Students'' Mathematical Capability
Yapin Tian
yinyuhui@bjbroadwin.com.cn
Weishanlu Middle School
The standard of new mathematical curriculum advocates students'' selfexploration, independent study, cooperative discussion, and the experience of the mathematical 'rediscover'. Thesis discusses the influence of graphing calculator on students’ mathematical capability of selfexploration under the new curriculum in three aspects by specific empirical research, mainly reflected in: (1) graphing calculator expands the space of students'' selfexploration; (2) graphing calculator inspires the students'' awareness of selfexploration; (3) graphing calculator enriches the ways of students' selfexploration.
HighQuality Statistical Plots in Latex for Mathematics Education Using an RBased KETpic PlugIn
Shunji Ouchi  Setsuo Takato
ouchi@shimonosekicu.ac.jp
Shimonoseki City University; Toho University
The KETpic software package is comprised of a library of macros to generate standard Latex source code for highquality scientific artwork. Such macros can be implemented in different Computer Algebra Systems. We have recently implemented them in R, which is a popular opensource software tool used in statistical analysis and for graphic output. It is often the case that the default or standard output from R is not exactly what the users requires, particularly when producing graphics for educational purposes. Through our KETpic plugin, finelytuned control of various graphical features such as line style, shading, and text display is enabled until the user’s needs are fully satisfied. Taking full advantage of the functionality of R and Latex, KETpic enables us to produce teaching/learning materials incorporating figures which are designed to help the learner better understand statistical ideas and theories. In this paper we look at the use of the plugin to generate two basic statistical plots, the histogram and boxplot, which are most useful in descriptive statistics. We will also describe KETpic functionality that can be used to produce enhanced graphic output.
Three Teaching Modes for Algorithm with a Graphing Calculator
Ling Yiguo
lingyg@163.com
Beijing No. 15 high school
I practice to use hp39gs Graphing Calculator in the algorithm teaching, summarizes the three teaching models for algorithm with the graphing calculator: learning algorithm with the graphing calculator in class; using the graphing calculator programming to support the learning of other knowledge; solving the problem with the graphing calculator afterschool. All three teaching models used in the new curriculum are well in the whole process of teaching algorithm.
The Use of Blended Learning in Development of Multimedia Courseware: Loci in Two Dimensions
ZURAINI HANIM ZAINI  WAN FATIMAH WAN AHMAD
tweetycute862003@gmail.com
UNIVERSITI TEKNOLOGI PETRONAS
Multimedia courseware has been widely used after the introduction of smart school project. This paper describes the development of the interactive courseware with embedment of Pedagogical Agents, Games Based Learning and Blended Learning elements. The focus of the courseware is Loci in Two Dimensions since most of the students have difficulties in understanding this topic. The combination of these three elements can provide an exciting, meaningful learning and at the same time assist them in learning the topic. A heuristic evaluation was conducted to evaluate the courseware’s interface and usability. 7 teachers from a school in Perak was involved in the evaluation. The structured questionnaire has been used to evaluate the content, interactivity, screen design and student preferences towards use of the Loci in Two Dimensions courseware. The results have shown positive feedback from evaluators.
The NonAbelian Tensor Square of a Centerless Bieberbach Groups With a Dihedral Point Group Of Order Eight: Theory and Calculation
Norashiqin Mohd Idrus  Nor Haniza Sarmin
norashiqin@fst.upsi.edu.my
Universiti Pendidikan Sultan Idris; 35900 Tg. Malim; Perak; Persatuan Sains Matematik Malaysia (PERSAMA); Universiti Teknologi Malaysia Skudai; Johor
Centerless Bieberbach group is a torsion free crystallographic group with trivial center. In this paper our focus is on the centerless Bieberbach groups with dihedral point group of order eight. With the method developed for polycyclic groups, we compute the nonabelian tensor square of one of the group of dimension four. Our approach of the computation of the nonabelian tensor square of the group is using both hand calculations and computer calculation by GAP. We explore how to use GAP to assist our hand calculation and gain insight into this group construction and look what are missing in just doing GAP calculation. We also illustrate the problems and solutions for mapping GAP calculation to hand calculation in computing the nonabelian tensor square of the group.
Factorization of Quadratic Polynomial with Fault Tolerance and Practice Oriented Learning Architecture
Hsiu Ju
Changhsiu108@ms41.hinet.net
Taipei County ShuLin High School
The main purpose of this research is to build automatic schemas for efficient and effective thinking, learning, and solving the quadratic polynomial factorization with crossmultiplication method for less able learners in junior high school. The Fault¡VTolerance and PracticeOriented (FTPO) Web Based Learning system are based on the comprehensible and recognizable learning objects with the well concept simplifications, linkage concatenations, and structure implementations to help learners to construct their own mental images. In supporting mechanism, the adaptive linkages and structures will be the essential components for the practicedriven learning system to maintain faulttolerance mechanisms which can build and share an interpretable knowledge framework for learners to interpret and imitate the new concepts and skills meaningfully and reasonably during learning and solving processes.
Implementing ProblemBased Learning in Mathematical Studies using Graphing Calculator
Wong Ling Shing  Betty Voon Wan Niu
lingshing79@yahoo.com.sg
Inti International University; University Tenaga National
Problembased learning is a focus in student center approach, which can be practically adopted into different learning styles, objectives, and subjects. However, creating of scenario appears to be the greatest challenge, especially in mathematical studies. The HP graphing Calculator with plug and play Stream Smart data streamer that we tested might be a supplement in scenario designs for mathematical studies. The parameters that can be captured by the data streamer are varied from height of students, temperature, to the speed of vehicle, or even level of oxygen. The real time data then can be stored and processed through graphing calculator. The vast measurable parameters can virtually bring students to the fields that mimicry their future working environments, where their mathematical knowledge can be applied. This paper shows the utilization of the calculator with the data streamer, as well as the sample of scenario created.
The Graphing Calculator(HP39GS) Based Numerical Experiment
Shihong Jiang
yinyuhui@bjbroadwin.com.cn
Wuhan Institute of Technology
Abstract: The college mathematics teaching program aims at cultivating undergraduate''s capabilities of innovation, mathematical modeling and problem solving by means of the computer. The Graphing Calculator is a professional and highly efficient tool that meets the need of the teaching program. With the help of the Graphing Calculator, we have designed and implemented many mathematical experiments in the past ten years, including calculus, linear algebra, probability and statistics, and so on. Some of these cases are described in detail in the paper.
GC &
Shaobing Wu  Mingming Lu  Lihong Zhao
yinyuhui@bjbroadwin.com.cn
suqian college; Suqian middle school; Jiangsu province
Using GC (abbr. Graphing Calculator) can have a positive effect on students¡¡¡ê¡è mode of learning and thinking. In macrocosm, GC can help students acquire knowledge autonomously and individually. In microcosm, GC is better to construct the teaching situation of conception formation, to promote students to comprehend Maths knowledge profoundly, to help students probe the essence of questions, and to facilitate students to form scientific mode of thought. Key words: GC cognitive represent mode of thought
Learning about Functions with a Geometrical and Symbolic Software Environment: a Study of Students' Instrumental Genesis along Two Years
JB Lagrange  Tran Kiem Minh
jeanbaptiste.lagrange@univreims.fr
LDAR Université Paris Diderot; Department of Mathematics; College of Education; Hue University; Vietnam. Laboratoire de Didactique Andre Revuz; Universite de Paris  Diderot; France.
Abstract: Software learning environments, especially those offering extended multi representational capabilities, are more and more complex. That is why researchers are now sensitive to the process of instrumental genesis that transforms this kind of artefact into an instrument for students mathematical work. The study reported here deals with Casyopee, a geometrical and symbolic learning environment dedicated to functions at upper secondary level. The same students have been observed along their 11th and 12th grade. Learning situations have been designed with the teacher, an experienced user of Casyopee. Consistent with the curriculum, these situations aimed at approaching functions by modelling geometrical dependencies, a task for which Casyopee offers special capabilities. The observation tried to capture how students developed together their use of the software and their mathematical knowledge. Although the situations had been prepared with students instrumental genesis in mind, the observation in the first year was relatively deceiving: students had little initiative and did not identify clearly key functionalities of the software in relationship with aspects of functions. In the second year, there was a clear improvement: while students used Casyopee more freely, they developed a flexible understanding of functions, associating the objects in the software to mathematical representations. The study suggests that such an instrumental genesis can be a real attainment, but needs to be achieved as a long term process.
Reducing Points In a Handwritten Curve (Improvement in a Notetaking Tool)
kaoru oka  Ryoji Fukuda
oka@oz.ces.kyutech.ac.jp
Faculty of Computer Science and Systems Engineering Kyushu Institute of Technology;
Faculty of Engineering Oita University Japan
To improve the performance of a handwriting input system for note takers, we attempt to reduce the number of points system contains. We construct an evaluation function for a ''''reasonable line segment'''' in a handwritten curve to create an adequate polygonal line for an input curve. We acquire training data using our experimental system, and we assign an evaluating value using ''''error sort model'''', that will be defined in the paper. Then we develop a method for reducing the number of points in the handwriting system. This method reflects the intentions of human being.
Learning mathematics with Computer Algebra Systems (CAS): Middle and senior secondary students’ attitudes achievement and gender differences
Tasos Barkatsas
Tasos.Barkatsas@education.monash.edu.au
Monash University; Australia
The Mathematics and Technology Attitudes Scale (MTAS) is a scale for secondary students which may be used to monitor five affective variables relevant to learning mathematics with technology. The subscales measure mathematics confidence, confidence with technology, attitude to learning mathematics with technology and two aspects of engagement in learning mathematics. The paper reports the responses of 835 students from 9 independent Victorian schools. The supplementary variables were the following: gender, mathematics grade, year level and learning setting. Principal Components Analysis (PCA), ttests, correlations and MANOVA have been used for the analysis of students’ responses. Statistically significant differences were found between gender, Mathematics Confidence and Technology Confidence, between achievement and Mathematics Confidence, Behavioural Engagement, and Affective engagement, between year level and Behavioural Engagement and between three years of CAS experience and one year of CAS experience.
Beyond Computation: Calculators Can Enhance Problem Solving Process
Yeo Kai Kow Joseph
kaikow.yeo@nie.edu.sg
National Institute of Education
Although the role that skill acquisition plays is being deliberated in the development of conceptual understanding, the key role of the calculator as a tool for exploring mathematics and solving problems at the primary level is unquestioned. In this paper, we show how pupils can use scientific calculators as a supporting medium to improve the quality of solving word problems. To this end a flexible sixstage process, acronymically named RESCUE, is presented. The process is illustrated using a nonroutine item that possesses the quality of complexity. In addition, the six stage process also deals with ways to use calculators to enhance multiple problemsolving strategies, encourage discourse and facilitate mathematical thinking through solving word problems at the primary level. The process of solving the problems allows pupils to become familiar with multiple ways of using a calculator to obtain an answer, learn to interpret the calculator display and identify the limitations of the calculator.
Dragging quadrilaterals into tetrahedra
Maria Flavia Mammana  Mario Pennisi
fmammana@dmi.unict.it
University of Catania; University of Catania  Italy
In this paper we present the results of an experimental sequence of classroom activities in Euclidean geometry, both plane and space geometry, proposed to high school students. During the activity students discover surprising analogies between quadrilaterals and tetrahedra, by means of analogy and of the dynamic geometry software they are working in.
How do students act with Dynamic Mathematics Software in Classroom?
HeeChan Lew  KyeongSik Choi  SeoYoung Jeong
syjeong78@gmail.com
Korea National University of Education; Seoul National University
In this paper, we will present the results of observation of students¡¯ action in mathematical modeling class with DMS(Dynamic Mathematics Software). Especially we chose GeoGebra for our research tool, because it is easytouse software and has the same grammar of command with school mathematics. In this research, we observed two students¡¯ actions with the video which was recorded in the computer and at the back of the classroom. They acted as researchers in the classroom and asked few questions to the teacher. Students modified their works many times and we could observe that students’ concept became better. Students also could understood vector adding according to operation in GeoGebra without the mathematical term.
Optimal control for linear singular fuzzy system using simulink
Kumaresan Nallasamy  Kuru Ratnavelu
drnk2008@gmail.com
University of Malaya
Malaysia
In this paper, optimal control for linear singular fuzzy system is obtained using Simulink. To obtain the optimal control, the solution of MRDE is computed using Simulink approach. The simulink solution is equivalent or very close to the exact solution of the problem. An illustrative numerical example is presented for the proposed method.
Teaching and Learning Probability in an Age of Technology
Barry Kissane  Marian Kemp
B.Kissane@Murdoch.edu.au
Murdoch University
Modern classrooms have access to a range of potential technologies, ranging from calculators to computers to the Internet. This paper explores some of the potential for such technologies to affect the curriculum and teaching of probability in the secondary school and early undergraduate years, rather than relying on the classical and formal approaches focusing on set theory and counting techniques. Different approaches to probability, including the study of risk, are identified. We describe some of the ways in which the teaching of probability might be supported by the availability of various forms of technology, including calculators, computer software and the Internet. We consider especially the role of simulation as a tool for both teachers and students, focusing on activities that are not possible without the use of technology. Modern technology provides an excellent means of exploring many of the concepts associated with probability. Many of these opportunities for learning were not available before the technology development and access within schools we enjoy today. This paper suggests some of the avenues for exploration, research and development and provides advice on where to get further information and resources.
Study on Instruction of elementary functions through geometric construction activity with dynamic geometry environment
Lew Hee Chan  Okyo Yoon
okyoyoon@hanmail.net
Korea National University of Education
Providing middle school students with an opportunity to construct function with dynamic geometry based on the proportion between lengths of triangle, this study aims to activate students'' intuitive relationship between the elementary algebraic functions and their geometric properties. In addition, emphasizing the process of justification about the choice of students'' construction method, this study aims to improve students'' deductive reasoning ability. This study will investigate the following research questions: (1) What are the characteristics of the students¡¯ thinking process when students construct elementary functions with the Geometer''s Sketchpad? (2) What are the roles of the teacher in the process? This study uses qualitative case study as its purpose to observe and analyze interaction between students and between students and teacher.
Graphing Calculator and the Algorithmic Questions in the2010 China College Entrance Examination
Guangming Wang, Guanghui Li, Nan Zhang
bd690310@163.com
Beijing Normal University, Tianjin Normal University
Algorithm is not only an important part of mathematics and its application but also an important foundation for computer science. As we can see, traditional teaching methods have obvious drawbacks when applied in algorithms teaching, and graphing calculator programming function can successfully allow students experience the transition process from mathematical algorithms to computer algorithms. The combination of Graphing calculator and mathematical algorithms teaching can help students understand and grasp the concept of algorithm and develop their application capability at the same time. In this paper, we take the algorithmic questions form 2010 Chinese University Entrance as an example to explore the application of Graphing calculator.
Solving Problems from Sangaku with Technology  For Good Mathematics in Education
Hideyo Makishita
makishita.hideyo.gu@un.tsukuba.ac.jp
Junior and Senior High School at Komaba
University of Tsukuba,
JAPAN
Wasan (traditional Japanese mathematics) as well as their important spinoffs the Sangaku (mathematics tablets) discussed in this article are a part of Japan’s unique cultural heritage. They were written on Ema (wooden votive tablets) and presented as offerings at shrines and temples in order to thank the gods. In the present article, I first will introduce a brief history of Wasan, with strong emphasis on the development of Sangaku, which is followed by two examples of Sangaku problems from Kon’ou Shrine and their modern mathematical solutions. Then, the procedure for drawing geometric constructions in Sangaku is explained, with the use of a graphics calculator Casio fx9860G II and a software Casio fx9860G II Manager PLUS which runs on the PC. Finally, one attempt to apply this procedure to mathematics education is presented. It is my sincere hope that the elegance of Wasan’s way of looking at things and way of thinking, the very essence of mathematics in Edo culture, will be brought to life once again in modern mathematics education.
TEACHING TEACHERS WITH MATHEMATICAL ACTIVITIES USING THE GRAPHIC CALCULATOR
Hajar Sulaiman
hajar@cs.usm.my
School of Mathematical Sciences, Universiti Sains Malaysia,
11800 USM, Penang, Malaysia.
This paper explains the teaching method used in introducing graphic calculator to teachers and preservice teachers in a master’s level course on mathematics and technology at the School of Mathematical Sciences, USM, Penang, Malaysia. This result is obtained after 5 weeks of lab exploration done in the first semester of the 2009/2010 Academic Session. Topics were mostly from linear algebra and calculus and activities were done based on materials found in the Texas Instrument (TI)’s websites and mathematics books. In this paper, we present 3 out of the 5 explorations done in the lab sessions. The conduct of each lab, which explored a specific topic of mathematics, is presented briefly. At the end of the 5week exploration, students were asked to answer survey questions regarding their experiences with the handheld tool. Analysis of the student survey is presented briefly to discuss the students’ perception towards the graphic calculator technology before and after the exploration.
