Track: Presenting a talk with only an abstract

Presentations in English

            Abstract for 12386
            A Comparison Theorem of the Improving Gauss-Seidel method for 
            H-matrix and its Comparison Matrix
            Authors: liying Sun, xingye xu
            Affiliations: Math Dept.of Guangdong Education Institute, Math Dept. 
            of Guangdong Education Institute
            Keywords: 

            In 1997, Kohno et al. have reported that the improving modified 
            Gauss-Seidel method, which was referred to as the IMGS method, was 
            superior to the classical iterative methods. H-matrix is a widely 
            used matrix. In this paper, we apply this method to H-matrix and its 
            comparison matrix, with a more general splitting we present the 
            corresponding convergence results and the comparison results of the 
            spectral radius. The convergence rates are as well as compared. Some 
            recent results are improved. 

            Abstract for 12680
            Using Computer Multimedia to Dissolve Cognitive Conflicts of 
            Mathematical Proof
            Authors: Chun-Yi Lee, Ming-Puu Chen
            Affiliations: National Taiwan Normal University
            Keywords: 

            This paper exemplified the design of an instructional support by 
            means of computer-multimedia to dissolve students¡¦ cognitive 
            conflicts during the process of a mathematical proof problem, the 
            pasture problem. Cognitive conflicts occur when there are 
            expectations which are not fulfilled. The pasture problem provides 
            cognitive conflicts and encourages students to explore and bridge 
            the gap between conjectures and proofs. In the beginning of the 
            problem-solving process, students made a conjecture concerning the 
            solution of the pasture problem and proposed a reason why it was 
            true. The reason was often rooted in common sense or based on 
            previous learning. Through multimedia-represented cognitive 
            conflicts, students are more capable of visualizing and accepting 
            the new conjecture. Then, it led them to construct a new explanation 
            for this new conjecture naturally. It is believed that through the 
            multimedia-supported exploration students were guided to use 
            deductive reasoning, construct reasons to support the new 
            conjecture, and be motivated to solve the pasture problem.
            Full paper will appear at the second issue of eJMT 
            (http://www.radford.edu/ejmt) 

Abstract for 12724 
Two explorations with Cabri 3D leading to two theorems 
Authors: Jean-Jacques Dahan 
Affiliations: IREM of Toulouse 
Keywords: 
 
Topics: Applications using Dynamic/Interactive Geometry or/and CAS  
Exploring the volume of the convex envelope of a net of a cube with Cabri 3D, as the net opens and closes will lead to a conjecture about the maximum of this volume. We will prove this conjecture. We will also solve experimentally the problem of the tessellation of a cylinder with equilateral triangles after the observation of a picture taken in the convention enter of Hong Kong. The proof will be exposed. Eventually we will present quasi-tesselations to illustrate the Schwarz paradox in relation with the lateral area of a cylinder  

Abstract for 12726
            The process of discovery of a theorem with Cabri 3D
            Authors: Jean-Jacques Dahan
            Affiliations: IREM of Toulouse
            Keywords: 

            We will show all the stages of our experimental research to prove a 
            theorem about the quasi tesselation of a cylinder with equilateral 
            triangles. These stages are discribed with the theoretical frame I 
            have developed in my research work (Ph D thesis). We will 
            particularly show the levels of geometry during this research 
            (praxeologies G1, G2, G1 informatique and G2 informatique). We will 
            compare to what we can expect from students during their process of 
            discovery. 

            
Abstract for 12727
            Helping teachers to Develop Self Learning Package using MicroSoft 
            Office
            Authors: Che-yin Suen, Boon Cheok Toh
            Affiliations: Hong Kah SEcondary School, Hong Kah Secondary School, 
            Singapore
            Keywords: 

            Many self-leaning packages have been developed. Parents are unhappy 
            to pay the on-line package subscription for their children to learn 
            mathematics. Teachers also feel that these packages are not tailored 
            for their own pupils. The authors used Excel to develop some lessons 
            so that pupils can learn in an environment which they are familiar 
            with. Parents need not to pay a single cent. Teachers can modify the 
            contents easily to fit their pupils’ need. As the author used Macro 
            and sliders in their development, all leaning is interactive. 
            Furthermore, the examples are not static. Pupils may have many 
            different examples during their learning. 

            Abstract for 12729
            Transfer of spatial visualization: Training with discrete, composite 
            transformations in USA, Taiwan and Turkey
            Authors: Helen Gerretson, Glenn Smith, Yuan Yuan, Sinan Olkun
            Affiliations: University of South Florida, Chung Yuan Christian 
            University, Ankara University
            Keywords: 

            Problem: The learning and transfer of spatial skills, such as 
            spatial visualization (SV) and mental rotation (MR), although 
            important to mathematics, remain resistant to educators and 
            researchers best efforts to teach them. Through re-testing and 
            practice, people improve spatial skills within a narrow context, but 
            such context-specific improvements have not transferred globally to 
            other contexts. 

            Research question: We investigated whether: a) composition of 
            discrete transformations (mental rotation, reflection, dilation, and 
            translation), b) in multiple contexts, c) using multiple 
            interventions could affect transfer to MR and SV. We also 
            investigated how such spatial learning played out in different 
            countries. 

            Method: The study investigated whether six weekly sessions involving 
            interactive software could aid female pre-service elementary 
            teachers in the USA, Taiwan, and Turkey in the transfer of MR and 
            SV, as measured by two standardized tests: Flags test of mental 
            rotation and the Differential Aptitude Test (DAT) space relations 
            subset (surface development). The study employed a pretest, 
            intervention, posttest design with experimental and control groups 
            to compare pre to post improvements in spatial skills between groups 
            within each country. The intervention consisted of six weekly 
            sessions (approximately 15 minutes each) of structured activities, 
            in the computer lab, that used interactive computer programs 
            involving composition of discrete spatial transformations (e.g. 90 
            degrees of rotation, dilations a factor of two, etc.): NCTM 
            Illuminations applets, Copycat and Mathmagic™. All students were 
            enrolled in the second of a two-course sequence of mathematics 
            methods, however the US course involved geometry content, while the 
            Turkish and Taiwanese courses did not. 

            Results: At this writing, data from USA and Turkey are in, but not 
            from Taiwan. See figures 1 and 2. All participants improved on MR 
            from pre to post, but the intervention did not make a difference for 
            MR. For the Turkish students, the training made a significant 
            positive difference for SV. 

            Table 1: Flags Mental Rotation test pre to post differences
            Country Within subjects (all groups) Between groups/between subjects
            USA SIG., .0001, t = 6.33 Not sig.
            Turkey SIG., .02, t = 2.47 Not sig.

            Table 2: DAT Spatial Visualization test pre to post differences
            Country Within subjects (all groups) Between groups/between subjects
            USA Not sig. Not sig.
            Turkey SIG., .001, t = 3.7 SIG., .05 (.04), F = 4.65

            Implications: Consistent with most prior studies, re-testing, but 
            not training, improved MR. However, based on the significant 
            between-group differences in improvements on the DAT for the Turkish 
            (who were not yet exposed to geometric transformation content), 
            training with composition of discrete transformations may improve 
            multi-step SV and effect transfer.

            Abstract for 12736
            A Study of School Teachers¡¦ Applications of Using Magic Board : a 
            Web-based Virtual Manipulatives
            Authors: Yuan Yuan
            Affiliations: Chung Yuan Christian University
            Keywords: 

            Usually, school teachers do not have the time neither the skills to 
            produce their own educational materials. Magic Board is a Web-based 
            instructional tool, which includes a virtual collection of pictures 
            and symbols, teachers can use to create learning materials and to 
            design context-oriented learning activities for elementary school 
            students. The researcher gave a three-hour workshop to elementary 
            school teachers in April, 2007. In June, a questionnaire was mailed 
            to those who registered as a member and used Magic Board to design 
            instructional materials on the Web. A total of thirty-one teachers 
            were surveyed and three elementary school teachers were interviewed 
            to collect their experience of using Magic Board in school. 
            Research results showed that most school teachers like to use this 
            tool to design instructional materials. They expected to include 
            more conceptual kits, such as fractions and fraction digits and 
            suggested to have ready made activities, so teachers may have more 
            wish to use these virtual manipulative and use them effectively. 
            Interviewing results showed that Magic Board could be used to teach 
            basic number concepts effectively. School students were surprised to 
            see and use this tool to learn mathematics. The three teachers 
            thought that this tool could be used to pose questions easily and to 
            promote students¡¦ conceptual understanding. Suggestions from 
            questionnaire surveys and interviews were useful and used as 
            directions to the improvement of Magic Board. 

            Abstract for 12746
            A Mathematical Lesson on the Applications of Differentiation 
            Principles
            Authors: Hong Eng Ding, Wooi Ping Hew, Mohd Hazhar bin Jamal
            Affiliations: University of Malaya
            Keywords: 

            Differentiation is an important topic in the Additional Mathematics 
            syllabus in the Malaysia upper secondary school curriculum. This 
            topic is used extensively in Engineering where it can be used to 
            investigate or predict the natural characteristics of machineries. 
            The Department of Electrical Engineering in the University of Malaya 
            has developed an E-Learning package for studying induction motor. 
            Differentiation principle was used to determine the maximum torque 
            the motor can generate. This paper presents a lesson on application 
            of differentiation that utilizes the relevant part of the Electrical 
            Engineering E-Learning package. The lesson was being taught to a 
            group of students in an upper secondary school in Malaysia.

            The lesson starts with showing pictures of induction motors from the 
            E-Learning package, so that the students have a clear idea on the 
            machine where differentiation can be applied. A small actual 
            induction motor can also be shown in the classroom. The teacher then 
            shows a PowerPoint slides on the applications of induction motor in 
            everyday life. The torque-speed equation is given. The students are 
            required to differentiate the given equation and equal it to zero 
            (the principle of finding maximum or minimum value). This condition 
            yields an optimum parameter that generates the maximum torque. The 
            students can choose different motors with different characteristics 
            to perform the required differentiation in order to obtain the 
            maximum torque. They can check their answers and view the 
            torque-speed curve using the E-Learning package. The teacher then 
            concludes on the practical implications of different torque-speed 
            curves. Furthermore, the students are free to explore other aspect 
            of the E-Learning package to learn more about application of 
            differentiation in Engineering. 

            As a result, the students are exposed to the application of 
            differentiation principles using real examples. Using this 
            contextual learning approach, Differentiation will no longer be an 
            abstract topic but actually it could be applied to a real machine 
            that they can see and touch. This arouses the interest of students 
            in the topic of Differentiation and Electrical Engineering. It is a 
            synergy between the tool (Mathematics) and the application 
            (Engineering).

Abstract. 12759
Visualization of Mathematics Against Misconceptions in Computer Graphics Course 
Authors: Vladimir Nodelman 
Affiliations: Holon Institute of Technology 
Keywords: 
 
Topics: Technology and Curriculum Issues  
The “Computer Graphics” course is one of intensively utilizing mathematics units in Computer Science studies. Related literature often refers to mathematical notions and techniques in not sufficiently correct, adequate and precise manner in order to obtain a quick result of calculations for real-time rendering (programming games, simulations etc.) 
This paper presents several ways to prevent misconceptions and mistakes by means of computer modeling and visualization of correspondent mathematical material: 
- Visual comparison of two 3D scenes: one, produced by traditionally used algorithms with wrong mathematical model, and the other, based on adequate mathematical understanding. 
- Taking into account mathematical features that are missed in studied algorithms and lead to more efficient performance. 
- Introduction of new, not studied previously mathematical notions that ensure appropriate and fruitful application.
Proposed educational methods and aids provide solutions in studies of both computer science and mathematics itself.

            Abstract for 12760
            A Graphical Explanation of Fundamental Vector Operations for 
            Engineering Students
            Authors: Hitoshi Nishizawa, Takayoshi Yoshioka
            Affiliations: Toyota National College of Technology, Dept. of 
            Electrical and Electronic Engineering
            Keywords: 

            At the achievement test of fundamental mathematics for third-year
            students of colleges of technology in Japan, the students in 
            linear algebra was lower than the ones of calculus, trigonometry, or 
            algebra. Many students failed to separate the equation of a straight 
            line in 3D space from the one of a flat surface. Interviews to the 
            students revealed that:
            1) they have memorized those equations just before term-end 
            examinations, but
            2) they didnft have the experience to relate them to graphic 
            objects, so
            3) they couldnft explain how the change in a parameter of the 
            equation affects on the position or direction of the related graphic 
            object, even qualitatively.
            Their knowledge in linear algebra seems to evaporate in thin air 
            because it is not related to the experiences which students feel 
            more reality.

            To improve this situation, we have been building some graphical 
            explanation of vector operations in 2D and 3D space with the help of 
            graphic software. In the explanation, we need:
            1) physical phenomenon which is familiar to engineering students, 
            and its mathematical model,
            2) graphic objects in the model, and
            3) vector operations and their graphical meanings.
            Our explanation and the implementation are described in this paper. 

            Abstract for 12767
            Designing Web-based Cognitive Tools to Enhance Teaching and Learning 
            of Mathematical Problem Solving
            Authors: Luis Tirtasanjaya Lioe, Yanping Fang, Kai Fai Ho
            Affiliations: Centre for Research in Pedagogy and Practice, National 
            Institute of Education, Singapore, Centre for Research in Pedagogy 
            and Practice, and Curriculum Teaching Unit, National Institute of 
            Education, Singapore., Centre for Research in Pedagogy and Practice, 
            National Institute of Education, Singapore.
            Keywords: 

            Many researchers and cognitive scientists have been exploring 
            effective professional development for teachers that offers 
            flexibility of time and a continuity to ensure successful transfer 
            of learning to teachers’ daily practices (Ball and Cohen, 1996; 
            Hapgood, Palincsar, Kucan, Gelpi-Lomangino, & Khasnabis, 2005). This 
            paper reports on a large research project which aims at building 
            web-based cognitive tools for teacher professional development in 
            the area of mathematical problem solving (MPS) in upper primary and 
            lower secondary schools in Singapore. To this end, we draw on a rich 
            variety of classroom data to design web-based cognitive tools, such 
            as video cases of teachers’ practices, students’ problem solving 
            processes (Boaler and Humphreys, 2005) and a databank of 
            mathematical problems. The video cases of teaching practices aim to 
            initiate, through guided discussion forums, a peer-sharing and 
            peer-learning among participant-teachers, while the video cases of 
            students’ pair work aim to open discussions among the teachers on 
            students’ challenges in solving problems and ways to help students 
            overcome them. Over time, such on-line discussions will be able to 
            build a virtual community of learners (Gee, 2003) through 
            interactive technologies and digital media as teachers pose 
            questions, analyse data, consider different perspectives, and apply 
            new knowledge to their own teaching practice (Baildon & Fang, 2007). 
            Meanwhile, our databank of problems, with wide variety of contexts, 
            rich problem types and multiple solution approaches (Foong, 2002; 
            Frobisher, 1994), serves as a resource to support problem solving 
            activities in classrooms as well as scaffold cognitive processes of 
            various problem-solving strategies. The development of these 
            web-based cognitive tools involves iterative process of improving 
            and evaluation based on feedback from teachers as users. This paper 
            will highlight the design and implementation processes of these 
            cognitive tools as well as the research implications for teachers’ 
            professional learning.

            Reference

            Baildon, M. & Fang, Y.P. (2007). A*Star Project Grant Proposal 
            (Science and Engineering Research Council, SERC)/Agency for Science, 
            Technology & Research (A*STAR), Singapore

            Ball, D., & Cohen, D.K. (1999). Developing practice, developing 
            practitioners: Toward a practice-based theory of professional 
            education. In L. Darling-Hammond & G. Skyyes (Eds.). Teaching as the 
            learning profession: Handbook of policy and practice (pp. 3-32). San 
            Fransisco: Jossey-Bass.

            Boaler, J. & Humphreys, C. (2005). Connecting mathematical ideas: 
            middle school video cases to support teaching and learning. 
            Heinemann, Portsmouth, NH.

            Foong, P. Y. (2002). The role of problems to enhance pedagogical 
            practices in the Singapore mathematics classroom. The Mathematics 
            Educator, 6(2), 15-31.

            Frobisher, L. (1994). Problems, investigations and an investigative 
            approach. In A. Orton & G. Wain (Eds.), Issues in Teaching 
            Mathematics (pp.150-173). London: Cassell.

            Gee, J. P.(2003). What Video Games Have to Teach Us About Learning 
            and Literacy. New York: Palgrave McMillan.

            Hapgoof, S., Palincsar, A.S., Kucan, L., Gelpi-Lomangino, A., & 
            Khasnabis, D. (2005). Investigating a new measure of teachers’ 
            pedagogical content knowledge for teaching informal text 
            comprehension. Paper presented at the annual meeting of the American 
            Educational Research Association. 

            Abstract for 12768
            An Online Study of Math Learning from Meta-Cognition Point of View
            Authors: Fu-Shiang P. Tsen
            Affiliations: National Chiao Tung University
            Keywords: 

            To get hold of the real math learning process of our students is the 
            key step to study their math learning problem. In this study, we 
            took the full advantage of our highly motivated students toward 
            preparing college exance examination. First,we formed 6 small 
            collaborative study groups among a class of students, so that they 
            may discuss about their math problems after class. Second, we 
            utilized an on line web conference tool to help us recording the 
            complete process of each group confernce after a reviewing written 
            test which was regularly held in school for the whole class, one 
            chapter per week. A short answer was given from their teacher to 
            check their answer right or wrong, but leave the detailed learning 
            activity been their on in their web conference. We focused our study 
            on their problem solving part of recording, so that A. Shonfeld''s 
            meta-cognition concept may be used to parse each problem solving 
            process into different sections. After the analysis on each problem 
            solving, we could summarize to form our important results. By 
            summarize our detailed analysis on all the recording, we found 
            several important results. First, the learning effect is heavily 
            related to their elaborate discussing process
            in terms of meta-cognitive procedure, and the effect could be 
            validated through individual basis because of the identify property 
            of the web based recording. Second, we found that group discussing 
            will promote the meta-cognitive functions well and hence the problem 
            solving process may go through a long road in stead of a short path. 
            Third, we found a misconception which confused a group of students of 
            4, that may have chance been cured through an elaborate use of a 
            technique in meta-cognition, plus an persistent on result against 
            time pressure. 

            Abstract for 12769
            Student-Centered Assessments in Mathematics
            Authors: Premjit Singh
            Affiliations: Dept. of Mathematics, Ohio University
            Keywords: 

           This presentation outlines the ways in which I involve my students'' 
            in reflecting on their performance as they learn mathematics. I 
            strongly believe that these class-room assessment techniques 
            including minute notes, visualization techniques with TI 
            calculators, etc...) keep them grounded and engaged during class and 
            ensures that they absorb course material at higher levels. 

            I also solicit their feedback on course materials and their 
            performance by asking them to fill out a questionnaire after each 
            exam. This exercise further promotes ownership of learning. Based on 
            their responses, they are asked to figure out what they should do 
            differently to improve their performance in the course as well as 
            get a better grade in the course. 

            Abstract for 12773
            How to motivate teachers to want to use technology
            Authors: Douglas Butler
            Affiliations: iCT Training Centre (Oundle School), UK
            Keywords: 

            The TSM (Technology for Secondary Math) workshops have a fantastic 
            reputation in the UK for motivating teachers to use computer-based 
            technology effectively. The annual 3-day residential workshop 
            concentrates on two areas: to become fluent in Word and Excel for 
            mathematics, and then to make the best use of dynamic software in 
            the classroom. 

            Abstract for 12789
            Engaging grade 7 and 8 students in using Cabri 3D: approaches to 
            instrumental genesis
            Authors: Kate Mackrell
            Affiliations: Cabrilog
            Keywords: 

            This paper reports on ongoing design research with grade 7 and 8 
            students in an Ontario school where tasks, materials and approaches 
            are being created to enable students to essentially treat Cabri 3D 
            as a microworld, using mathematically mediating tools to pursue 
            their own goals, such as exploring polyhedral or building houses and 
            animated figures. The focus will be on the means by which students 
            have been enabled to gain familiarity with the software. A variety 
            of materials and approaches have been trialed and it has been found 
            that both Flash demos and pre-constructed files to replay are 
            perceived by students to be effective in facilitating their use of 
            the software. Questions arise, however, as to whether these 
            materials provide the optimum scaffolding to enable students to move 
            forward or whether too much is provided and hence opportunities for 
            student creativity and challenge are restricted. 

            Abstract for 12806
            What is the function y^(n) = y ?
            Authors: Shin Watanabe
            Affiliations: Tokai University
            Keywords: 

            We will be using Taylor Series with technological tools to explore 
            the functions which could be a solution of the differential equation 
            y^(n) = y. There are functions, which are number of n.

            Before we use the Fundamental Theorem of Algebra, which states 
            that every non-zero single-variable polynomial, with complex 
            coefficients, has exactly as many complex roots as its degree, if 
            repeated roots are counted up to their multiplicity. We will use the 
            fact that there are n linearly independent vectors to form a basis 
            in the space of R^n to solve the equation. 

            Abstract for 12807
            TI-Nspire CAS - A New Generation Math Teaching and Learning Tool
            Authors: Bernhard Kutzler
            Affiliations: ACDCA - Austrian Center for Didactics of Computer 
            Algebra
            Keywords: 

            Texas Instrument’s new product TI-Nspire CAS carries the technology 
            of the legendary TI-92 further into a new generation Math/CAS tool. 
            Its innovative double-platform design (handheld + 100 % compatible 
            computer software) and the seamless integration of the various 
            applications make it a very powerful teaching and learning aid for 
            teachers and students.
            In this lecture presentation we demonstrate all applications (CAS, 
            graphing, dynamic geometry, spreadsheet, word processing, and data 
            collection) with live examples and show how to create powerful 
            experimentation and visualization examples by combining the modules.

            Abstract for 12887
            The Effect of the Use of a Computer Algebra System on Junior College 
            Students'' Achievement in Mathematics
            Authors: Wee Leng Ng
            Affiliations: National Institute of Education, Nanyang Technological 
            University
            Keywords: 

            The purpose of this study was to investigate the effect of the use 
            of the Voyage 200 graphing calculator, a portable computer algebra 
            system (CAS), on the achievement of junior college students in 
            mathematics. Positive results were obtained though the gain was not 
            statistically significant. 

            Using the CAS Attitude Scale (CASAS), which comprises four 
            sub-scales, developed by the researcher, students'' attitudes 
            towards CAS were also examined and statistically significant results 
            were found. The reliability index, Cronbach’s alpha, for each of the 
            four subscales of the CASAS was found to be high and the reliability 
            for total scale was 0.96. The four sub-scales of the CASAS were also 
            found to be highly correlated with each other and with the total 
            scale. 

            Abstract for 12894
            A Study of Interactive Mathematical Environments for Teacher with 
            Trigger-based Animation
            Authors: Ming Jang Chen, Ning-chun Tan
            Affiliations: National Chiao Tung University, National Taipei 
            University of Education
            Keywords: 

            Teaching strategy in information age usually needs close cooperation 
            between teachers and technique professionals from the very beginning 
            when the original ideas for teaching come out. Moreover, the 
            performing of teaching information usually need to be reorganized 
            within a single screen structurally, flexibly and interactively. The 
            costs needed in man power and in time are high; it will be even 
            higher if drawing software or the programming languages are applied. 

            For the purpose of reducing digital divide while promoting its 
            popularity simultaneously, the system ¡§Mathematical Presentation 
            System (MathPS)¡¨ is developed as an interaction model for dynamic 
            presentation on the platform of Microsoft PowerPoint in terms of 
            trigger-based animation by reorganizing its original functions of 
            interaction. 
            This system MathPS provides an environment with friendly interface, 
            and it is good for mathematical multi-presentations with the ability 
            of dynamic interaction as well as an efficient environment for 
            drawing. Under this system, the occurrences of information can be 
            handled efficiently, which will help the performance needed in 
            teaching. For example, it can help to present abstract mathematics 
            concepts dynamically and even to demonstrate possible connections 
            among those patterns found. In addition to its interactive ability, 
            structural cloning method is also developed, leading to drawing 
            environments for complicated figures efficiently and friendly. 
            The purpose of this research is to provide an environment for course 
            material preparation in a user-friendly manner, so that teachers can 
            integrated their ideas into the material; moreover, the MathPS 
            environment will also provide a chance for teachers to keep these 
            material lively by using in class practically and revising 
            continuously. Therefore, teaching pedagogy, teaching strategies, and 
            teaching activities deserve further studies within the environment 
            supported by the system of MathPS .

            Abstract for 12899
            Developing Mathematical Thinking and Problem Solving Skills through 
            Card Tricks
            Authors: Poh Yew Teoh
            Affiliations: Creative Wizard Pte. Ltd., Malaysian Invention and 
            Design Society, Malaysian Association of Profesional Speakers
            Keywords: 

            Useful mathematical knowledge only becomes really useful when they 
            can be recalled and used in other contexts than those in which they 
            have been learned. This requires the development of mathematical 
            thinking and problem solving skills; not just the proficiency in 
            handling mathematical operations. Cognitive theory suggests that 
            instruction that actively involves children is the best means in 
            helping them to construct mathematical understanding and develop 
            more mature thinking patterns. One of the most effective ways to 
            actively involve pupils in learning is through mathematical magic. 
            Of all branches of mathematical magic, that which is concern with 
            playing cards is perhaps the most prolific and exciting. Playing 
            cards are one of the most effective, low cost and easily accessible 
            manipulative materials that can do wonders in mathematics classroom. 
            Mathematical card tricks can serve as an effective means of 
            motivation at almost all levels of instruction. In this 
            presentation, participants will see two very creative and powerful 
            examples of how a single card trick can be made relevant to develop 
            mathematical thinking and problem solving skills from preschool to 
            high school level. Mathematical concepts involved in these examples 
            include ascending/descending orders, addition/subtraction, inductive 
            reasoning and arithmetic progression.

            Key Words: 
            card tricks, recreational mathematics, mathematical thinking, 
            problem solving, constructivism, creativity.

            Target audience: 
            Preschool, Primary and Secondary schools mathematics teachers as 
            well as teacher trainers.

	Abstract for 12915 
Graphical Differentiation with ClassPad300Plus 
Authors: Mutlu AKAR, Mustafa Bayram, Hasan Unal 
Affiliations: Yildiz Technical University 

Topics: Implementation of Technology from K-12 Level, Mathematics Research with Technology, Assessment of Implementation of Technology in Education, Technology and Curriculum Issues, Mathematics Teaching, Learning and Assessment using Technology, Applications using CASIO technologies  
Research studies (e.g. Vinner, 1989) have shown that students’ mathematics understanding is typically analytic not visual. The use of multiple representations (visual and analytic) of mathematical concepts, in instruction can be beneficial for to students develop conceptual understanding of mathematics. The process of calculating the derivative f’ of a given function f is called differentiation. The graph of f’ can often be sketched directly from that of f by visualizing slopes, a procedure called graphical differentiation. In this poster presentation, authors will share the results of graphical differentiation activity done with ClassPad300+. We have tried activity with high school students and will share the results in detail. The results revealed that graphical differentiation have a positive effect on students understanding of differentiation concept compare to those received traditional instruction  

Abstract for 12920
            Teaching with Autograph
            Authors: Mun Chou Fong
            Affiliations: QED Education Scientific
            Keywords: Intermediate

            Autograph is the signature software for secondary mathematics 
            education. It incorporates the 3 main principles in the teaching and 
            learning of Mathematics: Flexibility-Reversibility- 
            Generalization. Autograph enables students with less vision to 
            follow the talk, deepen and excite them further. The teacher 
            will be motivated to promote mathematical thoughts by asking 
            students to write out what they see on screen. It will help both 
            teacher and student to see the connections between visual 
            representations and symbolic ones. The discourse that follows would 
            create the environment for the correct vocabulary to be used, and 
            for concepts to be internalized. Autograph can be used for the 
            learning and teaching of Transformations, Graphs, Trigonometry, 
            Statistics, and 3-D activities and the author believe that if 
            correctly used it is bound to excite secondary students in their 
            study of Mathematics. 

            Abstract for 12969
            Transforming a Mathematical Data into a Visual Form Through the Use 
            of Graphic Calculators
            Authors: Fatih YILDIZ, Nuray GOKDAL
            Affiliations: Mersa Technological Producs Co., Math Teacher in 
            Ministry of Education in Turkiye
            Keywords: Novice, Intermediate, Undergraduate Level, K-12 Level, 
            ClassPad 300, Casio, Comprehensive teaching, Graphics calculators, 
            new methods of teaching, new curriculum, easy learning, visual and 
            easy mathematics

            Mathematics is a subject that relies on a solid foundation from 
            which to build on. The learning process is more effective when 
            enhanced by visual representation to assist cognitive learning.

            Graphics calculators have become an essential tool to transfer, 
            store and manipulate mathematical data in both scientific and 
            business fields.

            The workshop will cover the graphics calculators use in mathematical 
            subjects from kindergarten to university level.

            We will begin by covering its use in teaching Trigonometry in year 8 
            and continue with Polar coordinates covered in year 11 and finish 
            with spherical coordinates used at a university level.

            Abstract for 13033
            Hartree _Fock Numerical calculations for Helium atom
            Authors: Sabri EL Atresh
            Affiliations: Department of physics, 7th October University, 
            Misurata, Libya
            Keywords: 

            The self-consistent field derived quantum mechanically by the 
            Hartree Fock approximation is used to calculate the ground state and 
            excited states of the helium atom (He). The electric potential, used 
            in this approach, is calculated by using Poisson''s equation. The 
            ground state value of He is found to be -2.89459 a.u which is below 
            the commonly accepted limit[1]. The excited states are found to be 
            -4.149 eV for 1s2s, -3.431 eV for 1s2p, -1.725 eV for 1s3s and 
            -1.521 eV for 1s3p. We should note that using Poisson''s equation 
            greatly simplified the mathematical calculation. 

            R. Celeste, H.F.M. da Costa, A.B.F da Silva and M. Trsic, J. Chem.. 
            Phys. 23 (1991) 1831 

            Abstract for 13127
            Development and Implementation of the Online Mathematics Course.
            Authors: Bakhodirzhon Siddikov
            Affiliations: Associate Professor of Mathematics, Department of 
            Mathematics, Ferris State University, 820 Campus Drive, ASC 2021, 
            Big Rapids, Michigan 49307, USA
            Keywords: 

            For the last ten to fifteen years there has been wide exploration of 
            innovative approaches to classroom instruction: the use of the 
            computer in teaching science courses. Rapid development of the 
            internet technology and improvements of mathematics software made 
            possible designing and implementing all levels of mathematics 
            courses to satisfy the nontraditional students’ need of being able 
            to take the mathematics courses off-campus. Today, a majority of 
            colleges and universities are offering the online mathematics 
            courses. 

            In 2006, Ferris State University has received a grant from the U.S. 
            Department of Education and Labor to develop the fully online the 
            Heating, Ventilation, Air Conditioning and Refrigeration (HVACR) 
            program, which leads to a Bachelor of Science degree. As part of 
            this grant project, an “Intermediate Algebra and Numerical 
            Trigonometry” online course has been developed, and implemented in 
            2007. Maple software has been used to make the new online 
            instruction platform more interactive and dynamic. 
            This talk is about the results of the development and implementation 
            of the online teaching platform for the “Intermediate Algebra and 
            Numerical Trigonometry” course. We will discuss advantages and 
            disadvantages of the developed online course. We will talk about the 
            different techniques of preventing academic cheating in taking the 
            online mathematics courses, as well as difficulties of designing 
            online tests, quizzes, lecture notes, and discussion of the homework 
            problems. We will share with the audience our experiences of 
            overcoming these difficulties. At the end of the talk, we will 
            discuss the statistical results of the implementation of the online 
            “Intermediate Algebra and Numerical Trigonometry” course at Ferris 
            State University, Michigan, U.S.A. in 2007. 

	Abstract for 13530 
Authors: Amy Leh, Lee Grafton 
Affiliations: California State University San Bernardino, USA, PSUSD 
Keywords: 
 
Topics: Implementation of Technology from K-12 Level, Assessment of Implementation of Technology in Education, Mathematics Teaching, Learning and Assessment using Technology  
This paper reports on the implementation and evaluation of an Enhancing Education Through Technology Competitive Grant (EETT-C) project. During 2005-2007, the project served 60 sixth to eighth grade mathematics teachers and approximately 6,500 students in Palm Springs Unified School District, a medium-sized, high-poverty school district in Southern California in the United States. The research-based program was designed to facilitate the delivery of a student program that effectively integrated technology into the curriculum to improve student achievement. Classroom observation and interview results indicated that the program was effective.

The presentation will start with an overview of the instructional strategies used to deliver the student program and the corresponding faculty development strategies. Descriptions of technologies used in the program are embedded. The overview is followed by the program evaluation, with a focus on classroom observations and interviews. 

Abstract for 13791 
Brief study of what high school students think about using technology tools in learning math and how they actually use them in learning math 
Authors: Tae Young Ha 
Affiliations: University of Hawaii, Kapolei High School, NCTM, PME 
Keywords: 
 
Topics: Implementation of Technology from K-12 Level, Mathematics Research with Technology, Technology and Curriculum Issues, Mathematics Teaching, Learning and Assessment using Technology  
In this study, students’ perceptions on using technology in learning mathematics were identified through questionnaire and interviews. Then their actual classroom  

Abstract for 13811 
Exploring Steiner''s Porism with Cabri Geometry 
Authors: Chien-Hsun Lu 
Affiliations: Shing-Hua High School maintained by Miaoli County Government 
Keywords: 
 
Topics: Applications using Dynamic/Interactive Geometry or/and CAS  
The purpose of this thesis is to explore Steiner''s Porism by the software "Cabri Geometry". There are two discussions referring to inversion and Steiner''s Porism. Definition, properties and applications of inversion are introduced in the first part and constructing Steiner Chain by inversion to explore Steiner''s Porism is the second one. The contents of this thesis are also presented dynamically on the website by CabriJava which is a Java program developed by the Cabrilog company.  

Abstract for 13902 
Google Earth and Spherical Geometry 
Authors: Hualun Li 
Affiliations: Chung Hua University 
Keywords: 
 
Topics: Internet Technology for Mathematics  
We investigated the relation between popular computer programs and geometry.
On the educational level, we focus on tools like paintbrush in Microsoft windows and Google earth. We discovered these (somewhat easy) tools provide interesting links between theoretical mathematics and experimental world.
In this talk, these new ideas for teaching and learning geometry will be presented.

Abstract for 13994 
Comparison Between Computer Supported Collaborative Learning and The Traditional Means in Learning Probability Concepts 
Authors: Carmelita Ragasa 
Affiliations: University of the East Manila, Philippine Normal University, MATHTED, Inc., Philippine E-Learning Society 
Keywords: 
 
Topics: Mathematics Education using Information & Communication Technology, Assessment of Implementation of Technology in Education, Mathematics Teaching, Learning and Assessment using Technology, Applications on Statistics with Technology  
Abstract
This study is a quasi experimental research involving 35 students in the experimental group (taught probability concepts using CD-ROM) and eight students in the control group (taught same topics using the traditional method of teaching). The experimental group were sophomore students taking up Information Technology while the control group were mixture of different courses. The statistical tools used were the t test of the difference of means for dependent and independent correlated samples, descriptive statistics, and the regression analysis using spss 11.5 version. The following were the findings of the study. There is a significant difference between the mean of the achievement test of the pretest and the mean of the achievement test of the posttest in the experimental group. There is no significant difference between the mean of the pretest and the mean of the posttest of the achievement tests in the control group. There is no significant difference between the pretests of both the experimental and the control group. There is a significant difference between the posttests of the experimental and the control groups. The variables that are correlated significantly at the .05 level of significance are: high school mathematics grade and the college entrance test total; the high school general weighted average with the college entrance test total. The posttest is not correlated with any of the variables and neither is the pretest correlated with any of the variables. The predictors of the posttest achievement test are the pretest achievement, the high school mathematics grade, the high school general weighted average, the college entrance test in mathematics, the college entrance test total score.

Abstract for 15000
Authors: Young-Wha Choi , Hee-Chan Lew, & Min-Shik Cho
Korea National University of Education
It has been noted in several international comparison studies on math achievement that Korean students demonstrate a high level of achievement.  When the data is disaggregated, it shows that urban students are achieving at much higher rates than rural students.  This significant difference between urban and rural students may result from an assortment of complex social factors associated with rural areas such as parents' relative indifference toward education, less competitive educational atmosphere, unfavorable working condition for teachers, poor educational surroundings, and insufficient instructional materials.
An understanding in Korea’s education requires a thorough acknowledgement of the stance of out-of-school education within the overall educational framework of Korea. According to Kim, Yang, Kim & Lee(2001), 84.1% of Korean parents provide some form of shadow education for their children (primary 91.1%, middle school 81.5, high school 70.2%) and it has been reported that such phenomenon is only getting more severe and public education fees including college tuition in 2000 equaled 33.5 billion US$, whereas out-of-school tutoring fees were calculated at 37 billion US$. In effect parents in Korea are using approximately 10% of their income on their children’s out-of-school tutoring fees.
Following the several reports and studies showing the significant differences in math achievement among rural and urban students and the social problem out-of-school tutoring fees have happened to parents, the Korean government proposed the plan to lessen the disparity of educational opportunities between rural and urban students and to reduce out-of-school tutoring fees of parents.  One such government-sponsored program is “E-learning” or commonly known as ‘cyber home school’.  The program targets low-income families throughout the country and provide them with a free computer, internet access, and cyber tutor. 
For this study analyzes 'cyber home school' impact on mathematics achievement and mathematical disposition of Korean 8th grade students.  The content focus for the study is Algebra, which is taken by all Korean students during the second year in middle school (8th grade). Generally, the course is tailored to students' different learning abilities.  In particular, middle- and low-level achieving students have opportunities to review elementary algebra as needed, whereas high-level achieving students have experiences to deepen their knowledge and to think at higher mathematical levels. Students may change their levels of studying, but most students remain in designated achievement levels. 
The study of ‘cyber home school’ was conducted for two months with 20 middle school students from one middle school at one small city in Korea. Students were divided into three achievement groups (high, middle, and low level) by the results of a pre-test. Teachers confirm the process of student ability; manage on-line meetings and e-board discussions to promote two-way communications with students.  Some of the students had difficulty using their computer at home, so they were given opportunities to use a computer at school before and after the class or lunchtime.
The post-test of mathematics achievement illustrated the degree of change resulting from the study.  This study did a comparison analysis between 20 students who were exposed to the on-line learning environment and another 20 students of the same school who enrolled out-of-school programs and had a similar achievement level averagely to the level of experimental group in the pre-test of mathematics achievement. 
This study suggests a powerful way for rural students or low-income brackets students who have insufficient educational opportunities to learn mathematics tailored to their levels, and provide an empirical foundation on how to promote substance of public education at small outlay.
References
Beaton, A.E., Mullis, I. V.S., Martin, M.O., Gonzalez, E. J., Kelly, D. L., & Smith, T. A. (1996). Mathematics achievement in the middle school years: IEA's third international mathematics and science study. Chestnut Hill, MA: TIMSS International Center, Boston College. 
Cho, Y.O., Song, D.H., & Lee, B.J.(2004). Short-term tasks for the activation of rural education and the establishment of special law. Presidential Committee on Educational Innovation.(in Korean) 
Chungbuk Education & Science Research Institute. (2006). Chungbuk Ccyber home school: Another classroom in internet. The Author. (in Korean) 
Han, T.M. (2004). School education and e-Learning. Kyungsangbuk-do Office of Education.(in Korean) 
Kim, Y.C., Yang, S.S., Kim, Y.H., Lee, J.H.(2001). Policy development for private tutoring expenditure reduction (in Korean). Research Report CR 2001-15. Seoul: Korea Educational Development Institute.
Kong, K. (2005). The analyses and remedies of educational conditions in rural communities. Thesis of Graduate School of Public Administration, Gyungsang National University.(in Korean) 
Mullis, I.V.S., Martin, M. O., Beaton, A.E., Gonzalez, E. J., Kelly, D. L., & Smith, T. A.  (1997). Mathematics achievement in the primary school years: IEA's third international mathematics and science study. Chestnut Hill, MA: TIMSS International Center, Boston College.

Chinese Presentations

Abstract for 12896 
以知覺理論為基礎的數學數位教材設計原則 
Authors: Po-chi Su, Ming Jang Chen 
Affiliations: Gung-Guan Junior High School, National Chiao-Tung University 
Keywords: 
 
數學課堂裡，教師將數學概念具象化為文字、圖像及口語等形式的訊息，透過各式的媒體傳達給學生。就學生的知覺歷程而言，上述訊息透過生理神經之感覺登錄為近側刺激；經由知覺組織形成知覺表象，再經辨識及操作形成其所理解的內部表徵。在此過程中，形成的知覺表象是否易於後續的辨識與操作是影響學習成效的關鍵之一，亦是教材設計上必須重視的課題。數學教材的設計，經常需要在單一畫面上將訊息切割重組，有組織、有彈性、有步驟的逐一呈現或互動呈現；使用教材時，亦須兼顧全班學生的差異性及進度的同步性。就上述課堂情境的觀察，以知覺理論為基礎，歸納數位教材設計的四面向原則：1. 在學生專注於理解訊息前，影響學生對訊息之初步理解的相關原則歸納為「基本安排面向」；2. 學生透過教材來觀察、學習時，就畫面上物件的變動與否，將教材呈現區分為「動態觀察面向」與「靜態觀察面向」；3. 課堂中師、生與教材三者間的互動，歸納為「師生互動面向」。初步觀察發現，妥善運用這些原則，可以降低雜訊之干擾，提升教材的品質，有效進行課程。  

Abstract for 12904 
數學數位教材設計之視覺原則 
Authors: ChinFu Lee ; Ming Jang Chen
Affiliations: FuHo junior high school; National Chiao-Tung University 
Keywords: 
 
電腦的即時運算及立即回饋功能，給了數學教學上一種新的面貌，電腦也成為學習上一種新的利器。但是在強大的工具之下若無正確地掌握訊息的傳遞，一味地追求電腦所可產生的效果，只是將原本不易學習的內容變得更加地複雜。因此在從事電腦輔助教學之前，必需先要了解訊息的傳遞技巧，才不會將電腦所提供的功能作誤用。視覺設計領域已存在著一套可以掌握訊息傳播的方式，我們可以藉用視覺設計的理論，結合數學學習時資訊呈現的特性，發展出適合數學數位教材設計的視覺原則。
以視覺設計的眼光看待教材設計，大致上有下列幾個原則可遵守：(1)畫面構圖：有圖形與文字各成一區塊的兩欄式構圖，和圖形與文字結合的整合式構圖，這兩種構圖方式各有其適用的時機。(2)配色原則：以色相環作為選色的依據，處理畫面上物件的差異性或相同性。(3)造形元素：改變點、線的樣式，但也不能改變點、線給予觀察者的感覺；文字則是以適合閱讀為原則，避免擾亂觀察者的閱讀動線。(4)視覺引導策略：利用幾個方式抓住觀察者的目光，游標、標籤、線條、圖地原理、開關。(5)動態呈現策略：動畫的使用必須遵守下列幾個原則，與視覺同步、一次一個、隨機使用。
以上的原則提供作為設計數學教材時的參考，讓教材設計者在發揮電腦功能的同時，也能掌握觀察者的視線。如此在課堂授課時，數位教材成為師生互動的良好媒介，將原本複雜不易理解的內容變得淺顯易懂。相信這也是設計教材的當初所欲達到的目的。

Abstract for 12906 
A Study of Using Mathematics Software, DERIVE, to Teach Polynomials in High School 
Authors: Tsai-Hung Lee 
Affiliations: High School 
Keywords: 
 
本研究的目的在使用數學軟體DERIVE應用於高中「多項函數的圖形」和「多項方程式」單元主題的教學，主要採行動研究的方式以了解高中學生對此試探性教學活動的看法與回饋，探究數學軟體DERIVE應用於高中數學教學之可行性。本研究以台北縣某完全中學8名高中一年級普通班學生為研究對象，依多項式之學習成就測驗前測的結果，將研究對象分為四組。前測階段8人同時進行二次共計110分鐘的電腦軟體教學課程，之後分組分次進行7小時的DERIVE教學活動，逐次地修正與調整教學活動，使教學模式能較佳化，在未來可作為大班教學的參考。藉由課堂觀察、學生電腦操作觀察、學習單、學生問卷、學生學習成就測驗以及訪談等資料之蒐集整理，來進行研究結果之分析。
研究結果發現在合適的學習單循序漸進引導下，DERIVE免除學生作單調繁雜的計算，讓學生有更多的時間去作數學思考；當抽象的數學變成可具體操作時，學生心中的解題策略在DERIVE的輔助下得以延續；DERIVE有別於傳統教室教學的呈現，除了給學生新鮮感，亦激發學生學習數學的興趣。以DERIVE來輔助教學的模式，學生反應可以適應、接受，並不會因此而分心，並依學生學習成就之前後測的整體結果及學生給予的回饋，研究者相信數學軟體DERIVE應用於輔助高中學生學習多項式是具可行性的。惟教師以DERIVE輔助教學時，對於教學環境的限制、軟體可能帶來的迷思概念等，應有相對的應變與調適。
最後根據研究結果與發現，提出若干建議以作為教師改進與未來研究之參考。

Abstract for 12914 
A Study of Using Mathematic Software, DERIVE, to Teach Inequality in a Vocational School 
Authors: Yu-Ling Chen 
Affiliations: High School 
Keywords: 
 
本研究主要是使用數學軟體DERIVE設計高職一年級學生學習不等式單元的數學科學習素材，並分析教師使用數學軟體DERIVE來進行不等式單元的教學活動後對學生學習的影響。本研究採單一組前後測準實驗設計，以新竹市某私立高職附設職業類科一年級學生86人為研究樣本。為檢驗學生在不同環境下的評量結果，將學生依前測分數進行S型分成A、B二組，其中A組學生在電腦教室進行後測，B組學生在一般教室進行後測。
本研究結果及發現如下：
1. 不論在電腦教室或一般教室進行評量，學生在接受DERIVE所設計的學習活動後，其後測成績均顯著高於前測成績。
2. 經逐題分析A、B兩組學生在後測的解題表現，顯示在電腦教室進行後測的學生已能嘗試使用DERIVE作為求解不等式的工具，因此在求解不等式的問題比在一般教室進行評量的學生表現較好，但對於圖形及不等式的解之間的聯結仍有不足，故兩組學生在此部分的解題表現並無顯著差異。
最後根據研究結果和發現，提出若干建議以做為教師教學改進與未來研究之參考。

Abstract for 12931 
Examples of Designing High School Mathematics Teaching Elements through the Use of Adaptive Software EXCEL 
Authors: Cheng-Feng Li 
Affiliations: high school 
Keywords: 
 
高中數學教材內容包括代數、三角、幾何、組合數學、機率統計、微積分等範圍。目前常用於製作高中數學教學元件的軟體有GSP、Cabri、Cabri 3D、Excel 、VBA、Maple、Mathematica、Visual Basic、MPS(Dynamic Math PowerPoint)、Flash、Java等類別。每一種軟體都有它獨特的功能與優勢，如果能夠將一個教材單元的內涵，根據它的特性，用最經濟、方便、有效、合適的軟體（單元適性化軟體）設計教學元件，以配合數學素材教學內容的呈現，將可達成最好的教學效果。
　　這個工作坊我將以Excel作為設計數學學習素材的工具，分享其應用實例。Excel具有計算、函數繪圖、處理演算法及遞迴關係等特性，而Excel VBA具有計算控制的功能。由這個工具可以發展的教學元件範例有：區隔式輾轉相除法、二元一次、三元一次整係數不定方程式的整數解、勘根定理高斯消去法、常態分配、信賴區間。期許未來教師能利用單元適性化軟體的優勢，呈現素材特點，希望本工作坊能帶動數學教師投入教學元件製作的興趣，並進一步提升數學教學效果。

Abstract for 12958 
題目：在電腦套裝軟環境下經營數學探究之研究
Authors: Cheng-Hua Tsai
Affiliations: National Taichung First Senior High School
    數學輔助軟體所具備的數學溝通與計算、動態呈現及操作-模擬-實驗等特性，為學生提供一個具有創新溝通及假設猜想的學習環境，是十分有利於學生的自主發現和樂於探索。因此，我們提出一個應用軟體輔助數學探索的模式--「提出問題─探究活動─成果交流」，作為一種體驗學習，亦是一種快樂學習，更是一種研究學習的基準。這樣的模式是以問題為主軸，透過數學軟體的輔助特性，藉以貫穿整個探索過程，並可作為指導學生進行數學探究或進行専題式教學的一個參考依據，讓學生在數學問題的探索過程中，不會被動地記憶或理解體會老師所講解的知識，而能敏銳地發現問題，主動地提出問題，積極地尋找解決問題的方法並能探知結果。