Automated online homework vs traditional paper and pencil

Automated online homework is an increasing trend in college mathematics courses over traditional paper and pencil. One university’s college algebra(pre-calculus) courses have moved the majority of homework assignments into the online environment, allowing for immediate feedback. We examined the degree to which online homework, specifically for algebra courses, affects perceptions of learning and motivation to learn. Online homework is an increasing trend in college mathematics courses over traditional paper and pencil. One such instance of this is at a large University of Qatar, where the college algebra courses have moved to comprising almost all homework as online assignments. Studies have been conducted on the use of online homework in physics courses (Bonham, Beichner, & Deardorff, 2001) and chemistry courses (Cole & Todd, 2003), but parallel research was not found in the field of mathematics. The aforementioned studies investigate exam scores and difference in online versus traditional methods of completing homework. Due to the considerable use of online homework in courses such as the college algebra course, it is necessary to investigate its effectiveness in a mathematics class. Furthermore, the investigation needs to go beyond test scores and examine its effects on student learning and motivation to learn mathematics. We examined the degree to which online homework, specifically for algebra courses, affects perceptions of learning and motivation to learn for this group of college students. The investigation, surveys involved all of the college algebra students enrolled in the course for one semester (n ~ 180). The Motivated Strategies for Learning Questionnaire (MSLQ) using both Likert-scale and open-ended response items Bonham, S., Beichner, R., & Deardorff, D. (2001). Online homework: Does it make a difference? The Physics Teacher. 39, 293-296. Cole, R. S., &Todd, J. B. (2003). Effects of web-based multimedia homework with immediate rich feedback on student learning in general chemistry. Journal of Chemical Education, 80, 1338-1343. Pintrich, P. R., Smith, D. A., Garcia, T., & McKeachie, W. J. (1991). A manual for the use of the Motivated Strategies for Learning Questionnaire (MSLQ) (Tech. Rep. No. 91-B-004). Ann Arbor, MI: University of Michigan. Lamberg, T., & Wiest, L. R. (Eds.). (2007). Proceedings of the 29 th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Stateline (Lake Tahoe), NV: University of Nevada, Reno

An investigation of geometry skills learning by dynamic geometry software

The aim of this paper reviews how to upgrade skills using geometry with dynamic geometry software (GeoGebra). And compare them with training and classes is common. Geometric skills, including skills in 5 categories logical, visual, verbal, constraction and applied. Researcher in this context, study their choice of a test group and control group. each consisting of 28 male students style sampling of available statistical community schools education students, boys with good computer facilities, during a school year has done. To control the progress of students learning skills, at the beginning of the school year, pre and post-test was held at the end. The data was analyzed by multiple Analizes of covariance Test (MANCOVA) for the research hypothesis. The results of MANCOVA test with 99 percent confidence the main research hypothesis based on geometric skills to be effective with the help of dynamic geometry software than the conventional lecture classes confirmed. In order to explain phenomena in the process of training and complete the correct conclusion, the qualitative findings were used. Researcher documenting observations, analysis of films recorded computer classes, analysis of survey and interview some students as case study, qualitative data will provide. Once the data documentation, categorization, and interpretation of significance, were analyzed. Results of research confirmed the original hypothesis.

Prospective Mathematics Teachers'' Technology-Based Presentations on Proportional Reasoning

This study investigated future teachers’ use of technology in teaching proportional reasoning lessons in a senior-level college seminar. Seminar participants were preparing to teach mathematics at an elementary, middle, or secondary school, and the technology-based 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 pre-service teachers used a common technology as well as a variety of particular technologies in presenting their lessons.

Promoting Mathematics and Technology in Social Media

Social media (e.g. Facebook®, blogger, youtube etc.) have become popular among students. The author has explored ways to use these common tools to connect with students and provide online learning resources. The idea of using these tools for teaching and learning was conceived to overcome some restrictions and limitations such as time allocation, institution policies and procedures. The author will share his experience of promoting mathematics and technology in facebook, blog, youtube, and of integrating the social media tools with existing course materials and curriculum. In particular, the author will show case his Youtube channel where the channel has attracted many views on technology (Casio ES series, Graphing calculators, ClassPad, Mathtype, Microsoft Equation Editor,MATLAB, SciLab etc).

SAMAP Mathematics Manipulatives

It is a well-known fact that mathematical manipulatives help students to concretize and exemplify the relationships between different abstract mathematical concepts. Hence, there is a great demand for online mathematical resources that provide interactive environments where users could investigate the properties of the concepts and reflect on them especially at primary and secondary schools. There are many such resources on Internet. We have also developed a comprehensive set of virtual mathematical manipulatives on the five strands of mathematics education at primary and secondary school levels and created a mathematics portal, called SAMAP, for the provision of interactive mathematics resources in a three-year national project sponsored by Turkish Science Foundation. In this paper, we will introduce a sample of the virtual mathematical manipulatives we have developed in our project. The implications of the usage of these virtual manipulatives in mathematics classrooms will also be discussed. SAMAP manipulatives are being currently used by thousands of pupils and teachers in mathematics lessons in Turkey. Preliminary findings about the effects of SAMAP manipulatives on Turkish primary and secondary school students’ mathematical skills and their perceptions of mathematics will also be discussed.

THE ROLE OF ICT IN MATHEMATICAL MODELLING: INITIAL PERSPECTIVES FROM SINGAPORE

Part 1: Mathematical Modelling and Curriculum Focuses by Lee Ngan Hoe (nganhoe.lee@nie.edu.sg)
Mathematical modelling is one of the current focuses of the mathematical curriculum in Singapore. This presentation will discuss the role of mathematical modelling with respect to other curriculum focuses, highlighting the role of ICT in the teaching and learning of mathematics. Particular references will be made to how ICT can further accentuate the potentials of modelling tasks. Suggestions of the incorporation of ICT and mathematical modelling in the day-to-day lesson planning of primary and secondary levels will be proposed. Task Design and ICT Use for Mathematical Modelling Ng Kit Ee Dawn (dawn.ng@nie.edu.sg)
Part 2: Task Design and ICT Use for Mathematical Modelling Ng Kit Ee Dawn (dawn.ng@nie.edu.sg)
The potentials of mathematical modelling tasks in teaching and learning come largely from the contexts in which the tasks are situated. The contexts provide rich stimuli for engaging students on two fronts. Firstly, the contexts invite multiple interpretations of the modelling tasks, hence drawing upon the varied repertoire of students’ prior knowledge of mathematical concepts and skills. Secondly, the interdisciplinary real-world challenges presented in the contexts of the modelling tasks lead students towards further mathematical discoveries as they progress through the tasks. As such, the integrated and purposeful use of ICT within the context of the modelling task is important. This presentation will discuss elements of task design and the incorporation of ICT for mathematical modelling.
Part 3: Paper Plane Task: Initial Experiences with Mathematical Modelling
Soon Wan Mei Amanda (wanmei.soon@nie.edu.sg), Chiok Hwee Fen (fenz_07@hotmail.com)
This presentation centres on the initial experiences of five groups of Year 8 (aged 13-14) students on a mathematical modelling task completed during a Mathematical Modelling Outreach event held recently in Singapore. Students worked in groups of three, either in within-school or between-schools grouping on a “paper plane task” over two days. They were tasked to design the “best” paper plane, given the historical contributions of paper planes in the aviation industry. Various approaches to the task were discovered. Of particular focus is the use of the TI-NSpire graphing calculator in investigating the relationship between variables and the mathematical decision making based on the results of the experimentations.

Integrating Computer Algebra Systems into Post-Secondary Mathematics Education

In the framework of an ongoing international research study that aims at analyzing the use of Computer Algebra Systems (CAS) in post-secondary mathematics instruction, we conducted a literature review pilot study (326 papers). The pilot study mainly aimed at informing and refining our theoretical framework, adapted from Lagrange et al. (2003)''s framework for literature reviews on technology use in (schools and universities) mathematics education and this will inform a more comprehensive literature review of 1,500 papers. The literature review will complement our study that also comprises a nation-wide, on-line survey of Canadian mathematics professors about their teaching practices in comparison with results of a similar international study (UK, USA, Hungary), and case studies of two universities (one in Canada; one in the UK) in which a mathematics department has sustained technology-related instructional change over time. In our talk, we will discuss the results of the literature review pilot study. Several themes have emerged from the review, which will be discussed in detail in our presentation: the diverse uses of CAS, the benefits to student learning, issues of integration into mathematics learning, common and innovative uses of CAS, and the scope of CAS integration into university curricula. Our analysis suggests that, perhaps contrary to popular belief, CAS integration in tertiary mathematics teaching occurs frequently in courses for mathematics majors and not only and mainly in-service courses designed for non-mathematics majors.

Impact of Contextual Lab Activity in Learning Engineering Statistics

With the introduction of computer in schools and higher learning institutions, students were exposed to use computer when learning certain subjects, including mathematics. In UTHM, lab activity is also used in the teaching and learning engineering statistics. Thus this research was done to test whether the use of statistics lab is effective in learning engineering statistics for the engineering students in UTHM. The population consisted of two groups: electrical engineering degree students using contextual lab activity and mechanical engineering degree students using non-contextual lab activity. A sample of 15 students from each group was selected: 5 weak students, 5 moderate students and 5 good students. Data were collected using an interview with semi-structured questions. The data were analyzed using NVivo Version 8. The findings showed that students in the contextual video lab activity understand statistics better than the other group. Students using the non-contextual lab activity do not help them with the lesson In conclusion; the contextual lab activity is able to help the engineering statistics students in their learning process. 

Development of a interactive multimedia courseware in learning mathematics subject for form two Loci in Two Dimension

This paper describes the development of an interactive multimedia courseware in learning mathematics. The focus of the courseware is Loci in Two Dimension since most of the students have difficulties in understanding this topic. The Pedagogical Agents, Games Based Learning and Blended Learning elements are embedded into the courseware. This would provide an exciting, meaningful learning and at the same time assist them in learning the topic. ADDIE Methodology together with Macromedia Flash 8 and Adobe Photoshop has been employed in the development of the games. A heuristic evaluation was conducted and the positive results have been obtained

FUN WITH GRAPHING CALCULATORS

With the advancement of ICT, handheld technologies such as graphing calculators are used in the classroom to enhance the understanding of concepts and mastering of skills in Mathematics and its applications in solving daily life problems. A series of interesting problem based activities on different topics in Mathematics and Additional Mathematics in Malaysian curriculum such as Graph Functions, Probability, Linear Programming, The Earth as a Sphere, Matrices, Linear Law, Progressions etc. are introduced. Students are engaged in solving challenging daily life problems using graphing calculators. The activities are designed to incorporate the Five Learning Principles (problem solving, mathematical communication, reasoning, making connection, and use of technology), emphasizing the Four Guiding Principles (fun, meaningful, challenging and useful), applying the Seven Interactive Teaching and Learning Approaches (directing, demonstrating, explaining and illustrating, questioning, consolidating, evaluating and summarizing).

Where are we heading after 12 years?

Information Communication Technology (ICT) is one of the main components that has been identified as a key foundation to drive Malaysia to become a fully developed country by the year 2020. Under the Eighth Malaysian Plan in year 1998, the Malaysian government announced to re structure and blend education system with ICT. After 12 years of planning and implementing, a constant study to measure the students’ usage and perception of learning with ICT should be conducted. This could record the progress and to understand the variables that are needed to boost up the students’ self exploration and engagement on learning using ICT.
This paper discusses the usage of ICT and the reasons that could be a catalyst variable to promote ICT in the education sector, particularly in Mathematics classes. The discussions are based on the findings from a survey of 330 Foundation Studies students at a private university in Malaysia. The objective of the study is to assess students’ perception towards learning Probability and Statistics subject using ICT; particularly the computer technology resources and the mobile learning approach. The findings indicated that the exposure of technology in Mathematics education is still low either formally in classrooms or informally outside classrooms. One of the main reasons is because of insufficient promotion of technology to be incorporated in their learning. This could also correlate with the students’ opinion on mobile learning where many of them are unsure whether to embark on mobile based learning or otherwise.

The Past Today and Future of the Tntegration of Mathematics Assessment with the technology in China

In China more and more teachers and students have considered it is very important to make the integration of mathematics teaching, learning and assessment with modern information technology. Almost every teachers and students feel the permeability of modern information technology will make the mathematics learning become more significant and more interesting. In the past, although modern information technology has been developed highly, the paper and the pencil always still are the main tools in Chinese students¡¯ mathematics learning and assessment. The uses of any form of information technology are prohibited. The problems on the daily life in the assessment are generally idealized with some special data. Today there are two exact opposite views and practices in China. The first is that information technology is an effective tool for mathematics learning and assessment, and adhere to integrate mathematics learning with information technology, insisted that information technology shch as the calculators can be used in the mathematics examination by students. For example, in Shanghai the students can use the calculators in their learning from 1999 and solving mathematics problems in the entrance examination of university from 2000. At the same time in some other place, the students can apply the calculators in their entrance examination of high school; The second is that information technology will greatly weaken the students¡¯ operating and thinking ability, in present we should strengthen training of students on these capabilities, should strictly prohibit the use of any information technology to solve mathematical problems. These two views and practices, may coexist for a long period of time. In future we are convinced that with the development of society, information technology, and the mathematics curriculum, the scientific calculator, graphic calculators and computers, etc. will become powerful tools for students to solve mathematical problems in their learning and assessment. By the aid of information technology the students can use the deduction and reasoning methods to build and solve the mathematical model with actual data. We can use modern information technology to describe the graph of mathematics problems, to demonstrate their mathematical beauty and mathematical properties. The spring of integration of mathematics learning and assessment with information technology would come as soon!

Mathematica Module Showing Dynamic Link of 3D Graphic Objects and Vector Equations

One of the reasons why some students suffered lower performance in three-dimensional linear algebra is because they had learned symbolic procedures without relating them to graphical representations. For the first time learners, we think, the link of symbolic and graphic representations has the essential importance. The Mathematica module, we demonstrate in this presentation, is one our current approaches to show the dynamic link of the two representations. It uses the new feature of computer algebra system Mathematica version 7, which connects the change of graphic objects, for example, lines and planes in 3D-space with the simultaneous change of vector equations. When a learner change a parameter in an equation with the slider on the screen, the vector equation change its form, and the related graphic object also changes the position or direction in the 3D-space on the screen. The Module uses Mathematica as the frontend program on studentsf computers and Mathematica source code stored in a remote database as gtextsh. The content of the module is dynamically downloaded from the database.

The creating of the function and the macro of Excel in high school math education in Japan

In the math education in the high school in Japan, it''s important for teachers to have the ability to create private functions and subroutines of Excel to help the understanding of a student in their class.
On the other hand, it is expected that students can create the implement that students themselves enjoy learning contents by and have skill to utilize for their studying by. Of course, to cultivate such a mind is valuable. More than 40 computers were installed in very high school in Japan, where each class consists of less than or equal to 40 students. These computers were not for the mathematics and were established for the new subject "information". Spreadsheet software "EXCEL" is installed in any computer.
I''ll show some examples about making the private function, using "EXCEL".
I think that they are interesting and useful for both of students and teachers.
Examples of private functions so-called macro
<1> The display of the graph
It defines private function "eval" to change to the graph immediately when
inputting a function-expression to the cell.
Function eval(a As String, dummy) As Double
eval=Evaluate(a)
End Function

By the way, "Evaluate" is one of functions of VBA, but it isn''t one which we can use on the sheet. If we use SpinButtons, the animation of the graph is possible, too. For example, let function typed on some cell be a*sin(b*x+_c)+d. Designate four cells to names a, b, _c, d,respectively. and do some cells to name x, too. Link four SpinButtons to cells a, b, _c, d ,respectively. If pushing the SpinButton , the graph moves and changes its shape.

<2> To animate the process of graph''s drawing, you can type expressions to cells, too.

<3> The way of recursive thinking appears in a lot of items of math learning. Creating of macroa by this thinking is interesting work for your studenta and you.

(1) Function "r_perm" returning repeated permutation

Function r_perm(n, k, ans)
If k = 0 Then r_perm = ans & " ": Exit Function
For i = 1 To n
r_perm = r_perm & r_perm(n, k - 1, ans & i)
Next i
End Function

Type =r_perm(3,2,"") on some cell, 11 12 13 21 22 23 31 32 33 appears on the cell. And modify function r_perm as follows.

Function r_perm4(n, k)
If k = 0 Then r_perm4 = 1: Exit Function
For i = 1 To n
r_perm4 = r_perm4 + r_perm4(n, k - 1)
Next i
End Function

Input =r_perm4(3,2), then it returns 8.

(2) Creation of the function returning all of the ways of selecting different k items among n number of items ,for example {1,2,3,.,n},and arranging them in one line.

Function perm(Lst As String, k As Single, ans As String)
If k = 0 Then perm = ans & " ": Exit Function
For i = 1 To Len(Lst)
perm = perm & perm(Mid(Lst, 1, i - 1) & Mid(Lst, i + 1, Len(Lst) - i), k -1,
ans & Mid(Lst, i, 1))
Next i
End Function

It''s easy to modify above macro returning the value nPk.

<4> Hanoi''s Tower
Hanoi''s tower is famous problem of the way to move n rings having different sizes on the first stand to third stand, following some rule to move each ring. It defines as follows the function hanoi(n,a,b,c) which returns a way of moving n rings on stand a to stand c, using stand b properly. Of course you must follow moving rule.

Function hanoi(n As Single, a As String, b As String, c As String) As String
If n = 1 Then hanoi = a & ">" & c: Exit Function
hanoi = hanoi(n - 1, a, c, b) & "," & a & ">" & c & "," & hanoi(n - 1, b, a, c)
End Function

Type =hanoi(3,"A","B","C") on cell, then it returns
A>B, A>C, B>C, A>B, C>A, C>B, A>B, A>C, B>C, B>A, C>A, B>C, A>B,
A>C, B>C.

There are many examples of permutation and combination related to examples <3>,<4> in math items

<5> Private functions which does high-precision computation, too, can be easily created using the way of recursive thinking.

<6> The example to verify the teaching materials which are in the book of the native mathematics of Japan (wasan)

<7> Creation of the macro which discovers the formula which computes the ratio of the circumference of a circle to its diameter "pi" using the computation of the complex number. I show some formulas found by easy macro. Of course it''s possible to find infinite number of formulas about pi/4.
1 * atan(1/2) + 1 * atan(1/3)
2 * atan(1/2) + -1 * atan(1/7)
1 * atan(1/2) + -1 * atan(1/3) + 2 * atan(1/4) + 2 * atan(1/13)
1 * atan(1/2) + 1 * atan(1/4) + 1 * atan(1/13)
1 * atan(1/2) + 2 * atan(1/3) + -1 * atan(1/4) + -1 * atan(1/13)

Mathematica for the Classroom

Mathematica for the Classroom is a product from Wolfram Research specifically designated for the teaching of undergraduate mathematics with Computer Algebra System. The lecture will show how teachers can use Mathematica for the Classroom effectively in teaching mathematics, preparing homework and teaching materials, and developing interactive notebooks that can be used both with Mathematica as well as with Mathematica reader. The lecture will show many important features of Mathematica for the Classroom as well as some new developments from Wolfram Research that support mathematics education. The lecture will be followed by a workshop sessions for teachers of mathematics.

Study on Instruction of Trochoid through Two Kinds of Representing Activity Using GeoGebra

Representing various situations we meet in everyday life in a mathematical way and providing opportunity for students to consider mathematics as a living knowledge are recommended strongly in the current mathematics education. In this study, students will represent kinetic phenomena of a bicycle wheel in everyday life algebraically and geometrically using Geogebra. It is expected that this will help them understand that mathematics is not just a list of concepts but something that has been developed with a significant meaning. This study will investigate following research questions: (1) What is the characteristics of thinking process when students represent various kinetic phenomena of a bicycle wheel in everyday life algebraically and geometrically using Geogebra? (2) What is the role of teachers in the process? This study uses Qualitative Case Study as its purpose is to observe and analyze interaction between students and between students and teacher.

Technology Makes Mathematics More Fun Accessible; Challenging; and Theoretical

How technology effect mathematics learning? The fact we all know is that technology makes mathematics more fun and accessible. In fact, technology can also make mathematics more challenging and make students to be more theoretical. In this presentation, by exploring and discovering some of our familiar life scenes or mathematics problems with the dynamitic geometry system SSP, we can get plenty of beautiful, excited but unfamiliar and not-too-easy mathematical results for students, which may simulate them more enthusiasm on mathematics leaning and problem solving, and promote them more desire on mathematical reasoning and deduction. With these examples the audiences will know the FACT of using technology in mathematics learning. Technology can make mathematics more Fun. Technology can make mathematics more Accessible; Technology can make mathematics more Changeling; and Technology can make mathematics more Theoretical.

DESIGN DEVELOPMENT AND EVALUATION OF AN INTERACTIVE MULTIMEDIA COURSEWARE IN ANALYTIC GEOMETRY

Schools are complex organizations, and as agents of changes, they have always been subjects of efforts for reforms. Bringing about these changes will never be easy but important changes, however, begin in the most critical location of change, the classrooms. This study will serve as an introduction to these changes at the Mapua Institute of Technology (MIT) and as guide for administrators and educators in the rapidly expanding world of educational telecommunications. This study included the design, development, evaluation, copyright registration and deployment in the Internet of an interactive multimedia courseware in Analytic Geometry as an aid to instruction. The first phase of the study (design and development of the courseware) went through the Software Development Cycle with the five steps, Defining the Content and Scope, Mapping Out the courseware Program Logic, Coding the Program, Testing the Program, and Documentation. This process was based on the Eclectic Model which was developed after reviewing developmental models presented by Boehm (1976), Jensen (1979), Heinich (1985), Asgresti (1986), Stanley (1988), Carey (1986) and Heinich (1977). Through the test item analysis performed on the departmental final examinations in Analytic Geometry at MIT, the researcher identified Circle and Parabola as relevant topics for study. Resource materials relevant to the subject matter, instructional development and instructional delivery system were reviewed. Subject matter experts, computer experts and students were consulted informally to find out how the courseware could be best developed. The researcher prepared the input-process-output specifications in designing the courseware program logic using flowcharts, pseudocodes, and storyboards. Since the courseware was intended as a supplement to classroom teaching, the materials were so designed as to follow the normal classroom teaching sequence. Authorware Version 4.0, a leading authoring tool for interactive web-based and multimedia-learning solutions, was used for coding the courseware program. A review of the courseware program was initially done to find out if it does what is supposed to do. In the final step, the researcher documented the procedures, logic tool and testing results. It included permanent record of what the courseware does, instructions for users (students), instructions for computer operators (teachers) and detailed documentation for programmers for possible modification of the program. This phase led to the initial version of the courseware, “Circle and Parabola@Net”, which was made available in CD-ROM for easy access to evaluators and as a preparation for its deployment in the Internet. In the second phase of the study (evaluation of the courseware) the completed courseware was presented to a group of MIT mathematics teachers and computer experts for final review and evaluation. Based on the comments and suggestions, modifications were made before the students in the experimental groups were exposed to the final form of the courseware, who later were asked to evaluate the courseware. The qualitative evaluation of the teachers (5), computer experts (5), and students (20) using a likert scale questionnaire revealed that the courseware was an effective aid to instruction. Worth mentioning is the unanimous decision that the students would recommend the courseware to their friends. A follow-up interview with students was conducted to affirm or negate some results of the evaluation. When asked about the contributing factors to courseware’s clarity of presentation, the respondents stated that the following were very good aspects: vocabulary and language used, figures and illustrations, organization of lessons, sequencing of lessons and sample problems and exercises. The respondents likewise considered the courseware as effective teaching aids because they are interactive. The feedback mechanism gave them immediate reteaching and relearning of lessons which were vague. They also found the lessons less threatening because they were self-paced. For quantitative evaluation, the Solomon four-group design was used. This involved 160 students randomly assigned to four groups (40 students per group), with two of the groups being pretested. One of the pretested groups and one of the unpretested groups were exposed to the experimental treatment. All groups were given the posttest which was used initially for the pretest. The results of the pretest and the posttest were analyzed using t-test for dependent samples, one-way analysis of covariance (ANCOVA) and two-way analysis of variance (ANOVA). Based on the findings, the following conclusions were drawn within the limitation and scope defined in the study. 1. The interactive multimedia courseware is an effective learning aid and it reflects the characteristics of an effective computer-aided material. 2. It was evident that learning took place after students were exposed to either the courseware or the lecture-discussion method. However, more learning took place with the use of the courseware. 3. Classifying the students based on testing (pretested and unpretested) is not needed to achieve better results. 4. Teaching method (the use of courseware and the lecture-discussion method) and testing (pretested and unprtetested) taken together can not be expected to have any significant effect on the student’s achievement. Combining them for improved students’ performance is not necessary. For the last phase of the study, the researcher applied for copyright protection of the courseware at the Philippine Copyright Office (PCO). He submitted an accomplished application form for copyright and two copies of the courseware in CD-ROM. As a trend-setter in Philippine researches and keeping with the new trends in education, the completed research materials finally found its way into the Internet for global consumption through the researchers homepage with Uniform Resource Locator (URL) at http://members.aol.com/dlsilva1/index. Based on the findings and conclusions of the study, administrators as planners, need to have critical analysis and evaluation of the courseware being considered for development or adoption, prepare an ongoing follow-up and assessment of the courseware in use to ensure its relevance and effectivity and to prepare the faculty for the curriculum change through faculty development sessions on computer-assisted instructions.

Enhancing Not Replacing; Teaching with CAS

As technology has evolved, teachers have struggled with its appropriate use and effect on teaching. This session will examine issues involving scientific, graphing, and CAS calculators, including topics still important to teach, those enhanced by technology, and those requiring less attention. Specific examples and teaching strategies will be discussed.

No! REALLY Match My Graph!

Most mathematics teachers in the US have used or at least seen the classroom activity in which a distance sensor is used to collect data as a student moves in front of the sensor. In these activities, the students are supposed to move to produce a graph that “matches” one that the teacher gives them. These sorts of activities give students physical experiences of linear functions, and can be extended to other non-linear functions. In this session, we extend this activity to other sensors (microphone, gas pressure, and others). We will also discuss the development of “habits of mind” for linear, exponential, and sinusoidal functions.

Safe and Simple Calculus Activities

This session will focus on a few easy-to-implement technology-enabled activities for a first year Calculus course. Specific topics will include the derivative at a point, the derivative as a function, the idea of the integral, and the Fundamental Theorem of Calculus. Once students are engaged with a particular mathematical scenario, questions become the critical component. A discussion of what makes good questions, and not-so-good questions, will accompany the activities.

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The Effect of Using The Geometer’s Sketchpad (GSP) on Iranian Students’ Understanding Geometrical Concepts

Technology has become a part of most of our activities in the everyday life. It entered to the educational field as well as the other fields. The use of technology in schools is growing in both technological equipments like computers and the structure for them, besides the training programs for the teachers and other users. The new technological tools, such as computers and their software, provide people with more opportunities to teach in new ways. This environment of using technology is growing in the general reform in mathematics education.
The purpose of this study was to investigate the effect of using the Geometer’s Sketchpad (GSP) on students’ understanding of some of the geometrical concepts. The sample consisted of 100 students from the Model School, Iran.
The students in the experimental group used the GSP software once a week and the book, while the students in the control group used only the book. Both groups took the same pretest and posttest, which was designed by the researcher.
The results of the study indicated that there was a significant difference between the means of the students scores on the posttest with favor to the experimental group. The results also indicated that there were more gain in the scores from the pretest to the posttest in the case of the experimental group. The researcher suggested more use of the GSP or Gabri softwares and more investigations in the area of using computers in education.

LESSON STUDY IN A MATHEMATICS CLASSROOM USING GRAPHING CALCULATORS

A team of Mathematics teachers in this school had implemented Lesson Study in order to improve their teaching and boast their students'' achievements in Mathematics by using graphing calculators. This study involved seven Mathematics teachers working together on a goal and developed lesson plans that were being observed, analyzed, and revised. Throughout this process, the focus is on improving students’ thinking, thus making their learning process more effective. Lesson Study is an ongoing, collaborative, and professional development process that was developed in Japan. The collaborative nature of Lesson Study helps strengthen relationships among teachers and improves teaching. The research focus of this Lesson Study helps to professionalize teaching. The greatest reward of this study is the benefit that students gain by improving their Mathematics performances and thinking using the graphing calculators to shade the area represented by the inequalities.

Using the Geometer's Sketchpad to Motivate Students in Learning Mathematics

Lack of student interest in learning mathematics has a long history, and is well documented. A majority of students experience mathematics as a dry and rigid field that is only about right or wrong answers. Teachers’ instructional practices should be carefully planned so as to challenge students’ perceptions. Teachers need to become aware of multiple instructional tools useful for teaching mathematics along with ways to motivate and engage students in learning. Selecting and using suitable curricular materials and using technology as an instructional tool are critical considerations. However, these are not sufficient to overcome the challenge of lack of student interest. Teachers also need to learn how to design environments and contexts that address the affective needs of the students. GSP is helpful to teachers as they develop pedagogical skills in this area. For instance, the transformations available in GSP and its animation feature, as well as the ease of using buttons make the software a wonderful tool to design and implement various projects that present engaging environments for learning mathematics. Observing and learning how to construct various designs and projects will enhance your ability to motivate your future students. This presentation introduces a set of such designs and projects created by students who have taken advantage of the motivational and recreational aspects of GSP.

Creative Applications of Excel for Calculus

The spreadsheet has proven to be an excellent tool for mathematics and its applications, especially for implementing algorithms, creating graphical visualizations, and designing mathematical models. In this paper we extend these applications to illustrate how Microsoft Excel can be used creatively in the study of calculus. We present examples to implement computational algorithms (Newton and Euler’s methods, Taylor series), to motivate definitions (limits, derivatives, integrals), and to create animated graphics for functions (real-valued, polar, parametric, and vector-valued. We create effective animated visualizations using standard Excel tools for use in teaching calculus and in developing mathematical proofs (mean value theorem, fundamental theorem of calculus). The paper discusses applications to both classroom teaching and teacher development. Our examples also demonstrate mathematical applications of such spreadsheet tools as scroll bars, data tables, recorded macros, and the solver.

Creating Multi-cultural Alphabet Books Using Excel and Mathematics

A spreadsheet is an excellent device to use for cooperative interdisciplinary work, providing a mathematical tool that is also accessible to non-mathematicians. This poster presentation illustrates an innovative way to use Microsoft Excel to integrate ideas from mathematics, linguistics, and traditional cultures through the creation of pictorial alphabet books. We display samples of pictures and text selected from newly developed alphabet books from Papua New Guinea, a nation with over 800 distinct languages. The alphabet books are the result of a joint project of staff from the Departments of Mathematics and PNG Studies at Divine Word University that produced alphabet books for the nation’s three national languages: English, Melanesian Pidgin, and Hiri Motu. Excel is used to create full-colored eye-catching images via mathematical equations (polar, parametric, and others). The materials are designed for developing language skills and reading interests of children, for preserving traditional culture, and for creating new and interesting ways to use university-level mathematics. In addition to showing printed and animated computer images along with a discussion of the project, the poster presentation will endeavor to produce on-the-spot illustrations from the languages of the conference participants.

Discovering Differentiation by Exploring the Idea of Limit and Modeling with Graphing Calculator

Idea of limit is basic and important concept in differentiation calculus. However, this idea is leased understood by students and probably by mathematics teachers too. Thus, new approach to teach the idea of limit and differentiation is rather essential for more meaningful application of limit into differentiation. Graphing calculator is able to provide such opportunity in teaching and was used in this study to explore the idea of limit and further used this approach together with modeling to discover differentiation. The experimental group had used graphing calculator TI 84-Plus in the teaching and learning of limit concept and control group used traditional approach. The post-test result showed a significant different in the achievement score in the experimental group. The study also found that students in experimental group are able to explore mathematical ideas beyond the normal boundaries.

To Use Graphing Calculator to Study the Subject: The Harm of the Increasing Individual Smoking Expenses

Smoking not only does harm to physical health, but also cost a great deal of money, which shouldn’t be ignored. Our groups that contain three members got a series of information by means of looking them up on books concerned, visiting typical character for information and then summed up and made up the data under guide of the teacher. We made use of graphing calculator functions, APLET, prediction and so on to help us study the harm and managed to find out the harm and effects smoking causes conveniently.

Using Graphing Calculators for Linear Algebra Examination

In the teaching of a first undergraduate course in Linear Algebra, the basic concepts of matrices and linear systems are covered. When students are solving linear algebra problems, it is very likely that they will need to perform tedious computation like matrix multiplication and Gaussian elimination. Most graphing calculators (GC) are capable of performing these computations. However, not all undergraduate students (in my university) are equipped with GC, and the common practice is that students are only allowed to use scientific calculators for their examinations. During a recent semester, I allowed a special group of students to use GC and restricted the rest of the students to use scientific calculators during the same examination. I studied and compared the examination results of the two groups of students. In this talk, I will present my findings.

Interactive way of finding Taylor coefficients with MuPAD

Most visualization of taylor series is to show f(x) and the taylor series of f(x) to the order of 3 to 4, and let the students to check the similarity. For example, y=exp(x) and y=1+x+x^2/2+x^3/6 on the screen. But can they really see the similarity? Don''t they simply believe in the teacher''s explanation? Surely these curves look really fit each other but it may exist even better osculate palabolas of f(x) of the same order somewhere. Thus it would be better to let THEM decide the coefficients of the series. By the animation and the magnifying glass of MuPAD, students can decide the coefficients with their own eyes.

Proof of Analytic Theorem for Zeta Function using Abel Transformation and Euler Product

In the prime number the Riemann zeta function is unquestionable and undisputable one of the most important question in mathematics whose many researchers are still trying to find the answer of some unsolved problems such as Riemann Hypothesis. In this study we proposed a new method that proves the analytic extension theorem for zeta function using Abel transformation and Euler product to understand the relation between zeta function and its properties which may help to solve some unsolved complex arithmetic problems including the Riemann Hypothesis. Euler used this formula principally as a formal identity and principally for integer values of s. Dirichlet also based his work in this field on the Euler product formula since Dirichlet was one of Riemann’s teacher and since Riemann refers to Dirichlet’s work in the first paragraph of his paper. It seems certain that Riemann’s use of the Euler formula was influenced by Dirichlet. Dirichlet, unlike Euler, used this formula with s as a real variable and, also unlike Euler he proposed rigorously that this formula is true for all real s >1. Riemann, as one of the founders of the theory of function of a complex variable, would naturally be expected to consider s as a complex variable. It is easy to show that both sides of the Euler product formula converge for complex s in the half plane Rez >1, but Riemann goes much further and shows that even though both sides of his formula diverge for other values of s, the function they define is meaningful for all values of s expect for the pole at s=1.

A Probe into MCL Teaching of Mathematics in High Schools

For the past two years, MCL (Mobile Calculator Lab) has been constantly applied in its own way to classroom teaching, and the application has proved to be greatly beneficial in optimizing teaching, making it possible to achieve some extending effects that might not be fully achieved in regular teaching. It deepens the students¡¯ understanding of mathematics, broadens their view on its application, and sharpens their creativity. In a sense, MCL has a significant influence on students¡¯ way of thinking.
Moreover, MCL has a positive impact on students¡¯ attitude to life. They have shown an amazing curiosity in their extracurricular activities and other self-motivated studies. And they keep on questioning, and feel at ease once they have found solutions they are looking for.
With our understanding of the application of the comparative information techniques and the essence of mathematics, we are directing students to think about questions such as what is the most important, and what is less important, and further to think about what is technique, what is science, and what is the relationship between them. To sum up, MCL, when applied in high school mathematics in-class education, seem to have a deep and lasting effect on student’s way of life. 

18468

Expression Method of Directed Graph For Graphical Information

We describe a simple method for constructing a directed graph to represent visual information. In this study, we propose a directed graph editor that can be used to express graphical contents with no visualization. Then, we describe a simple method to translate some graphical contents into non-graphical contents that can be accessed by visually impaired persons. We assume that there exist some properties that are expressed as relations between two information elements. Then, we can define a fuzzy measure on the unit set, and estimate the contribution of each node using Banzuf Interaction indices. 

18488

Graphical user interface for drawing 3D plot by KETpic

Yasuyuki Nakamura, Setsuo Takato
Nagoya University, Toho University

KETpic is a macro package for Computer Algebra System (CAS) to convert plot data created by CAS to LATEX picture data. We are able to draw ne pictures including 3D plots in LATEX documents with aid of KETpic. We develop a graphical user interface (GUI) for producing 3D plots by KETpic. The GUI is implemented by Maplets package of Maple. Only small amount of input and mouse operation can produce 3D plots by the use of the GUI for KETpic. It is expected that the GUI helps many potential users of KETpic begin to use KETpic.

Electricity Consumption Analysis of steel mill using regression analysis

This paper presents a regression analysis model to forecast the daily maximum demand of Malaysian steel mills. It attempts to employ the regression model with top down approach to obtain the annual steel mill electricity consumption. A bottom up approach that uses the Model for Analysis of Electric Demand _ Electric Load (MAED_EL) then converts the results from the regression analysis model into hourly load of the steel mill.

On Diffusion equation with the Pinsky phenomenon

First we prove the Pinsky phenomenon for non-spherical partial sums of $n$-fold Fourier integrals of piecewise smooth functions. Then we consider an initial-value problem for diffusion equation with a piecewise smooth initial condition in three-dimensional Euclidian space $R^3$. Due to the Pinsky phenomenon, Fourier integrals of a piecewise smooth function does not converge everywhere. Therefore this kind of initial-value problems cannot be solved by direct use of classical Fourier transform method. In order to obtain the solution numerically we make use of Riesz summation method.

An Interactive Visualization Software of a Four-Dimensional Space Based on the Relationship of Subspaces

We present an interactive visualization software of a four-dimensional space in which four-dimensional objects, which are prepared by the system or defined by users, are visualized and manipulated in a dynamic and interactive way. There are two display modes: single and multiple display modes. At the single display mode, an object in the four-dimensional space is projected to one of the four three-dimensional subspaces and one can see the three-dimensional 'shadow' of the object and furthermore, one can seamlessly move from this three-dimensional subspace to the other subspace by fixing the two common axes and changing the remaining axes. At the multiple display mode, all of the four orthogonal three-dimensional subspaces are displayed simultaneously. In both modes, objects are displayed, moved, and transformed interactively by users. Furthermore, one axis can be used as time and tempo-spatial expression, that is, a four-dimensional object which is made by moving a three-dimensional object is visualized. In the presentation, we show many examples of visualizing and manipulating three- and four-dimensional objects.

Teaching and Learning Calculus with calculator

Over the last decades, mathematics educators have recognized the need for pedagogical approaches that are clearly more student-centered. This includes the realization that traditional math instruction based almost entirely on symbolic (or formulaic, or algebraic) representation of mathematics does not serve students well. Much progress has been made towards teaching mathematics curricula employing verbal, numerical, and graphical approaches, rather than relying primarily on abstract symbol manipulation. We would like to present at this presentation a problem, named as the “Emergency medical clinic” problem, we have written to demonstrate this multi-representational approach and its experimentation in class room. We have designed the problem to be solvable by parallel graphical, numerical, or algebraic approaches, based on fundamental, important principles of calculus. It is intended to present a fairly complex, yet realistic and plausible, problem scenario that world capture the interest of typical Vietnamese calculus students who are teacher students at the last year of their 4 years of training at our university. Some remarks and observations of the experimentation have been also introduced in this presentation.

Study the Technology-based Method of Mathematics Education and Compare it with other methods at IAU

In this paper, we argue about some important and effective factors on quality of mathematics Education and Learning. Also we study some problems in math teaching about the different conditions of students in a same classroom at the Islamic Azad University (IAU). Some conditions such as age of students (adult and young students), employment (employee and non-employee students), programs of prior education and etc. In order to improving quality of teaching and learning, determining the differences of students and their points of view about the methods of math education, can be useful and efficient. This paper is one of the outputs of an academic research project at the Islamic Azad University of Toyserkan. IAU is a non-governmental and great university in Iran which has different students in the sense of age, employment and etc. In the present paper, we study the effects of the new methods of math education on improving the learning of different students. This research was designed to present standards for development in Elementary Mathematical sciences Education in Islamic Azad University of Toyserkan (IAU). In this paper we study the effective and important factors on improving quality of teaching and learning in elementary mathematics and statistics at IAU of Toyserkan. If we want to achieve the ideal goal that state good teaching leads to good learning we have to have a two way understanding between teachers and learners. Tacking information about the students conditions, backgrounds, potential, prior knowledge of students at the previous studies at high schools and determining the differences of students and their points of view about the methods of math education, can be useful and informative. IAU is a great non-governmental university with several branches (more than one hundred and fifty branches at different cities and countries) and it has various fields of study and many students with different conditions in the sense of age (adult and young students), employment (employee and non-employee students), programs of prior education and etc. For determining and modelling these factors and variables, we conducting a research project in this connection at IAU. In the research some of mathematics education methods were briefly introduced to Engineering and Nursing students then we asked the students to rank the methods from their points of view. In following by this ordinal scale question, some well known methods of math education such as classic math education, conceptual education, algorithmic education, active education and technology-based methods were contrasted. In the technology-based methods we used the Power Point, Microsoft MS Word, Acrobat Reader, mathematical and statistical software and data projector in teaching math sciences. Our research project is a survey research which was done in the 2009-2010 academic year at IAU of Toyserkan. The students of four classes were participated in the research as the sample students and a questionnaire was designed in consultation with mathematics psychology teachers. The purpose of the questionnaire was to identify students level of interest of learning math and satisfaction with each of the math teaching methods. Also in most of the items (questions) of questionnaire we measure both the score of satisfaction and importance of each item. Participants were asked to indicate the score of each item in present status and the amount of importance of each item from his/her points of view in ideal situation. The minimum score was 1 and the maximum score was 5 (Likert Scale). There are six general factors (one dependent factor and five independent factors) in the questionnaire: Quality of Education (QE), New Teaching Methods (NTM), Teaching Skills of teachers (TS), Students Participating in classroom (SP), Education Curricula of departments (EC) and Learning Assessment (LA). The Questionnaire also had an open-ended response section that was designed to elicit more information about other effective variables and factors which can be connected with QE. In the pilot survey we used 20 questionnaires and in the final survey sampling we have had 125 questionnaires which some of them have not returned or have not accomplished entirely (missing data problem). The Reliability of the questionnaires measured by Cronbach alpha which the results (0.85) improved the questionnaires reliability.

Vedic Math - An Ancient Supplement to Modern Mathematics

Vedic Math is a name given to ancient system of math which is far more systematic, coherent, and unified than the conventional system. There are sixteen jaw-dropping formulae which solve all known mathematical problems in the branches of arithmetic, algebra, geometry, and calculus. They are easy to understand, easy to apply, and easy to remember. It is a mental tool for calculation that encourages the development and innovation and complements the math curriculum conventionally taught in schools and colleges. History: - The 'Vedic Mathematics' is called so because of its origin from the Vedas. Vedas are the ancient sacred Hindu texts which are often referred to as the “inexhaustible mind of profound wisdom.” - Vedic Math is said to have originated from 'Atharva Veda“, known as the fourth Veda. - Atharva Veda' deals with branches like Engineering, Mathematics, sculpture, Medicine, and many other sciences. All of mathematics is based on sixteen Sutras or word-formulae. - These formulae describe the way the mind naturally works, and are therefore a great help in directing students to an appropriate method of problem solving. [“…& the natural development of critical thinking skills”] - Vedic Math is an introduction to an ancient civilization. It takes us back many millennia to India’s mathematical heritage. Rooted in the ancient Vedic sources which heralded the dawn of human history. - Indian mathematicians gave the world the numerals which are now in universal use. Points to Ponder: - Do our students know that in some countries, people in ancient times solved mathematical problems when there were no computers, and still made calculations easy? -How do you design activities that help every one to know each other, value their uniqueness, and to create an atmosphere of mutual respect? - Do we have activities that are not routine based. As teachers, do we allow ourselves the “time” to invest in building community? - Are my students able to think innovatively with respect to numbers? - How do we create love for numbers? - How do we make our students understand that there is so much more to be discovered with numbers? - Let’s go back thousands of years, and learn how to have fun with numbers. Why Vedic Math should be a part of the curriculum? - Students can discover their very own methods, which leads to more imaginative, interesting, and intelligent techniques. For which research is being carried out in multiple disciplines. [critical thinking skill development] - Researches are currently studying Vedic Math’s effects on children; while developing powerful applications of the Vedic Sutras in different fields, such as Geometry, Calculus, Computing, and more.

Developing a tool for teaching mathematics on the multiple-points touch environment

Developing virtual Manipulative is a new trend in designing mathematics instructional materials. Usually virtual manipulatives created on the Web were manipulated with a mouse in a computer environment. This application is not a coincidence with the traditional teaching approach. If these virtual manipulatives can be manipulated in a multiple-points touch and control screen, it is likely these manipulations on the computer interface can be similar to those of the concrete manipulatives. This development might increase the easiness of usage and presentation of virtual manipulatives. Further, this might also increase school teachers’ will to apply technology into their teaching. In thia presentation, I will discuss control signals used for teaaching matheamtics on the multiple-points touch environment. Two instructional activities with geometry virtual manipulatives will also be shared.

IT WOULD BE FUN TO LEARN MATHEMATICS BY PROGRAMMING

The purpose of this study is to apply an object-oriented educational programming language(EPL), ''Dolittle'' which has developed in Japan, to teaching and learning of mathematics. We have attempted to apply Dolittle in teach mathematics in elementary geometry with Geoboard, a secondary function using coordinates plane and trigonometric plane which had been made by the researcher. Then, we have implemented case studies with secondary school students in order to show the feasibility of programming activities with Dolittle programming. The results indicated that programming activities with Dolittle give students an opportunity to encourage them to explore the concepts of interior angle and exterior angle in learning of geometry, and it was effective in learning the concept of functions

The latest version of the TI-nspire V2.1 has enhancement to facilitate programming. This session will demonstrate how to write, edit and run some programs on the Ti-nspire.

An Analytical Finite Element Analysis Tool for Optimizing Parameters of Axial Flux Permanent Magnet Machines

This paper presents an analytical approach to calculate the magnetic field in a slotted axial flux permanent magnet machine. The analytical modeling is based on the simple nonlinear magnetic analysis for axial flux permanent magnet machine. The proposed analysis consists of an equivalent magnetic circuit with the saturable magnetic reluctance in the core. It is capable of calculating the flux distribution and torque characteristic under various operating conditions. The accuracy of the proposed analysis is verified by comparing with a finite element analysis model. This method can serve as an assistant design tool for FEA especially to expedite the design optimization process of the electrical machine. After verification of the analysis, sensitivity to design variables using the proposed model is presented. The sensitivity analysis through the proposed magnetic circuit of the AFPM machine provides an effective way for selection of design parameters which are iteratively adjusted through the multi objective optimal design in order to obtain maximum output torque and efficiency. The simulation results indicate that machine efficiency is significantly less sensitive to thickness of the back iron and more sensitive to both inner and outer diameter of the AFPM machine in comparison with the other design variable

A Linear Time Solution of the Molecular Distance Geometry Problem

We formulate the molecular distance geometry problem as a dynamical folding of a chain of atoms described by a potential based on the native inter-atomic distance matrix with a damping term. Numerical solutions applied to protein folding capture physical folding pathways and leads to solutions that scale with the number of atoms in the chain.

THE APPLICATION OF THE CREATIVE PROBLEM SOLVING LEARNING MODEL USING DYNAMIC SOFTWARE AUTOGRAPH TO ENHANCE STUDENTS’ MATHEMATICAL UNDERSTANDING

The general objective of this research was to investigate the effectiveness of the learning of mathematics through the study of Creative Problem Solving (CPS) using dynamic software Autograph. In particular the purpose of the study were (1) to explore students’ mathematical understanding by using the learning model the CPS with Autograph ; (2) to describe the effectiveness of the learning models with the CPS Autograph in teaching the volume of 3-D objects. The data was collected through 2-cycle of Classroom Action Research (CAR). The subjects were high school students of Istiqlal, Delitua, grade XII/science of Academic Year 2009/2010. Thirty one students with heterogeneous ability levels were involved in this study. The research object was the application of CPS learning model using as Autograph as a teaching tool. Each cycle spent four meetings. The instrument used were the prerequisite material tests and the posttest of students'' understanding of mathematics and a questionnaire to obtain students'' responses on CPS model using Autograph. The result of the study showed that: (1) the application of CPS learning model using Autograph can enhance students'' level of mathematical understanding , (2) the application of CPS learning model using Autograph was effectively applied by teachers in teaching the volume of 3-D objects, (3) The use of dynamic software Autograph lead to the positive response of students towards learning mathematics. From the test results it was obtained that there was significant increment on students’ mathematical understanding as indicated by the score improvement from 68.78 on the average score of the test of the first cycle to 85.66 of the average score on the second cycle. While the final average test score on mathematical understanding was 88.56. The study documented that the use of CPS with Autograph enhanced students'' mathematical understanding, student’s learning activities and teachers activity in classroom.

Effective Use of CAS in Mathematics Education

The computer-based mathematics education was studied enthusiastically in 1990’s in Japan and the effective use of Computer Algebra System (CAS) was a part of this attempt. The incorporation of CAS in mathematics education in Japan, however, has not been able to become an indispensable tool in teaching mathematics. On the other hand, we have seen that the use of Dynamic Geometry Software (DGS) in mathematics education has got many attentions and resulted in many important research results in recent years. In this talk, we shall analyze if the incorporation of DGS in addition to CAS can make positive impacts in mathematics education.

Sociological reflections of use of technology in mathematics

This study aims to evaluate the sociological reflections of the results of the use of technology in mathematics. The use of advanced technology in mathematics both facilitated the systematic understanding of mathematics and abolished the time and location restrictions. The technology accelerated the reflections of mathematics into daily life. In this article, the effects of usage of technology in mathematics will be evaluated in terms of researchers, teachers and students with respect to both the benefits and harms of usage of technology in mathematics education. Sociological evaluation of the socio-cultural identity and status of those teachers and researchers who have actively used technology in mathematics will be analyzed.

MHD PROPULSION THRUSTER via MODELING ANALYTICAL and NUMERICAL SIMULATION

In this work we introduce some new techniques for the solution of a complex case of MHD propulsion thruster problems. Here a magnetohydrodynamics (MHD) refers to the study of the motions of electrically conducting fluids dynamics and their interactions with magnetic fields. Plasmas, liquid metals, salt water and fluid motion in the earth's core are some examples. We study different approaches and investigate such problems proposing utmost promising methods, technique and approaches. We present a construction of a new MHD plasma convection and magnetoconvection force theory. Different theoretical and computational aspects are presented. We mainly proposed the auxiliary variational inequality as well as the projection method as a replacement of asymptotic analysis for the solution of some complicated MHD as well as MHD turbulence and thruster problems. We also suggest some variational formulation extension for a similar class of mathematical and engineering problems.

Title Teaching of Mathematics and Fundamental Engineering subjects using Scilab

Today, mathematics and engineering software play a major role in moving from classrooms to research laboratories. A number of proprietary softwares are developed for this purpose; however, most of them costs a lot of money for government and private sectors in acquiring the software.
SCILAB is one of the fastest growing open source numerical computation software in the world. By adopting the software in universities/polytechnic/school levels, it could save millions of dollar yearly. It would also building up a knowledge community to provide solutions and services base on their knowledge on the software. SCILAB is used as a tool for teaching and learning mathematics. Students can work independently and responsibly while learning mathematical concepts. Freely available at school or at home, the use of SCILAB by students and teachers is favored. In this paper, we would present how's Scilab could be adopted in the teaching of mathematics and fundamental engineering subjects.

The Teaching Experiment of Linear Function with Dynamic Mathematics Software GeoGebra

Abstract: In this study, based on the framework of DeFT, we design a learning environment with dynamic linking multiple representations to instruct linear function. Under this environment, we also investigate 7th grade-students’ performances as learning the meaning of the coefficient and the constant of linear function. According to two facets, the form of representation and flexibly to utilize representations, we design a diagnosis questionnaire and randomly pick students who have learned linear function from one class of school to take pre-tests, post-tests, and experimental instructions. In addition to statistic analysis, we have deep interviews with students to realize their understanding for value-m and value-b of the function, y = mx + b. Research results are as the following: (1) under the environment of dynamic multiple representation, students’ post-learning performances show significant differences from their pre-learning performances; (2) the environment of dynamic representation have impact on students’ thoughts to deal with the relationship of linear function, and facilitates students’ comprehension to straightly apply value-m and value-b; (3) this teaching environment not only helps promote students’ understanding for algebraic, tabular, and graphic representations but also raise students’ abilities to deal with context representations and integrate representations. In this study, the learning environment of linear function provides a pragmatic way to assist teachers’ instructions in junior high schools.

An innovative DVD model for teaching Mathematics in South Africa

The serious crisis in secondary school mathematics education in South Africa has led to many different intervention models by universities, non-governmental organizations and other stakeholders. Identifying a modern and innovative approach to the teaching and learning of mathematics, that will appeal to both learners and educators, remains elusive. The Govan Mbeki Mathematics development unit at the NMMU recently developed a DVD based presentation model that has shown promising results. Every mathematics topic DVD that was developed, contains a set of structured micro-lessons that integrate animated PowerPoint slides with narration and the use of the latest dynamic graphics software. Various techniques to enhance the visual effects of DVD lessons were integrated as part of the DVD architecture. These include colour schemes, curser focus, font size and the timing of animations.
For educators, the series of content DVD’s represents a complete and independent teaching resource which allows new degrees of freedom in the way technology is used to teach mathematics in the classroom. At the same time, this DVD model offers learners a quality learning resource which is modern, affordable, flexible and user-friendly. The seven distinct phases of the production of each DVD are described in chronological order. Information about the modern screen capturing software that was used to create a virtual DVD production studio is also presented.

The Experimental Research on the Mathematics Instruction Integrated with Graphing Calculator in China

The reform of mathematics curriculum in China stresses the integration of information technology in the 21st century. The graphing calculator (GC) is particularly worth receiving attention due to its portability and usability for experimentation. In the October of 2007, Ministry of Basic Education Centre in China reached the collaboration agreement to spin off some research projects with Hewlett Packard of America (HP) which was named the “Integrating the mobile technology with new mathematics curriculum in middle School”. This project is undertaken and implemented by Key Laboratory of Mathematics and Complex Systems of Education Centre in Beijing Normal University. The research topics had been planned to take place between 2008 and 2011 and to cover 14 local areas for experiments. There are 100 schools in China chosen where teachers’ training workshops will be conducted for implementing new way of teaching when technological tools are incorporated. To name a few, there are creative and innovative materials designed for instructions, and students are engaged in the process by solving concrete and real-life problems when technological tools are incorporated during the instructions. In essence, our goal is to design a curriculum by incorporating technology.

Customize Learning of Mathematics to Students Learning Styles

Premjit Singh
Dept. of Mathematics, Ohio University, USA

In this talk, we report how the use of Webassign in teaching of College Algebra, which integrates technology with the pedagogy, has helped students’ diverse learning styles.. Furthermore, the program is customized to students’ needs whether they are visual learners, auditory learners or textual learners.

Success in Mathematics in a Click or Two?

M Naidoo
naidoom1@tut.ac.za
Department of Mathematics and Statistics
Tshwane University of Technology
South Africa

The challenges facing nations referred to as 'developing' (or rather nations with less access to credit than others) extend to the arena of tertiary education. These challenges are clearly seen in the tertiary terrain in South Africa with these challenges augmented by the perculiar socio-economic history of the nation. A history of marginalisation of the majority of the population has seen gallant attempts by institutions to redress artificially created demographic imbalances. As the Industrial Revolution in the 18th and 19th centuries marginalised large sectors of the population, the Technological Age of the 21st century threatens to accentuate the wide gaps in society