Mass Production of Theorems in Solid Geometry
Jenchung Chuan
jcchuan@gmail.com
Department of Mathematics; National Tsing Hua University; Hsinchu;
Taiwan
Before Cabri 3D came to existence, Solid Geometry was treated just like any other theorectical science and very little could be experimented. After Cabri 3D was released, Solid Geometry gradually became an experimental science! We shall explore in this workshop how two types of plane geometric results can be directly converted into theorems in 3D: those involving circles only and those involving straight lines only. Laboratory setup: Cabri 3D with Internet connection. Hardware requirement: graphic card with 256K of memory.
GeoGebraSpreadsheet and GeoGebraCAS workshop
Zsolt Lavicza
zl221@cam.ac.uk
University of Cambridge
United Kingdom
GeoGebra is free, multiplatform, opensource dynamic mathematics software with rapidly growing worldwide popularity. The basic idea of the software is to join dynamic geometry, algebra, and calculus, which other packages treat separately, into a single easytouse package for learning and teaching mathematics from elementary through university level. In this workshop, I will introduce new features of GeoGebra using the spreadsheet and the new symbolic algebra (CAS) view.
Old Wine in New Bottle: a fresh look at Casio fx 991 ES Plus Scientific Calculator
Wei Ching Quek
quekwc@sp.edu.sg
Singapore Polytechnic
Singapore
Casio fx 991 ES Plus Scientific Calculator is widely regarded as an ideal choice for university students. This scientific calculator is equipped with more functions, awareness of these “new” or 'notsofamiliar' features will help us to (i) squeeze more computation power from calculator (ii) introduce new and more efficient, and relaxing way to teach and do mathematics. (iii) devise strategies for a valid, reliable assessment, This 1.5hour sharing session will provide fresh insights of some features of Casio fx 991 ES plus Scientific Calculator, which will include the following: 1) Statistics computations, reference to standard normal distributions (2) Table functions for graph, Simpson’s rule, Fourier coefficients (3) Matrix and vector computation (4) Modulo computation (5) Solving general equations such as xe^(x) = 0, (6) Demonstrations and Handson Practice (7) Discussion on assessment strategies
Analytic 3D geometry with TI N’Spire
JeanJacques Dahan
jjdahan46@yahoo.fr
IREM of Toulouse
France
In this workshop we will learn how to represent very easily 3D objects in parallel perspectives in the geometry application of TI N’Spire. We will use the connections between the different applications of this environment to create activities for the classroom. We will show that, dealing with the tools of this software during that sort of activities, helps students to deeply understand mathematical concepts of 3D representations.
Folding and unfolding cones and cylinders with Cabri 3D
JeanJacques Dahan
jjdahan46@yahoo.fr
IREM of Toulouse
France
We will first model cones and cylinders respectively with pyramids and prisms. Secondly, we will use plane symmetries and rotations to open them. At last we will design our figures to obtain a realistic response to our problem. Even a beginner will be able to follow this session and enter easily the world of 3D dynamic geometry.
Let's Develop Interactive eTextbook for Classroom: Your Innovation by Freeware ''dbook''
Masami Isoda
isoda@criced.tsukuba.ac.jp
CRICED; University of Tsukuba
Japan
In any countries, teacher and students use textbooks for teaching and studying mathematics even if they do not use the software or calculator. Now, a number of schools in many countries equipped projectors as well as Blackboard. Interactive board is also good equipment. On this demand, the software ''dbook'' was developed by Masami Isoda, CRICED, University of Tsukuba. It aimed for editing eTextbook from ordinary printed materials such as students’ textbooks, distributing it through the web and using it with projector. ''dbook'' supports free Dynamic Geometry Software (DGS) by GCL (Geometric Construction Language) and flv video format. Now, we are preparing to support graphing. If you use dbook, you can use DGS and Graphing tool on your textbook by free. This workshop provides you how to develop eTextbook from ordinal printed textbook with DGS. http://mathinfo.criced.tsukuba.ac.jp/software/dbook/dbook_eng/
Let's Use Freeware ''GRAPES'' on your language: Easier Access for your students
Masami Isoda
isoda@criced.tsukuba.ac.jp
CRICED; University of Tsukuba
Japan
GRAPES is best freeware in Japan for teaching mathematics. It can work on your language if you would like to develop on your language version. Thai version developed by Maitree Inprasitha and Masami Isoda recognized and it recommended by Center of Excellence in Mathematics. Masami Isoda, CRICED, University of Tsukuba has been developing and supporting it to the world users. This workshop will show you how to use GRAPES and explain you how to develop your language version. http://www.criced.tsukuba.ac.jp/grapes/
Exploring space with Autograph and the algebraic power of its constant controller
JeanJacques Dahan
jjdahan46@yahoo.fr
IREM of Toulouse
France
Even a beginner can attend this workshop where we will explore space with the 3D version of Autograph. Step by step we will learn how to represent points, lines, planes by their coordinates or equations and how to move them in using the constant controller which is the core of the teaching power of this software. We will also represent surfaces and learn how to transform continuously one surface onto another. We will show also how to use this 3D software to investigate the solutions of trigonometric equations as the intersection of a surface with the horizontal plane xy. Rotations and symmetries will be used dynamically in order to understand better some other problems.
Interactive Geometry on the ClassPad Calculator
Ian Thomson
ian.thomson@postgrad.curtin.edu.au
Curtin University
Australia
Visual representations of mathematical ideas are stimulating and motivate students to think mathematically. Using the touch screen interface of the calculator, students are able to create and interact with geometric constructions. The dynamic power of the calculator allows the students to make observations and perceive patterns. Participants in this session will gain experience in using the ClassPad calculator to create geometric constructions and animations. Activities will be used that have been trialled on students in the mathematics classroom. The workshop will be predominantly hands on in nature. A booklet of activities will be provided for participants.
Getting going with Autograph 3.3 – teaching and learning ages 1116
Alan Catley
alan@catley.org
Tyne Metropolitan College; NCETM
United Kingdom
This handson workshop is aimed at developing confidence at utilizing the many interactive features of Autograph in algebra, graphing, geometry, trigonometry and data handling. Delegates will have the opportunity to work from carefully structured lesson plans and worksheets designed to ensure that learners are totally focused on the mathematics being studied. As well as catering for delegates with no prior knowledge of using Autograph experienced users will also benefit by providing a variety of innovative uses across the curriculum.
Getting going with Autograph 3.3 – teaching and learning ages 1619
Alan Catley
alan@catley.org
Tyne Metropolitan College; NCETM
United Kingdom
This handson workshop is aimed at developing confidence at utilizing the many interactive features of Autograph in teaching and learning algebra, graphing, calculus, geometry, trigonometry, vectors (in 2D and 3D) and statistics. Delegates will have the opportunity to work from carefully structured lesson plans and worksheets designed to ensure that learners are totally focused on the mathematics being studied. As well as catering for delegates with no prior knowledge of using Autograph experienced users will also benefit by providing a variety of innovative uses across the curriculum.
Learning about equations with a graphics calculator
Marian Kemp
m.kemp@murdoch.edu.au
Murdoch University
Australia
This handon workshop will illustrate how graphics calculators can be used to support teaching and learning about equations in secondary school and early undergraduate mathematics classrooms. The use of graphics calculators enables students to develop key concepts in an interactive and exploratory way not possible without such technology, and to explore relationships between functions, graphs and equations. Workshop participants will examine the opportunities provided by calculators to represent and solve equations of various kinds, including polynomial equations and simultaneous linear equations, as well as others. We will build upon this experience to consider the place of exact and numerical solutions of equations in the school curriculum. No previous experience with graphics calculators will be assumed; beginners are very welcome.
What does technology offer teachers and students of trigonometry?
Marian Kemp  Barry Kissane
m.kemp@murdoch.edu.au
Murdoch University
Australia
Trigonometry has ancient roots, but was little changed in schools until recently, when the scientific calculator removed the need for trigonometric tables to be used. These days, modern technology provides an excellent means of exploring many of the concepts associated with trigonometry, both trigonometric and circular functions. This workshop suggests some of the avenues for exploration and considers the opportunities for effective teaching and enriched learning they offer in the senior secondary school. This workshop will explore the use of a range of technologies, including graphics calculators, Java applets and computer software. We will consider circular measures, graphs of functions, trigonometric identities, equations and statistical modelling with a focus on activities that are not available without access to technology.
Rethinking introductory calculus with a graphics calculator
Barry Kissane
B.Kissane@Murdoch.edu.au
Murdoch University
Australia
This handon workshop will explore how graphics calculators can be used for learning introductory calculus concepts in senior secondary school and early undergraduate mathematics. The use of graphics calculators enables students to develop key concepts in an interactive and exploratory way not possible without such technology. The workshop will explore the role of graphics calculators to examine calculus concepts including derivatives, continuity and limits and discuss how teachers can use informal and intuitive methods to build students’ understanding, in contrast to the more formal approach typically adopted. No previous experience with these calculators will be assumed; beginners are very welcome.
Mathematica for the classroom workshop
Miroslaw Majewski
mirek.majewski@yahoo.com
New York Institute of Technology
United Arab Emirates
Mathematica for the Classroom is a product from Wolfram Research specifically designated for the teaching of undergraduate mathematics with Computer Algebra System. The workshop 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 workshop will include three parts: (1) Introduction to Mathematica for the Classroom (editing documents for screen presentation, for printing, styles, basic commands, handling errors), (2) Mathematical graphics with Mathematica (2D and 3D graphs of functions, parametric equation, graphs in polar and spherical coordinates), (3) animation and manipulation (developing interactive panels, types of manipulation and animation, preparing interactive panels to be used with Mathematica reader).
Integration of Graphing Calculator in Mathematics Teaching in China
Lijun Ye
yeatsylj@126.com
Hangzhou Normal University
China
This study investigated the benefits of using the graphic calculators in mathematics teaching and examined the effects of the TI graphing in secondary mathematics classroom. In addition, this study discussed the advantages of using the graphic calculators in mathematics education programs in higher education institutions and in professional development.
The importance of graphing and interpretation in high school Mathematics.
Christopher Longhurst
longhurstster@gmail.com
Hewlett Packard
Australia
This is a hands on workshop, which will show participants how to draw graphs and interpret their findings. It will be geared to the secondary classroom and focus on a graphical approach to investigating in mathematics.
Some useful and interesting investigations for classroom use.
Christopher Longhurst
longhurstster@gmail.com
Hewlett Packard
Australia
With the introduction of many different types of technology, it is not just getting the answer that is important, but understanding the mathematics. Investigations sometimes are tedious and time consuming. However, using technology, the tedious nature can be taken away and students can discover some interesting and important mathematical ideas. In this workshop some investigations will be presented, worked through and discussed with reference to classroom use.
SPICE UP YOUR LESSONS WITH ANIMATED MATHS MAGIC AND PUZZLES!
Poh Yew Teoh
teohpy@tm.net.my
Creative Wizard Pte. Ltd.; Malaysian Invention and Design Society; Malaysian Association of Professional Speakers
Malaysia
Getting students excited about learning is the teachers’ constant challenge. The answer lies in incorporating creative techniques into our classroom practice. Spicing up our lessons with some mathematical magic and puzzles could easily help increase attention, understanding and retention significantly. Appropriate recreational problems stimulate intellectual curiosity, develop problem solving skills, promote discovery and thinking skills, as well as unleash creativity. In this workshop participants will be participating in deciphering some interesting mathematical magic and puzzles (using Flash programming). These problems appear to be recreational or magical in nature but they are actually based on sound mathematical concepts. In solving these problems, students actively participate in discovering or deciphering the hidden principles underlying each problem and in the process construct their own knowledge of mathematics. This presentation also stress on the need for excitement to encourage mathematical thinking. Mathematical magic can serve as an effective means of motivation at almost all levels of instruction. The major purpose of its use in the classroom is to enable students to discover that mathematics is easy and interesting, and thus stimulate interest in their further study of mathematics. Target audience: Upper primary and lower secondary schools mathematics teachers as well as teacher trainers
Casyope an open environment for learning about functions at upper secondary level
JB Lagrange  Tran Kiem Minh
jeanbaptiste.lagrange@univreims.fr
LDAR Université Paris Diderot; LDAR; University Paris Diderot
France
Modeling geometrical dependencies by way of algebraic functions, and studying the geometrical properties of curves representing functions are essential mathematical activities that Casyopee makes very accessible for students. They allow students a better link between syntactical and semantic points of view in algebra and an easy introduction into calculus. Casyopee has two main windows closely linked. The first one, (called the symbolic window) provides students with symbolic computing and representation capabilities as well as facilities for proving. The second one is a Dynamic Geometry (DG) window. Casyopee uses the Maxima kernel and can be freely installed on Windows based ystems. (http://casyopee.eu). Casyopee has been extensively experimented in France and other countries. Participants in the workshop will be introduced to Casyopee main features and to learning situations for their classes.
Linearization and Interpolation with HP Graphing Calculator
Betty; Wan Niu Voon
bvwn56@yahoo.com
Universiti Tenaga Nasional
Malaysia
Usually, data collected are analyzed using linearization. Otherwise, other functions would be chosen to find the best fit for the data. In this workshop, the steps to do linearization will be shown using HP graphing calculator. Attendees will be provided with the calculators to learn to do the linearization. Besides that, other functions would be chosen to find the best fit using another set of data. From the best fit, attendees would be able to learn how to find properties of graph such as extremum points, zeros, yintercept etc.
DESIGNING A MATHEMATICAL MODELLING TASK: THE ROLE OF ICT
Ngan Hoe Lee  Kit Ee Dawn Ng
nganhoe.lee@nie.edu.sg
National Institute of Education; Nanyang Technological University; National Institute of Education; Nanyang Technological University
Singapore
Mathematical modeling is one of the new focuses of the mathematical curriculum in Singapore. Training has been underway for teachers on task design, facilitation and evaluation of learning during modeling tasks. This handson workshop will bring teachers through a process of designing a mathematical modeling task. In particular, the workshop will also address the role ICT plays during task design.
Exploring TINspire Handheld Technology in Mathematics
Puteri Anis Aneeza Zakaria
anis@statwks.com
Statworks Group
Malaysia
TINspire handheld is the latest math and science learning technology from Texas Instruments, creating a dynamic dimension for students and educators to visualize concepts and take an engaging, interactive role in their learning. This technology goes beyond graphing to help students and educators see math and science in new and different ways. With its own unique features, TINspire technology let you: • See multiple representations of a problem, individually or together on a single screen • Dynamically link representations of a problem to see how changes to one affect others • Grab and move graphed functions in real time to observe relationships and patterns • Save and review work in documents, similar to a computer This workshop session will explore the features in TINspire Graphing Calculator which will use various applications in Mathematics to engage the students and educators to solve problems in realworld mathematics.
Problem Solving with TINspire CAS Graphing Calculator
Puteri Anis Aneeza Zakaria
anis@statwks.com
Statworks Group
Malaysia
TINspire CAS technology makes it possible to recognize, simplify and calculate math expressions, preserving the symbols including variables and terms such as e and π. This ability to enter and view equations and expressions on screen as they appear in textbooks may be especially useful for stepbystep, arithmetic, algebraic and calculus calculations. Educators have the option to incorporate CAS into their instruction, using TINspire CAS technology that is designed to help students • Learn to solve equations stepbystep while avoiding common arithmetic errors. • Spend more time on specific math topics, from algebra through calculus. • Factor and expand expressions and solve common denominators. • See patterns and grasp the math behind the formulas. • Find common denominators recognizing that TINspire CAS Handheld Technology has the teaching and learning of mathematics education in Malaysia, this workshop session will explore the usage of TINspire CAS to engage the participants to solve more than 10 different problembased mathematics activities.
FATHOM2 Based Mindware for Developing Inferential Reasoning in Statistics
Norjoharuddeen Mohd Nor  Noraini Idris
norjo@um.edu.my
University of Malaya; Malaysia
Malaysia
Students learning statistics at the university level usually learn formal inferential statistics to enable them to make inference about the population from data collected from a sample. However, a number of students have difficulty understanding the reasoning underlying the statistical inference process. Students do not understand the importance of ideas such as resampling, sampling distribution and hypothesis testing used in inferential statistics. In this workshop students will undergo through a mindware which consist of two tasks that will provide them with opportunities to experience informally ideas like resampling, sampling distribution and hypothesis testing through the use of a dynamic statistical software known as Fathom2.
The educational use of scientific calculators
Barry Kissane  Marian Kemp
B.Kissane@Murdoch.edu.au
Murdoch University
Australia
Over the last four decades scientific calculators have been used for calculations in trigonometry, for handling logarithmic and exponential functions and for simple and more complicated arithmetic calculations. More recently, modern scientific calculators have been developed more widely to extend the mathematical capabilities to equations, vectors, matrices, complex numbers, probability and statistics, as well as elementary calculus operations of integration and differentiation. In this workshop suitable examples will be used to consider ways that fairly sophisticated mathematical and statistical concepts can be developed, with the use of these modern scientific calculators. We will use the Casio fx570 series of calculators, but do not expect that participants will have prior experience with these calculators.
