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- Plenary session #1
Ferdinando ARZARELLO, Ornella ROBUTTI, Italy 
Plenary speakers: Ferdinando ARZARELLO, Ornella ROBUTTI
University of Turin, Italy
Multi-representations in TI-Nspire and TI-Navigator environments
We consider students multimodal learning processes within TI-Nspire and TI-Navigator environments. We compare them analysing the different cognitive dynamics that the different instruments trigger and support. We argue that their differences are originated by the different nature of the multiple-representations they allow. As a conclusion, we use our analysis to investigate students processes while working in TI-Nspire environments with and without handheld. The presentation is exemplified showing some video-clips of students activities within the two TI-environments.
[Summary] [Presentation]
Chair: Bärbel BARZEL
- Plenary session #2
Truus DEKKER, Netherlands
Plenary speaker: Truus DEKKER
Freudenthal Institute, Netherlands
Using technology to assess mathematics: threat or treat?
It is obvious that the use of technology will change the nature of mathematics assessment. The format of the questions to be posed, the possibility of immediate feedback, less emphasis on algorithms...most teachers have already experienced this shift in focus. How can we make sure that the use of technology really improves the possibilities for assessment rather than limiting them?
[Presentation] [Handout] [Questions & Answers]
Chair: Paul DRIJVERS
- Plenary session #3
Pierre BRZAKALA, Wolfgang FRUHAUF, Belgium
Presentation of the decision process in the European Shools regarding the introduction of CAS calculators in the mathematics syllabus on all levels in the 4 years before the baccalaureat.
Presentation of the European Schools: Language sections,options,exams and baccalaureat.
[PDF]
- Plenary session #3
Gilles ALDON, France
Report on the work of the french research team e-CoLab ; sharing and constructing resources : presentation of the frame of our work.
[PDF]
- Plenary session #3
Angelika REIß, Germany
Abstract of the presentation of teacher with students
during the conference “Sharing Inspirations”, Berlin, May,2008
Angelika Reiß & students
Detecting a primitive of 1/x
Students report on their math lessons-
During the course the students found a primitive of 1/x with the aid of different applications of TI-Nspire CAS. They measured the area below the graph of 1/x between the lower bound x=1 and the variable upper bound. The values of the upper boundary and the values of the area are transferred one after another into a spreadsheet and these points are plotted in a coordinate system. Then the students tried to model the scatter plot by an appropriate function – the primitive.
After this they investigate how the primitives depend on the lower boundary by using the locus tool. The students will report on their lesson and the used technology from their point of view.
[PDF]
- Plenary session #4
Kaye STACEY, Australia
Plenary speaker: Kaye STACEY
University of Melbourne, Australia
Pedagogical Maps for Describing Teaching with Technology.
Kaye STACEY will present a graphic display which enables us to visualise the variety of purposes of technology in a teacher's pedagogical repertoire. She will show maps of different teachers' practices and discuss differences. The maps could be used for teacher development or research.
[Presentation, with notes]
Chair: Alison CLARK-WILSON
- Workshop 101
Alison CLARK-WILSON, Truus DEKKER, Betty GASQUE, Laurent HIVON, Andreas PALLACK, Annette ZEIDLER, Sweden
In many countries, there is a greater emphasis on the development of students’ problem solving within mathematics. However, assessing such competencies presents a challenge to teachers and assessment designers. This session will offer a framework for thinking about the nature of the interactions that are afforded when technologies (TI-Nspire and TI-Navigator) are used to promote such interactions. An international team from different European Countries (France, Germany, Netherlands, Sweden, UK) and the US will offer a series of classroom-based examples.
- Workshop 102
Marc GARNEAU, Canada
The Case for CAS in Secondary School - A Canadian Experience
The secondary mathematics curriculum in Ontario, Canada, has embedded CAS as a powerful learning tool - the first jurisdiction in North America to do so. Come explore how the TI-Nspire CAS can be used effectively to enhance the learning of mathematics in a profound and meaningful way, with specific references to course expectations from the Ontario mathematics curriculum.
Additional files used during the Tips & Tricks for Teachers (202) workshop:
Tips_Tricks.zip
- Workshop 103
Brian OLESEN, Denmark
Cryptography with TI-Nspire as project for Danish high school students:
- Short introduction to programming
- Number theory used in the mono-alphabetic affine cryptosystem
- Affine encryption and decryption with programming
- Workshop 103
Bjørn FELSAGER, Denmark
Interdisciplinary teaching combining mathematics with the humanities: Mathematics and Danish: The common theme is argumentation and logic. The role of TI-Nspire in introducing propositional logic and its relationsship with mathematical proof. As in other interdisciplinary subjects part of mathematics contibution will be very specific dealing with propositional logic and part of it will be philosophical (metathinking) relating logic in mathematics to logic in other subjects, e.g. modal logic.
- Workshop 104
Benno FREI, René HUGELSHOFER, Robert MAERKI, Switzerland
New ideas and concepts of teaching quadratic functions and equations
Worldwide a lot of nice but unrelated examples are produced for TI-nspire. Innovative and early-adopting teachers are able to integrate these examples into their classroom activities. The less innovative teachers or those who reject technology should be provided with ready made teaching sequences that show the way to integrate TI-nspire (especially CAS) in the classroom, not just by adding additional examples. We made such a teaching sequence with new ideas, based on graphing and variable concepts (as shown in P. Drijver's dissertation and in “The case for CAS”). The sequence includes a variety of nice and interesting applied examples, demonstrating convincingly the didactical and pedagogical surplus of TI-nspire CAS. The concept and some examples will be demonstrated.
- Workshop 105
Jim NAKAMOTO, Canada
The Nspire is a discovery tool that allows the IB student to conduct investigations, particularly in portfolio work where the use of technology is required. The multiple representations possible with the Nspire lends itself very well to the work required of students. This presentation will look at one sample of a portfolio task.
- Workshop 106
Peter RANSOM, UK
Fun with the Sun
The session will show how to convert the TI Nspire into a universal sundial. This uses Cabri geometry to draw the sundial on the screen. Learners combine rotations and reflections to draw the basic dial, then the properties of circle geometry are used to explain why the gnomon of a sundial has to be parallel to the Earth's axis. Learners then use the spreadsheet and linked scattergraph to examine the 'equation of time' which is needed to calculate the mean time from a sundial. The final part of the file allows the learner to convert local solar time to mean time.
If time permits, some other types of sundial will be explored, linking historical mathematical texts and science with the technology of today via geometrical constructions.
- Workshop 106
Michael ROSER, Switzerland
Bungee jumping
forces, work and energy conservation
- Workshop 106
Gert SCHOMACKER, Denmark
Can you turn the ladder into the other corridor?
How long a ladder can be turned from one corridor into another one perpendicular to the first one? The acticity includes geometrical construction, graphing and calculus.
- Workshop 202
Paul DRIJVERS, Netherlands
Workshop 202 - Tips & Tricks for Teachers
- Workshop 203
Stephen ARNOLD, Australia
What are the lessons we have learned from the last twelve months using TI-Nspire with teachers, students, authors and publishers. What are the qualities we might associate with effective TI-Nspire documents? In this session, we share the experience gained from writing, reviewing and editing dozens of TI-Nspire documents from Australia and the United States, identifying the "Golden Rules" for working with the new TI-Nspire document system.
- Workshop 204
Thomas DICK, US
A framework for creating TI-Nspire electronic learning documents: the action-consequence principle
Opportunities for learning are enhanced and amplified if a TI-Nspire document provides for user initiated actions that are mathematically meaningful, and for immediately apparent and mathematically meaningful consequences. Dynamic links on TI-Nspire effectively make it a "microworld maker." Two issues that arise are:
1) mathematical fidelity to the objects represented
2) cognitive fidelity to the user's perceptions.
Amplified opportunities will not be realized unless the teacher asks questions that require the student to reflect and make sense of the mathematics embodied in the document.
- Workshop 204
Dominique RAYMOND-BAROUX, France
Two didactic screenplays for a single problem: comparing the mathematical activity of pupils.
Leaning on an example, a problem about fonctions level "seconde" in France, our idea is to show how and why the terms of a problem can evolve.
Starting from observations made in two classrooms, we analyse the impact of the terms on the pupils'instrumental and mathematic activity. We also compare the teacher's interventions during the lesson.
This problem allow to use all the applications of the calculator. We intend to lead our analyse application by application.
Each time we were two observers. So we can cross the observations between four pupils' groups.
Our tools of analysis are the notes taken by the observers, the audio recording, the pupils'written works, some pupils'files tns, and four movies taken with hypercan(pupils searching the problem on computer with TI-Nspire CAS).
- Workshop 204
Ruhal FLORIS, Switzerland
Evaluating TI-Nspire student documents.
This communication is descriptive in nature. It is based on the instructions given to pupils, on the tns files made by these students and on the feedback from the teacher.
I relate the evolution of these interactions through the year and how were evaluated documents made by students about the problems they had to solve. The communication focuses on the interaction made possible by the digital documents. These interactions have focused firstly on the mathematical shortcomings of the documents, and secondly on the presentation of the resolution of problems (comments, organization of pages and parts of pages, eliminating calculations irrelevant).
In conclusion, I try to identify certain characteristics and difficulties in the instrumentation process of TI-Nspire documents for the presentation by students of a problem’s study.
- Workshop 205
Alison CLARK-WILSON, UK
A Report on the outcomes of the UK TI-Nspire Pilot 2007-8, focussing on the issues surrounding teachers' professional development.
- Workshop 301
Wolfgang PROEPPER, Germany
Libraries; how to create and how to use them
A library is a collection of data and procedures which can be accessed from any documents and problem of a Nspire system.
In this workshop we will first show, how libraries are created. Among others we proceed from the frame of a library (a function, not implemented in Nspire). In a second step it will be enlarged by some functions and we will see how to call them.
Participants can include this library into their Nspire (software or handheld) and use it.
This workshop adresses to colleagues who had (until now) no experience with that new feature of Nspire.
- Workshop 301
Karl-Heinz KEUNECKE, Germany
Simulation of stochastic processes
Programming functions
Dr. Karl-Heinz Keunecke
Simulations of stochastic processes are an important part of statistic courses. With a CAS simulations can be done stepwise, but this method is often rather long-winded. Therefore it is much more comfortable to put the procedures in a program or a function.
It is reported on statistic lessons in class 12 (age 17-18). The used programs have a modular structure so that students can combine them accordingly to their own ideas.
- Workshop 302
Isabella SOLETTA, Italy
A module about vector with some simulations and some lab activities.
- Workshop 302
Stephen ARNOLD, Australia
What do we know about geometric thinking and how does this impact upon teaching and learning? In particular, what opportunities are provided within the TI-Nspire environment for building improved access to geometric reasoning? Finally, how does knowledge of geometric thinking inform our teaching and learning of mathematics in general. This session explores some of these questions and offers the chance for participants to pursue some of the implications for their own situations.
- Workshop 303A
Maria WAERN, Sweden
An introduction of the trigonometric ratios with TI-NspireCAS as I have done with my classes this year.
By creating a trigonometric table "live" there is a great opportunity to improve the understanding of how to use the trigonometric ratios for the students. To visualize the table also creates a better knowledge of the difference between the functions tan and tan^(-1) on the calculator.
- Workshop 303A
Hans-Georg WEIGAND, Germany
The Bavarian M3-Project - The TI-Nspire in calculus classes
A long term project was started in the school year 2003/04 to test the use of symbolic calculators (SC) grammar schools in Bavaria (Germany). In school year 2006/07 students in grade 11 used the TI-Nspire (and the Voyage 200) for the whole school year in calculus. The evaluation of the project was intended give answers to the following questions: how basic mathematical skills (algebraic transformations, solving equations, working with tables and formulas) changed; how the questions posed in examinations changed if the students were allowed to use a symbolic calculator; how the students evaluated the use of the new tool; This article presents the results of this project. A rough overview about this project and the first results of the project are given.
- Workshop 303A
Ishak GÜRLEYIK, Denmark
Construction of the derivative funktion and the integral function.
The slope of the tangent line and the secant.
- Workshop 303B
Eberhard LEHMANN, Germany
Construction of "Nspire-landscapes" – and how to work with this idea in teaching mathematics.
The idea is to create pictures by using geometry oder graphs of functions, among other things looking at real landscapes!
- Workshop 304
Øystein NORDVIK, Norway
A suggestion of how to present and study hypergeometric distributions and also a comparison between binomial and normal distributions.
We will construct various sliders for each parameter to enable us to dynamically see the effect of change in these probability distributions.
- Workshop 304
Marie-Claire COMBES, France
Rolling lucky dice: The genetics of an activity or its variation into hybrid resources.
We will present how a single resource generated diverse activities adapted to different school levels, raising different mathematical issues.
- Workshop 305
Betty GASQUE, US
Use the TI-Nspire CAS to Assess Students’ Solutions of Optimization Problems
In the past, optimization problems were often relegated to the calculus curriculum. These problems provide a rich connection to mathematics history and the applications of geometric and algebraic concepts. Using the TI-Nspire CAS’ linked applications, students can explore these problems, make conjectures, and report their results. A problem considered by Heron of Alexandria in the 1st Century A.D will be presented.
- Workshop 305
Margaret BAMBRICK, US
This presentation will focus on activities designed for students enrolled in an introductory algebra course. The activities and discussion will focus on how TI-Nspire can assist struggling students in learning basic algebraic concepts such as slope, linear functions, etc. covered in the Algebra 1 course. This will be an interactive session.
- Workshop 306
Lars JAKOBSSON, Sweden
The session will show the present status of Data Collection possibilities and primarily how to use the enhanced features of modeling data using TI-Nspire.
- Workshop 401A
Anne GUASCH, Alain VESIN, France
Developping TI-Nspire activities to help students prepare the practical mathematics subject of their final exam (baccalauréat).
This session will include a presentation of the new math test currently experimented in France.
- Workshop 401B
Robert CABANE, France
I will briefly present the recent introduction of practical mathematics (e.g maths with tools) in the scope of the french scientific baccalauréat (=Matura/Abitur), with some examples.
The discussion will be given in english, and I will be glad to answer to related questions in either language (e.g. french, english or german).
- Workshop 401B
Jaime CARVALHO e SILVA, Portugal
The challenges of designing exams where graphics calculators can be used.
- Workshop 402A
Laurent HIVON, France
Our purpose is to describe a course aimed at French pupils of Grade 10. By using TI Navigator starting from a simple geometrical situation, this course makes allows the pupils to create the concept of the curve of a function and to introduce the graphic calculator to meet a need.
The unit will be presented within the theoretical framework of the processes of instrumental genesis and will approach the notion of collaborative work in the classroom.
- Workshop 402B
Hans KAMMER, Switzerland
TI-Navigator™, A computer-aided classroom learning system for graphing calculators (TI-84)
- Description and presentation of the Navigator™ system (hardware and software)
- Classroom-Experiences in Austrian and Swiss High Schools (Gymnasium)
- TI-Navigator™ for TI-Nspire-/TI-NspireCAS handhelds: What could be
better done (ease of operation)?
- Discussion
- Workshop 403
Epi van WINSEN, Bert WIKKERINK, Netherlands
"Move to prove" Interactive documents that invite to experiment, form
hypotheses and prove them geometrically and/or algebraically.
Using C2C (Connect to Class) to collect students answers.
Examples of class work, discussion on the questions asked by the pilot
teachers.
TNS files for every participant.
Duo presentation by Bert Wikkering and Epi van Winsen
- Workshop 403
Pierangela ACCOMAZZO, Giovanni MARGIOTTA, Italy
M@t.abel. a training project for italian teachers that proposes an integrated use of the mathematics laboratory in teaching and learning: how does it change didactic practices?
- Workshop 404
Ewald BICHLER, Hubert LANGLOTZ, Germany
Minute Made Math – Inspiring Colleagues To Use Technology. A Conceptual Design for Training Material.
- Workshop 404
Heike JACOBY-SCHÄFER, Germany
The TOP 10 in getting started:
pupils working with TI-Nspire for the first time are to learn the “10 principal control elements” of TI-Nspire based on a concrete example (the trajectory of a basketball).
Is this approach also conceivable for further training of colleagues?
43 shared contributions - 188 files uploaded
www.sharinginspiration.org
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