CTI Mathematics Workshop Report
Taking advantage of hand-held technology and calculator networks

This one day workshop, organised by CTI Mathematics and sponsored by Texas Instruments, was held in the InterActive ClassRoom at the University of Strathclyde on Friday 8 January 1999

The TI-89 with Advanced Mathematics Software is a portable symbolic, numeric, and graphing solution for advanced mathematics and engineering coursework. Such tools can replace skills looked for in the past but not the understanding that those skills brought. This workshop, sponsored by Texas Instruments, investigated benefits and drawbacks to the use of handheld technology by students in and out of the classroom, the effect it will have on assessment and the way it can be integrated into courses.   A printed version of this report is available on request, including an article from Micromath relating to how these issues are being addressed in schools.

1.    Using Classroom Communication Systems with large classes - Jim Boyle, University of Strathclyde
2.    Modelling with differential equations ­ case study from Diana Mackie, Napier University
3.    Hands-on session: Using ClassTalk with the TI-86 - Jim Boyle
4.    The evolution to the TI-89 - Harry Gretton, Sheffield Hallam University
5.    Case study - the experience of integrating technology at Sheffield Hallam University
6.    Hands-on session: Getting a grip on the TI-89
7.    Discussion on the implications of the TI-89 and calculator networks
8.    Further reading


1.     Using Classroom Communication Systems with large classes - Jim Boyle, University of Strathclyde

At Strathclyde funding is available for the Natalie project, investigating new approaches to training and learning in engineering. The Vice-Chancellor served on the Dearing Committee, and recognises that education is in transition ­ traditional ways of teaching are not appropriate to the culture of mass higher education. In particular, there is a different motivation; students have a shorter attention span, but can multi task better, and want breadth rather than depth. Changing one's teaching is hard, but there is evidence that the way we teach is no longer working.

The introduction of technology into the classroom will not be effective unless it is based on our understanding of the way students learn, which means looking at studies of experiential learning or those carried out by Piaget. This has not been a feature in the discipline of mathematics, where the professor of old would still feel at home in today's classroom, unlike the teacher of medical students. Lectures have become too passive, and this is exacerbated by the use of the OHP and printed notes. What is missing is a dialogue between teacher and student, such as takes place using a Socratic method - teaching by questioning.

This is the basis for ClassTalk, a network software system based on TI calculators which provides an effective way to enter into a dialogue with large classes. In a Strathclyde first year mechanics course up to 95 students collect calculators on their way into the InterActive ClassRoom, and log into the network built into the seats. The instructor presents a question, problem or information task, sent via the network. Students discuss and respond with words, sentences, numbers, formulas or multiple choice; the latter can be used to see whether concepts are understood. Group or individual responses are allowed, also dissent; alternatively a confidence level can accompany the answer. The InterActive classroom is also fitted out with a number of radio mikes for instructors and students to use.

The results are displayed on a seating plan management system, so the instructor can see who is logged in and can address students by name. The system also analyses student progress - feedback, tests and grading are available and the instructor can send messages via the network. There can then be discussion of the different views held by students - peer instruction reinforcing the idea of groupwork. As a side benefit, students enjoyed the more creative atmosphere. At Harvard class sizes can reach up to 350 using this software. PRS (Personal Response System) is a simpler system allowing multiple choice only.

The three members of staff involved spend some time assessing the capabilities of the new students on the mechanics course. They seem to have developed strategies for problem-solving without understanding basic concepts, and to have manipulative skills without knowing how to apply them. In the real world experts have a set of models to draw on and tweak to suit a particular problem, and the course therefore uses a model-based (or concept-based) problem-solving approach. A few basic models are presented for use with minor modifications, and students identify or create a model and make inferences to produce a solution. Modelling examples include rectilinear motion and damping mechanisms.

2.     Modelling with differential equations ­ case study from Diana Mackie, Napier University

The TI-85 is used in one module of the four-year course "Science with Management Studies". This module requires students to investigate the graphical solutions of first and second order ODEs, plot solutions and phase paths of systems of ODEs and explore solutions to first and second order difference equations. A set of TI-85 instruments is available on loan to the 15-20 students taking the course, and are used for the course and the exam. Students may also go to the maths lab and use software learned on other courses, but usually find the calculators more convenient. There is no hard copy output ­ they are expected to sketch graphs displayed on the screen.

One example of its use is the investigation of damped and forced vibrations. The TI-85 can cope with up to nine variables, and students can examine over-, under- and critical damping by changing parameters. They can look at a transient phase and steady state oscillation, and how this matches the frequency of the forcing function, and the enhancement of the amplitude when the natural frequency is close. Epidemic modelling provides another example; students can view changes in the numbers of infectives and susceptibles within a population and examine the phase plots. Traditional methods are also used to teach simpler linear models using ideas of eigenvalues, but students then find the phase plots difficult to understand. With the calculators they can try things out for themselves, and get a better feel for the mathematics.

3.     Hands-on session: Using ClassTalk with the TI-86 - Jim Boyle

Delegates had the opportunity to log in for themselves and get a student eye-view of the system. Currently this runs off an Apple Mac, with any number of calculators going into one serial port. The network is live - once students have logged in, they can unplug and plug back in without logging in again. They seem to enjoy learning in this environment, since attendance at lectures is now running at 90%. A typical question or task would be of the following form:

Do you think graphing calculators are:
1.  a good thing
2.  a bad thing
3.  don't care
4.  don't know
Discuss in groups of four for 90 seconds and input the result on your calculator

The results can be displayed as a bar chart to provide the basis of discussion on the merits of each answer and the total class response.

4.    The evolution to the TI-89 - Harry Gretton, Sheffield Hallam University

Harry summarised the features of a whole range of TI calculators. Their evolution matches the change in the skills base of our students. The TI site contains software downloads, examples of good practice and contacts for the different user groups.

5.    Case study - the experience of integrating technology at Sheffield Hallam University

Initially in service teaching to 400 engineers and now for 50 mathematics honours students, the aim is to integrate technology (graphic calculators, spreadsheets, CAS, CDROM) into practice, review the curriculum, teaching style and the way students are encouraged to learn, incorporate key skills and review assessment. Harry described the impact of these changes on staff, students and innovators, and pointed out that mathematicians are in a position of being able to deliver all six key skills outlined by Dearing. Sheffield Hallam's mathematics degree is now designed on the assumption that students will have good access to a range of technology - they are given a copy of the departmental Web site on disc before they come to the university. Virtually all mathematics students buy a graphic calculator, and this year many have bought a TI-92 or TI-89. The full version of this talk is appended under its title "Slings and Arrows of Outrageous Fortune".

6.    Hands-on session: Getting a grip on the TI-89

This session was made possible by the loan of a TI-89 class set by Texas Instruments. It was based on an introduction to the TI-89 written by Sally E Fischbeck, Rochester Institute of Technology, Rochester NY.

7.    Discussion on the implications of the TI-89 and calculator networks

Concerns regarding the technology itself

 The need for different assessment practices

The effect of technology on the curriculum

 Teaching and learning issues

Motivation

8.    Further reading

Publications List