Initially, the CALM Project built a computerised tutorial system to enhance the teaching of calculus to students of the Heriot-Watt University. CALM started in 1985 following funding from the Computers in Teaching Initiative (CTI). The award from CTI provided both the computing expertise to produce the CALM courseware and a laboratory of 32 networked Research Machines microcomputers for student use. The first CALM Project was completed on time by October 1988.
CALM courseware is the result of strong teamwork and dedicated teaching. It has already exceeded our expectation in its impact. There is an enthusiastic response to it by each new group of students. Lessons learnt over the last decade have been built into the courseware wherever possible. We are still listening to what the students tell us from their experiences and we continue to develop courseware which aims to help students learn more effectively and more efficiently.
Calculus is an ideal medium to bring applications of mathematics to life. The 22 units of CALM courseware produced cover the syllabus of a typical course on calculus with differentiation, integration, an introduction to numerical methods and elements of ordinary differential equations. Each unit includes the topics first encountered in approximately two lectures of the course. Mathematical modelling and the development of mathematics in Engineering and Applied Physics is an important feature of CALM. For example:
- State the Rate invites the students to work through a problem involving the filling of a cup from a coffee dispenser encouraging design considerations;
- Fireman is a model of the trajectory of water from a hose which properly directed puts out a fire; and
- Escape from Colditz asks the students to work with calculus and numerical methods to solve an optimisation problem.
From the outset our teaching
strategy for each unit has been constructed around:
- Theory sections, to consolidate the conventional lecture;
- Worked example sections, to teach the methods of calculus;
- Motivating examples, including mathematical "games", experimental elements and mathematical models; and
- Test sections, to enable students to assess their own strengths and weaknesses and to allow the teacher to monitor individual progress.
The units are designed to allow the students complete control over their route through the tutorial. The course for which these units are part, is mainly assessed in a conventional way. The test section of each unit can be taken at any one of three levels to cater for a spectrum of ability. The design of the multi-level test was guided by specific requests from the students themselves. The test offers different types of help at each level. Students can start a topic at the easiest level and progress to the hardest level as they gain in confidence. They are free to use the CALM tutorials in whatever way they choose.
The students' marks and test answers are recorded so that the teacher can monitor their progress. Students who are working well are sent encouraging messages. Those who are in difficulty are detected early in the year and given extra attention. By viewing the recorded answers, the teacher is able to identify the source of a student's problem and send an appropriate message.
We have worked as a team throughout
with regular meetings a central feature. We have presented our
results and demonstrated our courseware at national and
international meetings (a list is provided elsewhere in these
screens).
In the course of the project, software tools like evaluation routines, test-making libraries and mathematical display procedures were produced. These have been packaged together and used by other developers of CAL courseware in the University and beyond. The details of these tools are described in our book "Software Tools for Computer Aided Learning in Mathematics" published in April 1991.
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Reactions to CALM
In 1986/7 and 1987/8 we compared the examination results of a pilot group with those of another group taking the same final examination, in categories of similar school qualification. On average, students in the computerised tutorial system performed 15% better in the common examination. It is estimated that the introduction of CALM has reduced student failure rates by 5% per annum.
Printed instructions and advice
gathered from previous CALM users are given out to all new
students. Their comments include:
"Great idea
--- you can come and learn when you want."
"Learning via the computer is less embarrassing."
"It is as if there is a tutor in front of you all the time."
"The tests make you work harder."
"The software is always under your control."
"I look forward to the CALM tutorials."
Information from students has been
collected through questionnaires, interviews, structured recall
and informal contacts. We assessed the advantages of the CALM
courseware in two ways:
- through feedback from the students
and their observations on the quality of learning that CALM
provides; and
- via enhanced examination
performances of two pilot groups.
Reviews on the Web
"We liked this program: its concept is simple and its delivery effective."
Electronic Telegraph
"My Sixth Form son loaded up the program, designed for use at A-level and Scottish Higher, suggesting that the user guide for this part is clear and accurate"
"The inputting must be extremely clever"
Review by Don Kite, a Secondary Schools Maths Teacher
"The program is oriented towards multi-pupil use in a school environment and for this reason may prove very useful as year-round practice, with the teacher being able to monitor each student's progress."
Educate Online Review
"This is a very useful tool for preparing for examinations. It is well worth considering for installation on single machines or more widely across a network."
"The interface is well suited to examination preparation activity."
BECTA CD-ROM Review
"The InputTool represents a considerable advance in providing a flexible and accessible user interface for supporting correct mathematical notation."
"Students who are prepared to spend time and effort with this professionally produced piece of software would enhance their revision programme and the content.
CTI Mathematics
Note: This document is in Adobe PDF Format and may have to be downloaded before viewing.
"The package is well designed, easy to use and can be configured to the needs of individual students, with all the topics in core advanced mathematics covered."
"The Computer Aided Learning in Mathematics team at Heriot-Watt University, who developed this program, have clearly used their expertise to good effect."
The Times Educational Supplement, December 19th 1997
"The software was extremely engaging to use and very satisfying. Much better than ploughing through past papers with no idea as you do them whether you are on the right track or not."
"This was considered to be good exam practice, easy to use and with lots of questions. Its other advantage is that it teaches layout and how much you need to write down in exams. It was possibly better than a set of past papers because of the instant feedback"
Mathematics Multimedia Courseware Review
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Some early CALM successes
- CALM courseware is being used by over 400 students each year at Heriot-Watt University
- In excess of 5000 undergraduates have regularly used CALM at the Heriot-Watt University alone
- CALM courseware has been bought by other FE and HE establishments; for example the universities of Southampton, Brunel, UMIST, Essex, Bangor, ITESO (Mexico) and Brussels
- There is an MS-DOS version of CALM running on PCs
- Particularly complimentary student comment has been received from the Universities of Brussels and Essex
- CALM has been translated into Spanish.
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