During 1994–95, first‐year maths for the BTechEd degree at the University of Glasgow was student‐centred, teacher‐supported A modular online maths course replaced a traditional, lecture‐based course. Students worked at their own pace, with timetabled and open access computer classes and/or paper handbooks. The course was evaluated by open‐ended measures, and study of examination outcomes, providing us with some pedagogical questions and some recommendations for change. With some adaptation, and with important questions still open, the new course will continue to run

Doughty, Gordon

McAteer, Erica

Pollock, Maggie

Turner, Ian

English

Name not available

Conversion of a mathematics courseto CAL: a case study of a large-scale rapid change ofresources and organizationMaggie Pollock,* Erica McAteer,** Gordon Doughty* and Ian Turner**Robert Clark Centre for Technological Education, University of Glasgow**Department of Psychology, University of GlasgowDuring 1994-95, first-year maths for the BTechEd degree at the University of Glasgow was student-centred, teacher-supported A modular online maths course replaced a traditional, lecture-based course.Students worked at their own pace, with timetabled and open access computer classes and/or paperhandbooks. The course was evaluated by open-ended measures, and study of examination outcomes,providing us with some pedagogical questions and some recommendations for change. With someadaptation, and with important questions still open, the new course will continue to run.BackgroundGlasgow University's Teaching With Independent Learning Technologies (TILT) project is aninstitutional initiative funded under Phase 1 of the Higher Education Funding Councils'Teaching and Learning Technology Programme (TLTP), We have developed or adapted andintegrated computer-assisted learning programs into a variety of courses in subjects rangingfrom Accountancy to Zoology.This paper reports a complete change of learning resources and teaching strategies in a Facultyof Engineering course. Overcoming 'not invented here' resistance, we used an externallyproduced program to deliver all maths teaching over a first-year class, and evaluatedeffectiveness for both teachers and students.The course is for first-year students in the Faculty of Engineering taking the Bachelor ofTechnological Education (BTechEd) concurrent initial teacher education degree, taught by theRobert Clark Centre for Technological Education in collaboration with St. Andrew's College,Glasgow. It produces school teachers of Technological Studies, Craft and Design and GraphicCommunication.28ALT-} Volume 4 Number IProblemsThe students vary widely in age and past experience, and in maths background. The 1994-95cohort entered with any of Scottish Higher 'A', 'B' or ' C \ A-level (pass), HND, HNC, ONC,Scottish Wider Access Programme, or SCOTVEC modules. Most qualifications were recent,but some were years old.For these students, the purpose of their maths learning is to acquire manipulative skills ratherthan high theoretical understanding. The level aimed for approximates that of first-yearengineers. Before 1992, the class was taught separately, with close co-operation between mathsteachers and technology teachers. Then partnership changes and timetabling problems put thestudents in with 200 first-year engineers and spread the (lecture-based) course over two years.The BTechEd students struggled, neglecting other subjects, and 29% (6 out of 21) failed thecourse and dropped out. Our teaching dilemma, ubiquitous in maths, was how tosimultaneously motivate the students by applying maths learning to real life problems ofconcern to them, and help them to quickly gain the basic skills to do the necessary mathsmanipulations almost automatically. In practice, students cycle between the two. The durationof a cycle may range from the few minutes required to tackle a real-life maths problem toseveral months' delay before an application to the maths skills learning emerges in anothercourse.Although the joint class of 200 did cycle between theory, example and practice within thelecture period, our target students were not able to keep up with the manipulative skills. Thedegree course organizers would have preferred to change to teaching all maths inside thetechnology courses, as and when needed, but could not get agreement from all course teachers.An efficient and manageable alternative was needed urgently.Solution?We designed a change to learning with long cycle times, providing the first year of a two-yearmaths course on basic skills, and treating their application in other courses. Integration of thecycles would be provided by two of the authors, who also teach or organize several othercourses.We bought in a computer-based maths course: CALMAT, developed by Jean Cook (Cook,1994, Cook and Hornby, 1995) and colleagues at Glasgow Caledonian University. Thisprovides 50 modules of drill and practice tutorial exercises, with self-assessment tests and abuilt-in diagnostic examination. A handbook with paper exercises is provided as a supplement(or even alternative) to each module. Although DOS-based (a Windows version is underdevelopment), it has a clear and easy-to-use interface, has evolved over many years use inhigher-education institutions with students much like our own (Tabor, 1993), and is supportedby a maths teaching team.We felt that its pedagogy suited our objectives: to provide practical maths knowledge andskills, applicable in engineering and technology project work and beyond, when students arethemselves teaching in secondary-school classrooms. For practical as well as pedagogicalreasons, we also needed to provide student-centred learning with independent study resourceswhile being able to access diagnostic information to promote appropriate teacher support.29Moggie Pollock et 0/ Rapid conversion of a mathematics course to CALCourse procedureAt the beginning of the course, all students sat a diagnostic test of 20 multiple-choicequestions. This allowed individual programmes of work to be scheduled for the first term. Aweekly three-hour (non-compulsory) class was timetabled in the computer laboratory for theyear's teaching period, which had at least one tutor present. Students were free to use thecomputer lab at other times during term or vacation, with teaching assistance available - oftenon demand, but always by appointment Copies of the software could be purchased for homeuse. No formal lectures or tutorials were run throughout the year, except to go over class-examination outcomes. Two text books were recommended to complement coursework. Arepeat of the diagnostic test was taken by students at the end of term 1. During term 2, allstudents followed the same work programme (rather than individualized programmes), but attheir own pace. 'Poor achievers', who reported themselves as falling behind schedule, weregiven extra tutor support.The course was assessed by a degree examination half-way through the third term. Exemptioncould be gained by students achieving an average of at least 60% by combining the results ofthe two class examinations, held at the end of the first term and the beginning of the third term.A summer re-sit examination was also available.Information from studentsComputer experience and attitudesMaths learning experience and attitudesConfidence about specific maths tasksCourse attitudes and experienceSkills gainInformation from teachersAdvantages, disadvantages, questions- questionnaire— focus group— checklist- questionnaire— focus group- diagnostic test and exam marks- interviews- debriefing sessionTable I: Evaluation targets and methodsEvaluationWith less than three evaluation staff, working across 20 sites, we could provide no more than aminimal evaluation of the course. Table 1 lists the information sought and the methods used.Students' attitudes to computers, and their knowledge and experience of basic computing, weresurveyed. Feelings about learning maths and preferred teaching methods were addressed byinformal interviews and a focus-group meeting. Students' statements of confidence aboutspecific mathematical principles and practices, before and after working through relevantmodules, were gathered throughout the course. A 'task experience' questionnaire wascompleted by students during term 1, to get an idea of how the course was progressing fromtheir point of view. At the end of the course, shortly before the examination, a second focusmeeting was held. The year's assessment grades were studied.30ALT-J Volume 4 Number ITeaching staff, who had collaborated in both the planning and the implementation of theevaluation exercise, as well as in the interpretation of interim findings, were interviewed.Evaluation outcomesStudent perspective *Table 2 summarizes findings from questionnaires and interviews. Most of the students cameinto the course computer-literate, in that 14 had had some training in computer use, either atschool or at college, with the software they had used ranging from MacWrite to C++. Mostused a computer at least once a week. Modestly they stated themselves as 'novice' more oftenthan 'competent' - almost all said they had at least some confidence about using a computer.Computing experienceAttitudes, practical knowledgeConfidence with computersMaths ExperienceExperiences with maths learningConfidence about practical mathsExperience of BTechEd coursePositiveNeutralNegative- high- middling to good- generally negative- increasingwith CALMAT- independent learning- own pace- immediate feedback- peer support- learning with computer- three-hour sessions— occasional incorrect feedback,- 'one method' teaching- need for tutorial support when 'losing it'Table 2: Student information summaryStudents' attitudes to and basic knowledge of computers were surveyed (with permission) byquestions from a questionnaire developed by Queen's University, Belfast. Almost all attitudeswere positive, and almost all knowledge questions were answered correctly.Their experience with maths learning was varied and, generally, negative. The mainimpression was that it worried them. Lectures were definitely not favoured: 'Once you getbehind, you stay there', 'Two hours and aching fingers', were two students' views aboutlistening and note-taking, a third adding: 'You're concentrating on getting everything down,not on taking it in'.Questioned at the end of term 1, students' experience with CALMAT was positive, with some31Maggie Pollock et al Rapid conversion of a mathematics course to CALcriticisms. The human-computer interaction presented no problems - except where they felt itgave them 'wrong' when it should not (an issue of decimal places), and when they could notretry a question without restarting a complete module. For the majority of students, three hours(with coffee break) at the computer screen was not a problem. However, for a few it was -these students would spend some time at the machine, then work through paper exercises in therelevant handbook: They very much liked the own-pace element, although there were stillsome fears of 'getting lost' or falling behind. Students were encouraged (rather than required)to complete their recommended exercises to a schedule - by three-quarters of the way throughthe term, many were behind on this. In general, they rated themselves more confident aboutmaths principles and practice as they went through the course, and most students activelyliked the working environment, which they felt included a lot of peer support.Teacher perspectiveDiscussions with teachers during the course and afterwards showed them to be even morepositive than the students. Table 3 summarizes the information. The feedback from theevaluation exercises fitted in with their own perceptions.• Importing established and supported software, in this case, has been very costeffective.• No time needed to prepare and deliver lectures.• Less stressful, allows support structures to be developed where needed rather thanglobally.• Possible improvement in students' practical application of maths in other courses.• Intend to provide weekly tutorial sessions and support further 'peer' tutorials atneed.• Intend to closely monitor next year's project work for evidence of practical mathsknowledge.Table 3: Teacher information summaryInformation from diagnostic test and class-examination resultsThe first class-examination posed 40 multiple-choice questions and 10 standard problems.Among the multiple-choice questions were the original 20 questions from the diagnostic test,to measure any improvement. The second class-examination set 10 problem-type questions.The degree examination had the same format as the second class-examination. Table 4 gives anoverview of the results.The diagnostic post-test at the end of term 1 indicates some improvement in their skills - therange is wide both before and after, and the central tendency is high. Ten students scored 70%or over at pre-test, so had little scope or need for improvement. Polynomials, equations ofstraight lines, and trigonometry were all topics which showed a significant overallimprovement.32ALT-J Volume 4 Number IDiagnostic test- significant overall improvement in scores- from high start 65% (range 30% to 85%)- at end of Term I 76% (range 40% to 100%)- better on some topics than others(e.g. improvement in algebra, co-ordinate geometry and trigonometry)Class exams- December multiple choice 69%- December open questions 36%(some students did not attempt these questions)- May open questions 38%. (five students obtained < 8%)ExemptionsI student with > 80%6 students with > 60%First year degree exam assessment grades 'I student with £ 70%I students with > 60%3 students with > 50%4 students with > 45%5 students with < 35%Resit ExamsI student with £ 45%4 students with > 35%Table 4: Diagnostic test, class- and degree-examination outcomesWe are concerned about the outcomes for the 'open' questions - standard mathematicalproblems which depend on knowledge of different topics covered in the course. We do not yetknow whether the material is not teaching, the learners are not learning, or the questions areinappropriate probes of their skills. It should be noted that the average in the May class-examination included five students whose marks were below 8%. Without these marks, theaverage would have been 48%.The first-year degree examination outcomes were acceptable in that they were on a par withthe previous year. It is encouraging that, unlike findings elsewhere (Noss, 1995), entryqualifications were not direct predictors of grades. The top six had entered with a mixture ofHighers, HNC and ONC, the lowest six with Highers, HNC, HND and Access.Although the assessment procedures, of necessity, differed from those for previous years, thesame external examiner's criteria had been satisfied. It is not, however, possible to make anydirect comparisons between the examination outcomes of 1994-95 and the previous year, apartfrom being encouraged that the number of failures after re-sits fell from six (after normative33Moggie Pollock et al Rapid conversion of a mathematics course to CALscaling was applied to the raw marks) to four (out of 21) with no normative scaling. A goodmeasure of their learning will be their competence and progress during next year's courses —electronics, energy, design, etc. - where much of their work will depend upon maths 'fluency'.The best predictor of examination performance was the post-test diagnostic scores - those whocame out best on this at the end of term 1 got the best degree grades, those at the bottom endstayed there.ConclusionsChanging the first-year maths course to student-centred, self-paced learning using a CALpackage, plus supplementary written material and textbooks, has been shown to be no worsethan if the course were delivered using traditional lectures, and in fact was preferred by boththe students and lecturers. The students responded well to self-paced learning and peer self-• help groups developed spontaneously. Staff found it less stressful to supervise the computerlabs than to prepare and deliver lectures. They could devote more time to those students whowere slow and struggling with the work.Every effort will be made to identify earlier those students who are having difficulty. Weintend to improve the learning of these students with the second year of the new course. Weare planning fortnightly tutorial classes, led by 'demand issues' and supported by some peertutoring. We also intend a closer monitoring of students' progress through the modules, thoughinterfering as little as possible with the student-centred, own-pace independent-learning model,which we feel is right for these students.ReferencesCook, J. (1994), 'Bridge the gap with CALMAT', Proceedings of the International Conferenceon Technology in Collegiate Mathematics, November 1994.Cook, J. and Hornby, J. (1995), 'CALMAT mathematics courseware for access to highereducation', Proceedings of the SMC Conference, Stirling, May 1995 (in press).Noss, R. (1995), Reading the Sines, final report of the mid-term evaluation of the TransitionalMathematics/Transmath Project, Institute of Education, University of London.Tabor, J.H. (1993), 'Using CALMAT in "levelling up" teaching', CTI Quarterly Newsletter, 4(1).34

Conversion of a mathematics course to CAL: A case study of a large‐scale rapid change of resources and organization

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Bridge the gap with CALMAT',

CALMAT mathematics courseware for access to higher education',

Reading the Sines, final report of the mid-term evaluation of the Transitional Mathematics/Transmath Project,

Using CALMAT in &quot;levelling up&quot; teaching',

Glasgow University's Teaching With Independent Learning Technologies (TILT) project is an institutional initiative funded under Phase 1 of the Higher Education Funding Councils' Teaching and Learning Technology Programme (TLTP), We have developed or adapted and integrated computer-assisted learning programs into a variety of courses in subjects ranging from Accountancy to Zoology.DOI:10.1080/0968776960040106</jats:p

Maggie Pollock

Erica McAteer

Gordon Doughty

Ian Turner

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Conversion of a mathematics course to CAL: a case study of a large-scale rapid change of resources and organization

Glasgow University&#x0027;s Teaching With Independent Learning Technologies (TILT) project is an institutional initiative funded under Phase 1 of the Higher Education Funding Councils&#x0027; Teaching and Learning Technology Programme (TLTP), We have developed or adapted and integrated computer-assisted learning programs into a variety of courses in subjects ranging from Accountancy to Zoology

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Conversion of a mathematics course to CAL: A case study of a large‐scale rapid change of resources and organization

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