[O5] e-learning: setting up a diploma in applied chemistry ... · 8 as HND/ year 2 of Scottish University, SCQF 9 as an Ordinary Degree and SCQF 10 as an Honours Degree. Thus SQA

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ABSTRACT

A new Diploma in Higher Education in AppliedChemistry has been set up through the VirtualCampus of The Robert Gordon University as aresult of demand by employers for training inchemistry for employees. This course replacesthe former SQA Higher National Certificate inApplied Chemistry which was taught by dayrelease. Demand for the day release coursehad shown a significant drop in numbersattending the course and yet the Universityreceived many enquiries for part-time modesof study. However the demand for the coursewas varied, some requiring distance learning,some twilight or evening classes and a few stillfor day release. This paper deals with ourexperience in setting up a distance learningcourse on a Virtual Learning Environment.

INTRODUCTION

For over 20 years The Robert GordonUniversity (formerly Robert Gordon’s Instituteof Technology and RGIT) has been delivering acourse in Applied Chemistry on a day releasebasis leading to the Scottish QualificationsAuthority (SQA) award of a Higher NationalCertificate (HNC) in Applied Chemistry.Students used to study for an OrdinaryNational Certificate (ONC) in Applied Chemistryat the local Further Education College beforeentering the HNC in Applied Chemistry course,

which was equivalent to year two of a ScottishUniversity degree programme.

Traditionally ONC and HNC were part timecourses whilst Ordinary National Diplomas(OND) and Higher National Diplomas (HND)were full time courses. There is also adifference in terms of the number of creditsthese qualifications carried: HNC courseshave 12 credits whilst their counterparts, HNDhave 30 credits. ONC courses have now beendropped and in its place Aberdeen Collegeruns an HNC in General Science (level 1),which gave entry into our level two HNC inApplied Chemistry. Considerable confusionwas therefore generated as studentsperceived that they were taking courses at thesame level rather than different levels.

The qualifications of ONC, OND, HNC, and HNDwere originally awarded by the ScottishVocational Education Council (SCOTVEC) whilstsecondary school qualifications – ‘Highers’ -were awarded by the Scottish ExaminationBoard (SEB). In a rationalisation of awardingbodies in Scotland, there was an amalgamationof SCOTVEC with the SEB to form the ScottishQualifications Authority (SQA). This has resultedin a review of courses and levels and thedevelopment of the Scottish Credit andQualifications Framework (SCQF). The SCFQlevel 6 is set as the Scottish secondary school‘Higher’ qualification, SCFQ 7 as ‘AdvancedHigher’ HNC, or year 1 Scottish University, SCQF

[O5] e-learning: setting up a diploma in appliedchemistry through the university’s virtual campus

Hazel J. WilkinsSchool of Life SciencesThe Robert Gordon [email protected]

Keywords: e-learning, chemistry, diploma, campus

The Science Learning and Teaching Conference 2005

8 as HND/ year 2 of Scottish University, SCQF 9as an Ordinary Degree and SCQF 10 as anHonours Degree. Thus SQA now regards all newHNC courses to be at SCQF 7 whilst an HND isat SCQF 8. The HNC in Applied Chemistry hadthus become an anomaly as its contents were atSCQF 8 yet its title now implied SCQF level 7.

We have also seen a large fall in the number ofstudents enrolling onto the day release courseas fewer and fewer employers were willing torelease their employees for a whole day. Therehas been however, an increased demand fromemployers and learners for courses in sciencefollowing a part time mode of learning butsome requests were for twilight or eveningclasses, some for distance learning whilstothers would still prefer the day release mode.The requests are also for a broadeningprovision of syllabus from chemistry intobiological sciences. To satisfy this demand itwas decided to provide a Distance Learningcourse delivered through the University’sVirtual Campus.

THE VIRTUAL CAMPUS

between staff, students and others, supportingcourse delivery, tutoring, and discussions. Itattempts to recreate facilities to be found on atraditional university campus, such as forexample the library and on-line resources,bookshop, meeting rooms, community groupsetc. A large part of the students’ learningexperience is delivered by tutorials online or bye-mail. The practical elements of the courseare taught by two one-week summer schoolsat which attendance is required.

THE COURSE AIMS

The course aims to develop students’knowledge and understanding of chemistry. Itis intended to provide a course on whichemployers may enrol their employees as partof a professional career structure and it willenable employees, who went into employmentstraight from school, to gain qualifications at aHigher Education level. It providesfundamental knowledge and scientific skills foremployees working in chemistry basedemployment.

THE COURSE CONTENT

On completion of eight modules (4 modulesper year) the students will be awarded aDiploma in Higher Education (AppliedChemistry) from The Robert Gordon University.The modules on the course are shown overleaf.

Students must study Analytical Science 1 andhave the free choice of seven other modulesfrom the remaining nine modules. However thestudents are strongly advised to take at leastone of the practical modules. Practical Work 1is taught by dry laboratory exercises and a oneweek summer school in late August. PracticalWork 2 has more extended work and could beundertaken in the place of work. For studentswho are employed in laboratories thenaccreditation of prior learning for the skills theyare already using and practising is also taken

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The University’s Virtual Campus, which hosts aconsiderable number of open and distance-learning courses, provides a comprehensiveinfrastructure for distance learning, providingthe flexibility for students to study in their owntime. The Virtual Campus facilitates interaction


into account when assessing these twomodules. Analytical Science 1 is a prerequisitefor Analytical Science 2.

For the award of the Diploma in HigherEducation in Applied Chemistry the studentsmust pass Analytical Science 1 and a furtherseven modules from those given above.

DESIGNING THE MATERIALS

to distance learning materials was not so easy.The material now had to be able to be studiedin isolation with no member of staff present.Lecture notes had therefore to be expandedand written in ways that are attractive tostudents. They had to be easy to follow andalso needed to contain all those points ofinformation and explanation which would begiven to the face-to-face learners.

Each module was divided into topics whichhad to be small enough for a distance learnerto be able to complete in a week. Stafftherefore decided to base the topic sizearound their lecture provision. As each of thesemesters at The Robert Gordon Universityhas twelve teaching weeks the modules werenot to contain more than twelve topics. A pagelimit on the topics was not set because therewould be varying numbers of diagrams andpictures in the topics depending on the natureof the material. For topics such asThermodynamics and Kinetics whichcontained numerical work – calculations,graphs etc, the staff were encouraged toinclude worked examples and several practiceexamples. Self assessed questions were alsoincluded in the text.

The first modules written were AnalyticalScience 1, Organic Chemistry and PhysicalChemistry. The production of the graphicalmaterial for these modules was well within thecapabilities of the members of staff writingthem, however production of some of theother modules such as Biological Chemistry,Microbiology and Inorganic Chemistry beganto show up problems which had not beenconsidered at the start of the project. Thesemodules all needed diagrams and pictureswhich were beyond the graphical skills of the

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Analytical Science 1 Analytical Science 2Biological Chemistry Organic ChemistryInorganic Chemistry Physical chemistryMolecular Biology and Modern Techniques MicrobiologyPractical Work 1 Practical Work 2

Course modules

The module content was based on the contentof the second year modules on the full timedegree programme of the BSc (Hons) AppliedChemistry course to ensure that studentscould progress further with the diploma if theywished. This course has been taught for manyyears and has undergone several revisions sothat we were confident that we had a viableprogramme of learning at second year level.Lecturers had well written lecture notes whichhad been tried and tested with the full-timestudents; however the conversion of this material


staff writing these materials. Under copyrightrules staff could not scan in diagrams from textbooks and hand drawn diagrams wereunacceptable to quality control staff of theVirtual Campus.

The writing team therefore decided that therewas need to employ a graphics artist who wasable to produce some excellent graphics forthe distance learning material. For biologicalchemistry two chapters of the recommendedtext book were made available in digitizedform by working with the Robert GordonLibrary which paid to have these chaptersconverted using the HERON project (1).HERON (Higher Education Resources OnlineNetwork) offers a national service to the UKacademic community for copyright clearance,digitisation and delivery of book extracts andjournal articles. Both of these solutions weresuccessful and for future projects we wouldemploy a graphics artist from the beginning.

ENGAGING THE STUDENTS

The Virtual campus is set up so that only thosestudents who are registered on the Diplomacourse can have access to the modulematerials for their course and the other facilitiesin the Virtual Campus. Students are enrolledonto the various modules by the courseadministrator as and when they are studyingthat particular module. This creates the variousmodule groups which consist of the studentsstudying the module, the module tutor, thesenior course tutor and the administrator.

E-mail contact with the students is carried outthrough the Campus although a copy of theirreply to the tutor appears in the tutor’s Outlooke-mail box. A direct link allows the tutor toreply through the Virtual Campus. In this waystudents e-mail addresses can be hidden fromeach other and complete security exists. Thetutor is able to post messages to the wholemodule group and students are able to emaileach other by setting up a contact list withinthe Virtual Campus.

However email doesn’t allow open discussionand so and alternative way of communicatinghas also been set up. This is by using aDiscussion Forum. Here the student or tutorcan post messages and everyone enrolled inthe group is able to read the message andpost a reply. This is particularly useful if astudent poses a question about the module aseveryone benefits from the tutor’s reply. TheDiscussion Fora have a number of strands tothem: Welcome, Module content, Moduleactivities and Module Administration.

However the most difficult task has been to getthe present students to use these fora tointeract. Ideally they should be able to answerqueries that are posted between themselvesrather than waiting for the tutor to answer eachquery. In the same way that full-time studentsmight sit around discussing problems they haveexperienced with the course. Some studentshave indicated that they feel isolated studyingthe material by themselves yet participation inthe Discussion Fora has been very poor to date.

Feedback from the students on the pilot studyhas indicated that it can be very boring readingmaterial on the computer or by downloadingand printing the material and so we areseeking ways of enhancing the modulematerial with a variety of computer aidedactivities. These have included the insertion ofsuitable websites, the use of formativemultiple-choice tests and the use ofcrosswords (2).

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Future plans are to further enhance the coursewith more interactive activities thus engagingthe students’ interest. The Virtual campus hasan introductory module for all studentsindependent of course but the development ofa more specific welcome and introductoryshort module would help to engage thestudents from the start.

REFERENCES

1. http://www.heron.ingenta.com/ (accessed28.04.05)

2. WISE, A., 2003. Web-based puzzleprogram to assist students’ understandingof research methods. active learning inhigher education 4 (2) 193-202.

This project was supported by funds from theESF.

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THE CONSORTIUM PARTNERS

Brunel UniversityUniversity of NewcastleOpen UniversityUniversity of PlymouthUniversity of Reading (Lead Institution)University of Salford

PRIME CONCERNS OF PPLATO

Teaching mathematics to physics under-graduates.

Widening participation in undergraduatephysics.

Using new learning technologies to addressthe two central issues above

PEDAGOGIC ISSUES

How can text-intensive subjects, such asmathematics and physics be presentedeffectively on screen?

To what extent can CAA technology help withassessment?

SCOPE OF PPLATO RESOURCES

A comprehensive flexible digital resource forthe support of physics and mathematics

teaching for physics undergraduates at Level 0and Level 1.

Includes materials for teaching, testing,diagnostics, practice and tutorial support.

Includes a Foundation Programme.

BRIEF DESCRIPTION OF RESOURCES

h-FLAP: A large hyper-linked teachingresource of Level 0 and Level 1 physics andmathematics, with links to a hyper-glossary.

Maths for Science: A hyper-linked teachingresource of Level 0 mathematics for sciencestudents.

Interactive Mathematics: A hyper-linkedtutorial package of Level 0 and Level 1mathematics topics for science students.

h-Tutorials: A hyper-linked tutorial package ofLevel 1 and Level 2 mathematics topics forscience students.

Computer assessment: A computerassessment package to generate aneffectively unlimited question bank withintelligent feedback on Level 0 and Level 1maths, useful for diagnostics, monitoring andfor formative or summative testing.

Online Foundation Programme: A completeflexible foundation programme for preparing

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[O6] Supporting maths and physics through thePPLATO resources

Mike TinkerDepartment of PhysicsUniversity of [email protected]


students for entry into physics-related andmathematics-related degree courses and foruse in continuing professional development inmathematics or physics for those inemployment.

INTEGRATION OF RESOURCES

Five resources, with different styles, accessedvia an HTML interface.

Flexible interface, can link a tutor’s course tothe PPLATO resources allowing flexiblelearning for students.

ASSESSMENT IN PPLATO

Teaching texts and tutorials have embeddedformative questions with rapid feedback & allunder student control. There is essentiallyunlimited CAA with intelligent feedback forsummative and formative use, includingmastery learning.

THE FOUNDATION PROGRAMME

This is a programme in physics andmathematics at Level 0 to prepare students foruniversity entry and to widen participation inundergraduate physics. It may also be used forindividuals seeking training in physics and/ormathematics and for continuing professionaldevelopment. The programme has extensiveCD resources and online tuition. It may bestudied full-time or part-time and eitherphysics or mathematics or both may bestudied. There is an optional laboratoryschool.

The programme is available to HEIs within theiraccredited programmes or to individualstudents with no institutional affiliation. Itprovides a benchmark programme foruniversity physics/engineering entry.

IMPLEMENTING THE RESOURCES

Departments select those parts that they wishto implement and in what way.

This may vary from full course design tobackground teaching support.

Departments agree to evaluate thoseresources used (instruments for evaluation areprovided). The resources are supplied free toHEIs in sector and there is support withimplementation and evaluation.

RESOURCE DEMONSTRATION

The full resource will be demonstrated at themeeting.

FURTHER ENQUIRIES

e-mail is [email protected] is www.pplato.rdg.ac.ukauthor contact is [email protected]

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ABSTRACT

This paper describes the development ofonline mechanics tests written as part of thePPLATO (2005) project. By using randomparameters within questions, including withinMathML for dynamic equations and SVG fordynamic diagrams, many millions of(algebraically and pedagogically equivalent)question realisations can be generated, atruntime, from a single question style. Wedescribe various technical features ofMathML, SVG and question & outcomemetadata and tagging, focussing on thepossibilities and problems they raise. We alsoreport on a FAST (2005) experiment designedto study the efficacy of feedback.

INTRODUCTION

This paper builds on recent work (Greenhow,2004; Gill & Greenhow 2004; Martin &Greenhow 2004; Nichols, Greenhow & Gill2003) that has resulted in a fairly extensiveCAA system called Mathletics. As the nameimplies, Mathletics seeks to provide a ‘trainingfacility’ whereby students at GCSE to secondyear undergraduate level can take diagnostic,formative or even summative assessments.The following are important Mathleticsfeatures:

(1) a variety of question types have beendeveloped with Question Mark’s open codeQML language (a type of XLM language that is

interpreted by a browser – specifically IE5 orabove – to display the question). These typesinclude the usual multi-choice, multi-responseand numerical input (with error range), but alsoresponsive numerical input where commonlyoccurring wrong answers are recognised,confidence-based questions similar to thoseof LAPT (Gardner-Medwin, 2005), hot linequestions where students usually have toidentify a line in a worked solution thatcontains a mistake, and sequential questionswhere a wrong answer in part i) is followedthrough in the rest of the calculation and usedto mark the method for subsequent parts ofthe question (the user’s input for parts ii) etcwill be wrong even if the correct method isused).

(2) roughly 1000 question styles have beenadded to the question database so far,grouped into libraries and sub-librariesaccording to mathematical topic. Where to putquestion styles can sometimes be a problem;the integral of e.g. xsin(x/2) could be includedin any of the integration: substitution, trigfunctions or by-parts sub-libraries. Wegenerally list according to the most advancedskill being tested, in this case by-parts, butthis requires a judgement. Each question styleresults in thousands or even millions ofrealisations seen by the users through the useof random parameters and, sometimes,words. These parameters are carried throughthe question, including MathML-basedequations and diagrams using SVG, and areused in the stem, correct answer (or key),marking and feedback.

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[O7] Learning and teaching via online maths tests

Mundeep Gill and Martin GreenhowDepartment of Mathematical SciencesBrunel [email protected] and [email protected]

Keywords: mathematics, online objective tests, MathML, SVG


(3) in the case of multi-choice or responsivenumerical input, distracters are generated byapplying algebraically/algorithmically encodedmal-rules. A mal-rule can be defined as astructured, but incorrect, way of doingmathematics, for example (a+b)(c+d) = ac +bd. An advantage of this approach is thattargeted feedback can be given for anystudent choosing that particular option formulti-choice questions or that particularnumber for responsive numerical input; theabove mal-rule might trigger a message ‘Youhave forgotten the cross-terms’.

(4) metadata is added to each questiondescription that characterises its algebraic andpedagogic structure. In the above example,negative values of any of the parameters a, b,c and d would change the skills set needed toanswer the question; thus although thealgebra is the same, the signs of theparameters also need including in the questionmetadata. For multi-choice questions,outcome metadata that characterises the mal-rule behind each distracter is needed to makesense of the answer files (these will include theparameter values so recognising whichdistracter has been chosen may not be easywithout this metadata).

(5) font size/colour and background colour canbe set up by each user in a cookie; on enteringa question, this information is read and usedby the question, including equations anddiagrams. For the resizing diagrams, linethickness can also increase with increasingfont size. We think this accessibility feature willbe of use to dyslexic and partially-sightedstudents.

(6) questions are tagged according to difficultylevel and national syllabus (we used Edexcel’sspecification 2005). The questions herepresented are all tagged M1, Mechanics 1. Oncreating an assessment, an author can searchon tags, specifying, for example, that onlyeasy questions are to be asked. Tags are alsoread by the ‘Related material’ button in thefeedback page.

(7) much of the above relies on callingfunctions, held within our template files, seee.g. Martin & Greenhow 2004. They arebasically of two types; those that return theresult of a calculation, e.g. multiply twopolynomials, and those that return MathML orSVG strings to display mathematics ordiagrams correctly e.g. x-2 not 1x+-2,cancelled fractions etc. As well as dramaticallysimplifying the coding of each question, thesefunctions can be used for any web page, forexample to produce learning material that, onreloading, generates equations and diagramsthat are consistent with the randomly chosenparameters and users accessibilitypreferences.

This paper demonstrates some of the abovefunctionality via the screenshots below. Wealso describe our approach to question designand the results of a study to determine theefficacy of the feedback we have written foreach question. Actually most of the authoringwork involved writing sufficient feedback, andat the correct level to engage the students andaffect their future attempts at similar questions(known as feed forward). With FAST (2005)funding we devised a series of pilot studieswith our first year students taking a mechanicsmodule aimed at quantifying their abilities andunderstanding their behaviour/use of thefeedback offered.

DISCOVERING MAL-RULES

In order to ask pertinent questions, tostructure the stem and feedback in a way thatrelates to students and to formulate the mal-rules built into some question types, it is veryuseful to have a clear idea of where studentsmake mistakes. At present there are two typesof source: teachers are a good source ofanecdotal evidence, but this can beunstructured and unquantified; and studentwork, such as their workings in class (seebelow) or their scripts from formal assessment.Chief examiners’ reports (see e.g. Edexcel2005) provide useful information on which

36


exam questions students found difficult, butare not specific enough on why they havedifficulties or how they actually went wrong.We have therefore analysed several hundredscripts from Brunel University’s foundation andfirst year mathematics and mechanicalengineering students, and ReadingUniversity’s foundation and first year physicsstudents. This has proved a rich source (!) ofmal-rules and their popularity, to be reportedon elsewhere. We have been able to build inmost of these into our questions; in the nextacademic year, we will have many hundreds ofanswer files with mal-rule (outcome) metadatathat will help us reformulate less successfulquestions, write new ones and inform teachingstaff and the curriculum in general.

TYPICAL QUESTION AND FEEDBACKSCREENS

Figure 1 (overleaf) shows a typical (annotated)feedback screen for a typical multi-choicequestion. It was wondered if the feedback wastoo extensive and might simply be ignored bystudents. In fact, students spent a lot of timestudying the feedback, even writing it all down(until we pointed out the helpful print button atthe top of the screen). Some students werealso found to be choosing ‘I don’t know’ orinputting random numbers so that they couldread the feedback before making a seriousattempt on similar questions. In short, thefeedback is seen by students as a primarylearning resource, rather than a check on theiranswers and knowledge.

TRIALS OF QUESTIONS

We set up and ran 6 staffed sessionsthroughout the autumn of 2004 to pilot thetests in controlled conditions (15 students tookpart and tests were available and used outsidethese sessions too). Each session was timedto follow material just covered in class. Inaddition to seeing if students could use thesoftware (very few problems were encountered

with the screen navigation/layout) and if thestudents enjoyed, or at least engaged with, thequestions (generally they did), we wanted tofind out how effective the feedback providedwas, in terms of:

" helping students do similar problemsimmediately/1 week/2 months, afterhaving read the feedback.

" helping students do related butdissimilar problems immediately/1week/2 months after having read thefeedback.

" getting students to spend time on taskand properly engage with the material toaffect a change in their learningbehaviour.

It quickly became apparent that we hadoverestimated the number of questions thatstudents could attempt in the 50-minute slot.Perhaps this arose because they spend solong looking at the feedback, but moststudents only completed 2 (out of an expected5) questions.

After four of the sessions, students wereunexpectedly asked to collect all their paperworkings, name them and give them in. Theaim was to see if students were emulating theworked solutions presented in the feedback.Conclusions were difficult to draw from this sowe decided to look specifically for fourindicators – units, diagrams, solution layoutand vector notation. We analysed the past 5years worth (1999/2004) of exam scripts forthe mechanics module, in total 125 scripts andthis year’s (2005) 15 exam scripts (in brackets).42% (45%) of students were using units whenstating their answer and/or throughout theirmethod. 35% (90%) of students were makinguse of diagrams in questions where they wereneeded. 37% (68%) of students were showingtheir method in a step-by-step layout wherethey explained or stated any formulas thatwere being used and any conclusions theyderived from their solution. 61% (65%) of

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Question is restated

in the feedback

Question parameters that change

within specified limits

SVG diagram has correct parameters displayed and

the angle is accurately drawn. The coding calls

component line functions within a template file

(themselves calling the accessibility data). The

resulting strings are concatenated in the question

and passed to the SVG viewer plug-in automatically

by the browser.

Fully-worked solution in

MathML with question

parameters taken through

Button reads syllabus tag and

displays a message about A level

module M1

General feedback

and advice


Figure 1: A typical feedback screen with annotation


students were indicating vectors correctly. Thesituation is complicated by a change oflecturer in 2002, which also was a low year, at30%, for correct showing of vectors, but twoof the trends are quite dramatic and providesome support for the notion that the feedbackis having a beneficial and lasting effect on thestudents.

CONCLUSIONS

Mathletics is due to be released this summer,ready for use in the next academic year. Bywriting a substantial number (about 100) ofquestion styles that incorporate randomparameters, we have built a useful resourcethat spans the M1 Mechanics module at Alevel and hence is useful to a range of school,college and university students. Although wewill be collecting further evidence about theeffectiveness and student reaction to thesequestions, results obtained the evaluationproject have been encouraging. Studentsspent a lot of time reading the extensivefeedback and this appears to have positiveeffects on them. The questions were beingused as a learning tool alongside lectures andseminars.

REFERENCES

Edexcel (2005) http://www.edexcel.org.uk/qualifications/QualificationAward.aspx?id=48823

FAST – Formative Assessment in ScienceTeaching (2005) http://www.open.ac.uk/science/fdtl/

Gardner-Medwin A. R. (2005) LAPT-lite forbrowsers. Available on http://www.ucl.ac.uk/lapt/laptlite/

M. Gill and M. Greenhow (2004) ‘Settingobjective tests in mathematics using QMPerception’ 8th CAA Conf, Loughborough,July. Available via the Conference Archiveat http://www.caaconference.com/

M. Greenhow (2004) Online video on CAA at:mms://bluerocket.caret.cam.ac.uk/talkatcaret/MartinGreenhow041207.wmv

E. Martin & M. Greenhow (2004) ‘Settingobjective tests in linear algebra using QMPerception’ MSOR Connections Volume 4,Number 3 Aug. Available on http://ltsn.mathstore.ac.uk/newsletter/vol4.shtml#no4

D. Nichols, M. Greenhow and M. Gill (2003)‘Pedagogic issues in setting onlinequestions’ MSOR Connections Volume 3,Number 4 Available on http://ltsn.mathstore.ac.uk/newsletter/vol3.shtml#no4

PPLATO: Promoting Physics Learning And TeachingOpportunities (2005) http://www.rdg.ac.uk/AcaDepts/sp/PPLATO/publish/

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ABSTRACT

‘mathtutor’ is a new mathematics e-learningresource for mathematics and scienceeducation, which delivers diagnostic tests,video tutorials, interactive exercises,animations and printable text via DVD andthe Internet. It has been designed to supportstudents through AS and A2 levelmathematics to 1st-year undergraduateprogrammes in engineering, mathematicsand the sciences, and represents theculmination of extensive collaborative workbetween the EBS Trust and the universitiesof Leeds, Loughborough and Coventry,supported by funding from HEFCE (FDTL4)and the Gatsby Foundation. This paperbegins by highlighting some of the currentproblems surrounding mathematics in thesciences and outlines the background to thedevelopment of ‘mathtutor’. It goes on todescribe the structure and key features ofthis learning resource and concludes bysummarising a proposal to apply the sametechnologies in the development of amultimedia and e-learning resource formathematics support for students of the lifesciences. The latter will apply a contextuallearning model in creating a problem-solvinge-learning environment.

BACKGROUND

There has been growing concern within thesciences about students’ mathematicalabilities. The problems have been welldocumented by disciplines ranging fromengineering, to the life sciences (Phoenix,1999; Lenton and Stevens, 1999; Savage andHawkes, 1999; Tariq, 2002a), and have beenhighlighted by some professions, such asnursing (Cartwright, 1996; Hutton, 1998;Bishop and Eley, 2001).

In the life sciences, which encompass a widediversity of disciplines, the range and level ofmathematical skills required of under-graduates inevitably vary; however, all requirea core of numerical ability (Phoenix, 1999).Over recent years concerns have beenexpressed that many students lack confidencein their ability to deal with basic mathematicalconcepts and are unable to calculateaccurately and efficiently even when using acalculator. They are often unable to manipulateor appreciate numbers and equations, to usescientific notation or to explain and makepredictions from data presented in graphs,charts and tables (Lake, 1999; Phoenix, 1999;Tariq, 2002a, 2002b, 2003). Many life sciencestudents enter their degree programmespossessing only GCSE Mathematics (or itsequivalent) and only a minority possess a

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[O8] Mathtutor: supporting students in learningmathematics

Jim Stevenson*, Vicki Tariq† and Tom Roper‡*Educational Broadcasting Services Trust†University of Central Lancashire‡University of [email protected], [email protected] and [email protected]

Keywords: mathtutor, mathematics, life sciences, e-learning, problem-solving, contextuallearning model


higher mathematics qualification (e.g. at AS- orA2-level). Concerns have been expressed thatchanges to GCSE mathematics curricula overthe years have reduced the expected level ofability of students entering life science degreecourses. But even allowing for this, universitydepartments should be able to assume thatmost students can manipulate fractions anddecimals, handle powers of ten and be able toplot and interpret graphs.

Universities have been forced to expand and thecohort of students arriving each year is not onlylarger but much more diverse in terms of thestudents’ prior academic experiences andachievements. Twenty years ago our scienceundergraduate populations were far morehomogeneous. Nowadays students embarkingupon science degree programmes possess amore diverse portfolio of qualifications, rangingfrom GCSE, through AS- and A2-levels, todiplomas, and may come from work-relatedbackgrounds, as well as from conventionalschools and further education colleges.Changes to secondary level mathematicssyllabuses in the 1980s and 1990s have allowedstudents to achieve good grades without havingbeen taught some of the more difficult conceptsand skills. In addition, Lenton and Stevens(1999) suggest that difficulties withmathematical concepts in science lessons mayarise from the teaching of facts and skills asopposed to teaching through conceptualunderstanding by science teachers andunqualified teachers of mathematics. The lattersituation has been compounded by thedifficulties associated with finding sufficientprofessionally qualified mathematics teachers(Smith, 2004). Today’s students need to beprovided with new ways of learning maths, andto be offered fresh perspectives on their chosendiscipline.

PROVIDING STUDENT SUPPORT INMATHEMATICS

Universities have had to implement a variety ofstrategies aimed at supporting their under-

graduates’ mathematical knowledge andskills. Many science disciplines have adopteda range of strategies to help identify entrants’specific difficulties regarding their basicnumeracy skills and the mathematics regardedas an essential foundation for subjectdisciplines, and to support students’academic development (Tariq, 2004). Learningsupport strategies adopted include:

" formal mathematics courses or teachingsessions – the latter may form part ofeither foundation quantitative subject-specific modules or more generic skillsmodules for first-year undergraduates.Their primary aim is to ensure that allstudents understand the basicmathematical concepts necessary withinthe discipline. But delivering suchcourses can often feel like an up-hillstruggle!

" tutor-led small group tutorial sessions orworkshops outside the formalcurriculum. The problem oftenencountered here is getting students toengage in a process that can appear tothem as offering few returns in terms ofany summative assessment and finalqualification.

" dedicated mathematics learning supportcentres. Some 50% of institutions havesuch facilities. Where available, thesehave proved successful and someprovide a most professional service.However, in the main they seem to beused by students of maths and maths-based subjects and the proportion ofstudents using them can be relativelylow. There is also the recognition thatthey might appeal to those students whoalready possess a high level of mathscompetence and seldom draw in thosestudents in greatest need of help andsupport.

" computer assisted learning (CAL)materials. These are often self-paced

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tutorials and assessment exercises,developed in-house, using software suchas QuestionMark™ or web-developmentsoftware (e.g. Macromedia® Dream-weaver®), and tailored to satisfy thedemands of a particular discipline orspecific module.

" self-help and independent learningresources, e.g. handouts, instructionalguides and/or textbooks (e.g. Phoenix,1997; Foster, 1998; Cann, 2003,www.mathcentre.ac.uk).

All these approaches are valid but are oftenlocal to one institution. What was needed wasto build on these activities and consider anational resource that would be available to allstudents and their teachers.

ENTER MATHTUTOR

‘mathtutor’ and its sister website‘mathcentre’ represent exciting new genericmathematics learning resources, based on thetutorial model of teaching and makingextensive use of video and animation (Fig. 1).‘mathtutor’ consists of a series of six DVD-ROMs covering over 80 topics in arithmetic,algebra, geometry, trigonometry, vectors,functions, graphs, sequences and series,differentiation and integration. The levelstraddles GCSE, AS and A2 mathematics, witha nudge into 1st-year undergraduateprogrammes. ‘mathtutor’ has been designedas a resource to support individual learning,rather than as a discrete course. Each topic isprefaced with a diagnostic test and hasassociated with it pages of interactiveexercises, some 2000 in all. There are over ahundred video tutorial sequences, some ofwhich are quite long – up to an hour – but eachvideo tutorial has a menu for easy navigation.Students appreciate the style of tuition, with a‘live’ tutor providing detailed explanations atan appropriate pace for the learner. The built-in facility to stop and re-play each videotutorial is particularly advantageous and the

feel of the tutorials is very much one ofpersonal and intimate teaching. When thealgebra section was evaluated in 2004, morethan 80% of students found the materialsuseful or very useful.

‘mathtutor’ has been produced by a team ledby the University of Leeds and the EBS Trustwho are experts in new media production. Onthe team are academics from the universitiesof Coventry and Loughborough together withtelevision producers and technicians. Fundinghas been jointly achieved through a HEFCE’sFDTL4 grant and a matching grant from theGatsby Foundation. It is anticipated that all thematerials will be published in summer 2005, inboth disk and web formats.

ADAPTING ‘MATHTUTOR’ FOR THELIFE SCIENCES

The challenge

A team of academics is currently working incollaboration with the EBS Trust to adaptaspects of ‘mathtutor’ for life scienceundergraduates. Our challenge is to try andaddress some of the key issues and concernshighlighted above. In short, our aim is toproduce a national multimedia e-learningresource to support students in their

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Figure 1: Sample screen from 'mathtutor'illustrating an animation for 'Calculus fromfirst principles'


acquisition, practice and application of thosemathematics skills essential to the lifesciences. Since the life sciences include aplethora of specific disciplines, the firstquestions we must answer in formulating astrategy to meet this challenge are ‘Which lifesciences will we cover?’, ‘What mathematicsare regarded as essential to these disciplines?’and ‘What learning model should we use?’

An initial pilot project will select a singlediscipline (e.g. microbiology) or aspect (e.g.cell biology) to cover. Few would argue that itis possible to identify a core level ofmathematical ability required by all studentsembarking on life science degree pathways(Phoenix, 1999; Tariq, 2004), e.g. theessentiality of basic arithmetic; the ability tomanipulate algebraic expressions andequations; the presentation and interpretationof graphical data; and if students are tounderstand movement and rates of changeand predict outcomes with confidence theywill have to get to grips with elements ofcalculus.

Our main challenge lies in increasing students’confidence in their ability to engage with themaths, both basic and more advanced, that isan integral part of their life science discipline.The first step involves persuading studentsthat maths can be exciting, that it can providefresh insights into biological phenomena andthat it is increasingly relevant to the lifesciences. So how can we get this messageacross?

Using the power of contextual problem-solving towards an innovative solution

We plan to adopt Coles’ contextual learningmodel (Coles, 1997) and apply it to problem-solving in an e-learning environment. Maths isan exciting subject and should be taught insuch a way as to complement the biology,rather than as an abstract necessity. So ratherthan present students with a range of mathstopics and then use biological examples tosimply illustrate the application of the

mathematical concepts, might it not be betterto take some exciting biological topics, casestudies and scenarios, present them in a highlyvisual manner and explore the mathematicswithin each – teaching students and enablingthem to practise the maths required for themto understand and master the topic? Eachcase study would demand mastery of one ormore particular mathematical concepts andskills. There would inevitably be overlap andreinforcement; several case studies mightdemand the same mathematical skills andthere might be several maths topicsassociated with any one case study. Theprinciple of this approach is that the context(i.e. the case study) triggers students to want(as opposed to need) to learn the maths. Thisshould appeal to students of the life scienceswho would see their own subject area asdistinct from others and immediately want todelve into a particular scenario. Associatedwith each case study would be a number ofquestions, tasks and calculations for studentsto complete. In addition, students would beprovided with online video-based tutorialsupport for those maths topics and conceptswith which they lacked confidence or withwhich they were unfamiliar; this would besimilar to the format successfully applied in‘mathtutor’. They would also be provided withthe opportunity to practise and apply theirskills to new case studies, thus linking theoryto practice.

The overall structure and navigation throughthis innovative learning resource aresummarised in Figure 2. Upon selecting aparticular discipline or specific aspect, astudent will be presented with a list of relevantcase studies from which they may make theirselection. Each case study will be delivered asa filmed and narrated story involving a realevent or biological phenomenon and thenecessary mathematics associated with it.From this case study learners will be able tonavigate to one or several sections of mathstopics required for their better understanding ofthe maths associated with the case studies.The latter would be presented by a real tutor as

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in ‘mathtutor’ and there would be an extendedtext version of each tutorial available forprinting. What would be interesting would be toexplore supplementary exercises which wouldenable learners to practise the maths they hadlearned, but to make such exercises relatedirectly to appropriate biological case studies,i.e. once again contextualising the maths. Herewe could also incorporate extensions to themaths, taking the learner to new and exciting

developments in biology which involvefascinating maths.

Although the aim is to create a form of problem-solving distance learning or mediated self-studytool, the resource developed could beintegrated into lectures, tutorials or practicalclasses within specific modules orprogrammes.

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e.g. mathguide 4 Cell Biology

Figure 2 Proposed model for a life sciences multimedia learning resource

ESTABLISHING THE CONTEXT

" present a selection of case studies directed at motivating students to wantto learn;

" case studies designed at an appropriate level for students' current state ofknowledge and understanding of cell biology;

" presented using video, accompanying narration and textual summary of the problem;

" student selects a case study

REFLECTION AND ADDITIONAL INFORMATION

" student reflects on existing knowledge and skills (biological and mathematical);

" acquires additional information and help (e.g. on specific maths topics) as necessary, via online maths tutorials and extended notes which relate to the learning context, in order to understand and solve the problem;

" tutorials may take the form of video presentations as in mathtutor

OPPORTUNITY TO HANDLE INFORMATION AND APPLY TO NEW CASE STUDIES

" student uses existing and/or acquired knowledge and skills to solve the current problem and applies what has been learned in new contexts (i.e. additional case studies and problems), as well as in a variety of interactive exercises;

" encourages student to make connections and link theory to practice


Scope of the project

The project aims to embrace most of theprincipal disciplines within the life sciencesand to cover the maths necessary for a fullunderstanding of all the case studiespresented. The resource will offer somethingof an alternative course in maths for the lifesciences, with the emphasis on the lifesciences first and then the underlying mathsthat students need. We aim to makeeverything highly visual, realistic and full ofmovement and excitement.

If you are interested in participating in this projectplease contact Jim Stevenson ([email protected]) orVicki Tariq ([email protected]).

REFERENCES

Bishop R. and Eley A. (2001) Microbiologistsand maths. Microbiology Today, 28, 62–63.

Cann, A. J. (2003) Maths from Scratch forBiologists. Chichester: John Wiley andSons

Cartwright M. (1996) Numeracy needs of thebeginning registered nurse. NurseEducation Today, 16, 137–143.

Coles C. (1997) Is problem-based learning theonly way? In D. Boud and G. I. Feletti (eds)The Challenge of Problem-basedLearning, 2nd edition, Kogan Page,London.

Foster P. C. (1998) Easy Mathematics forBiologists. Amsterdam: HarwoodAcademic Publishers.

Hutton B. M. (1998) Do school qualificationspredict competence in nursingcalculations? Nurse Education Today, 18,25–31.

Lake D. (1999) Helping students to go SOLO:teaching critical numeracy in the biologicalsciences. Journal of Biological Education,33, 191–198.

Lenton G. and Stevens B. (1999) Numeracy inscience. School Science Review, 80,59–64.

Phoenix D. A. (1999) Numeracy and the lifescientist! Journal of Biological Education,34, 3–4.

Phoenix D. (1997) Introductory Mathematicsfor the Life Sciences. London: Taylor andFrancis.

Savage M. and Hawkes T. (1999) Measuringthe Mathematics Problem. A reportpublished under the auspices of: the LTSNfor Maths, Stats and OR, the Institute ofMathematics and its Applications, theLondon Mathematical Society, and theEngineering Council.

Smith, Adrian (2004) Making MathematicsCount: Inquiry into Post-14 MathematicsEducation, DfES.

Tariq V. N. (2002a) A decline in numeracy skillsamong bioscience undergraduates.Journal of Biological Education, 36(2),76–83.

Tariq V. N. (2002b) Numeracy skills deficitamong bioscience entrants. LTSN Bio-science Bulletin, No. 7, p. 8.

Tariq V. N. (2003) Diagnosis of mathematicalskills among bioscience entrants. InDiagnostic Testing for Mathematics, LTSNMaths TEAM Project, pp.14–15.

Tariq V. N. (2004) Numeracy, mathematicalliteracy and the life sciences. MSORConnections 4(2), 25–29.

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ABSTRACT

Key skills are an important element of theUnited Kingdom Government’s educationalagenda (Dearing, 1996; NCIHE, 1997).Nationally recognised key skills includeapplication of number (numeracy). Dearing(1997) emphasised the need for HE institutionsin the UK to deliver ‘numerate graduates’.Subsequently the Department for Educationand Skills’ Numeracy Task Force proposed adefinition framing the skills that are attributedto a numerate individual (DfES, 1998); howeveracross a range of subject disciplines evidencesuggests that a significant number ofundergraduates do not match this definition(Phoenix, 1999; Engineering Council, 1995;LMS, 1995; Engineering Council, 2000; Tariq,2002a; Tariq, 2002b).

Decline in the mathematical fluency ofstudents embarking upon HE courses appearsto coincide with low confidence and negativeattitudes to learning related to the use andapplication of numbers (Mackenzie, 2002).This project explores self-efficacy of studentswhen applying numeracy skills and whether adissonance in perception between studentsand staff exists. During induction studentscompleted a questionnaire that included itemson prior learning experience in numeracy,attitude to numeracy, and perceivedconfidence in applying particular numeracyskills. Staff completed a related questionnaireof their perceptions of students’ abilities in

applying particular numeracy skills. There is aclear dissonance in staff and studentperceptions and an apparent lack ofconfidence and some negative attitudes andconcern towards numeracy. Positive attitudesto prior maths learning are noted; as studentsrecognise the situation of numeracy inacademic and work contexts. Staffperceptions appear more consonant with malestudents. The results of the project will beused to inform provision of appropriatesupport strategies to enhance numeracy skillsand increase confidence and capability in theirapplication.

INTRODUCTION

Concern about levels of basic numeracy hasengaged politicians, educators and employersalike. Qualifications for 16-19 Year Olds(Dearing, 1996) and the report of the NationalCommittee of Inquiry into Higher Education(Dearing Report) (NCIHE, 1997), in additionOFSTED (1993) and the Basic Skills Agency(1997) following evidence of poor levels ofnumeracy in the UK school and adultpopulations. Low levels of numeracy forstudents entering higher education (HE),across a range of subject disciplines are welldocumented in the literature (Phoenix, 1999).

Decline in the mathematical fluency ofstudents embarking upon HE courses appearsto coincide with affective issues, a so called

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[O9] Counting on numbers – squaring the numeracydivide

Adam WattsSchool of Applied Sciences, Biomedical Science DivisionUniversity of Wolverhampton

Keywords: numeracy, dissonance in perceptions, confidence


‘maths anxiety’ (Mackenzie, 2002). Presage(Biggs, 2003; Ramsden, 2003) is a key issue,particularly against the backdrop of the‘massification’ of higher education (Barrington,2004; Coaldrake, 2001) and many HEinstitutions strong commitment to wideningparticipation and lifelong learning. Studentsenter university with a range of qualitativelydifferent conceptions of and approaches tolearning; this will be no different for numeracyand mathematics (Crawford et al., 1998). Theaims of this study were to explore theconfidence and attitudes to numeracy amonglevel one students studying at the Schoolof Applied Sciences, University ofWolverhampton, and to investigate studentand staff perceptions of numeracy and identifyany consonance or dissonance that may exist.

METHOD

A questionnaire was prepared, the constructionof which was influenced by the ideas ofMackenzie (2002) and Tariq (2004), and issuedto year 1 Applied Science students duringinduction week. Questions related to threethemes; prior experience of numeracy, attitudeto numeracy and perceived confidence innumeracy application. This third theme wasfurther subdivided into student and staffperceptions. A five-point Likert scale of‘Strongly agree’, ‘Agree’, ‘Neither agree nordisagree’, ‘Disagree’ and ‘Strongly disagree’was used for assessing prior experience andattitude, and a four-point scale for ratingconfidence C=0 (not at all confident), C=1, C=2and C=3 (very confident). Students were askedto rate their personal confidence (self-efficacy)in each of twenty eight numeracy skills (afterTariq, 2004) and staff asked to rate theirperceptions of what level of confidence wouldbe expected of a level one undergraduateentrant in the same numeracy skills. Allstudents completing the questionnaire wereasked to indicate formal mathematicalqualifications. The questionnaire was producedusing Surveyor by ObjectPlanet software,hosted online and distributed via a URL link

from the University virtual learningenvironment, WOLF (Wolverhampton OnlineLearning Framework) and the University emailsystem. Statistical analysis using Mann-Whitney U Test was performed in SPSS version11.5.

RESULTS

Summary of Questionnaire Findings

160 fully completed questionnaires werereturned, from across the School of AppliedSciences, which comprises four Divisions:Biomedical Sciences, Biosciences, Environ-mental Sciences, Analytical Sciences andGeography (EAS) and Psychology. 31academic staff, all involved in year 1undergraduate teaching returned fullycompleted questionnaires.

Prior Experience and Attitude toNumeracy in year 1 undergraduates

67% of the student respondents were female,and 33% male, which mirrors the genderdemographic of the School. A significantproportion of the students (85%) have passedGCSE maths or equivalent, with 28% ofstudents having studied maths at AS level and8% at A2 level. This prior learning profile issimilar to that reported by Mackenzie (2002).The age profile of the students is 18-41 years;hence non-traditional entrants may well havemore distant experience of maths; however8% of students have gained a qualification inmaths during an Access course, and 17%report Key Skills qualifications in maths.

The majority of students (75%) report havingenjoyed maths at primary/first school; thispositive view of maths is continued atsecondary/high school, with 67% ofrespondents agreeing with the statement. Halfof the students (57%) say that they find doingnumber skills (sums) easy, and 61% intimate awillingness to learn new number skills.

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Although fewer than half of the students (49%)report that they like working with formulae andequations (mathematical constructs), there iswidespread acknowledgement and recognitionthat numeracy is implicit both in terms ofacademic study and employability, withstudents expecting to use number skills inmodules (92%) and at work (95%). Expectationto work with formulae and equations in modules(83%) and at work (71%) is also recognised.

Approximately a third of students agree withthe statement ‘I am concerned about learningnew number skills’, 29% are male and 71%are female congruent with the respondentdemographic. There are identical percentagesfor ‘concern’ shared by Bioscience and EASstudents (39%) with a smaller, yet stillsignificant proportion of Biomedical Sciencestudents reporting ‘concern’ (32%). Data forPsychology students demonstrates amarkedly lower percentage of 10%.‘Avoidance’ as evaluated by agreement withthe statement ‘I avoid formal number work’

demonstrates a similar trend overall with 21%admitting to such avoidance, of which 22%are male and 78% are female.

Student and Staff Perceptions ofConfidence with Numeracy Skills

Students generally express high levels ofconfidence about basic statistics; these mightbe termed basic numeracy skills. Low levelsand no confidence are noted for unitconversion, integration, differentiation,molarity and modelling, a common factorbeing the applied nature of the numeracyskills.

Differences in student and staff perceptions ofconfidence in numeracy application areevident in 9 out of the 28 numeracy skills.There is a dissonance in perception of thefundamental skills of multiplication, division,decimals, the size of numbers andcommunicating data, with staff expectation of

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NeitherStrongly agree nor Stronglyagree Agree disagree Disagree disagree(%) (%) (%) (%) (%)

I enjoyed doing maths at primary/first school 36 39 13 8 4I enjoyed doing maths at secondary/high school 27 40 12 13 8I find doing number work (sums) easy 19 38 27 13 3I want to learn new number skills 19 42 29 8 2I am concerned about learning new number skills 9 23 40 23 5I avoid formal number work 4 17 28 40 11I use number skills in everyday life 24 59 13 4 -I expect to use number skills in the world of work 42 53 4 1 -I expect to use number skills in modules for my 46 46 5 3 -degree I like working with mathematical constructs 16 33 26 17 8 (formulae and equations)I expect to work with mathematical constructs 34 49 12 5 -(formulae and equations) in my degree I expect to work with mathematical constructs 23 48 23 5 1(formulae and equations) at work

Table 1: Prior learning experience and attitude to numeracy of students expressed aspercentage frequency (to nearest whole number) (after Mackenzie, 2002)


confidence in ability to apply such skillssignificantly higher than students’ perceivedconfidence. Conversely, compared to staff,students report higher levels of confidence inthe more advanced skills of integration,differentiation and basic statistics.

Differences in perception analysed by Divisionusing a Mann-Whitney U Test indicated asignificant difference in staff and studentperceptions in all four Divisions of the School.

DISCUSSION

The study revealed that a majority of studentsdemonstrated positive attitudes to their priorlearning experience in mathematics at bothprimary/first school and secondary/highschool, 75% and 67% respectively (Table 1).This is consistent with previously reportedfindings for primary/first schools (Mackenzie,2002); however the two-thirds of studentsreporting to have enjoyed maths atsecondary/high school is in contrast toMackenzie’s findings. This may be a reflectionof the cohort surveyed, in this study thestudents are level one entrants onto an appliedsciences based degree programme;consequently a more pragmatic view might beanticipated, with students viewing maths asintegral to pursuing their chosen future

studies, whilst Mackenzie (2002) drawsrespondents from a range of disciplines thatinclude English, Design and Technology andPE. This pragmatism is reflected by thewidespread acknowledgement andrecognition that numeracy is implicit both interms of academic study and employability.This has positive implications for embeddingappropriate quantitative tasks in teaching andlearning activities, as there appears to be aclear expectation that numeracy skills will berequired, a recognition that numeracy skills areimportant in an academic and broader contextthat includes employability, Edwards andRuthven (2003) have reported that youngpeople are more aware of the mathematicsembedded in everyday activities thanpreviously thought.

Lack of confidence and negative attitudes,sometimes bordering on the irrational fear of‘all things numerical’ (Tariq, 2003; Mackenzie,2002), is reported by 32% of the students. Agreater proportion of those reporting concernwere female (71%). Highest levels of concernare shared by Biosciences and EAS students(39%), a trend that is mirrored for avoidance,this may be linked to students opting toundertake academic studies in these areaswith the notion that this is a way of studyingscience whilst avoiding the maths. Despite the high level of confidence reported

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Environmental& Analytical

❍ ▲ Biomedical Science & All students Science Bioscience Geography Psychology

(%) (%) (%) (%) (%)

I am concerned about 32 29 71 29 39 39 10learning new number skills

I avoid formal number 21 22 78 17 26 22 10work

Table 2: Percentage frequency (to nearest whole number) of students agreeing or stronglyagreeing with statements relating to maths anxiety and avoidance (Mackenzie, 2002)analysed by Division. Male (❍ ) and Female (▲) students.


by the majority of the students, a dissonancein perception for the fundamental skills ofmultiplication, division and decimals isapparent, with staff expectation of confidencein ability to apply these basic numeracy skillssignificantly higher than students’ perceived

confidence. This is of particular disquiet giventhe widespread infusion of such fundamentalmathematical concepts in quantitative tasksboth within the context of both degree andworkplace and links in with the decliningstandards in numeracy reported. Interestingly,

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Table 3: Differences in student and staff perceptions of confidence in 28 numeracy skillsanalysed by cohort and Division

Complete BiomedicalCohort Science Biosciences EAS PsychologyP < 0.05 P < 0.05 P < 0.05 P < 0.05 P < 0.05

Numeracy skill (two-tailed) (two-tailed) (two-tailed) (two-tailed) (two-tailed)

Addition n/s n/s n/s n/s n/sSubtraction n/s n/s n/s n/s n/sMultiplication sig. sig. n/s sig. n/sDivision sig. sig. n/s sig. n/sFractions n/s sig. n/s n/s n/sDecimals sig. sig. n/s n/s n/sPercentages n/s sig. n/s n/s n/sRatios/Proportions sig. sig. n/s n/s n/sProbabilities n/s n/s n/s n/s n/sLogarithms n/s sig. n/s n/s n/sCalculating things mentally n/s n/s n/s n/s n/sJudging whether your answer makes sense n/s n/s n/s n/s n/sBasic Algebra e.g. rearranging and solving n/s n/s n/s n/s n/sequations, using formulaeUsing a calculator n/s n/s n/s n/s n/sAppreciating the size of number sig. sig. n/s n/s n/sExponentials and Powers n/s sig. n/s n/s n/sScientific notation n/s sig. n/s n/s n/sUnit conversion n/s n/s n/s n/s n/sReading scales (measurements) n/s sig. n/s n/s n/sIntegration sig. n/s sig. sig. n/sDifferentiation sig. n/s n/s sig. n/sInterpreting/transforming data from Graphs n/s n/s n/s n/s n/sInterpreting/transforming data from n/s n/s n/s n/s n/sSpreadsheetsInterpreting/transforming data from n/s n/s n/s n/s n/sCharts and TablesMolarity n/s n/s n/s n/s n/sBasic Statistics e.g. mean, mode, median, sig. n/s sig. n/s sig. standard deviationModelling e.g. understanding how n/s n/s n/s n/s n/svariables interact, creating formulaeCommunicating data sig. sig. n/s n/s n/s


compared to staff, students report significantlygreater levels of confidence with the moreadvanced mathematical skills of integration,differentiation and application of basicstatistics. However evidence from practiceand diagnostic tests suggests that there couldbe an overconfidence expressed. Dissonancein appreciating the size of numbers is also ofconcern, as many quantitative tasks areunderpinned by this concept. Some studentsappear to have difficulty conceptualising andrationalising calculated values, demonstratinga greater trust in a calculator display, than theirown judgement. Staff also expected a higherlevel of confidence to be displayed incommunicating data a key skill for scientists.

Dissonance is most prevalent in theBiomedical Science Division. A high degree ofcorrespondence is noted for the other threeDivisions; as a caveat, response rates forstudents as a percentage of the total studentcohort are: Biomedical Science, 49%;Biosciences, 34%; EAS, 11% and Psychology,6%. This dissonance has implications for bothlearning and teaching activities and learnersupport, and will inform appropriateintervention strategies.

CONCLUSION

This study contributes to the debate onattitudes and confidence in applying numeracyand the wider discourse considering decliningstandards of numeracy in HE entrants. With anagenda for widening participation and lifelonglearning, students will enter university withdifferent conceptions of and approaches tolearning; and this will be no different fornumeracy and mathematics. Clearly negativeattitudes and low levels of confidence areincompatible with deeper approaches tolearning so staff must avoid perpetuatinggender stereotypes. Reassuringly the majorityof students in this study report positiveattitudes to maths and appreciate theacademic and vocational relevance ofnumeracy; however there is evidence of

concern about and avoidance of maths andlower levels of confidence in ‘appliednumeracy’. Appropriate support and inter-vention strategies are required to empower thestudents, and the results from this study will beused to shape the process. The relationshipbetween students perceived levels ofconfidence in numeracy application, actualskills and progress need further investigationas the ‘problem’ of numeracy is a potentialbarrier to effective learning.

REFERENCES

Basic Skills Agency (1997) Internationalnumeracy survey. London: Basic SkillsAgency

Barrington, E. (2004) Teaching to studentdiversity in higher education: how multipleintelligence theory can help, Teaching inHigher Education, 9 (4), p 421-434.

Biggs, J. (2003) Teaching for quality learning atuniversity: what the student does. 2nd ed.Buckingham: SRHE and Open UniversityPress.

Coaldrake, P. (2001) Responding to changingstudent expectations, Higher EducationManagement, 13(2), 75-92.

Crawford, K., Gordon, S., Nicholas, J. andProsser, M. (1998) Qualitatively differentexperiences of learning mathematics atuniversity. Learning and Instruction, Vol 8(5)

Dearing, R. (1996) Review of Qualifications for16–19 Year Olds (Middlesex: SCAA).

Department for Education and Skills (DfES)(1998) The Imlementation of the NationalNumeracy Strategy. The Final Report ofthe Numeracy Task Force. London:Department for Education and Skills

Edwards, A. and Ruthven, K. (2003) Youngpeople’s perceptions of the mathematicsinvolved in everyday activities. EducationalResearch, Vol 45 (3)

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Engineering Council (1995) The changingmathematical background of under-graduate engineers (R. Sutherland and S.Pozzi), Engineering Council, London.

Engineering Council (2000) Measuring themathematics problem, EngineeringCouncil, London.

LMS, IMA, RSS (1995) Tackling the math-ematics problem, London MathematicalSociety, London.

Mackenzie, S. (2002) Can we make mathscount at HE? Journal of Further andHigher Education 26(2) p159-171.

NATIONAL COMMITTEE OF INQUIRY INTOHIGHER EDUCATION (NCIHE) (1997)Higher education in the Learning Society(The Dearing Report) (London, HMSO).

OFSTED (1993) Unfinished business: full-timeeducational courses for 16-19 year olds(UK, HMSO)

Phoenix, D. A. (1999) Numeracy and the lifescientist! Journal of Biological Education34(1), p3-4.

Ramsden, P. (2003) Learning to teach inhigher education. London: Routledge.

Tariq, V. N. (2002a) A decline in the numeracyskills among bioscience undergraduates.Journal of Biological Education 36(2), p76-83.

Tariq, V. N. (2002b) Numeracy skills deficitamong bioscience entrants. LTSNBioscience Bulletin, Autumn 2002, no. 7,p8.

Tariq, V. N. (2003) Diagnosis of mathematicalskills among bioscience entrants. InDiagnostic Testing for Mathematics, pp.14-15, LTSN Maths TEAM Project,Birmingham.

Tariq, V. N. (2004) Numeracy, mathematicalliteracy and the life sciences. MSORConnections May 2004 Vol 4 No 2

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Documents

[O5] e-learning: setting up a diploma in applied chemistry ... · 8 as HND/ year 2 of Scottish University, SCQF 9 as an Ordinary Degree and SCQF 10 as an Honours Degree. Thus SQA