Roper, T

Stevenson, J

Tariq, Vicki

English

Vicki Tariq

Jim Stevenson

Tom Roper

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MSOR Connections

Maths for Biosciences: Towards Developing an Innovative E-learning Resource for Post-GCSE Students

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1Vicki TariqUniversity of CentralLancashirevtariq@uclan.ac.ukJim StevensonEBS Trustjim@ebst.co.ukTom RoperUniversity of Leedst.roper@education.leeds.ac.ukMaths for Biosciences Towards Developing an Innovative E-learning Resource for Post-GCSE StudentsMSOR Connections May 2005 Vol 5 No 2At a two-day conference in January 2005, participants from universitybiological sciences departments were asked to write down three words orphrases which summed up their perceptions and feelings about the mathsknowledge and skills of life science undergraduates.  Participants’ answers aresummarised in Table 1.Table 1 Summary of some bioscientists’ viewsThere is undoubtedly concern within the sciences about students’ mathematicalabilities.  From engineering, through physics, to chemistry, to medicine andthrough all the life sciences the problems are well documented [1, 2, 3, 4, 6,7, 9].  Universities have been forced to expand and the cohort of studentsarriving each year is not only larger but in many disciplines is also much morediverse in terms of the students’ prior academic experiences.  There arestudents coming not only from conventional schools and FE colleges, but alsofrom a variety of work-related backgrounds.  Consequently, their qualificationsrange very widely from GCSE, through AS and A2 levels, to HNDs and tailored‘access’ courses.  Older colleagues will remember a time when theundergraduate population was more homogeneous, and a higher educationenvironment where teaching was something of an adjunct to learning ratherthan the driving force.  Today’s students need new ways of learning, newroutes to the subject, and to be offered a different view of things.  Learningmaths is a particular conundrum of overlapping skills, conceptual understandingand contexts, where relevance jostles with charm and difficulty.For those teaching in the life sciences the task of ensuring that students possessthe necessary mathematical knowledge and skills for the discipline is not aneasy one.  The minimum mathematics entrance qualification for manyundergraduate life science programmes remains grade C at GCSE.  However,changes to secondary level mathematics syllabuses in the 1980s and 1990shave allowed students at GCSE to achieve good grades without having beentaught the harder algebraic skills.  In addition, Lenton and Stevens [6] suggestthat difficulties with mathematical concepts in science lessons may arise fromthe teaching of facts and skills, as opposed to teaching through conceptualunderstanding, by science teachers and unqualified teachers of mathematics;ecneicsefiLerewsetaudargrednu...sadebircsed'setaudargrednuecneicsefiLslliks&egdelwonkshtam...sadebircsederew...scimedacaecneicsoiBetaremunnIdegagnesid&cibohp,lufraeFycaremunhtiwyrtotgnilliwnUerehwshtamgnidiovAelbissopsrotaluclacnogniyler-revOslliksniecnedifnocgnikcaLEHotroirpdenraeldnagninosaerlacigolgnikcaLhcaorppalufthguohtatseretnignikcaLgnidnatsrednugnikcaLylppaotytilibaehtgnikcaLsmelborpotegdelwonkriehtetauqedanIcitehtaPgnisirpruSgniyrroWsuoregnaDkaewnetfo,elbairaVrooPelbixelfnIstneduts-citehtapmysleeFehttcepxet'ndidnetfosdnamedelttilwohtadeifirroherAstnihehttadnallacerstnedutsgnihcaetroopfoenodebdluoceromhsiWdnalaitnetops'erehtleeFepohfoytisrevidehtesingoceRfostnedutstsgnomasmelborpnoitacifilauqralimisehtfoweivrevonaleeFgnikcalsimelborpMaths for Biosciences Vicki Tariq, Jim Stevenson and Tom RoperMSOR Connections May 2005 Vol 5 No 22the latter situation has been compounded by thedifficulties associated with finding sufficientprofessionally qualified mathematics teachers [8].In the life sciences, which encompass a wide range ofdisciplines from molecular biology to ecology and frommicrobiology to medicine, the range and level ofmathematical skills required of undergraduates vary,although all require a core of numerical ability [7].Many life science students enter their degreeprogrammes possessing only GCSE Mathematics (or itsequivalent) and only a minority possess a highermathematics qualification (e.g. at AS or A2-level).Concerns have been expressed that changes to GCSEmathematics curricula over the years have reduced theexpected level of ability of students entering life sciencedegree courses.  But even allowing for this, universitydepartments should be able to assume that most studentscan manipulate fractions and decimals, handle powersof ten and be able to plot and interpret graphs.  Manystudents, however, lack confidence in their ability todeal with basic mathematical concepts and are unableto calculate accurately and efficiently even when usinga calculator.  They are often unable to manipulate orappreciate numbers and equations, to use scientificnotation or to explain and make predictions from datapresented in graphs, charts and tables [5, 7, 9, 10, 11].Our challenge is to do something that goes a long wayin a short time to address this deficit in students’confidence, knowledge and skills, and that engagesstudents in the process.  In short, we aim to produce anational learning resource to support post-GCSE pupilsand students in their acquisition, practice and applicationof those mathematics skills essential to the life sciences.Since the life sciences include a plethora of specificdisciplines, our initial questions when formulating astrategy to meet this challenge have been ‘Which lifesciences?’ and ‘What mathematics?’  Plotting mathstopics against individual life science disciplines canyield a cat’s cradle of relationships where, if you’re notcareful, everything becomes relevant and essential toeverything! (See Fig 1)At the January conference attendees were asked torelate broad topics in maths to selected biologicalapplications.  There are, of course, many combinationsbut Fig 1 illustrates examples of just a few of therelationships that emerged.Fig 1  Examples of some relationships between life science disciplines and maths topics3Maths for Biosciences Vicki Tariq, Jim Stevenson and Tom RoperMSOR Connections May 2005 Vol 5 No 2Few would argue that it is possible to identify a corelevel of mathematical ability required by all studentsembarking on life science programmes.  Nobody wouldquarrel with the essentiality of basic arithmetic for allareas; the interpretation of graphs is as essential a skillin molecular biology as it is in behavioural psychology;and if students are going to understand movement andrates of change and predict outcomes with confidencethey will have to get to grips with algebra and elementsof calculus.Our proposalSo what can we do to try and remedy this situation?  Howcan we get the message across to students that maths isexciting and increasingly relevant to all the life sciences?Perhaps the maths should be taught in such a way thatit complements the biology rather than being presentedas a turgid necessity.  So rather than begin with themaths and then demonstrate how relevant it is tobiological topics, might it not be better to start with aseries of biological topics, case studies and scenariosand explore the mathematics within each?  The latterwould be supported by online video-led maths tutorials,to assist students to understand and master the mathscontained within each biological topic.  For argument’ssake we could develop fifty biological case studies,each one of which would relate to a particular lifescience discipline.  Each case study would demandmastery of one or more particular skills in maths.  Therewould of course be overlap and reinforcement; severalcase studies might demand the same mathematicalskills and there might be several maths topics in any onecase study.  The principle of this approach is that the‘context’ (i.e. case study) drives the learning.  Thisshould appeal to students of the life sciences who wouldsee their own subject area as interesting and distinctfrom others, and who would therefore be inclined towant to delve into a particular subject story.  Ourapproach will therefore include:• setting the mathematics in context• capturing students’ imagination by motivatingthem to want to learn the mathematics inherent inthe disciplines• providing brief straightforward case studies andproblem based scenarios• providing the opportunity for extensive practice• ensuring clear and enjoyable navigation throughthe resource• evaluating the usefulness of a pilot resource inschools and universities.The authors’ experiences of developing video-ledteaching in pure and applied maths have convincedthem that the power of web and disk delivery should beexploited in designing a new learning resource for thebiosciences.  With DVD-ROM anything can be included:high quality film, animations, video tutorials, interactiveexercises – and we propose to lead into each componentof the resource with a specially filmed case study of abiological event or phenomenon and to include withinthat case study the maths essential for a full understandingof the biology presented.  Links will enable the studentto navigate from each case study to video-led tutorialson the relevant maths topics, as well as to practiceexercises and printable textual support.The project will build on the experience of developingmathtutor, a new web and disk-based resource designedto teach maths between GCSE and 1st-yearundergraduate levels.  mathtutor delivers pure mathsand contains more than 100 video tutorial and extensionfilms.  Together with 80 diagnostic tests and about 1300interactive exercises, the disks represent an easilynavigable forest of maths packaged for clear and easyaccess.  mathtutor is being generally praised as a uniqueapproach which will do much to repair inadequacies instudents as they embark on courses where maths isrequired and also those students studying at AS and A2-levels where they need help.  Those who work in thebiosciences are already considering mathtutor as anadditional plank in the fight for biological numeracy,but recognise the limitations of such a pure mathsresource in supporting a predominantly maths-phobicpopulation of students.The case study approach – biology with embeddedmaths and then focussing on the maths – is similar to thatused in the earlier project Maths for Engineers whichwas structured around 15 films of mathematical modellingof mechanical events in the real world.  But in Maths forEngineers the maths was ‘up front’.  In Maths forBiosciences the maths will be less obvious and more anunderlying theme, since bioscience students tend to bemore apprehensive about maths.  That said, the wholestructure of the teaching will follow a pattern where theroute to the maths is through the biology rather than theother way round, the normal approach in many textbooksand courses.The project will endeavour to embrace most of theprincipal disciplines within the life sciences and themaths necessary for a full understanding of all casestudies.  As an additional aspect we suggest that theproject could contain extended materials of a researchkind – we are keen to stretch the brightest students aswell as those most in need of support.  We plan to makeeverything very visual, real and full of movement andexciting.Maths for Biosciences Vicki Tariq, Jim Stevenson and Tom RoperMSOR Connections May 2005 Vol 5 No 24A pilotIn order to develop a project of this size, it is necessaryto develop and test a sample first.  We envisage thewhole product consisting of about fifty short biologicalfilms and believe it may be more sensible to divide theproduct into major biological fields, with perhaps tentopic films in each.  For the purposes of the pilot wepropose to produce two filmed case studies within thebroad field of cell biology, since this forms a significantcomponent of AS/A2-level specifications, as well asmany undergraduate programmes.• Case study 1: A patient with anaemia.  A sampleof blood is taken and diluted to a stage when acount can be made.  This results in a diagnosis.The same blood sample is used to count thebacteria within it.  This is a more complexprocess needing dilution followed by plating outsamples and measuring colony numbers.• Case study 2: Population growth in bacteria, birdsor people, involving observation and forecasting.These two filmed case studies will be linked to associatedmaths topics:ydutsesaC scipotshtamfoselpmaxEsllecgnitnuoC ,noitidda,slamiced,srewoPsnoitcarf,noitacilpitlumhtworgnoitalupoP dnasecneuqes,gnilpmaSsuluclac,noitamitse,seiresThe maths will be supported by six to eight video-ledtutorials, printable text, exercises and diagnostic tests.The pilot will draw on materials already recorded formathtutor, but will be tailored for this very differentaudience.  The practice exercises will be designed toattract biologists as well as the more mathematicallyinclined.  It is envisaged that as the pilot is designed anddeveloped, other ideas will surface which willcomplement each case study.And further...The pilot will inform full development of approximatelyfifty case studies across four or five major life sciencedisciplines.  We believe it is important that biosciencestudents not only be encouraged to embrace the mathscontained within their chosen programmes, but also beencouraged to explore how maths can impinge on thefrontiers of biological research.  The following examplesmight stimulate, inspire and open the eyes and ears ofindividuals who have never really imagined how closelythe disciplines of biology and maths are linked.1.  How do birds fly?The answer could be illustrated with a film of birdsflying, incorporating slow motion and overlaid graphicsillustrating the forces involved.  The maths modelswould include an analysis of flight into components andsimple modelling of these.  The maths topics includeforces, vectors, velocity/acceleration, mechanics,graphs.  Links could be provided to other examples ofmovement, including dolphins, pterodactyls, wormsand bacteria.2.  When will I die?The answer could be illustrated with longevity data formen and women, highlighting why people die, thefactors affecting lifespan, as well as demographicchanges, providing students with the opportunity tocalculate the potential time of their own demise! Themaths models would include forecasts from observation,birth and death rates, futures.  Maths topics includesequences and series, probability, logarithms, statistics,distribution curves and calculus.  Links could be providedto bacterial growth, the spread and decline of disease,Malthus and war, Napoleon and the march on Moscow.3.  Why is DNA a double helix?The answer could be illustrated with films of Watsonand Crick, the dimensions of the model and forces onthe various chemical groups.  The maths models wouldinclude real models of the molecule and the necessityto express molecular interaction in mathematical terms.Maths topics include geometry, trigonometry and Fourieranalysis.  Links could be provided to biochemicalreaction times, protein structure and enzymology.The project we propose to embark upon is obviously avery large one, embracing most of the principaldisciplines within the life sciences and the mathsnecessary for a full understanding of all the case studiespresented.  This online and disk-based learning resource,with its associated support materials, will offer analternative course in maths for students of the lifesciences.  The emphasis will be on contextualisedlearning, with highly visual and exciting examples fromthe life sciences encouraging students to want (ratherthen need) to understand the underlying mathematicalprinciples.Maths for Biosciences is a topic for discussion at the conferenceHelping Everyone Learn Mathematics, 14-15 September 2005 (see page 7)5Maths for Biosciences Vicki Tariq, Jim Stevenson and Tom RoperMSOR Connections May 2005 Vol 5 No 2References[1]   Bishop, R. and Eley, A. (2001). Microbiologistsand maths. Microbiology Today, 28, 62–63.[2]   Cartwright, M. (1996). Numeracy needs of thebeginning registered nurse. Nurse EducationToday, 16, 137-143.[3]   Green, J. M., Shearn, D. C. S. and Bolton, N.(1983). A numeracy course for artsundergraduates. Studies in Higher Education, 8,57-65.[4]   Hutton, B. M. (1998). Do school qualificationspredict competence in nursing calculations?Nurse Education Today, 18, 25-31.[5]   Lake, D. (1999). Helping students to go SOLO:teaching critical numeracy in the biologicalsciences. Journal of Biological Education, 33,191-198.mathtutor is an 80+ topic-led DVD Rom and web-based series.Provides pure maths bridgingGCSE – AS/A2 – 1st yearessential maths within mathsand science disciplines.To be published June, 2005.[6]   Lenton, G. and Stevens, B. (1999). Numeracy inscience. School Science Review, 80, 59-64.[7]   Phoenix, D. A. (1999). Numeracy and the lifescientist! Journal of Biological Education, 34, 3-4.[8]   Smith, A. (2004). Making Mathematics Count:Inquiry into Post-14 Mathematics Education,DfES.[9]   Tariq, V. N. (2002). A decline in numeracy skillsamong bioscience undergraduates. Journal ofBiological Education, 36(2), 76-83.[10] Tariq, V. N. (2002). Numeracy skills deficitamong bioscience entrants. LTSN BioscienceBulletin, No. 7, p. 8.[11] Tariq, V. N. (2003). Diagnosis of mathematicalskills among bioscience entrants. In DiagnosticTesting for Mathematics, LTSN MathsTEAMProject, pp.14-15.mathtutor Pythagoras illustrated with ‘The pizza on the hypotenuse’mathtutor animation for ‘Calculus from first principles’These and examples of mathtutormay be viewed at:www.ebst.co.uk/differentiationwww.ebst.co.uk/trigonometrywww.ebst.co.uk/integration andwww.ebst.co.uk/algebramathtutor is funded by a HEFCE FDTL4 grant and the Gatsby Foundation.  It is a collaboration between the universities ofLeeds, Loughborough and Coventry with the EBS Trust.

A decline in numeracy skills among bioscience undergraduates.

A numeracy course for arts undergraduates.

Do school qualifications predict competence in nursing calculations?

Helping students to go SOLO: teaching critical numeracy in the biological sciences.

Making Mathematics Count: Inquiry into

Microbiologists and maths.

Numeracy and the life scientist!

Numeracy in science.

Numeracy needs of the beginning registered nurse.

Numeracy skills deficit among bioscience entrants.

Maths for Biosciences: towards developing an innovative e-learning resource for post GCSE students.

http://clok.uclan.ac.uk/3672/1/Maths%20for%20Biosciences.pdf

Maths for Biosciences: towards developing an innovative e-learning resource for post GCSE students.

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