Jason Feser|Helen L. Vasaly|José Palazón Herrera
On the Edge of Mathematics and Biology Integration: Improving Quantitative Skills in Undergraduate Biology Education
Division of Undergraduate Education|National Science Foundation|Truman State University|Division of Undergraduate Education|National Science Foundation|Truman State University|Division of Undergraduate Education|National Science Foundation|Truman State University
cbelife sciences educationvol 12 2 featuresfree accesson edge mathematics biology integration improving quantitative skills undergraduate biology educationjason feser helen vasaly jose herrerajason feseraddress correspondence jason feser email address email protectedsearch papers author helen vasalysearch papers author jose herrerasearch papers authorpublished online13 oct 2017httpsdoiorg101187cbe13030057aboutsectionsview pdf toolsadd favoritesdownload citationstrack citations shareshare onfacebooktwitterlinked inredditemail introductionthe challenges future biologists face dictate change way prepare undergraduates wish pursue career life sciences new biology 21st century national research council nrc 2009 four main challenges articulated enabling sustainable food plant growth changing environments sustaining ecosystems biodiversity rapidly changing environs expanding sustainable alternatives fossil fuels understanding human health solutions 21stcentury challenges involve complex systems single discipline fully address many key problems involve biology future biologists must ready work diverse settings interdisciplinary collaborations equipping biologists current disciplinary knowledge essential biologists also need develop strengths outside specialty fully contribute engage problems rich history interdisciplinary work mathematics biology producing exciting sometimes unexpected new knowledge discoveries jungck 1997 insure continued success interdisciplinary work publics ability absorb understand implications work important mathematical approaches become integral component undergraduate biology education even within biology increasing use large data sets requires biologists acquire skills mathematics particularly statistics computer science goal best accomplished incorporating mathematical tools approaches biology courses example molecular forensics program california polytechnic state university integrates theme across curriculum integrating biology applied areas include database design strong emphasis data analysis kitts 2012deficiencies quantitative knowledge approaches biology curricula noted past decade gross 2000 bialek botstein 2004 frequently mathematics biology courses taught near independence gross 2000 approach often leaves students parallel tracks knowledge unable understand discipline informs influences students difficulty applying knowledge one course another often unable synthesize knowledge cohesive framework decadelong survey plant physiology students revealed persistent weaknesses students abilities answer quantitative questions llamas et al 2012 limitations basic quantitative abilities real implications biology health students study australian nursing students demonstrated conceptual computational errors calculating drug concentrations skills commonly used workplace eastwood et al 2011fostering quantitative competencies important professional biologists virtually subdisciplines well recent analysis fawcett higginson 2012 shows greater concentration mathematical equations presented main text papers published ecology evolution journals lowers number citations paper biologists judged information science citation index fawcett higginson paper raised lively conversation possible causes effect one possibility drawn commentary biology audience lacks comfort mathematically dense papers limits impact ideas findings within providing quantitative approaches early education biologists would improve ability handle mathematical models therefore ability contribute benefit key approaches within fields interest quantitative competencies critical analyzing data analysis behavioral systems cognitive neuroscience studies found multiple articles incorrectly used statistical analyses leading potentially wrong conclusions went undetected researchers reviewers editors nieuwenhuis et al 2011 quantitative competencies essential skills professional biologists enabling effectively interpret communicate complex datathe vision change undergraduate biology education report calls focus core competencies quantitative reasoning modeling simulating complex systems undergraduate students learn apply quantitative skills biological topics use quantitative reasoning interpret data students also proficient use modeling exploring systems computational approaches american association advancement science aaas 2011 bio2010 transforming undergraduate biology education future researchers nrc american association medical collegeshoward hughes medical institutes scientific foundations future physicians college board advanced placement biology test acknowledge importance quantitative reasoning skills modern biology nrc 2003 2009 association american medical collegeshoward hughes medical institute 2009 college board 2012 cbelife sciences education dedicated entire issue mathematics biology see marsteller 2010 despite attention given need improve quantitative competencies many biology courses remain unchanged however prime opportunities exist biologists introduce innovative courses curricula best use resources institutions provide biology undergraduates quantitative competencies need meet demands current future challengesin paper describe two institutions helping undergraduate biology students build quantitative competencies incorporation quantitative skills reasoning biology framed discussion two cases concern introductory biology courses differ complexity mathematics type changes involved first university marylandcollege park mathbench biology modules via interactive webbased instructional service providing supplemental materials illustrate develop quantitative competencies basic biology second example davidson college uses unique text introduce wide range students including calculus experience challenging mathematical concepts biology textbook emphasizes learning modeling data analysis activities integral developing understanding biologymathbench biology modulesproject descriptionbeginning biology students start introductory classes diverse set mathematical experiences students may need assistance integrate mathematical knowledge biology courses even develop basic quantitative skills essential success updated introductory biology courses mathbench biology modules designed kren nelson colleagues university maryland college park interactive web modules detailing critical beginning concepts biology students thompson et al 2010these modules foster numerical literacy reinforce biological themes lay foundational competencies required advanced biology courses modules cover range topics measurements statistics growth rates diffusion core concepts biological processes table 1 40 modules developed date contains interactive examples problems illustrate realworld applications doubling time bacteria diffusion different environments incorporates important quantitative concepts modules written accessible style making appealing easily understood modules succinct hosted online httpmathbenchumdedu completed within students schedules biology educators use modules number ways class presentation reinforce selected concepts prelab activity intervention students needing assistance become proficient essential quantitative skillstable 1 examples mathbench topics demonstrated conceptssectionexamplesmeasurementbasic techniques logs ph metric conversionsvisualizationgraphing threedimensional becomes two dimensionalprobability statisticsnormal distributions science process se punnett squaresstatistical testst test chisquare goodnessoffit simulationsmiscellaneous34 scaling lawcellular processesdiffusion osmosis nernst equationmicrobiologymeningitis case study growth ratespopulation dynamicsescherichia coli population dynamics mutation equilibriumenvironmental sciencesampling evolved immunity watershed coal mountaintop removalclimate changegraphs climate change co2assessment outcomesthe modules positively impact number factors biology students thompson et al 2010 importantly students navigating modules show improved outcomes relative starting quantitative skills measured pre posttests effects noted include improved understanding regarding mathematics used biology increased student engagement biology classmathbench biology modules represent one example biology educators incorporate materials improve quantitative skills reasoning introductory courses materials standalone nature freely available educators utilize materials needed experiment implementation modules beyond use reinforce concepts classroom modules particularly beneficial students taking laboratories typically accompany biology coursesintegration mathematics biology use new textbooktextbooks central components introductory courses textbook design influence students incorporate information relate new knowledge cognitive framework textbooks shape students perceive biology however examination current popular biology textbooks reveals presentation biology focused facts images presented conclusions takehome messages process science involves interpreting data inform understanding develop concepts largely absent duncan et al 2011 understanding process science clearly stated vision change core competency aaas 2011 advanced reports cited altering introductory biology textbooks focus process presents opportunity emphasize integration quantitative competencies early biology studentsproject descriptionbiologists malcolm campbell chris paradise teamed mathematician laurie heyer redesign introductory course davidson college writing textbook de novo book tested classes diverse institutions takes approach rejects encyclopedialike biology textbooks opts focus core themes ideas central biology rather feeding overwhelming amounts information students new biology textbook provides real data challenges students construct knowledge key concepts biology many current textbooks noted milewide inch deep approach provides broad coverage minimizes process science leading shallow perspective biology duncan et al 2011 interpreting data essential biological researcher makes sense teach students think critically examine visual quantitative information means constructing clarifying concepts book utilizes published research data sets key papers allowing students work data organize interpretations develop scientific meaning use figures data rather decoration collection takehome messages helps biology students see discipline science rather foreign language long lists terms memorize texts emphasis data analysis interpretation developing concepts greatly facilitate activelearning practices classroom already demonstrated gains students barsoum et al 2013mathematics incorporated throughout text accompanying pieces termed biomath explorations bmes bmes designed enhance biological concepts interactive mathematical examples maximize accessibility text assumes high school mathematics including algebra calculus basic mathematics preparation students entering course basic quantitative skills developed explorations highlight close relationship mathematics biology throughout explorations students manipulate data sets develop concepts data one exploration students curvefitted data understand abiotic vesicles steal lipids competitors discover possible mechanisms origins life another exploration helps students calculate genetic distances correlate geographic distance using plant populations better understand gene flow third exploration uses simple geometry area triangle approximate amount dna present band meselsonstahls classic experiment semiconservative dna replicationassessment outcomesskeptics often raise concern students using process science learn content suffer lack fundamental knowledge due decreased content throughout one semester introductory biology authors measured effects new textbook students comparing students revised course students two sections using traditional text barsoum et al 2013 teaching approaches consisted socratic discussion mixed teacher presentations across three sections teaching methods consistent measure impact textbook content examinations revealed similar levels knowledge students using new text students using traditional text indicating reducing factual content focusing central themes detrimental student outcomes related content furthermore students using new text exhibited better retention content surveyed several months later perhaps importantly students using new text demonstrated better abilities interpret novel data sets students using new textbook also likely disagree viewing science biology set definitions processes memorizeresourcesthe preceding descriptions illustrate two examples incorporate quantitative competencies biology instruction additional examples textbooks online resources integrate mathematics biology found table 2table 2 resources integrating mathematics biologynamedescriptionwebsitemodeling dynamics life calculus probability life sciences textbookexamines mathematics diverse biology fields connects principles central biological concepts emphasis modeling mathematicscalculus life sciences modeling approach online textbooksfree online texts cover concepts without calculushttpcornettepubliciastateeduclshtmlundergraduate mathematics life sciences models process directions booka collection courses diverse institutions portraying varied attempts integrate mathematics biologywwwmathunledugledder1mathbioedmaanotesprefacetocintropdfesteemmodules excel allow students explore learn concepts transformed contemporary biological practicehttpbioquestorgesteemnumbers countemphasizes biological problem solving contemporary biological problems using real datahttpbioquestorgnumberscountbedrockinquirybased approach use bioinformatics solving biological questionshttpbioquestorgbedrockproblemspacesuniversity californiadavis quantitative computer labscomputer labs covering variety biological topicshttpbiosci3ucdaviseduqcoursessociety mathematical biologyupcoming 2013 annual meeting arizona state universityhttpmathasuedusmb2013enabling changeas faculty consider ways merge quantitative reasoning mathematical skills core content biology process bringing new materials concepts classroom difficult due limited time resources assistance funding agencies exists advance new educational opportunities support faculty changing teaching practices help biology students meet 21stcentury challenges external support foster relationships among faculty support faculty invest curricula development national science foundation nsf programs transforming undergraduate education stem tues program research coordination networksundergraduate biology education rcnube science talent expansion program research experiences undergraduates aimed supporting changes nsf 2006 2011 2012a 2012bfaculty talent interests often segregated discrete diverse disciplines challenge faculty bring quantitative skills attitudes biology courses levels finding likeminded colleagues sister disciplines time develop strong working relationships critical therefore opportunities bring faculty together prove invaluable facilitating spread knowledge enabling partnerships form bridging gap biology mathematics interdisciplinary workshops helped shape field nrc 2009 marsteller et al 2010 making biomath happen 2012 future gatherings educators critical sharing practices exploring rich variety ways mathematics biology intersect one effort hhmi quantitative biology conference httpbioquestorgqb2013 organized pat marsteller scheduled june 1114 2013 emory university cover highprofile efforts bioquest national institute mathematical biological synthesis hhmi quantitative biology consortium tues rcnube programs support efforts bring educators together explore issues development courses materials support goals nsf 2006 2012a community strongly encouraged seek opportunities work warrants supportconclusionthe goal change biology teaching match biology opportunity educators creatively explore forge interdisciplinary relationships mathematics biology biology research integrated quantitative methods knowledge creation becomes paramount future generations biologists appropriately educated paper highlight two cases help frame scope mathematical quantitative competency issues improve student quantitative competencies reasoning contribute future success students examples may provide details ways institutions incorporate quantitative skills biology see marsteller 2010 next article series provide many examples provide overview challenges advantages varied approaches merge mathematics biology charge clear nsf ready help biology community meet challengeacknowledgmentswe thank terry woodin steady comments shaping manuscript kaci thompson malcolm campbell generous assistance assure proper description projects glenn ledder richard yamada pat marsteller mathematics biology community advice information enthusiasm encouragement provided course writing paperfootnoteson assignment truman state university kirksville mo 63501any opinions findings conclusions recommendations expressed material authors necessarily reflect views national science foundationreferences american association advancement science 2011 vision change undergraduate biology education call action washington dc google scholar association american medical collegeshoward hughes medical institute 2009 scientific foundations future physicians washington dc aamc wwwhhmiorggrantspdf08209aamchhmireportpdf accessed 3 december 2012 google scholar barsoum sellers pj campbell heyer lj paradise cj 2013 implementing recommendations introductory biology writing new textbook cbe life sci educ 12 106116 link google scholar bialek w botstein 2004 introductory science mathematics education 21stcentury biologists science 303 788790 medline google scholar college board 2012 ap biology quantitative skills guide teachers new york college board httpapcentralcollegeboardcomapcpublicrepositoryapbioquantitativeskillsguide2012pdf accessed 3 december 2012 google scholar duncan db lubman hoskins sg 2011 introductory biology textbooks underrepresent scientific process j microbiol biol educ 12 143151 medline google scholar eastwood kj boyle mj williams b fairhall r 2011 numeracy skills nursing students nurse educ today 31 815818 medline google scholar fawcett higginson 2012 heavy use equations impedes communication among biologists proc natl acad sci usa 109 1173511739 medline google scholar gross lj 2000 education biocomplex future science 28 807 google scholar jungck jr 1997 ten equations changed biology mathematics problemsolving biology curricula bioscene 23 1136 google scholar kitts c 2012 cal polys library pyroprints transcurricular program molecular forensics powerpoint presentation coast council ocean affairs science technology 2012 annual meeting long beach ca april 25 2012 google scholar llamas vila f sanz 2012 mathematical skills undergraduate students tenyear survey plant physiology course biosci educ 19 google scholar making biomath happen 2012 making biomath happen conference home page httpbiomatharizonaedumbh accessed 26 november 2012 google scholar marsteller p 2010 beyond bio2010 integrating biology mathematics collaborations challenges opportunities cbe life sci educ 9 141142 link google scholar marsteller p pillis l findley joplin k pelesko j nelson k thompson k usher watkins j 2010 toward integration quantitative biology mathbiobiomath cbe life sci educ 9 165171 link google scholar national research council nrc 2003 bio2010 transforming undergraduate education future research biologists washington dc national academies press wwwnapeducatalogphprecordid10497 accessed 3 december 2012 google scholar nrc 2009 new biology 21st century washington dc national academies press wwwnapeducatalogphprecordid12764 accessed 3 december 2012 google scholar national science foundation nsf 2006 transforming undergraduate education science technology engineering mathematics program solicitation nsf 10544 wwwnsfgovpubs2010nsf10544nsf10544htm accessed 26 november 2012 google scholar nsf 2011 science technology engineering mathematics talent expansion program step program solicitation nsf 11550 wwwnsfgovpubs2011nsf11550nsf11550htm accessed 26 november 2012 google scholar nsf 2012a research coordination networks program solicitation nsf 13520 wwwnsfgovpubs2013nsf13520nsf13520htm accessed 12 december 2012 google scholar nsf 2012b research experience undergraduates reu program solicitation nsf 12569 wwwnsfgovpubs2013nsf13542nsf13542htm accessed 16 april 2013 google scholar nieuwenhuis forstmann b wagenmakers e 2011 erroneous analyses interactions neuroscience problem significance nat neurosci 14 11051107 medline google scholar thompson kv nelson kc marbachad g keller fagan wf 2010 online interactive teaching modules enhance quantitative proficiency introductory biology students cbe life sci educ 9 277283 link google scholarfiguresreferencesrelateddetailscited bystudent responses creative coding biomedical science education10 november 2022 biochemistry molecular biology education vol 18bridging statistics life sciences undergraduate education14 september 2022 journal biological education vol 7teaching basic calculations introductory biology labjournal microbiology biology education vol 23 1implementation new quantitative biology course assessment students abilities confidence13 july 2020 primus vol 32 3supporting computational apprenticeship educational software infrastructure case study mathematical oncology research lab18 february 2021 primus vol 32 3early undergraduate biostatistics data science introduction using r r studio tidyversethe american biology teacher vol 84 3experiments data mining using digitized natural history collections introduce biology students data science12 may 2022the conceptualization quantitative reasoning among introductory biology facultyjournal microbiology biology education vol 22 3reimagining introductory math curriculum life sciences studentserin sanders oleary hannah whang sayson casey shapiro alan garfinkel william j conley marc levisfitzgerald kevin eagan blaire van valkenburghjennifer knight monitoring editor30 november 2021 cbelife sciences education vol 20 4hits harnessing collaborative training network create case studies integrate highthroughput complex datasets curricula9 august 2021 frontiers education vol 6datarich textbook figures promote core competencies comparison two textbooks9 january 2021 biochemistry molecular biology education vol 49 3student perceptions towards introductory lessons r27 october 2021 natural sciences education vol 50 2how prepared students feel quantitative nature biological sciences degree10 december 2020 journal biological educationyes mathematicians x students x x think25 july 2020 zdm vol 52 6mathematical biology expand expose educate10 september 2020 bulletin mathematical biology vol 82 9community college instructors perceptions constraints affordances related teaching quantitative biology skills conceptslisa corwin stacey kiser sondra lore jillian miller melissa l aikenskimberly tanner monitoring editor29 november 2019 cbelife sciences education vol 18 4review predatorprey model two limit cycles20 august 2018 international journal mathematical education science technology vol 50 6is undergraduate microbiology curriculum preparing students careers field assessment biology majors conceptions growth control microorganisms19 october 2018 international journal stem education vol 5 1orientation pill bugs interdisciplinary activity engage students concepts biology physics circular statisticsthe american biology teacher vol 80 8climate change energy technologies undergraduate introductory science textbooks29 april 2018 environmental communication vol 12 6incorporating interactive statistics workshop introductory biology coursebased undergraduate research experience cure enhances students statistical reasoning quantitative literacy skillsjournal microbiology biology education vol 19 1technology tool teaching quantitative biology secondary undergraduate levels review1 january 2018 letters biomathematics vol 5 1addressing digital divide contemporary biology lessons teaching unixtrends biotechnology vol 35 10gender math confidence grit relationships quantitative skills performance undergraduate biology coursek flanagan j einarsonmarshall sundberg monitoring editor13 october 2017 cbelife sciences education vol 16 3interdisciplinary education predatorprey model developing skill set mathematics biology technology6 february 2017 international journal mathematical education science technology vol 48 6yeast mathematicians ferment discovery model competition describe data19 december 2016 bulletin mathematical biology vol 79 2killing two birds one stone model plant systems tool teach fundamental concepts gene expression analyzing biological databiochimica et biophysica acta bba gene regulatory mechanisms vol 1860 1the poisson distribution biology instructionthe american biology teacher vol 79 1development evaluation tigriopus coursebased undergraduate research experience impacts students content knowledge attitudes motivation majors introductory biology coursejeffrey olimpo ginger r fisher sue ellen dechennepetersgraham f hatfull monitoring editor13 october 2017 cbelife sciences education vol 15 4the impact interactive statistics module novices development scientific process skills attitudes firstsemester research foundations coursejournal microbiology biology education vol 17 3development assessment modules integrate quantitative skills introductory biology courseskathleen hoffman sarah leupen kathy dowell kerrie kephart jeff leipsjanet batzli monitoring editor13 october 2017 cbelife sciences education vol 15 2deriving population growth models growing fruit fly coloniesthe american biology teacher vol 78 3using active learning teach concepts methods quantitative biology12 august 2015 integrative comparative biology vol 55 5authentic research experience big data analysis classroom maize response abiotic stressirina makarevitch cameo frechette natalia wiatrosa malcolm campbell monitoring editor13 october 2017 cbelife sciences education vol 14 3incorporacin de la programacin informtica en el currculum de biologamagister vol 27 2integrating interactive computational modeling biology curricula19 march 2015 plos computational biology vol 11 3assessment student memo assignments management science6 november 2014 journal education business vol 90 1a reverse engineering approach teach biology students mathematical complexity ecology interdisciplinary teaching connects mathematical literacy outdoor practicenexusphysics interdisciplinary repurposing physics biologistsamerican journal physics vol 82 5teaching basic numeracy predictive models socioeconomics marine ecologists bayesian belief networks22 december 2014 f1000research vol 3 vol 12 2 june 01 2013117314 metrics downloads citations downloads 641citations 40 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