AdaptedfromFoster,C.,Swan,M.andWake,G.(2015)TheLessonStudyProcessLessonsforMathematicalProblemSolving,Nottingham:TheUniversityofNottingham)

TheLessonStudyProcess–Algebraicpatternsandexpressions

CornerstoneMathsProjectAlisonClark-WilsonandCeliaHoyles

Lessonstudycycle

2

ResearchfocusTodeveloppupils’appreciationofanalgebraicvariableasadynamicconcept.

Identifyresearchfocus

Planresearchlesson

Teachresearchlesson

Analyseresearchlesson

Reviseresearchlesson

Disseminate

Lessonstudycycle

3

Teacherscollaborativelyplan:TheplaceofthelessoninthesequenceThephasesofthelessonandtheirpurposeThekeyprompts,questionsandactionsthatareplannedAnticipatedpupilresponsesResponsestotheanticipatedpupilresponses

Identifyresearchfocus

Planresearchlesson

Teachresearchlesson

Analyseresearchlesson

Reviseresearchlesson

Disseminate

Lessonstudycycle

4

Whenplanningbemindfulof:

NotingexactlywhatYOUwillsayanddo–especiallyduringwholeclassteachingwhenyouplantousethesoftware! Includingdescriptionsofwhenandhowthepupilswillusethesoftware-andhowyouwillsupportthis. Keepingthefocusonthemathematics–i.e.algebraicvariableandhowthevaluesofthetwovariablesneedtoincrease/decreasetogether! Thevocabularyofthelesson–themaths(variable,multiple,increase,decrease);thetechnology(light,block,pattern,linketc.)andthecontext(growingpatternsoflights).

Lessonstudycycle

5

Teachresearchlesson:Observeanddescribe:Teaching:

Whatarethemosteffectiveprompts,questionsandactions?Howwasthesoftwareusedandtowhateffect?Learning:Whatdopupilsdiscuss?

Howdopupilsreason?Mathematics:

Howdoesthedynamicconceptofavariabledevelopduringthelesson?Whatmathematicalsurprisesorchallengesdoyouobserve?

Identifyresearchfocus

Planresearchlesson

Teachresearchlesson

Analyseresearchlesson

Reviseresearchlesson

Disseminate

Lessonstudycycle

6

Analyseresearchlesson:Same-day*(orsoonafter)debriefingincludesafacilitator,theteacher,observers,acommentator.

1. Teacherdescribesthelessonandreasonsbehinddecisionsmadeanddeparturesfromtheplan.

2. Observersdescribewhattheysaw–supportedbyevidence!

3. Generaldiscussionandsuggestionsforrefiningthelesson.

4. Implicationsforotherlessons.5. Commentatormakesasignificant

contribution,wherepossible.*Ifitispossibletoorganise

Identifyresearchfocus

Planresearchlesson

Teachresearchlesson

Analyseresearchlesson

Reviseresearchlesson

Disseminate

Lessonstudycycle

7

Teachersrevisethelessonplan.• Reviewthelessonobjectives.

• Revieweachphaseofthelesson,theflow,thetimings,theprompts.

• Revisethetasksandquestions.

• Revisedtheanticipatedpupilresponses–usingactualpupilresponses.

• Usesamplepupilworktoillustratesuccesscriteria.

• [Ifchangesareextensivethelessonmightberetaught.]

Identifyresearchfocus

Planresearchlesson

Teachresearchlesson

Analyseresearchlesson

Reviseresearchlesson

Disseminate

Lessonstudycycle

8

Sharingtheoutcomes.• Othersreviewthelessonplanandalsoaskquestionswhereanythingisunclear.

• Teachersproduceacopyofthelessonthatmaybedisseminatedamongallteachersinvolvedintheproject.

• OtherteacherstryoutthelessonandbecomeCMChampionsfortheirschool.

• [Schoolpresentsapubliclessonstudyforothers.]

Identifyresearchfocus

Planresearchlesson

Teachresearchlesson

Analyseresearchlesson

Reviseresearchlesson

Disseminate

Lessonstudycycle

9

Moreaboutlessonstudy:FromtheTeacherDevelopmentTrust http://tdtrust.org/what-is-lesson-studyLessonStudyisaJapanesemodelofteacher-ledresearchinwhichatriadofteachersworktogethertotargetanidentifiedareafordevelopmentintheirstudents’learning.Usingexistingevidence,participantscollaborativelyresearch,plan,teachandobserveaseriesoflessons,usingongoingdiscussion,reflectionandexpertinputtotrackandrefinetheirinterventions.FromtheNationalCentreforExcellenceinTeachingMathematicshttps://www.ncetm.org.uk/resources/18729AresourcetosupportmathematicsdepartmentstouseaLessonStudyapproachforprofessionaldevelopment.FromcolleaguesatNottinghamUniversityhttps://www.nottingham.ac.uk/research/groups/crme/projects/lemaps/index.aspxTheprojectbuildsonaninternationalpilotstudywhichexploredthepotentialofusinganadaptedmodelofJapanese'LessonStudy'todeveloptechniquesforteachingmathematicalproblemsolving.Problemsolvingisatopicwhereevenhigh-performingnationssuchasJapanrecogniseaneedformoreprofessionallearning.