Eightprinciples foreffectiveteaching(SwainandSwan,2007)BuildontheknowledgelearnersbringtosessionsEffectiveteachersandtrainersassessandusepriorlearningandadapttheirteachingtotheneedsoflearners.

ExposeanddiscusscommonmisconceptionsEffectiveteachersandtrainerssystematicallyexpose,challengeanddiscusscommonmistakesandmisconceptions.

DevelopeffectivequestioningEffectiveteachersandtrainersuseavarietyoflower-levelandhigher-levelopenquestionsratherthanacontinuousdietofclosedrecallquestions.

Useco-operativesmallgroupworkEffectiveteachersandtrainersusecooperativesmallgroupworksothatalllearnersareabletodiscussimportantideas.Thishaspositiveeffectsonlearning,socialskillsandself-esteem.

EmphasisemethodsratherthananswersEffectiveteachersandtrainersdonotworrytoomuchaboutwhetherornotlearnerscompleteeverytask,butinsteadtheytrytoincreasethepoweroflearnerstoexplainandusemathematicalideas.

UserichcollaborativetasksEffectiveteachersandtrainersuserichcollaborativetasksthat:

• areaccessibleandextendable;• allowlearnerstomakedecisions;• involvelearnersintesting,proving,explaining,reflecting,interpreting;• promotediscussionandcommunication;• encourageoriginalityandinvention;• encourage‘whatif?’and‘whatifnot?’questions;• areenjoyableandcontaintheopportunityforsurprise.

CreateconnectionsbetweenmathematicaltopicsEffectiveteachersandtrainersuseactivitiesthatcreateconnectionsbetweencloselyrelatedconceptsandnotations(suchasdivision,fractionandratio).

UsetechnologyinappropriatewaysEffectiveteachersandtrainersusetechnologytopresentmathematicalconceptsindynamic,visuallyexcitingwaysthatengageandmotivatelearners.SwainJ.,andSwan,M.,(2007).Thinkingthroughmathematics:researchreport.[online]Availableat:http://dera.ioe.ac.uk/22296/1/doc_3631.pdf[Accessed13March2017].