Learning the work of ambitiousmathematics teachingProfessor Glenda AnthonyIEFE, Feb 2013, Saudi Arabia
Challenging goals of education• Changing educational targets for knowledgesociety.• Awareness of academic and social outcomes• Expectations of equitable opportunities andaccess for diverse students.
Mathematical proficiency• Must include both cognitive and dispositional/participatory components.• A way of knowing in which:– conceptual understanding,– procedural fluency,– strategic competence,– adaptive reasoning, and– productive dispositionare intertwined in mathematical practice andlearning.
New social and academically ambitiouslearning goals within the maths classroomNew forms of pedagogy to developmathematical proficiency in its widest sense
Ambitious Teaching• Supports learners not only to do mathematicscompetently, make sense of it and be able to useit to solve authentic problems in their everydaylife.• Our views are informed by research about whatteachers need TO DO and what they need toKNOW.• Anthony, G., & Walshaw, M. (2009). Effective pedagogy inmathematics No 19 in the International Bureau of EducationsEducational Practices Series: www.ibe.unesco.org/en/services/publications/educational-practices.html
Ambitious mathematics teachers:ü Have specialised knowledge for teaching andteaching mathematicsü Have high expectations for all studentsü Place students’ reasoning about maths at thecentre of instruction.
Create classroom inquiry communities• Skills in orchestrating instructional activities thatprovide opportunities for mathematical talk.• Ability to notice, elicit, and interpret students’mathematical reasoning.• Promote and ethic of care , building relationshipsthat are inclusive, and expect all students toengage.
Ambitious teaching requires investmentin TEACHER LEARNINGTeacher learning (at all stages of one’s careerpathway) is a “major engine for academicsuccess”• Wei, R. C., Andree, A., & Darling-Hammond, L. (2009). How nationsinvest in teachers. Educational Leadership, 66(5), 28-33.
Supporting teacher learning• Initial teacher education• Beginning teacher mentor and guidanceprogrammes• School based and external professionaldevelopment experiences• Further study/research contexts.
Professional development in mathseducation in New ZealandInformed by two sources from the Ministry ofEducation Iterative Best Evidence Synthesis (BES)programme1. synthesis on effective mathematics pedagogy(Anthony & Walshaw, 2007, 2009).2. synthesis on teacher professional learning anddevelopment (Timperley, Wilson, Barrar, & Fung,2007, 2008) andSee <http://www.educationcounts.govt.nz/topics/BES>
Teacher inquiry and knowledge buildingcycleWhat knowledge and skills do we as teachers need to enable our student to bridge the gap between current understandings and valued outcomes? How can we as leaders promote the learning of our teachers to bridge the gap for our students? Engagement of teachers in further learning to deepen professional knowledge and reﬁne skills Engagement of students in new learning experiences What has been the impact of our changed ac=ons on our students ? What educa=onal outcomes are valued for our students and how are our students doing in rela=on to those outcomes?
Case 1:Learning the work of ambitious mathematics teaching• Building on the work of a team of U.S.researchers in the Learning in, from and forTeaching Practice (LTP) we have introducedpublic rehearsals of purposefully designedInstructional Activities (IAs) into our teachereducation math methods courses.• See http://sitemaker.umich.edu/ltp/home for LTP project
Instructional Activities• Examples include quick images, choral counting,strings, and launching a problem and facilitatinga discussion.• Designed to be activities that enable noviceteachers to practice the key routines andknowledge involved in ambitious teaching.
Choral Counting:Count by 6 starting at 55 11 17 23 2935 41 47 53 5965 71 77 83 8995 ?• These activities provide opportunities forlearners to develop the mathematical practicesof reasoning, explaining, and justifying - in thecontext of pattern seeking/exploringmathematical structure.
RehearsalsIn rehearsals we work with teachers to learn howto:• Support their students to know what to shareand how to share• Support their students to be positionedcompetently• Work towards a mathematical goal.
Approximations of practicee.g., talk moves• Revoicing – a students’ thinking• Repeating – asking students to restate someoneelse’s reasoning• Reasoning - agree/disagree• Adding on to another student’s reasoning–connects mathematical ideas• Wait time
Case 2:Encouraging Mathematical Talk• Teacher inquiry supported by a Communicationand Participation Framework (CPF) tool.• Maps out possible teacher actions and studentpractices within the classroom.• Supports trajectory of change of teacherpractices.• Provides a shared language to support teachers’reflection within a professional community.
CommunicationPhase One Phase Two Phase ThreeM a k i n gc o n c e p t u a lexplanationsUse problem context tomake explanationexperientially real.Provide alternative ways to explainsolution strategies.Revise, extend, or elaborate onsections of explanations.M a k i n ge x p l a n a t o r yjustificationIndicate agreement ordisagreement with anexplanation.Provide mathematical reasons foragreeing or disagreeing withsolution strategy. Justify using otherexplanations.Validate reasoning using own means.Resolve disagreement by discussingviability of various solution strategies.M a k i n ggeneralisationsLook for patterns andconnections. Compare andcontrast own reasoningwith that used by others.Make comparisons and explain thedifferences and similarities betweensolution strategies. Explain numberproperties, relationships.Analyse and make comparisonsbetween explanations that aredifferent, efficient, sophisticated.Provide further examples for numberpatterns, number relations and numberproperties.U s i n grepresentationsDiscuss and use a range ofrepresentations to supportexplanations.Describe inscriptions used, toexplain and justify conceptually asactions on quantities, notmanipulation of symbols.Interpret inscriptions used by othersand contrast with own. Translateacross representations to clarify andjustify reasoning.U s i n gmathematicallanguage anddefinitionsUse mathematical wordsto describe actions.Use correct mathematical terms.Ask questions to clarify terms andactions.Use mathematical words to describeactions. Reword or re-explainmathematical terms and solutionstrategies. Use other examples toillustrate.
Active listening and questioning• Discuss and role-play active listening.• Use inclusive language: “show us”, “we want toknow”, “tell us”.• Emphasise need for individual responsibility forsense-making• Provide space in explanations for thinking andquestioning.• Affirm models of students actively engaged andquestioning to gain further information or clarifyparts of a solution.
Norms of collaborative participation/responsibilities• Provide students with problem and think-time thendiscussion and sharing before recording.• Establish use of one piece of paper and one pen.• Expectation that students will agree on one solutionstrategy that all members can explain.• Explore ways to support students indicating need toask a question during large group sharing.• When questions are asked of the group selectdifferent members to respond (not the recorder orexplainer)• During large group sharing change the explainermid explanation.
What are the common features of theseresearch-based tools?• Support partnerships between teachers andteachers and researchers /facilitators.• Enable teachers to develop a common languageabout pedagogy.• Provide approximations of practice, reduce thecomplexity.• Highlight students’ as learners, building onstudents’ mathematical thinking.• Link teaching actions to create opportunities tolearn with student outcomes.• Focus on equitable and responsive teaching.
Development of adaptive expertise• Adaptive experts are constantly attentive aboutthe impact of teaching and learning routines onstudents’ engagement, learning, and wellbeing.• Tools enabled teachers to learn not just aboutambitious teaching but rather how to doambitious teaching.