استراتيجيات التعلم الاحترافية لتخريج معلمين متمرسين مستقبلًا

Learning the work of ambitious mathematics teaching

Professor Glenda Anthony IEFE, Feb 2013, Saudi Arabia

Challenging goals of education

•  Changing educational targets for knowledge society.

•  Awareness of academic and social outcomes

•  Expectations of equitable opportunities and access 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 disposition

are intertwined in mathematical practice and learning.

New social and academically ambitious learning goals within the maths classroom

New forms of pedagogy to develop mathematical proficiency in its widest sense

Ambitious Teaching •  Supports learners not only to do mathematics

competently, make sense of it and be able to use it to solve authentic problems in their everyday life.

•  Our views are informed by research about what teachers need TO DO and what they need to KNOW.

•  Anthony, G., & Walshaw, M. (2009). Effective pedagogy in mathematics No 19 in the International Bureau of Education's Educational Practices Series: www.ibe.unesco.org/en/services/publications/educational-practices.html

Ambitious mathematics teachers:

ü Have specialised knowledge for teaching and teaching mathematics

ü Have high expectations for all students

ü Place students’ reasoning about maths at the centre of instruction.

Create classroom inquiry communities

•  Skills in orchestrating instructional activities that provide opportunities for mathematical talk.

•  Ability to notice, elicit, and interpret students’ mathematical reasoning.

•  Promote and ethic of care , building relationships that are inclusive, and expect all students to engage.

Ambitious teaching requires investment in TEACHER LEARNING

Teacher learning (at all stages of one’s career pathway) is a “major engine for academic success”

•  Wei, R. C., Andree, A., & Darling-Hammond, L. (2009). How nations invest in teachers. Educational Leadership, 66(5), 28-33.

Supporting teacher learning

•  Initial teacher education •  Beginning teacher mentor and guidance

programmes •  School based and external professional

development experiences •  Further study/research contexts.

Professional development in maths education in New Zealand

Informed by two sources from the Ministry of Education Iterative Best Evidence Synthesis (BES) programme 1.  synthesis on effective mathematics pedagogy

(Anthony & Walshaw, 2007, 2009). 2.  synthesis on teacher professional learning and

development (Timperley, Wilson, Barrar, & Fung, 2007, 2008) and

See <http://www.educationcounts.govt.nz/topics/BES>

Teacher inquiry and knowledge building cycle

What  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 for Teaching Practice (LTP) we have introduced public rehearsals of purposefully designed Instructional Activities (IAs) into our teacher education 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 facilitating a discussion.

•  Designed to be activities that enable novice teachers to practice the key routines and knowledge involved in ambitious teaching.

Quick Image: How many dots are there?

Choral Counting: Count by 6 starting at 5

5 11 17 23 29 35 41 47 53 59 65 71 77 83 89 95 ?

•  These activities provide opportunities for

learners to develop the mathematical practices of reasoning, explaining, and justifying - in the context of pattern seeking/exploring mathematical structure.

Rehearsals

In rehearsals we work with teachers to learn how to: •  Support their students to know what to share

and how to share •  Support their students to be positioned

competently •  Work towards a mathematical goal.

Approximations of practice e.g., talk moves

•  Revoicing – a students’ thinking •  Repeating – asking students to restate someone

else’s reasoning •  Reasoning - agree/disagree •  Adding on to another student’s reasoning–

connects mathematical ideas •  Wait time

Cycle of Enactment and Investigation

Case 2: Encouraging Mathematical Talk

•  Teacher inquiry supported by a Communication and Participation Framework (CPF) tool.

•  Maps out possible teacher actions and student practices within the classroom.

•  Supports trajectory of change of teacher practices.

•  Provides a shared language to support teachers’ reflection within a professional community.

Communication

Phase One Phase Two Phase Three M a k i n g c o n c e p t u a l explanations

Use problem context to make explanation experientially real.

Provide alternative ways to explain solution strategies.

Revise, extend, or elaborate on sections of explanations.

M a k i n g e x p l a n a t o r y justification

Indicate agreement or disagreement with an explanation.

Provide mathematical reasons for agreeing or disagreeing with solution strategy. Justify using other explanations.

Validate reasoning using own means. Resolve disagreement by discussing viability of various solution strategies.

M a k i n g generalisations

Look for patterns and connections. Compare and contrast own reasoning with that used by others.

Make comparisons and explain the differences and similarities between solution strategies. Explain number properties, relationships.

Analyse and make comparisons between explanations that are different, efficient, sophisticated. Provide further examples for number patterns, number relations and number properties.

U s i n g representations

Discuss and use a range of representations to support explanations.

Describe inscriptions used, to explain and justify conceptually as actions on quantities, not manipulation of symbols.

Interpret inscriptions used by others and contrast with own. Translate across representations to clarify and justify reasoning.

U s i n g ma thema t i ca l language and definitions

Use mathematical words to describe actions.

Use correct mathematical terms. Ask questions to clarify terms and actions.

Use mathematical words to describe actions. Reword or re-explain mathematical terms and solution strategies. Use other examples to illustrate.

Active listening and questioning

•  Discuss and role-play active listening. •  Use inclusive language: “show us”, “we want to

know”, “tell us”. •  Emphasise need for individual responsibility for

sense-making •  Provide space in explanations for thinking and

questioning. •  Affirm models of students actively engaged and

questioning to gain further information or clarify parts of a solution.

Norms of collaborative participation/responsibilities

•  Provide students with problem and think-time then discussion and sharing before recording.

•  Establish use of one piece of paper and one pen. •  Expectation that students will agree on one solution

strategy that all members can explain. •  Explore ways to support students indicating need to

ask a question during large group sharing. •  When questions are asked of the group select

different members to respond (not the recorder or explainer)

•  During large group sharing change the explainer mid explanation.

What are the common features of these research-based tools?

•  Support partnerships between teachers and teachers and researchers /facilitators.

•  Enable teachers to develop a common language about pedagogy.

•  Provide approximations of practice, reduce the complexity.

•  Highlight students’ as learners, building on students’ mathematical thinking.

•  Link teaching actions to create opportunities to learn with student outcomes.

•  Focus on equitable and responsive teaching.

Development of adaptive expertise

•  Adaptive experts are constantly attentive about the impact of teaching and learning routines on students’ engagement, learning, and wellbeing.

•  Tools enabled teachers to learn not just about

ambitious teaching but rather how to do ambitious teaching.