استراتيجيات التعلم الاحترافية لتخريج معلمين متمرسين...
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. جليندا أنتوني المدير الموازي لمركز الامتياز لبحوث الرياضيات في التعليم. كلية التربية والتعليم, جامعة ماسي. نيوزيلنداTRANSCRIPT
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.