This document discusses research-based tools and frameworks to support ambitious mathematics teaching. It describes instructional activities designed for novice teachers to practice key routines of ambitious teaching. Rehearsals are used for teachers to learn how to facilitate mathematical talk and position students competently. A communication and participation framework maps teacher actions and student practices to support teacher reflection and trajectory of change. Common features of these tools include supporting teacher-researcher partnerships, developing a shared pedagogical language, approximating practice, highlighting student thinking, and linking teaching to learning outcomes. The goal is to develop teachers' adaptive expertise.

1. Learning the work of ambitious
mathematics teaching
Professor Glenda Anthony
IEFE, Feb 2013, Saudi Arabia

2. 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.

3. 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.

4. New social and academically ambitious
learning goals within the maths classroom
New forms of pedagogy to develop
mathematical proficiency in its widest sense

5. 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

6. 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.

7. 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.

8. 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.

9. Supporting teacher learning
• Initial teacher education
• Beginning teacher mentor and guidance
programmes
• School based and external professional
development experiences
• Further study/research contexts.

10. 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>

11. 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?

12. 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

13. 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.

14. Quick Image:
How many dots are there?

15. 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.

16. 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.

17. 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

18. Cycle of Enactment and Investigation

19. 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.

20. 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
mathematical
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.

21. 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.

22. 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.

23. 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.

24. 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.