Teaching Better Mathematics Learning Better Mathematics

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Teaching Better MathematicsLearning Better
Mathematics

• A Research and Development Project supported by
  NFR and SKF

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Teaching/learning better mathematics?

• How can students learn mathematics better?
• How can teachers provide better opportunities for
  students to learn mathematics?
• What kinds of activity in classrooms contribute
  to deeper mathematical understandings?
• How can didacticians contribute to improving
  mathematics learning and teaching?
• What roles should/can students, teachers and
  didacticians play in the developmental process

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Aim, motive, goal

• A developmental aim is that students learning
  of mathematics will improve as teachers and
  didacticians come to know more about learning
  processes and the tasks and tools that promote
  learning.

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Learning communities
Working
Asking questions
Thinking
TOGETHER
Tackling problems
Seeking answers
Exploring
Seeking new possibilities
Discussing outcomes
Looking critically
In learning mathematics
In teaching mathematics
In researching mathematics learning and teaching
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Inquiry Processes

• Questioning
• Exploring
• Investigating
• Searching
• Finding out

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Inquiry

• Ask questions
• Seek answers
• Recognise problems
• Seek solutions
• Invent
• Wonder
• Imagine
• Look critically

to
Inquiry as a way of being
from
Inquiry as a tool
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Community

• Working together
• Talking together
• Knowing together
• Shared aims
• Shared practice
• Shared activity
• Shared responsibility
• Engagement in a joint enterprise knowledge
  grows in the community

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WHO?

• School owners
• School leaders
• Teachers
• Didacticians
• Student teachers
• Pupils
• Using inquiry together to develop knowledge and
  understanding

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Inquiry communities

• Working together and asking critical questions
  about what we do, how and why we do it
• What?
• Why?
• How?

Learning through critical exploration of our
own thinking and practice
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Research

• is systematic inquiry made public
  (Stenhouse)

Systematic Inquiry Public
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Three complexly inter-related learning
communities

• Pupils learning mathematics
• Teachers learning about teaching mathematics
• Didacticians learning about ways in which
  mathematics teaching can develop

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Researching together

• By engaging together in inquiry processes in a
  systematic way we are all researchers
• The focus of research is
• our own practice,
• our own learning,
• our own growth of knowledge

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An inquiry cycle

• Thinking and planning
• Action in practice
• Observation of action
• Reflection and review
• Feedback

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In the project

• Schools and teachers decide own goals for
  development
• Didacticians work with schools and teachers to
  use inquiry in the developmental process
• Workshops or seminars at the university college
• Action in teacher team in a school
• Research into the action process

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Own goals in school

• Better learning for pupils.
• What is it that you want to achieve?
• For example,
• Using tasks that really get pupils thinking
• Asking more open mathematical questions
• Working on pre-algebra with young children
• Finding effective ways of using computers
• Finding new ways of addressing a text book topic
• Be realistic and not too ambitious

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How didacticians can help

• Talking with teachers about what is possible in
  school
• Providing workshops to open up mathematics and
  discuss possibilities
• Offering courses in areas that teachers want e.g.
  
• in a mathematical topic
• in use of computers
• in approaches to classroom research
• Researching the developmental process

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Teachers and didacticians are researchers
Research is systematic inquiry made public.

• Teachers inquire into what is possible for the
  classroom and into their pupils mathematical
  learning
• Didacticians inquire into how to support teachers
  and into the developmental process
• ALL learn from the research activity new
  knowledge results in both practice and theory

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Research that promotes development

• Research

Development