improving learning in mathematics. perception, taste & priorities pearls before breakfast
TRANSCRIPT
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Improving learning in mathematics
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Improving learning in mathematics
Perception, taste & priorities
Pearls before breakfast
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Improving learning in mathematics
Programme for Day 2
0930 Welcome & Introduction
0945 Review
1045 Coffee
1115 Talking Maths
1245 Lunch
1330 Teaching Maths
1500 Next Steps
1530 Close
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Improving learning in mathematics
Programme Aim:
To enhance the learning experiences of all pupils by promoting quality teaching of
mathematics
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Every School a Good Every School a Good SchoolSchool
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Better Mathematics
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Characteristics that Determine Effective Provision
December 2008
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Improving learning in mathematics
By the end of the two day programme participants will be better able to:
Challenge pupils understanding through skilful questioning;
Learning Intentions:
Explore a variety of teaching activities and learning strategies
Encourage pupils to think and talk about how they learn mathematics and what they have
learntContribute to departmental planning and the dissemination of good practice within and across
schools.
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Improving learning in mathematics
How would you Estimate:
The number of hairdressers in N. Ireland?
The population of N. Ireland
(male/female)
The area of Lough Neagh
The height of Slieve Donard
The number of pubs in
Ireland
The number of churches in N. Ireland
The number of mobile phones
in the worldThe number of
Teachers in Northern Ireland
Bowland Maths – You Reckon
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Feedback
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Improving learning in mathematics
Challenged pupils understanding through skilful questioning?
Explored a variety of teaching activities
and learning strategies?
Encouraged pupils to think and talk about
how they learn mathematics and what
they have learnt?
Contributed to departmental planning
and the dissemination of good practice within and
across schools.
Review
Have you:
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Different types of questions
Improving learning in mathematics
Creating example
s & special cases
Evaluating & correcting
Comparing &
organisingModifying & changing
Generalising &
conjecturing
Explaining &
justifying
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Improving learning in mathematics
Types of activity
Classifying mathematical objects
Creating problems
Evaluating mathemati
cal statements
Interpreting multiple
representations
Analysing reasoning
and solutions
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Improving learning in mathematicsReview
Mind Map Activity
Skilful questionin
g
Variety of teaching activities
and learning strategies?
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Feedback
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Improving learning in mathematics
Personal Reflection
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Improving learning in mathematics
Please be back in 30 minutes
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Improving learning in mathematics
Buses, Buses, & more Buses!!
All the pupils in this school are going on a trip.
There are 423 pupils at this
school.
How many buses will be needed?
Show all your work.
Each school bus has 42 seats.
Every bus must have a teacher on board, who will sit in one of
the seats.
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Improving learning in mathematics
Buses, Buses, & more Buses!!
How did you solve this problem?
What benefits would have been gained by pupils working in small groups to
solve this problem as opposed to carrying out the task individually?
Consider the pupil responses
what do you see?
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Improving learning in mathematicsTalking Maths
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Sadly, children are frequently expected to
write mathematics before they have
learned to imagine and to discuss, and those
who do not easily make connections are offered more pencil and paper
work instead of the vital talk and discussion.
Yet in other subjects it would be unthinkable
to ask children to write what they cannot say.
Talking Points in Mathematics,
Anita Straker (1993)
Improving learning in mathematics
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If you can get students to articulate their views, and you get them to
argue amongst themselves, in a way,
you're moving the responsibility to them.
Improving learning in mathematics
You have a role of making little interventions that
might steer the group in the right direction.
Professor Celia Hoyles – Talking Maths
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Learners:When you explain, you go through what you've
already done, so it's sort of like revising it.
Improving learning in mathematics
Every time you explain something, you're reinforcing it in your own head as well. So every time you give an answer to something, you have to be sure of that yourself. And
every time you do it, you become more sure of it.
Teacher: As they're talking to
each other they're exploring ideas out
loud. They're correcting each other, they're
discussing things and coming to conclusions.
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Learners tell us that they get satisfaction out of
understanding something, making sense of it, being able to
explain it and justify their reasoning.
It gives them a lot of confidence, but it also makes sense to them, and they can
then fit it into other things they know.
Improving learning in mathematics
Lyn Churchman
Ofsted Inspector
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We know from research that mathematical discussion is an essential component of
thinking and reasoning. Yet, as many OfSTED reports confirm, collaborative discussion is rare among pupils in most mathematics classrooms.
Improving learning in mathematics
Many inspection reports echo this
sentiment!
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Mathematics Wall of Mastery
Intuitive
Concrete
Pictorial
Abstract
Application
Communication
2 + 2 = 5
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Functions
Improving learning in mathematics
How good are your communication skills?
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Curves
Improving learning in mathematics
How good are your communication skills?
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Integrals
Improving learning in mathematics
How good are your communication skills?
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Feedback
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Improving learning in mathematics
Lunch
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25536477251
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Types of Talk
Improving learning in mathematics
Types of learner-learner talk
• Cumulative
• Disputational
• Exploratory
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Types of Talk
Improving learning in mathematics
Read the two examples of learner-learner talk
Which type of talk do you think they
represent:Cumulative;
Disputational; or Exploratory?
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Types of Talk
Improving learning in mathematics
Okay then I’ll show the
DVD!!
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Improving learning in mathematics
Personal Reflection
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Improving learning in mathematics
Encourage Talking and Listening
Developing communication, discussion and the skills of working
with others
Develop discussion opportunities
and
the skills of working with others
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Improving learning in mathematics
Encouraging the communication skills of
talking and listening
Paired Activities
‘Back-to-back’ ‘Fourbidden’
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Wacky RacesWacky Races
Improving learning in mathematics
Developing discussion and the skills of working with
others
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and in group composition
(consider size of group and ability)
Improving learning in mathematics
Developing communication, discussion and the skills of working
with others
Plan for progression
in developing communication skills
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Improving learning in mathematics
In pairs:
Consider the advice cards about the role of the teacher and if possible, add 2 extra advice cards
‘Diamond 9’ the advice cards according to their relevance
Role of the Teacher
during pupil discussion and collaborative work
As a table group discuss:
Does the Teacher’s role change when managing a whole class discussion? If so, how?
As a table group agree on the 3 most relevant
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Improving learning in mathematics
In your table groups:
Prepare your own list of
‘Ground Rules for pupils to use as they work in groups’
Role of the Pupil
during pupil discussion and collaborative work
As a table group discuss:
How could you encourage pupils to adhere to a similar
list ?
Compare your list with the sheet
Agree your top 3 rules
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Improving learning in mathematics
Theory into practice?
Choose one topic that you plan to teach next week
Think of some ways in which you might build in pupil mathematical
discussion of the important ideas in that topic
Share your outcomes on LNI
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Improving learning in mathematicsLearning NI
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Improving learning in mathematics
Personal Reflection
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Improving learning in mathematics
Evaluation & Travel forms
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Go 4th + X
Improving learning in mathematics