Improving learning in mathematics. Perception, taste & priorities Pearls before breakfast

Improving learning in mathematics

Perception, taste & priorities

Pearls before breakfast

Programme for Day 2

0930 Welcome & Introduction

0945 Review

1045 Coffee

1115 Talking Maths

1245 Lunch

1330 Teaching Maths

1500 Next Steps

1530 Close

Programme Aim:

To enhance the learning experiences of all pupils by promoting quality teaching of

mathematics

Every School a Good Every School a Good SchoolSchool

Better Mathematics

Characteristics that Determine Effective Provision

December 2008

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.

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

Feedback

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:

Different types of questions

Creating example

s & special cases

Evaluating & correcting

Comparing &

organisingModifying & changing

Generalising &

conjecturing

Explaining &

justifying

Types of activity

Classifying mathematical objects

Creating problems

Evaluating mathemati

cal statements

Interpreting multiple

representations

Analysing reasoning

and solutions

Improving learning in mathematicsReview

Mind Map Activity

Skilful questionin

Variety of teaching activities

and learning strategies?

Feedback

Personal Reflection

Please be back in 30 minutes

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.

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?

Improving learning in mathematicsTalking Maths

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)

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.

You have a role of making little interventions that

might steer the group in the right direction.

Professor Celia Hoyles – Talking Maths

Learners:When you explain, you go through what you've

already done, so it's sort of like revising it.

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.

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.

Lyn Churchman

Ofsted Inspector

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.

Many inspection reports echo this

sentiment!

Mathematics Wall of Mastery

Intuitive

Concrete

Pictorial

Abstract

Application

Communication

2 + 2 = 5

Functions

How good are your communication skills?

Curves

Integrals

Feedback

25536477251

Types of Talk

Types of learner-learner talk

• Cumulative

• Disputational

• Exploratory

Types of Talk

Read the two examples of learner-learner talk

Which type of talk do you think they

represent:Cumulative;

Disputational; or Exploratory?

Types of Talk

Okay then I’ll show the

Personal Reflection

Encourage Talking and Listening

Developing communication, discussion and the skills of working

with others

Develop discussion opportunities

the skills of working with others

Encouraging the communication skills of

talking and listening

Paired Activities

‘Back-to-back’ ‘Fourbidden’

Wacky RacesWacky Races

Developing discussion and the skills of working with

others

and in group composition

(consider size of group and ability)

Developing communication, discussion and the skills of working

with others

Plan for progression

in developing communication skills

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

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

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

Improving learning in mathematicsLearning NI

Personal Reflection

Evaluation & Travel forms

Go 4th + X

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