Fiona Allan

Adults Do Count

Adults Do Count

Aims

To think about the effective teaching and learning Maths

To enjoy doing Maths!

Compare these two equations.

What is the same and what is different?

4)2()3(

4)5()2(

22

22

yx

yx

Let’s do some Maths!

LSC leads on Themes 1 &

4

Meeting needs, improvingchoice

Developing leaders, teachers, trainers & support staff of the future

Developing a framework for quality and success

Putting teaching, training and learning at the heart of what we do

Accelerating Quality

Improvement

Success for All - launched 19 November 2002

DfES Standards Unit leads on

Theme 2, 3 & 6

Policy Coherence and

Communications

Background

Putting teaching, training and learning at the heart of what we do

Priority areas phase 1 –

Business, Construction, E2E and

Science.

Priority areas for phase 2 –

Mathematics, ICT, Health & Social

Care, and Land-Based Studies. Building

on the work of phase 1 - delivery

undertaken by LSDA, supported by

regional and national Standards Unit

teams.

Priority areas for phase 3 –

Modern Foreign Languages,

Engineering, ACL, ITT.

The resources were to be

• of world-class quality

• interactive

• developed with practitioners in trials and pilots

They had to contain

• activities for learners

• CPD resources for managers, teachers and trainers

• tutor guides

The resources were to be• part of a national transformation programme.This programme would have • an unique focus on teaching, training and learning and would include •a national coaching programme • high quality resources and approaches.• subject specific regional networks.

“All students can think hard about mathematics and thus do better at mathematics”

Deep Progress in Mathematics 2003

Research

“There are two aspects to low attainment in mathematics: not knowing enough mathematics and not knowing how to learn mathematics.”

Deep Progress in Mathematics 2003

“It is vital that society fully recognises the importance of mathematics

for its own sake, as an intellectual discipline;

for the knowledge economy;for science, technology and engineering;for the workplace;for the individual citizen.”

Post 14 Mathematics Inquiry, February 2004

The following makes a significant contribution to high achievement in mathematics:

“Teaching that focuses on developing students’ understanding of mathematical concepts and enhances their critical thinking and reasoning, together with a spirit of collaborative enquiry that promotes mathematical discussion and debate”.

Evaluating mathematics provision for 14-19-year-olds, (Ofsted 2006)

All students (Source: Allan 2005)

I enjoy Maths

0

10

20

30

40

50

60

70

Maths AoN Sociology

Frequently or sometimes (Source: Allan 2005)

0

20

40

60

80

100

120

Computer

s

Graph

ics ca

lcs.

Teach

er(s

) lectu

red

Notes f

rom

boa

rd

Group

work

Pairs.

Puzzle

s

Videos

Mad

e up e

xerc

ises

Textb

ook e

xerc

ises

Past p

apers

Maths

AoN

Sociology

Teacher(s) stood at the front of the classroom and lectured (Source: Allan 2005)

0

10

20

30

40

50

60

Never Occasionally Sometimes Frequently

With IAW

No IAW

We copied notes from the board (Source: Allan 2005)

0

10

20

30

40

50

60

70

Never Occasionally Sometimes Frequently

With IAW

No IAW

Lessons were sometimes or frequently boring (Source: Allan 2005)

0

5

10

15

20

25

30

35

40

45

Never Occasionally Sometimes Frequently

With IAW

No IAW

Students’ learning styles (Source: Allan 2005)

0

2

4

6Activist

Reflector

Theorist

Pragmatist

Maths

AoN

Sociology

http://tlp.excellencegateway.org.uk/teachingandlearning/downloads/?#math

Improving learning

"When you explain something to someone else then you really understand it."

"When you really understand

something, you don't need to revise - you've got it for life!"

https://www.ncetm.org.uk/resources/5845

Learning Mathematics in Contexthttp://tlp.excellencegateway.org.uk/tlp/xcurricula/lmic/

Teaching and learning functional mathematics

http://www.excellencegateway.org.uk/pdf/TandLMathematicsHT281107.pdf

Mathematics Mattershttps://www.ncetm.org.uk/resources/12491

Principles for effective teaching

• Build on the knowledge learners already have. • Expose and discuss misconceptions.• Develop effective questioning.• Make appropriate use of whole class interactive teaching,

individual work and cooperative small group work. • Encourage reasoning. • Use rich collaborative tasks.• Create connections between mathematical topics and the real world. • Use technology in appropriate ways.• Confront difficulties rather than seek to avoid or pre-empt them• Develop mathematical language• Recognise both what has been learned and how it has been learned

Adults Don’t Count

https://www.ncetm.org.uk/community/8207

Build on the knowledge learners already have

Write down everything you know about

Triangles

Develop effective questioning

Spread out the fraction cards on the table in front of you.

How many questions have you answered in the last few minutes?

Encourage reasoning.

Mathematical Moments

Topic: Percentages (Encouraging reasoning rather than ‘answer getting’)

Create connections between mathematical topics

Write the following numbers at the top of your flipchart paper: 5, 12, 15

Write down beneath the numbers anything which links any two of the numbers.

Use mathematical language appropriately and also be imaginative!

…… and the real world

Golf Course Measurements

“The only way to avoid the formation of entrenched misconceptions is through discussion and interaction. A trouble shared, in mathematical discourse, may become a problem solved.”

Wood 1988

Thinking Through Mathematics

Expose and discuss misconceptions

1. Cut out the cards

2. Stick the Always True, Sometimes True and Never True cards on to a sheet of flip-chart paper.

3. Stick each of other cards under an appropriate title card and explain why you have put it there.

Use rich collaborative tasks Multiple representations

Evaluating statements

Creating problems

Analysing Solutions

Classifying

Tarsia jigsaws and dominoes

Use a Range of Activity Types

Multiple representations Evaluating statements Creating problems Analysing Solutions Classifying Questioning Use of IT Card activities Ideas for open questions Encouragement to develop and extend ideas

Use technology in appropriate ways

ICT and Digital Technology used in mathematics teaching 

Develop mathematical language

Mathematical Moment 2D and 3D shapes (Developing mathematical language)

Make appropriate use of whole class interactive teaching, individual work and cooperative small group work.

When?

What?

Recognise both what has been learned and how it has been learned

What I Learned from Reading the Entire Encyclopaedia A.J.Jacobs

And now ….

Look again at the list of principles for effective teaching.

Which of these are you going to concentrate on for the rest of this term?

Start by focusing on one.

When you have embedded it into your practice, choose another one.

Principles for effective teaching

• Build on the knowledge learners already have. • Expose and discuss misconceptions.• Develop effective questioning.• Make appropriate use of whole class interactive teaching,

individual work and cooperative small group work. • Encourage reasoning. • Use rich collaborative tasks.• Create connections between mathematical topics and the real world. • Use technology in appropriate ways.• Confront difficulties rather than seek to avoid or pre-empt them• Develop mathematical language• Recognise both what has been learned and how it has been learned

And now ….

What will you do next week?

What will you do for the rest of the term?

Fiona Allan

Thinking Through Mathematics