Primary PGCELearning and Teaching the

CurriculumMathematics - Introduction

25x88=

Irene Wooldridgeirene.wooldridge@beds.ac.uk

Maria McArdleMaria.mcardle@beds.ac.uk

Sarah CousinsSarah.cousins@beds.ac.uk

If you are unable to attend a session, please inform your tutor.

Aims of session Part 1

•To acknowledge that some people find maths scary

• To communicate the structure of the course

•To communicate some key principles embedded in the course

Success Criteria

• I am feeling a bit more confident about the mathematics element of the course

• I am aware of the aspects of subject knowledge I need to develop

•I know of sources that can support the development of my subject knowledge for teaching mathematics

Our Maths Stories

I Wooldridge & S Cousins10/03/12

About the course -The challenge …• How children learn maths

• What to teach

• When to teach it

• How to teach it

• How to assess it

… in approx 20 hours .....+ Pause points

Hmmmm… quarts and pint pots ?

.........we can’t cover everything!

Our aim is to develop a broader understanding, general principles and approaches that you can apply in a wide variety of contexts as you develop your mathematics teaching career.......

The course• Seminars - looking at approaches to developing mathematical skills and understanding• School placement experience• Tasks M1 M2, & M3• And personal study ....You might want to do your research project with a mathematical perspective

Shulman, 1986 ‘Those who understand: knowledge growth in teaching’, Educational Researcher, 15(2):4-14

 Knowledge bases needed by teachers.

Generic in nature:• general pedagogical knowledge;• knowledge of learners;• knowledge of the context;• knowledge of the purposes of teaching

and learning

Content specific knowledge:• subject-matter knowledge • (facts, skills, concepts & processes and the links

between them, awareness of purpose, knowledge of errors and misconceptions, theoretical underpinning and beliefs about mathematics)

• pedagogical content knowledge • (the mathematical pedagogy which the teacher

brings to the teaching situation and how teachers transform their knowledge into a form that makes it accessible to learners)

• curriculum knowledge • (knowing what it is that children are expected to

learn and knowledge of related resources)

Cockcroft Report (1982)Mathematics teaching at all levels should

include opportunities for

• exposition by the teacher; • discussion between teacher and pupils and

between pupils themselves; • appropriate practical work; • consolidation and practice of fundamental

skills and routines; • problem solving, including the application of

mathematics to everyday situations; • investigational work.

Jerome Bruner’s 3 Modes of Representation

The Enactive Mode:- This involves representing ideas through undertaking some form of action. For example, manipulating physical objects.

The Iconic Mode:- This involves representing ideas using pictures or images.

The Symbolic Mode:- This involves representing ideas through language or symbols.

ELPS helps

The Williams Review

• The importance of scribbles and mark-making

• Thinking made visible• The importance of having

a skilled workforce to support children’s mathematical development

I Wooldridge & S Cousins10/03/12

I Wooldridge & S Cousins10/03/12

Some of our key messages:• Maths isn’t just about doing sums, it’s about

learning to think mathematically• Develop your own subject knowledge• Representation is key – find ways to

communicate concepts through images• Make the connections between different bits

of maths and previous learning• Talking is an important part of learning• Observe and listen to children explaining

their maths• Solve problems with the children

Mathematics is everywhere

I Wooldridge & S Cousins10/03/12

Real resources

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Maths and routines

I Wooldridge & S Cousins10/03/12

Corporeal knowledge

• Children need to experience learn with their whole bodies

• Adults need to support children in the process

• How can adults do support chidlren to develop their thinking?

I Wooldridge & S Cousins10/03/12

NCETM: www.ncetm.org.ukRegister with this site (email address and password required) and then start to explore it.

Look at the self-evaluation tools. These will help develop understanding of ways to teach different topics.

ATM - The Association of Teachers of Mathematicswww.atm.org.uk

Click on Resources, then Gaps and Misconceptions.Information, ideas and resources relating to subtraction, division, and fractions decimals and percentages (FDP) – areas that teachers find harder to teach and children find harder to learn.

Core subject knowledge reference book:

Understanding Mathematics for Young Children: A guide for the Foundation Stage and Lower Primary Teachers. (2008), Haylock, D. & Cockburn, A.

Read relevant sections BEFORE each week’s seminar

Look at relevant sections when you are planning your teaching in school

Follow-up maths subject knowledge audit: (‘Clouds; Links sheet’ introduced at start of course )

http://www.cimt.plymouth.ac.uk

• Click on Resources, Tests and Audits, Mathematics Attainment Test, Pick A Test At Random• Make sure you are working in full screen• Enjoy!

QTS Skills test

Do this earlier in the year in order to get it out of the way. For practice material go tohttp://www.tda.gov.uk/skillstests/numeracy/practicematerials.aspx

People who find this test hard usually find the timed mental arithmetic section hard – it’s often about finding easy ways to do sums that look hard.For example you could do 25 x 88 by first doing 100 x 88 (easy!) and then dividing by 4 (also easy with these numbers)

Thank you for participating in the session

Sarah.Cousins@beds.ac.uk