- The document outlines an introductory session for a Primary PGCE course on teaching mathematics. - It introduces the tutors for the course and provides aims and success criteria, focusing on developing confidence in mathematics and awareness of required subject knowledge. - Key course content is discussed, including how children learn maths, what to teach, when to teach it, and how to assess, all in approximately 20 hours. - Educational theories and frameworks that underpin the teaching of mathematics are referenced, including the Cockcroft Report, Bruner's modes of representation, and the Williams Review.

1. Primary PGCE
Learning and Teaching the
Curriculum
Mathematics - Introduction

2. 25x88=

3. Irene Wooldridge
irene.wooldridge@beds.ac.uk
Maria McArdle
Maria.mcardle@beds.ac.uk
Sarah Cousins
Sarah.cousins@beds.ac.uk
If you are unable to attend a session,
please inform your tutor.

4. 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

5. 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

6. Our Maths Stories
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7. About the course -The challenge …
• How children learn maths
• What to teach
Hmmmm… quarts
• When to teach it and pint pots ?
• How to teach it
• How to assess it
… in approx 20 hours
.....+ Pause points

9. .........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

10. 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

11. 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)

12. 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.

13. 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

14. 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
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16. 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

17. Mathematics is everywhere
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18. Real resources
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19. Maths and routines
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20. 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?
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21. NCETM: www.ncetm.org.uk
Register 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.

22. ATM - The Association of Teachers of
Mathematics
www.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.

23. 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

24. 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!

25. QTS Skills test
Do this earlier in the year in order to get it out
of the way. For practice material go to
http://www.tda.gov.uk/skillstests/numeracy/prac
ticematerials.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)

28. Thank you for participating in the
session
Sarah.Cousins@beds.ac.uk