1. Teaching and learning functional mathematics
Fiona Allan

2. Teaching functional mathematics
Aims of today:
To think about the needs of students studying Functional Mathematics
To reflect on approaches to teaching and learning which are appropriate for these students
To explore some of resources/activities which can be used with these students

3. Teaching functional mathematics

4. Teaching functional mathematics
Work in a group
Write down EVERYTHING you know about
triangles
Everyone must take part
You have ten minutes

5. Teaching functional mathematics
“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
Deep Progress in Mathematics - The Improving Attainment in Mathematics Project
Watson, Anne; De Geest, Els and Prestage, Stephanie (2003). Deep Progress in Mathematics - The Improving Attainment in Mathematics Project. Oxford, UK: University of Oxford, Department of educational studies.

6. Teaching functional mathematics
“All students can think hard about mathematics and thus do better at mathematics”
Deep Progress in Mathematics 2003
Deep Progress in Mathematics - The Improving Attainment in Mathematics Project
Watson, Anne; De Geest, Els and Prestage, Stephanie (2003). Deep Progress in Mathematics - The Improving Attainment in Mathematics Project. Oxford, UK: University of Oxford, Department of educational studies.

7. Teaching functional mathematics
Compare these shapes.
In what ways are they the same?
In what ways are they different?

8. Teaching functional mathematics
“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
Wood, D. (1988) How Children Think and Learn, Oxford

9. Teaching functional mathematics
Take it in turns to choose a card
Decide whether the statement on the card is true, false or if you are not sure whether it is true or false. Explain your answer to the others in your group.
If you not agree with what someone says, say so!

10. Teaching functional mathematics
Reflect on your discussion
Has anyone learnt anything? If so, how did this happen?
What was good about the activity?

11. Teaching functional mathematics
“When you explain something to someone else then you really understand it.”
A-level Maths student
“When you really understand something, you don’t need to revise - you’ve got it for life!”
GCSE Maths student

12. Teaching functional mathematics
Find the errors in this bill
Explain to the others in the group your reasoning

13. Teaching functional mathematics
(first video only)
(first video only)

14. Teaching functional mathematics
Teaching is more effective when it:
Builds on the knowledge learners already have
Exposes and discusses common misconceptions
Uses higher-order questions

15. Teaching functional mathematics
Makes appropriate use of whole class interactive teaching, individual work and cooperative small group work
Encourages reasoning rather than ‘answer getting’
Uses rich, collaborative tasks
Creates connections between topics

16. Teaching functional mathematics
Uses resources, including technology, in creative and appropriate ways
Confronts difficulties rather than seeks to avoid or pre-empt them
Develops mathematical language through communicative activities
Recognises both what has been learned and also how it has been learned

17. Teaching functional mathematics
Today we are going to look at:
Building on the knowledge that learners already have
Exposes and discusses common misconceptions
Uses higher order questions

18. Teaching functional mathematics
Sort the shapes in any way you want
Now sort them again
Write down all the ways you have sorted them

19. Teaching functional mathematics
Divide your flip chart paper into 3 columns
Write 5, 12 and 24 at the top of the columns
Under each number write down all the facts that make it different or the same as the other two numbers

20. Teaching functional mathematics

21. Teaching functional mathematics
Write down all the mathematical misconceptions that learners bring with them to college

22. Teaching functional mathematics
Learners have worked enthusiastically with the tutors, and motivation, attendance and achievement have increased.
Attendance in the classes taking part is 90% compared to 78% for those not taking part
The pass rate for GCSE Mock has increased to 77% in the classes taking part, compared to a College pass rate of 52% in 2009/2010.
In an AS Level mock exam learners achieved an average of 1.57 grades higher than the grades predicted by their GCSE scores.
North Hertfordshire College ‘Teaching is more effective when it uses higher-order questions’
Professional development opportunities for mathematics teachers in Post-16 colleges (
North Hertfordshire College ‘Teaching is more effective when it uses higher-order questions (

23. Teaching functional mathematics
Open questioning
Lay out the fraction cards in front of you
Please don’t mix up the sets!

24. Teaching functional mathematics
Teaching functional maths

25. Teaching functional mathematics

26. Teaching functional mathematics

27. Teaching functional mathematics

28. Teaching functional mathematics

29. Resources Don’t reinvent the wheel!

30. Let’s explore some resources!

32. Essentials collection https://www.ncetm.org.uk/resources/35530

41. http://www. nationalstemcentre. org. uk/elibrary/maths/search

42. http://www. nationalstemcentre. org. uk/elibrary/maths/search

43. http://www. nationalstemcentre. org

45. Preparing to teach students resitting GCSE Mathematics
Preparing to teach students resitting GCSE Mathematics
Resources and CPD for those working with students resitting GCSE Mathematics
Tarsia Resources

47. Teaching functional mathematics
archive.excellencegateway.org.uk/pdf/TandLMathematicsHT pdf

48. Teaching functional mathematics
What are you going to do tomorrow?
Join Resitting GCSE Mathematics community
What are you going to do next week?
What are you going to do before the end of term?

49. Teaching functional mathematics
Aims of today:
To think about the needs of students studying Functional Mathematics
To reflect on approaches to teaching and learning which are appropriate for these students
To explore some of resources/activities which can be used with these students

50. Teaching functional mathematics