1. Adults Don’t Count
Fiona Allan

2. Adults Don’t Count Aims
To think about the effective teaching and learning Maths
To explore questioning further
To revisit the principles for effective teaching
To network and learn from each other
To enjoy doing some Maths!

3. 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

4. Starting with Starters
Using only 1, 2 and 3, how many numbers between 0 and 10 can you make using addition, subtraction, multiplication and division? For example: – 3 = 0

5. Starting with Starters
Using 2,4 and 6, can you make an odd number? Using 3, 5 and 7, can you make an even number?

6. Starting with Starters
Using 2, 3, 4 What is the biggest number you can make? What is the lowest number you can make? Make an even number Make an odd number Make a square number Make a multiple of 2 Make a multiple of 4

7. Developing effective questioning
Results from North Hertfordshire College project Attendance in the classes taking part is at 90% - for those not taking part the attendance rate was 78%. 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/ In an AS Level mock exam learners achieved an average of 1.57 grades higher than the grades predicted by their GCSE scores.

8. Focusing on Questioning
Why do teachers ask learners questions? Write one reason on a post-it. On another post-it write an example of this type of question.

9. Focusing on Questioning
In your group, compare your answers and group them. Can you think of any other reasons and types of questions?
Handout after task:
Resource Sheet 1 from NCETM Departmental Workshop Questioning

10. Focusing on Questioning
‘Twas brillig, and the slithy toves Did gyre and gimbal in the wabe; All mimsy were the borogoves, And the mome raths outgabe.” (from Jabberwocky by Lewis Carroll)

11. Focusing on Questioning
1. What were the slithy toves doing in the wabe? 2. How would you describe the state of the borogroves? 3. What can you say about the mome raths? 4. Did you need to understand the text in order to answer questions 1 to 3? 5. Why were the borogroves mimsy? 6. How effective was the mome raths’ strategy?

12. Focusing on Questioning
Questions 1, 2 and 3 ask “What?” and seek facts. Question 4 is a follow up to questions 1, 2 and 3. Question 5 asks “Why?” Question 6 seeks an opinion. Questions 5 and 6 cannot be answered by extracting information from the text. They require thought and understanding as well.

13. Focusing on Questioning
The answer is 7 What is the question? Write your answer on a Post-It and then compare your answers with the others on your table.
Write y

14. Writing open questions
Writing open questions using Resource Sheet 2 and Resource Sheet 3 from the NCETM Departmental Workshop on Questioning

15. Writing open questions
Writing open questions using a Mathematical Moment: Money (Using higher order questions)

16. Write down 3 closed questions which you might ask your students.
Writing open questions
Write down 3 closed questions which you might ask your students.

17. Now change the questions you have written into open questions.
Writing open questions
Now change the questions you have written into open questions.

18. When is it appropriate to use closed questions?
Writing open questions
When is it appropriate to use closed questions?

19. Developing language
Write down all the words that are used in exam questions on a piece of poster paper (spread them out with a space around each) Pass your poster to the next group Rewrite the words in language your learners will understand

20. Asking the right questions!
Think before you ask! If you don’t ask the right questions, you won’t get the right answers!

21. Review of last term’s session
One step at a time …….

22. 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

23. Range of Activity Types
See Improving learning in mathematics
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

24. Building on the knowledge that learners already have
‘If I know this I also know that ..’ Write a multiplication sum in the centre of an A4 sheet of paper Pass it to the person on your left. They should write down

25. Encouraging reasoning
New York
Rio de Janeiro
London
Dubai
Moscow
Cape Town
Ibiza
Tokyo
Sydney
Do the task from Air Miles produced by the More Maths Grads project

26. Describe ….. using as many mathematical words as you can.
Developing language
Describe ….. using as many mathematical words as you can.

27. Creating connections with the real world
See the Channel Tunnel task
Do the estimation task from Channel Tunnel

28. Using rich collaborative tasks
Choose one of the Durham Maths Mysteries and work on it with the others on your table.
Link edmondsley.itss-durham.org.uk/resources/index.html?_Action=viewrecord&_Id=134&_Where=AllValidated

29. Confronting difficulties
Play the Biggest take away game and then think about how and why you would ask your learners to play it.
See Biggest Take Away

30. Always, Sometimes, Never True
Exposing misconceptions
Always, Sometimes, Never True

31. Developing language
Write down all the words that are used in exam questions on a piece of poster paper (spread them out with a space around each) Pass your poster to the next group Rewrite the words in language your learners will understand

32. And now …. What will you do next week?
What will you do for the rest of the term?

33. Adults Don’t Count
Fiona Allan