Adults Don’t Count

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: 1 + 2 – 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, 4What is the biggest number you can make?What is the lowest number you can make?Make an even numberMake an odd numberMake a square numberMake a multiple of 2Make a multiple of 4

7. Developing effective questioning Results from North Hertfordshire College projectAttendance 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 2009/2010. 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 ‘Twasbrillig, and the slithytoves Did gyre and gimbal in the wabe; All mimsy were the borogoves, And the momerathsoutgabe.” (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 7What is the question?Write your answer on a Post-It and then compare your answers with the others on your table.

14. Writing open questions Writing open questions usingResource Sheet 2 andResource Sheet 3 fromthe NCETM Departmental Workshop onQuestioning

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

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

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

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

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

27. Creating connections with the real world 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.

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

30. 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 groupRewrite 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