1. Skills for Life Support Programme T: 0118 902 1920 F: 0845 838 1207 E: sflenquiries@cfbt.com W: www.excellencegateway.org.uk/sflsp The Skills for Life Support Programme is delivered on behalf of the Learning and Skills Improvement Service by CfBT Education Trust and partners CfBT Education Trust 60 Queens Road Reading RG1 4BS Helping learners progress with their maths

2. Skills for Life Support Programme Activity 1: Starter task Identifying the levels Work in groups of 2 or 3 with the people sitting next to you. For each question card, decide on the level of the question, and place under the appropriate heading. (If you are not familiar with these level headings, place the cards in what you think is the order of difficulty.) When you have finished, ask for a feedback sheet. Please note, this is not a test – it is an activity designed to encourage discussion!

3. Skills for Life Support Programme Identifying the levels – some thoughts There are a number of factors that can determine the level of a maths question. Everyone has a spiky profile, with narrow spikes. Progress in learning is an individual process. Learners are not levels. Curricula and standards are tools to support teaching (i.e. descriptive, not prescriptive).

4. Skills for Life Support Programme Aim To explore teaching and learning strategies to maximise learner achievement in maths, and to consider the skills critical to learner progress.

5. Skills for Life Support Programme Learning outcomes By the end of the training session, participants will have: Described and classified some of the different ways in which learners can progress with their maths Identified a range of teaching approaches thought to be effective for maths learning Discussed the role of formative assessment in maths teaching Developed some ways of turning errors, misconceptions and difficulties into opportunities for progressing learning and understanding Experienced a range of numeracy and maths learning activities and adapted one for a different level or context

6. Skills for Life Support Programme Example of learner progress Think of a numeracy/maths learner whom you know. Write down an example of a way in which this learner has made progress (it could be something small or large, directly or indirectly related to their learning). Keep hold of your example to refer to later.

7. Skills for Life Support Programme What do we mean by progress in learning maths and numeracy? Knowledge of mathematical facts Technical skills (fluency) Process skills –Representing situations mathematically –Selecting, using, checking and evaluating appropriate methods –Interpreting and communicating results Levels are determined by –complexity of problem and familiarity of context –level of independence (or of support needed)

8. Skills for Life Support Programme What else do we mean by progress in learning maths and numeracy? Understanding of concepts Other areas include: –Attitudes and emotions –ICT skills –Motor skills –Communication skills –Group work and interpersonal skills –Transferability Which category does your example come under?

9. Skills for Life Support Programme Activity 3a – Matching learning goals to types of progress Work individually or as a pair. You will be given a card with an example of learner progress on it. Place the example under the appropriate heading. Have a look at where others have placed their examples – do you agree? Do any examples fit under more than one heading?

10. Skills for Life Support Programme Activity 3b – analysing a maths task Look at the sample maths task you have been given. Identify some examples of technical skills or knowledge required to complete this task. What are the equivalent skills or knowledge at the level below? Are there any other underpinning skills needed in relation to the chosen example?

11. Skills for Life Support Programme Numeracy and maths teaching is effective when it... Builds on the knowledge learners already have Exposes and discusses common misconceptions and other surprising phenomena Uses higher order questions 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 Mathematics Matters (NCETM 2008)

12. Skills for Life Support Programme And when it... Creates connections between topics both within mathematics and with the real world 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. Mathematics Matters (NCETM 2008)

13. Skills for Life Support Programme Other research on effective teaching NRDC Effective Teaching and Learning (Numeracy) report cautioned against any attempt to promote a single method or approach that can be applied across all settings but made some similar recommendations to NCETM. Similar findings in Beyond the Daily Application (NRDC 2005) Increased learner achievement on vocational courses where LLN is embedded – You wouldnt expect a maths teacher to teach plastering (NRDC 2006)

14. Skills for Life Support Programme Self-assessment task Work individually and use task sheet R4a. Place or stick the cards onto page R4b according to how confident you feel in these areas (see example R4c). Add some comments, doodles and/or illustrations! Fill in and add some of the blank cards as you wish. Share and discuss the results with your neighbours. Keep as a self-assessment record to be revisited and reviewed at a later date.

15. Skills for Life Support Programme How do you know what progress is being made and what do you do about it? Assessment for Learning DVD – Maths for Kitchen Design Northern College, Barnsley – residential college for adults returning to learning. This course aims to develop the maths skills needed to design a kitchen. Intended as a fun way to hook people into maths! It is non-accredited. Learners levels are from E3 to L1. 9 learners aged 30–60 (plus 2 support assistants). Not an embedded course as such but contextualised.

16. Skills for Life Support Programme Assessment for Learning Day 1 Approaching kitchen design Using metric lengths Calculating area and perimeter Day 2 Using scale diagrams Positioning units along a wall (adding, subtracting and converting lengths) Using design software Day 3 Calculating storage space (volume) Working out tiling problems Keeping within budget Maths for Kitchen Design course This DVD focuses on Day 2

17. Skills for Life Support Programme Activity 5 – Assessment for Learning Group A – Note down the questions that Carol, the class tutor, uses. Afterwards, compare your notes. What types of questions are they (e.g. factual recall, checking understanding, etc)? Group B – Note down the ways in which Carol uses learners answers, questions and task results to develop progress in learning. Afterwards, compare your notes. In particular, how does she respond to wrong answers?

18. Skills for Life Support Programme Assessment for Learning is a key professional skill Read through Handout 7 on Formative Assessment (also known as Assessment for Learning, AfL). Focus on the ten principles for AfL. Where would you place Assessment for Learning on the poster that you designed as part of the self- assessment task earlier? To what extent do you plan how you will assess progress during your lessons? What kinds of questions do you use? How do you use information from learner activities to support progress? Please take a few minutes to reflect on these questions.

19. Skills for Life Support Programme Find the floor area for the room in this sketch: Learner answer: 22 m 2 Errors, misconceptions and difficulties

20. Skills for Life Support Programme Errors, misconceptions and difficulties The learner has probably multiplied 4 by 3 and then 5 by 2 and added. She has remembered that finding the area of a non-composite shape involves multiplying and adding, but does not know which numbers to begin with. She could draw a scale plan on squared or graph paper (1cm to 1m) and find the area by counting squares, which will give a different answer (this creates cognitive conflict!). Through discussion and reflection she could then be encouraged to develop a method for finding the area of any L-shaped room. Other ideas?

21. Skills for Life Support Programme Errors, misconceptions and difficulties Work in groups of 2 or 3. For your given error, Write down what has happened and why you think it might have happened (e.g. a slip of the pen, a misconception, a possible learning difficulty, etc) Write down a strategy that could be used to support the learner to progress in this area. Walk round the tables to look at what others have done. Add further comments to other peoples sheets if you wish!

22. Skills for Life Support Programme Cognitive Conflict and Exposing Errors and Misconceptions Summary of research findings Teaching becomes more effective when common mistakes and misconceptions are systematically exposed, challenged and discussed. Cognitive conflicts occur when the learner recognises inconsistencies between existing beliefs and observed events. Such conflicts, when resolved through reflective discussion, lead to more permanent learning than conventional, incremental teaching methods. (Swan 2005)

23. Skills for Life Support Programme Sample learning activities – ways to support learner progress Work in groups of 3–4. You will be given a maths learning activity. Choose one of the following tasks: 1.Suggest a way to scaffold this activity for learners who might struggle with it 2.Suggest a way to extend this activity or follow on from it for learners who need to be challenged further 3.Suggest a way to contextualise this activity for a particular individual or group of learners in a specific context Set up a market stall to present your results.

24. Skills for Life Support Programme Sample learning activities – ways to support learner progress Its market time! Have a look around the stalls and try out the activities. Dont forget to look at the results of the previous task (supporting/extending/contextualising) As you try out the activities, consider the types of progress being supported (e.g. technical knowledge and skills, process skills, language and communication, understanding etc) Handout HO9 lists where you can find these resources

25. Skills for Life Support Programme Liked this? Try these... Move On NCETM OFT Skilled to Go Adult Numeracy Core Curriculum For more, see Handout HO9

26. Skills for Life Support Programme Aim To explore teaching and learning strategies to maximise learner achievement in mathematics, and to consider the skills critical to learner progress.

27. Skills for Life Support Programme Learning outcomes By the end of the training session participants will have: Described and classified some of the different ways in which learners can progress with their maths Identified a range of teaching approaches thought to be effective for maths learning Discussed the role of formative assessment in maths teaching Developed some ways of turning errors, misconceptions and difficulties into opportunities for progressing learning and understanding Experienced a range of numeracy and maths learning activities and adapted one for a different level or context

28. Skills for Life Support Programme Next steps Write on a sticky note one thing you will take from todays session and apply either in your own practice, or within your institution. You can also make a note of further CPD needs if you wish. Put your note on the wall and have a look at what others have written.

29. Skills for Life Support Programme References (All web-based resources accessed on 31/01/10) Baker, E. et al. (2005) Beyond the Daily Application, NRDC http://www.nrdc.org.uk/publications_details.asp?ID=29 http://www.nrdc.org.uk/publications_details.asp?ID=29 Casey, H. et al. (2006) You wouldnt expect a maths teacher to teach plastering..., NRDC http://www.nrdc.org.uk/publications_details.asp?ID=73 http://www.nrdc.org.uk/publications_details.asp?ID=73 Coben, D. et al. (2007) Effective Teaching and Learning: Numeracy, NRDC http://www.nrdc.org.uk/publications_details.asp?ID=86 http://www.nrdc.org.uk/publications_details.asp?ID=86

30. Skills for Life Support Programme References continued NCETM (2008) Mathematics Matters – an executive summary. https://www.ncetm.org.uk/files/274681/NCETM+Mathem atics+Summary.pdf https://www.ncetm.org.uk/files/274681/NCETM+Mathem atics+Summary.pdf Swan, M. (2005) Improving Learning in Mathematics: challenges and strategies, DfES Standards Unit. https://www.ncetm.org.uk/files/224/improving_learning_i n_mathematicsi.pdf https://www.ncetm.org.uk/files/224/improving_learning_i n_mathematicsi.pdf

31. Skills for Life Support Programme Contacts Add contact details here: Presenter Email Address Presenter Telephone (optional) Skills for Life Support Programme Office Contacts: CfBT Education Trust Tel: 0118 902 1920 Email: sflenquiries@cfbt.comsflenquiries@cfbt.com www.excellencegateway.org.uk/sflsp