CCEA Developing Pupils’ Problem-Solving Skills in Your Classroom Mark Simmons

1. CCEA Developing Pupils’ Problem-Solving Skills in Your Classroom Mark Simmons

2. Welcome! • Today’s session outline: • Reviewing Geoff’s Talk on Problem-Solving • Exploring a CCEA exemplar problem using ‘boxing up’ • Understanding the Problem-Solving Cycle and working on strategies to help pupils to succeed

3. What IS Reasoning? Reasoning is… The because to our Why? Thinking (Pace is a measure of total thinking) Thinking time will be needed Talking together helps us to comprehend our own reasoning better

4. Some thoughts on Qing Pose Pause Pounce (Bounce) Wait time T chooses (three?) and scribes Poker face Subtle ‘praise’ T tries to avoid re-stating (stage voice), Probe? NVcues? Focus away from ‘the answer’ Use mwbs

5. understand organise what? R E X P L O E try why? how? D S C R I B E E Assume… and justify solve find E X P L A I N P R O P O S E check compare show J U S T I F Y V E R I F Y improve O C N C L U D E challenge steps L G I C A L O How good is your mathematical reasoning? N O V I N C E C E V I D E N C E Implies that => hence… evaluate exemplify E Q D generalise conjecture Therefore :. constrain If… then.. so… exclude because… counter-example :. => ≠

6. What IS Problem-Solving? What distinguishes Problem-Solving from just doing exercises? What is the connection with Reasoning? Elements of the Problem-Solving Cycle. Affective elements

7. What do I need?

8. Problem solving / modelling cycle Representing/formulating representing mathematical problem mathematical problem problem problem analysing -reasoning ‘employing’ -procedures evaluating evaluating mathematical solution mathematical solution solution solution Reporting/communicating interpreting interpreting

9. Have a go. • What might your pupils write in each box as they tackle this problem? • Notice the range of approaches. • Notice any English words used to communicate your solution? • Critique the context and the assumptions the writer is expecting us to make

10. Boxing Up (a self-questioning training tool)

11. Boxing Up (a self-questioning training tool) Compare your work vs teacher notes? Compare ‘What I did’ in teacher notes vs ‘Formulating and ‘Employing’ in PS cycle

12. Problem-Solving Pedagogy – some thoughts • We work on PS in contexts • The lesson begins when the problem is solved: PLENARY(s) crucial in SHARING approaches and ideas. • We might focus in only on a section of the cycle • Examining/assessing ‘Sample pupil work’ is powerful • 2-year rule, accessibility, • Use similar problems set in various contexts together, and various problems in one context.

13. Problem-Solving Pedagogy – some more thoughts • Do I U all the WORDS? • Can I say the problem (with feeling?) • Can I re-state in my own words? • What am I being asked to find/show? • What units are things measured in? • Could I pose another problem in the context? • Do I have enough info? • Is there any redundant info? • Do I know a similar problem? • Can I make a relevant numerical example with ‘easy numbers’? • HOW will I solve this? Steps? • Can I make assumptions? • Guess & Check? • Could I draw a diagram? • Orderly list? Table? • Can I work backwards? • Could algebra help me?

14. Problem solving: Questions my teacher might ask. What could you assume… and can you justify that? What do you want to know? What do you already know? How could you organize this info..? Can you find a general example? What patterns do you notice? How can you be certain? Is this a general rule? Will it always happen? Are you sure? How can you check/test? What was your thought process? What could it NOT be? If that’s true, then what? Anything else? What have you done? How did it help? Can you convince me?

15. Keep in touch mark.simmons@nottingham.ac.uk UoNSoE @UoNSoE