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

Reviewing Geoff’s Talk on Problem-Solving 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

Thinking (Pace is a measure of total thinking) 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

Pose Pause Pounce (Bounce) Wait time T chooses (three?) and scribes 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 What do we think of these – how do they align with the stuff on PD5.1?

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

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

What do I need?

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

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

Boxing Up (a self-questioning training tool)

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

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.

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?

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

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