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Problem Solving

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Overview of Session Problem solving overview Three aspects to problem solving Planning, doing, assessing, recording reporting for problem solving Reflection and identify next steps

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Effective Learning and Teaching Development of problem solving skills and analytical thinking skills Science opportunities for the development of problem -solving skills RME development of curiosity and problem solving skills and capacity to take initiatives Social studies the development of problem-solving skills and approaches English and literacy curiosity and problem solving skills, a capacity to work with others and take initiative Technology uses a variety of approaches including active, cooperative and peer learning and effective use of technology HWB opportunities to analyse, explore and reflect. Expressive arts create meaningful relevant contexts for learning including the appropriate use of ICT Modern languages

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Learning and Teaching Active learning ContextInterdisciplinaryTechnology AIFL AIFL Problem Solving

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Approaches to Assessment AttitudeProcessEvaluateStickability

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Developing a Problem Solving Programme Teaching the Strategies and developing the process model Creating the Problem Solving Environment Providing a range of Problems CfE AiFL Planning Progression Developing a Problem Solving Approach to Teaching and Learning

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Aims of Problem solving. 1. Attitudes To motivate children to accept the challenge of problem solving by providing stimulating activities set in a ‘ Can do ’ environment. To develop children’s confidence in their ability to solve mathematical problems by the successful application of skills, knowledge and strategies. Creating the Problem Solving Environment Providing a range of Problems

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2. Skills and Knowledge To equip children with the ability to apply an appropriate process. To enable children to select appropriate strategies to solve mathematical problems To develop the children’s ability to think and to logically evaluate their ideas when working towards a solution. Developing a Problem Solving Approach to Teaching and Learning Teaching the Strategies and developing the process model

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Aspect 1 Investigation Adopting an investigative approach to learning concepts, facts and techniques. Thinking lessons e.g. CAME Developing a Problem Solving Approach to Teaching and Learning

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Angles in a Triangle A B C A + B + C = 180 o

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Investigating angles in triangles

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Tessellating Triangles

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Aspect 2 Processes and Strategies Working on tasks designed specifically to highlight the merits of certain approaches to mathematical thinking Process and strategy models

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Principles Problem solving strategies can be taught. Children need a variety of strategies to build up a repertoire. Children need to solve problems in different contexts using the same strategy. Children need to discuss why some strategies are more appropriate for certain problems. They need to test different approaches. They need problems at appropriate levels of difficulty. The teacher needs to think aloud Teachers and children need to reflect upon the effectiveness of procedures used.

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Starting / Doing/ Reporting linked to evaluation Understand – Plan – Solve – Report Read – choose – experiment – consider - report TASC wheel gather – identify – generate – decide – implement – evaluate – communicate – learn from experience RACE CAR read – ask – choose – experiment – check – agree - report Developing the Process model Some process models (handout) Teaching the Strategies and developing the process model

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Discussion Reflect on the process models given on the last slide Have a look at the models described in the handout and compare with what is used in your school/class (PMI) What would work for you and your pupils? How would you plan for and assess progression?

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Strategies These are taken from page 13 of the 5-14 national guidelines: Look for a pattern Make a model Draw a picture/diagram Work together Guess, check and improve Act it out Produce an organised list/table Reason logically Try a simpler case Work backwards Make a conjecture and test it

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Aspect 3 Enquiry Using mathematics in an enquiry that could be part of a cross-curricular study. Some criteria –Problems could arise naturally from the class or school –Problems should be of interest to the children and will seek to change or have an impact on their school lives and environment –The children will make decisions, decide on which questions to ask and where to find the answers –There will normally be no ‘right’ answer or clear boundaries, but the children will always have an end product in mind –There may be an element of ‘risk’ and the teacher may have to be prepared to relinquish a degree of control –There should be on-going opportunities for the children to discuss their work, to report to the class and the teacher CfE AiFL Planning Progression

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Enquiry Discuss with your group where ‘enquiry’ is already happening and if there are any opportunities to use enquiry more often in the curriculum.

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Structure of lesson: investigative, process, enquiry or all/some? Role of teacher: questioning, modelling, scaffolding, reviewing Language development Making connections Links to Play / Cross Curricular Groupings Strategies for recording and presenting their work. Consideration of skills, attitudes and strategies to be assessed, recorded and reported. Developing a problem solving approach to teaching and learning Developing a Problem Solving approach To learning and teaching

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Structure of the lesson Getting started –Starter –Introduction of the ‘problem’ through discussion –Group members organised with set tasks While working on the problem –Encourage collaborative learning (wilf social) –Act as a mediator if required –Show you value sustained effort –Scaffold to help with problem and model ways of working At the finish –Draw upon ideas –Share thinking (Time!) preparation – construction – sharing

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Characteristics of beginner problem solvers Hesitancy Wait for instructions from the teacher Can’t get started Difficulty with reading/interpreting the question Scared to make a mistake Only interested in the answer Unaware of strategies Lacking in perseverance Lindsay Logan

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Characteristics of experienced problem solvers More ideas of how to get started Willingness to have a go Expectation of initial failure and being stuck Able and willing to cooperate Asks the teacher as a last resort Prepared to discuss and explain strategies Knowledge of a variety of strategies Lindsay Logan

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Supporting Learners to be Reflective TASC and BC handout

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Assessment How do you assess problem solving now and does this need to change? InformalInformal FormalFormal FormativeFormative How do we record this?

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A Few Words About Resources http://www.ltscotland.org.uk/5to14/problem solving/index.asp http://www.ltscotland.org.uk/5to14/problem solving/index.asp http://www.ltscotland.org.uk/5to14/problem solving/index.asp http://www.nzmaths.co.nz/node/449 http://www.nzmaths.co.nz/node/449 http://www.cut-the-knot.org/ http://www.cut-the-knot.org/ http://nrich.maths.org/public/ http://nrich.maths.org/public/ CAME Thinking skills ICT? E.g. Problem Solving in Action Hundreds of black line masters

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Reflection and next steps Look back at the belief statements and reflect with your group on what we have covered today.

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Prioritising next steps Look at this list of tasks. Prioritise them and make notes on what needs to be done: –To devise a whole school structure to provide progression of strategies –To select strategies for coverage at different levels –To acquire and collect resources to support this structure –To design a system for organising PS resources in each room or at each stage and audit current provision –To build in to this structure a way of identifying investigative PS or enquiry activities –To consider ideas for assessing, recording and reporting

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Reading and References http://www.ltscotland.org.uk/5to14/problemsolving/index. asp http://www.ltscotland.org.uk/5to14/problemsolving/index. asp http://www.ltscotland.org.uk/5to14/problemsolving/index. asp http://www.nzmaths.co.nz/node/449 http://www.nzmaths.co.nz/node/449 “Primary CAME Thinking Maths” Beam “Thinking Skills and Problem Solving” Wallace et al, David Fulton Publishers Lindsay Logan inservice materials Mathematics 5-14 national guidelines CfE principals and practice papers http://www.bced.gov.bc.ca/irp/mathk72007.pdf http://www.bced.gov.bc.ca/irp/mathk72007.pdf http://www.cut-the-knot.org/ http://www.cut-the-knot.org/ http://nrich.maths.org/public/ http://nrich.maths.org/public/

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