Overview of Session • Problem solving overview • Three aspects to problem solving • Planning, doing, assessing, recording reporting for problem solving • Reflection and identify next steps
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
Learning and Teaching • Active learning • Context • Interdisciplinary • Technology • AIFL • Problem Solving
Approaches to Assessment • Attitude • Process • Evaluate • Stickability
Developing a Problem Solving Programme Developing a Problem Solving Approach to Teaching and Learning Teaching the Strategies and developing the process model CfE AiFL Planning Progression Providing a range of Problems Creating the Problem Solving Environment
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. Providing a range of Problems Creating the Problem Solving Environment
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. Teaching the Strategies and developing the process model Developing a Problem Solving Approach to Teaching and Learning
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
Angles in a Triangle A + B + C = 180o A B C
Aspect 2 Processes and Strategies • Working on tasks designed specifically to highlight the merits of certain approaches to mathematical thinking • Process and strategy models
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.
Developing the Process model Some process models (handout) • 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 Teaching the Strategies and developing the process model
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?
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
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
Enquiry • Discuss with your group where ‘enquiry’ is already happening and if there are any opportunities to use enquiry more often in the curriculum.
Developing a problem solving approach to teaching and learning • 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 learning and teaching
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
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
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
Supporting Learners to be Reflective • TASC and BC handout
Assessment • How do you assess problem solving now and does this need to change? • Informal • Formal • Formative • How do we record this?
A Few Words About Resources • http://www.ltscotland.org.uk/5to14/problemsolving/index.asp • http://www.nzmaths.co.nz/node/449 • http://www.cut-the-knot.org/ • http://nrich.maths.org/public/ • CAME Thinking skills • ICT? E.g. Problem Solving in Action • Hundreds of black line masters
Reflection and next steps • Look back at the belief statements and reflect with your group on what we have covered today.
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
Reading and References • http://www.ltscotland.org.uk/5to14/problemsolving/index.asp • 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.cut-the-knot.org/ • http://nrich.maths.org/public/