Problem Solving

Overview of SessionOverview of Session

Problem solving overview Problem solving overview Three aspects to problem solvingThree aspects to problem solving Planning, doing, assessing, recording Planning, doing, assessing, recording

reporting for problem solvingreporting for problem solving Reflection and identify next stepsReflection and identify next steps

Effective Learning and Teaching Development of problem solving skills and analytical thinking skills ScienceScience opportunities for the development of problem -solving skills RMERME development of curiosity and problem solving skills and capacity to take initiatives Social studiesSocial studies the development of problem-solving skills and approaches English and literacyEnglish and literacy curiosity and problem solving skills, a capacity to work with others and take

initiative TechnologyTechnology uses a variety of approaches including active, cooperative and peer learning and

effective use of technology HWBHWB opportunities to analyse, explore and reflect. Expressive artsExpressive arts create meaningful relevant contexts for learning including the appropriate use of

ICT Modern languagesModern languages

Learning and TeachingLearning and Teaching

Active learningActive learning

ContextContext

InterdisciplinaryInterdisciplinary

TechnologyTechnology

AIFLAIFL

Problem SolvingProblem Solving

Approaches to Assessment

AttitudeAttitude

ProcessProcess

EvaluateEvaluate

StickabilityStickability

Developing a Problem Solving Developing a Problem Solving ProgrammeProgramme

Teaching the Strategiesand developing

the process model

Creating the

Problem Solving Environment

Providing a

range of Problems

CfEAiFL

PlanningProgression

Developing a Problem Solving Approach

to Teaching and Learning

Aims of Problem solvingAims of Problem solving..

1. Attitudes1. Attitudes To motivate children to To motivate children to accept the challengeaccept the challenge of of

problem solving by providing stimulating problem solving by providing stimulating activities set in a ‘ Can do ’ environment.activities set in a ‘ Can do ’ environment.

To develop children’s To develop children’s confidenceconfidence in their ability to in their ability to solve mathematical problems by the solve mathematical problems by the successful successful application of skills, knowledge and strategies.application of skills, knowledge and strategies.

Creating the

Problem Solving Environment

Providing a

range of Problems

2. Skills and Knowledge2. Skills and Knowledge To equip children with the ability to apply an To equip children with the ability to apply an

appropriate appropriate process.process.

To enable children to select appropriateTo enable children to select appropriate strategiesstrategies to solve mathematical problems to solve mathematical problems

To develop the children’s ability to To develop the children’s ability to thinkthink and to and to logically evaluatelogically evaluate their ideas when working their ideas when working towards a solution.towards a solution.

Developing a Problem Solving Approach

to Teaching and Learning

Teaching the Strategiesand developing

the process model

Aspect 1 InvestigationAspect 1 Investigation

Adopting an investigative approach to Adopting an investigative approach to learning concepts, facts and techniques.learning concepts, facts and techniques.

Thinking lessons e.g. CAMEThinking lessons e.g. CAME

Developing a Problem Solving Approach

to Teaching and Learning

Angles in a TriangleAngles in a Triangle

A

B C

A + B + C = 180o

Investigating angles in trianglesInvestigating angles in triangles

Investigating angles in trianglesInvestigating angles in triangles

Tessellating TrianglesTessellating Triangles

Aspect 2 Processes and StrategiesAspect 2 Processes and Strategies

Working on tasks designed specifically to Working on tasks designed specifically to highlight the merits of certain approaches highlight the merits of certain approaches to mathematical thinkingto mathematical thinking

Process and strategy modelsProcess and strategy models

PrinciplesPrinciples Problem solving strategies can be taught.Problem solving strategies can be taught. Children need a variety of strategies to build up a Children need a variety of strategies to build up a

repertoire.repertoire. Children need to solve problems in different Children need to solve problems in different

contexts using the same strategy.contexts using the same strategy. Children need to discuss why some strategies are Children need to discuss why some strategies are

more appropriate for certain problems.more appropriate for certain problems. They need to test different approaches.They need to test different approaches. They need problems at appropriate levels of They need problems at appropriate levels of

difficulty.difficulty. The teacher needs to think aloudThe teacher needs to think aloud Teachers and children need to reflect upon the Teachers and children need to reflect upon the

effectiveness of procedures used.effectiveness of procedures used.

Starting / Doing/ Reporting linked to evaluationStarting / Doing/ Reporting linked to evaluation Understand – Plan – Solve – Report Understand – Plan – Solve – Report Read – choose – experiment – consider - reportRead – choose – experiment – consider - report TASC wheel TASC wheel

gather – identify – generate – decide – implement – evaluate – gather – identify – generate – decide – implement – evaluate – communicate – learn from experiencecommunicate – learn from experience

RACE CARRACE CARread – ask – choose – experiment – check – agree - reportread – ask – choose – experiment – check – agree - report

Developing the Process modelDeveloping the Process model

Some process models(handout)

Teaching the Strategiesand developing

the process model

Discussion Discussion

Reflect on the process models given on Reflect on the process models given on the last slidethe last slide

Have a look at the models described in Have a look at the models described in the handout and compare with what is the handout and compare with what is used in your school/class (PMI)used in your school/class (PMI)

What would work for you and your What would work for you and your pupils?pupils?

How would you plan for and assess How would you plan for and assess progression?progression?

StrategiesStrategies These are taken from page 13 of the 5-14 national guidelines:These are taken from page 13 of the 5-14 national guidelines:

Look for a patternLook for a pattern Make a modelMake a model Draw a picture/diagramDraw a picture/diagram Work togetherWork together Guess, check and improveGuess, check and improve Act it outAct it out Produce an organised list/tableProduce an organised list/table Reason logicallyReason logically Try a simpler caseTry a simpler case Work backwardsWork backwards Make a conjecture and test itMake a conjecture and test it

Aspect 3 EnquiryAspect 3 Enquiry Using mathematics in an enquiry that could be part of a Using mathematics in an enquiry that could be part of a

cross-curricular study.cross-curricular study. Some criteriaSome criteria

– Problems could arise naturally from the class or schoolProblems could arise naturally from the class or school– Problems should be of interest to the children and will seek to Problems should be of interest to the children and will seek to

change or have an impact on their school lives and environmentchange or have an impact on their school lives and environment– The children will make decisions, decide on which questions to The children will make decisions, decide on which questions to

ask and where to find the answersask and where to find the answers– There will normally be no ‘right’ answer or clear boundaries, but There will normally be no ‘right’ answer or clear boundaries, but

the children will always have an end product in mindthe children will always have an end product in mind– There may be an element of ‘risk’ and the teacher may have to There may be an element of ‘risk’ and the teacher may have to

be prepared to relinquish a degree of controlbe prepared to relinquish a degree of control– There should be on-going opportunities for the children to There should be on-going opportunities for the children to

discuss their work, to report to the class and the teacherdiscuss their work, to report to the class and the teacher

CfEAiFL

PlanningProgression

EnquiryEnquiry

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

Structure of lesson: investigative, process, enquiry or Structure of lesson: investigative, process, enquiry or all/some?all/some?

Role of teacher: questioning, modelling, scaffolding, Role of teacher: questioning, modelling, scaffolding, reviewingreviewing

Language developmentLanguage development Making connectionsMaking connections Links to Play / Cross CurricularLinks to Play / Cross Curricular GroupingsGroupings Strategies for recording and presenting their work.Strategies for recording and presenting their work. Consideration of skills, attitudes and strategies to be Consideration of skills, attitudes and strategies to be

assessed, recorded and reported.assessed, recorded and reported.

Developing a problem solving Developing a problem solving approach to teaching and learningapproach to teaching and learning

Developing a Problem Solving approachTo learning and teaching

Structure of the lessonStructure of the lessonGetting startedGetting started

– StarterStarter– Introduction of the ‘problem’ through discussionIntroduction of the ‘problem’ through discussion– Group members organised with set tasksGroup members organised with set tasks

While working on the problemWhile working on the problem– Encourage collaborative learning (wilf social)Encourage collaborative learning (wilf social)– Act as a mediator if requiredAct as a mediator if required– Show you value sustained effortShow you value sustained effort– Scaffold to help with problem and model ways of workingScaffold to help with problem and model ways of working

At the finishAt the finish– Draw upon ideasDraw upon ideas– Share thinkingShare thinking (Time!)(Time!)

preparation – construction – sharing

Characteristics of beginner Characteristics of beginner problem solversproblem solvers

HesitancyHesitancy Wait for instructions from the teacherWait for instructions from the teacher Can’t get startedCan’t get started Difficulty with reading/interpreting the questionDifficulty with reading/interpreting the question Scared to make a mistakeScared to make a mistake Only interested in the answerOnly interested in the answer Unaware of strategiesUnaware of strategies Lacking in perseveranceLacking in perseverance

Lindsay Lindsay LoganLogan

Characteristics of experienced Characteristics of experienced problem solversproblem solvers

More ideas of how to get startedMore ideas of how to get started Willingness to have a goWillingness to have a go Expectation of initial failure and being stuckExpectation of initial failure and being stuck Able and willing to cooperateAble and willing to cooperate Asks the teacher as a last resortAsks the teacher as a last resort Prepared to discuss and explain strategiesPrepared to discuss and explain strategies Knowledge of a variety of strategiesKnowledge of a variety of strategies

Lindsay Lindsay LoganLogan

Supporting Learners to be Supporting Learners to be ReflectiveReflective

TASC and BC TASC and BC handouthandout

AssessmentAssessment

How do you assess problem solving now and does this need to change?

•InformalInformal•FormalFormal•FormativeFormative

How do we record How do we record this?this?

A Few Words About ResourcesA Few Words About Resources

http://www.ltscotland.org.uk/5to14/problemhttp://www.ltscotland.org.uk/5to14/problemsolving/index.aspsolving/index.asp

http://www.nzmaths.co.nz/node/449http://www.nzmaths.co.nz/node/449 http://www.cut-the-knot.orghttp://www.cut-the-knot.org// http://http://nrich.maths.orgnrich.maths.org/public//public/ CAME Thinking skillsCAME Thinking skills ICT? E.g. Problem Solving in ActionICT? E.g. Problem Solving in Action Hundreds of black line mastersHundreds of black line masters

Reflection and next stepsReflection and next steps

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

Prioritising next stepsPrioritising next steps Look at this list of tasks. Prioritise them and make notes on Look at this list of tasks. Prioritise them and make notes on

what needs to be done:what needs to be done:– To devise a whole school structure to provide progression To devise a whole school structure to provide progression

of strategiesof strategies– To select strategies for coverage at different levelsTo select strategies for coverage at different levels– To acquire and collect resources to support this structureTo acquire and collect resources to support this structure– To design a system for organising PS resources in each To design a system for organising PS resources in each

room or at each stage and audit current provisionroom or at each stage and audit current provision– To build in to this structure a way of identifying To build in to this structure a way of identifying

investigative PS or enquiry activitiesinvestigative PS or enquiry activities– To consider ideas for assessing, recording and reportingTo consider ideas for assessing, recording and reporting

Reading and ReferencesReading and References http://www.ltscotland.org.uk/5to14/problemsolving/index.http://www.ltscotland.org.uk/5to14/problemsolving/index.

aspasp http://www.nzmaths.co.nz/node/449http://www.nzmaths.co.nz/node/449 ““Primary CAME Thinking Maths” BeamPrimary CAME Thinking Maths” Beam ““Thinking Skills and Problem Solving” Wallace et al, Thinking Skills and Problem Solving” Wallace et al,

David Fulton PublishersDavid Fulton Publishers Lindsay Logan inservice materialsLindsay Logan inservice materials Mathematics 5-14 national guidelinesMathematics 5-14 national guidelines CfE principals and practice papersCfE principals and practice papers http://www.bced.gov.bc.ca/irp/mathk72007.pdfhttp://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/