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Teaching Problem Solving from Junior Infants ILSA Spring Conference March 2015 Prepared and presented by Dr Pauline M Cogan

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Why is teaching of problem solving so difficult ? Ideas/Suggestions

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Problem Solving Requires multiple processes: Problem Solving processes called on are: Psychological Linguistic Cognitive/memory Emotional

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Problem Solving Requires activity in several domains Problem Solving processes called on are (among others): Auditory processing (reading/listening) Comprehension (technical language of Maths) Depersonalised/abstract situation Reach into LTM (Long Term Memory) and extract possible solutions from (huge) field of alternatives Have confidence in the plan Use number facts and correct algorithms Execute the plan Look back/check Accept solution

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All of the above steps are difficult for older students Solution: Teaching Problem Solving in a stratified way from Junior Infants to prepare for Problem Solving

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All class levels: 4 Steps of Problem Solving UNDERSTAND Plan Solve Look back/check

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Junior Infants prepare for Problem Solving by Teach Maths concepts through the day by integration/organisation activity Chairs and tables Table A has X chairs Table B has Y chairs Which table has more chairs? Which table has fewer chairs? Teacher - I need groups of 4. How many more do I need for this group? 4 2

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Sorting Objects according to colour Ask What other way could these things be sorted? All birds together All horses together All bears together Headband (on children) idea. All reds here, All greens here, etc

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First formal Problem Solving strategy DRAW A PICTURE Make your own from Clip Art or draw them and photocopy (more needed than TEXT book)

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Draw the next thing and continue the colour pattern. Headband idea/box idea Child reads and hears each pattern and decides if its correct BlueYellowBlueYellowBlue Yellow ? RedPinkRedPink ? Blue Pink ?

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Extend the skill Read back your pattern. See does it look/sound right BlueYellow Red Blue Yellow ? Pink Blue Pink Blue Pink ? YellowBlue YellowBlue Red Pink YellowBlue

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Draw and colour your pattern to continue it. Red ? Blue Red Blue Red Blue ? Red Blue Red BlueRed ? Yellow Red Blue Red Yellow

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Read the word pattern CatDogCatDogCat?? Dog Cat Dog Jump Sit Jump ? Sit ?

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Junior Infants Problem Solving UnderstandPlan SolveLookback (check) Secondary strategy Make a Pictograph Blue Pink Yellow You can do this with real balloons first for a fun activity and sellotape to grid on board Cut these out and glue them in the correct place on the grid

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Exploring number e.g. to 5 Three birds were sitting on a wall One more bird came How many in all ? How many altogether? How many birds were sitting on the wall now We will write the number sentence 3 + 1 = Extend this by asking children to make up a story. Then show them how to write the number sentence. Strategy Draw a Picture Listen to this story and then complete or finish the picture

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Problem Solving Strategy: ACT IT OUT Listen to my story and act it out. Then we will write the number sentence 1 girl stands 1 girl jogs How many girls are there ? 1 + 1 = 2 2 girls UnderstandPlan SolveLookback (check)

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Problem Solving Strategy: ACT IT OUT Listen to my story and act it out. Then we will write the number sentence 2 boys eat 2 boys drink How many boys are t the table ? 2 + 2 = 4 UnderstandPlan SolveLookback (check)

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You have taught addition & subtraction within e.g. 5 Problem Strategy: Choose an Operation (Addition or subtraction) UnderstandPlan SolveLookback (check) Tell a story. Children Listen. Choose Add or Subtract Whiteboard Ring the operation you choose ADD SUBTRACT

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Get a child to tell his/her story. Story : - number within 5. Addition or subtraction Volunteers to say whether its add or subtract

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Problem Solving Strategy: Choose the question UnderstandPlan SolveLookback (check) Tell a story. Write addition or subtraction options on the board Dan sees 4 cows Then another cow comes How many cows are there in all ? (altogether) How many are left?

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Problem Strategy: Use a picture UnderstandPlan SolveLook back (check) Teach Counting on: Counting 1,2,3 3 cent 2 cent 4 cent How much must you pay? 3 C 1 C += 4 2 C 4 C += ? 1 cent Make up other combinations

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Cross out the information you do not need. Then find the answer Joe has 4 red cars. Then he got 1 yellow bus. Then he got 2 blue cars. Now how many cars has he got altogether ? Problem Solving Strategy: Recognise too much information 4+ 2 = 6

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There are 5 dogs. Then 1 dog ran away How many are left? Problem Solving Strategy: Make a Model. Represent items by cubes UnderstandPlan SolveLook back (check) Work Workpad

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These are number clues Problem Solving Strategy: Guessing and Checking UnderstandPlan SolveLook back (check) The sum is 5 The difference is 1 Guess the number pair 4 + 1 = 5 3 + 2 = 5 4 1 = 3 3 2 = 1 Which number pair fits the clues ?_____ and ____

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Problem Solving Strategy: Make a Bar Graph UnderstandPlan SolveLook back (check) 012345 6 7

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Problem Solving Strategy: Find a Pattern UnderstandPlan SolveLook back (check) Find the pattern. Draw the missing shape. Colour the pattern greenpinkgreenpinkgreen blue green ? ? blue yellow

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Throw out X number of objects Get children to estimate Draw a ring around each group of 10 (for older or more able children) Problem Solving Strategy: Use Estimation

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How many in the next boxes Problem Solving Strategy: Use Estimation ??876543 ??123456 ??1357911

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Problem Solving Strategy: Make a Bar Graph (favourite colours etc) UnderstandPlan SolveLook back (check) Which colour did most children like ?

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Name Week 1Week 2Week 3Week 4Week 5Week 6Week 7 Mary Joe Ann Cian Molly David Problem Solving Strategy: Write/Talk/Ask appropriate questions Each child sows bean/pea/bulb Each child measures its growth

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Problem Solving Strategy: Visualising the correct answer You want each of 2 children to have a fair share. How will you cut the pizza? Circle the fair share. You want each of 3 children to have a fair share. How will you cut the pizza? Circle the fair share. You want each of 4 children to have a fair share. How will you cut the pizza? Circle the fair share. You want each of 6 children to have a fair share. How will you cut the pizza? Circle the fair share.

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Get a child to pretend an activity (piano, painting, writing, reading) Listen to the story Mary started reading at 1 o clock. She reads for 1 hour. At what time will she stop? Draw /turn the hands on this clock to show what time she will stop. Joe and Mum arrive at the cinema at 2 o clock. The movie starts in 30 minutes. At what time will the move begin? Draw/turn the hands on the clock to show the time the movie will begin. Problem Solving Strategy: Use a model (clock,coins,counters)

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Tom has 1 five cent coin and 2 one cent coins. How much money does he have in all (altogether) ? John has 1 ten cent coin. He swaps it for the same amount in cent. How many cent should be get ? Problem Solving Strategy: Use model money to act out stories

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Molly has 2 sweets. She gets 3 more. How many sweets does she have now? Ring the reasonable answer. Tell why. She has 10 sweets She has 20 sweets She has 5 sweets Mike has 10 marbles. He lost 5. How many has he now ? Ring the reasonable answer. Tell why. Mike had 15 marbles Mike had 5 marbles Mike had 12 marbles Problem Solving Strategy: Pick the best (most reasonable) answer

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About how much money did I spend? about 50 cent about 40 cent Problem Solving Strategy: Use estimation 32c 12c 13c 21c19c 22c About how much money did I spend? about 30 cent about 40 cent About how much money did I spend? about 30 cent about 40 cent

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The children choose pizza or chips. This table shows the childrens favourite food. Problem Solving Strategy: Make a Table (tally marks) Favourite Food PizzaChips Tally marks Favourite Food PizzaChips Number 1615 Expand this to tally from other classes Ask questions

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There are 4 sweets There are 2 children Give an equal number of sweets to each child Problem Solving Strategy: Make a Model (use counters) Model this using counters, cubes, etc Extend this to larger number of items and children Child

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Problem Solving Strategy: Classes Problem Solving Strategies Junior Infants Senior Infants FirstSecondThirdFourthFifthSixth Act it out Draw a Picture Colour the pattern Read the pattern Make a pictograph Choose an operation Choose the question Use a picture Recognise too much information Make a model Guessing and checking Make a Bar Graph Find a pattern

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Problem Solving Strategy: Classes Problem Solving Strategies Junior Infants Senior Infants FirstSecondThirdFourthFifthSixth Extend and Create patterns Make a decision Use Data Too little information Identify reasonable results Use a graph Organise data Use a Bar Graph Use a table Use a schedule Make and use a line graph Analyse data to make decisions Choose the method of computation

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Problem Solving Strategy: Classes Problem Solving Strategies Junior Infants Senior Infants FirstSecondThirdFourthFifthSixth Use estimation Use a pattern Make and use a Bar Graph Ask (write) appropriate questions Visualise the correct answer Use a model Use a model to act out stories Pick the reasonable answer Make a table Make a model Write a number sentence

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Problem Solving Strategy: Classes Problem Solving Strategies Junior Infants Senior Infants FirstSecondThirdFourthFifthSixth Choose the method of computation (calculation, Mental Math, Objects, paper, pencil Make a vertical Bar Graph Multi-step problems Work Backwards Choose the best strategy from a range of strategies Find the hidden question Interpret the remainder Use logical reasoning Relevant/Irrelevant information Make a diagram Evaluate answers for reasonableness Use a formula (area, perimeter) Conduct a simulation

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Problem Solving Strategy as stated in Planet Maths Problem solving is an integral part of all mathematics learning. It should not be an isolated part of the curriculum but should involve all the strands. Good problems give students the change to solidify and extend their knowledge and to stimulate new learning. The problems students encounter in Planet Maths are based on familiar experiences coming from students lives. Planet Maths encourages students to develop a range of strategies for solving problems, such as using diagrams, looking for patterns and making organised lists.

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All problem solving techniques presented here are used in an excellent programme called Mathematics Plus and Math Advantage published by Harcourt Brace Jovanovich available in the United States. This Maths programme is now also used throughout Australia.