Teaching Problem Solving from Junior
Infants
Prepared and presented by
Dr Pauline M Cogan
ILSA Spring Conference March 2015
Why is teaching of problem
solving so difficult ?
 Ideas/Suggestions
Problem Solving Requires multiple processes:
 Problem Solving processes called on are:
 Psychological
 Linguistic
 Cognitive/memory
 Emotional
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
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
All class levels: 4 Steps of Problem Solving
 UNDERSTAND
 Plan
 Solve
 Look back/check
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
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
First formal Problem Solving strategy

DRAW A PICTURE
 Make your own from Clip Art or draw them and photocopy (more
needed than TEXT book)
Draw the next thing and continue the colour
pattern.
Blue
Yellow
Red
Pink
Blue
Pink
Yellow
Red
Blue
Blue
Pink
Pink
Yellow
?
?
Pink
?
 Headband idea/box idea
 Child reads and “hears” each pattern and decides if it’s correct
Extend the skill
Yellow
Blue
Yellow
Red
Blue
Yellow
Pink
Blue
Pink
Blue
Pink
Blue
Yellow
Blue
Red
 Read back your pattern. See does it look/sound right
?
?
Yellow
Pink
Blue
Draw and colour your pattern to continue it.
Red
Red
Red
Red
Blue
Red
Red
Blue
Red
Red
?
Yellow
?
Red
Blue
Red
Red
Yellow
?
Blue
Red
Blue
Red
Red
Blue
Red
Blue
Red
Red
Yellow
Read the word pattern
Cat Dog Cat Dog Cat ??
Dog Dog Cat Cat
Dog Dog ?
Jump Sit Jump
Jump
?
Sit
Junior Infants Problem Solving
Understand

Plan
Solve
Lookback (check)
Secondary strategy – Make a Pictograph
Blue
Pink
Yellow

Cut these out and glue them in the correct place on the grid

You can do this with real balloons first for a fun activity and
sellotape to grid on board
Exploring number e.g. to 5

Strategy – Draw a Picture

Listen to this story and then complete or finish the picture
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.
Problem Solving Strategy: ACT IT OUT
Understand
Plan
Solve
Lookback (check)
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
Problem Solving Strategy: ACT IT OUT
Understand
Plan
Solve
Lookback (check)
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
You have taught addition & subtraction within
e.g. 5
Problem Strategy: Choose an Operation (Addition or subtraction)
Understand
Plan
Solve
Lookback (check)

Tell a story. Children Listen. Choose Add or Subtract

Whiteboard

Ring the operation you choose
ADD
SUBTRACT
Get a child to tell his/her story.
•
Story : - number within 5. Addition or subtraction
•
Volunteers to say whether it’s add or subtract
Problem Solving Strategy: Choose the question
Understand
•
Plan
Solve
Lookback (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?
Teach – Counting on: Counting 1,2,3
Problem Strategy: Use a picture
Understand
Plan
Solve
Look back (check)
4 cent
3 cent
1 cent
2 cent
How much must you pay?
3C
+
1C
=
4
2C
Make up other combinations
+
4C =
?
Problem Solving Strategy: Recognise too much information
 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 ?
4+ 2 = 6
Problem Solving Strategy: Make a Model. Represent items by cubes
Understand
Plan
Solve
Look back (check)
Workpad
There are 5 dogs.
Then 1 dog ran away
How many are left?
Work
Problem Solving Strategy: Guessing and Checking
Understand
Plan
Solve
Look back (check)
These are number clues
 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 ____
Problem Solving Strategy: Make a Bar Graph
Understand
0
1
Solve
Plan
2
3
Look back (check)
4
5
6
7
Problem Solving Strategy: Find a Pattern
Understand
Solve
Plan
Look back (check)
Find the pattern. Draw the missing shape. Colour the pattern
green
blue
yellow
pink
green
green
?
pink
green
blue
yellow
?
green
green
Problem Solving Strategy: Use Estimation
 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
 How many in the next boxes
1
2
3
4
5
6
?
?
8
7
6
5
4
3
?
?
1
3
5
7
9
11
?
?
Problem Solving Strategy: Make a Bar Graph (favourite colours etc)
Understand
Plan
Solve
Look back (check)
Which colour did most children like ?
Problem Solving Strategy: Write/Talk/Ask appropriate questions
 Each child sows bean/pea/bulb
 Each child measures its growth
Name
Mary
Joe
Ann
Cian
Molly
David
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
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.
Problem Solving Strategy: Use a model (clock,coins,counters)
 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 model money to act out stories
 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: Pick the best (most reasonable) answer
 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: Use estimation
32c
21c
19c
12c
13c
 About how much
money did I spend?
 about 50 cent
 about 40 cent
 About how much
money did I spend?
 about 30 cent
 about 40 cent
22c
 About how much
money did I spend?
 about 30 cent
 about 40 cent
Problem Solving Strategy: Make a Table (tally marks)
The children choose pizza or chips. This table shows the children’s favourite food.
Favourite Food
Tally marks
Favourite Food
Number
Pizza
Chips
Pizza
Chips
16
15
 Expand this to tally from other classes
 Ask questions
Problem Solving Strategy: Make a Model (use counters)

There are 4 sweets

There are 2 children

Give an equal number of sweets to each child
Child
Child
 Model this using counters, cubes, etc
 Extend this to larger number of items and children
Problem Solving Strategy: Classes
Problem Solving
Strategies
Act it out
Junior
Infants
First
Second
Third
Fourth
Fifth





Draw a Picture





Colour the pattern


Read the pattern


Make a pictograph





Choose an operation





Choose the question









Make a model


Guessing and checking






Make a Bar Graph



Find a pattern






Use a picture
Recognise too much
information

Senior
Infants


Sixth
Problem Solving Strategy: Classes
Problem Solving
Strategies
Junior
Infants
Senior
Infants
First
Extend and Create patterns
Second
Fifth


Use Data
Too little information

Identify reasonable results


Use a graph




Organise data
Use a Bar Graph

Use a table
Make and use a line graph
Analyse data to make
decisions
Choose the method of
computation
Fourth

Make a decision
Use a schedule
Third












Sixth
Problem Solving Strategy: Classes
Senior
Infants
First
















Pick the reasonable answer


Make a table


Problem Solving
Strategies
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
Make a model
Write a number sentence
Junior
Infants




Second


Third
Fourth
Fifth











Sixth
Problem Solving Strategy: Classes
Problem Solving
Strategies
Junior
Infants
Senior
Infants
First
Second
Third
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
Fourth
Fifth













Make a diagram
Evaluate answers for
reasonableness
Use a formula (area,
perimeter)

Conduct a simulation



Sixth
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.
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.