Thinking About My Thinking

Working With Friends to Solve Problems

Prep students working together

Students were focusing on their problem solving skills as a group

and as individuals to find a solution to a seemingly simple problem

Develop a drawing to represent the game “Cat and Mouse”

Problem Solving

• Is there a situation or process that has some major constraints or limiting condition?

• Is there a situation or process that could be better understood if constraints or limiting conditions were placed on it?

Problem Solving Organiser Goal:

Constraining/limiting conditions:

Possible solution Possible solutionPossible solution Selected solution

Try another solution

Did not work well

Problem solved

Worked well

Problem Solving Organiser Goal: Draw the game cat and mouse

Constraining/limiting conditions: Has to be an accurate drawing in terms of positional concepts.

Student 1 solution Student 3 solutionStudent 2 solution Selected solution

Try another solution or adopt one of the original plans.

Did not work well

Problem solved

Worked well

We all played Cat and Mouse

We then had to draw us playing the game.

“I drew my circle first so I would not forget what the game looked like. Then I can draw my friends around the outside” - Chelsea

“You have to make sure the children you draw are on the circle; otherwise they are not in the game” - Alana

We talked about our drawings“You have to draw some of the people upside down; they are the ones on the other side to me.” - Daffy

“I did that too, but they are not really upside down; you just have to draw them that way so you know how they really look.” - Nick

Deciding which drawings were the best and why

Our Thinking

“Greta’s drawing looks best because everyone is on the line, but we are not really

upside down” – Daffy

“I think Kelsie’s drawing is right, because nobody is

upside down in her drawing” – Matt

Daffy’s Picture

“This is my game of cat and mouse. Everyone

is in the circle and they are holding

hands”.

Checking our ideas Re-enacting the drawings

• The students had a go of Matt’s drawing first. They agreed that Matt who was the only one with his legs facing inwards was probably drawn wrong. Then they all stood up to see what it really looked like. After lots of giggles they realised that Matt was the only one that was drawn correctly “This isn’t right, we are all the

wrong way except for Matt” - Chelsea

What about this drawingStudents decided to have a go at Kelsie’s drawing next. They were asked to predict if this was more

accurate and why: “Yes it is a better drawing because we

all have our legs facing downwards like Matt did before” – Nick

“Nobody is upside down doing it this way”- Daffy

 The students then stood up.

Maybe this one is right!Students decided they wanted to

have a go at Nick’s drawing to see if it was right. They were

asked if they thought there was any difference between Nick

and Kelsie’s drawing, but they were not sure.

When the students stood up they were surprised again that this picture

was not right.

Thinking about their drawings“Everyone is wrong here; I had a few

people right in my drawing” - Kelsie

“Maybe we have to draw everyone differently and think about where

our faces are” – Greta

“Maybe we can draw it while we are standing up so we can see where we

should be” - Daffy

Proof

Prediction: If legs face away from circle, when you stand up you will be facing the wrong way.

Prediction: When you can see each other you must be facing the same way.

Conclusion or Final Prediction:Drawing must have legs facing inwards and faces looking at each other.

Legs have to all face towards the middle of the

circle.

Faces have to be looking towards middle of circle.

Proof

YesNo

No conclusion – new theory

NoYes

No conclusion – new theory

What type of thinkin

g is this?

Teacher Direction

• It is suggested the each individually take turns standing outside the circle and drawing the position of only one person considering, the body, head, legs as well as any distinguishing facial features e.g. could they see the nose or eyes.

Individual Drawings

Profiles

Front and Back

Students then cut and pasted their drawings onto a poster

“It was easy drawing my position as I could look closely at how they were standing” – Matt

“Everyone was standing differently, we just had to look carefully” - Daffy

Final Team Drawing

Us playing Cat and Mouse

Self-assessment

Children compare their initial drawings with their final drawings and try and explain the

changes they have made

Zone of proximal developmentLearners advance their understanding

Vygotsky

Reflecting on Predictions

Students reflected on their initial drawings and to talk

about what they have learnt.

Reflection & Feedback “ Your ring-around the rosy is great!

The second drawing is a lot more Ring-around-the-rosy!

“See that line? That was my first Ring-around-the –rosy but it was not right!

Giovanni helped me get a picture of a ring-around-the-rosy in my mind…it was just like

I was seeing it, so copying from my mind I got it right”

Our Reflections

“This was easy when we did everyone one at a time, we could really think about where everyone was

standing” - Daffy“I didn’t look at where our faces and our legs where

when I first did my picture. That really helped me when I did” – Kelsie

“We are all different when we stand in different spots, we just need to look” – Matt

“Drawing people upside down is not right, as we are never playing with our feet in the air” - Greta

“Language shapes the way we think, and determines what we can

think about.”Benjamin Lee Whorf

American linguist noted for his hypotheses

regarding the relation of language to thinking and cognition 1897-1941.

Daffy’s Projection

“I would like to be able to draw ring around the rosie by myself”.

Final Drawing – (produced with guidance and advice from her

friends)

More Than Just Play…..Learning process through problem solving:• Development of vocabulary

• Development of verbal language through communication of ideas

• Development of spatial concepts

• Deductive thinking as a process of refining thinking

• Fine tuning of visual representation

• Construction of hypotheses

• Formulation of theories

• Strategies of action

• Team work and cooperative thinking

Children become smart by being treated as if they already are

intelligent.Resnick & Hall, 1998Pressed to

raise questions

Accept challenges

Risk take

Make predictions

Justify reasons

Seek information