« This is not math ! » Problem solving in early childhood

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« This is not math ! » Problem solving in early childhood

DEL NOTARO, Christine

Abstract

The context of this research is initially, an order from a private school in Geneva, to give a few hours of continuous training to teachers. It is a primary school, with children from 4 to 12 years old. The request concerned the organization of the teaching of problems, called "open problems". The project started in September 2017 and is still running until June 2019 or more.

It is a longitudinal study. Two years to implement the teaching of problem-solving. My part of researcher is to understand how teachers and students cope with these problems. A first question to be problematized is "If we practice open problems from early childhood, can we measure an impact in grade six, or even before, on the students' reasoning". The first results I will present concern the following difficulties, for example: • implement what we call the devolution of the task, which appears as a long process to appropriate the task, • manage the organization of the sheet space for the pupils, • etc. Among these difficulties, I will highlight the positive contributions such as the fact that the students had fun, participated well and learned [...]

DEL NOTARO, Christine. « This is not math ! » Problem solving in early childhood. In: Winter GETL (Global Education Teaching & Learning) , Tignes (France), 28th Jan.-1st Feb., 2019

Available at:

http://archive-ouverte.unige.ch/unige:134613

Disclaimer: layout of this document may differ from the published version.

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1. Christine Del Notaro: Problem-solving in Early Childhood

2. Orrie Dan, Adi Laredo and Sivan Raz: Short Term Memory of Emotional Facial Expressions Among Young Adults with ADHD

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4. Tatjana Brkic: Teaching Social Innovation in Entrepreneurship through Applied Business Research

5. Loulou Malaeb: Teaching Philosophy in Dubai

Coffee Break

SESSION 2-1

Session Chair : Christine Del Notaro

PROBLEM-SOLVING IN EARLY CHILDHOOD

« THIS IS NOT MATHS ! »

CP-CE1

5 – 6 years

INTRODUCING PROBLEM SOLVING IN EARLY CHILDHOOD

Context : a private school in Geneva, French education system Project: Longitudinal study started in January 2018

Research question: What is the impact of introducing problem solving from 6 or 7 years of age on reasoning skills at the end of primary education?

Observations: problems encountered in implementation, long process of devolution

PROBLEM SOLVING

”PROBLÈME OUVERT”

DEFINITION

Arsac, Germain, Mante (1991, 2007)

• Concise wording

• Does not infer the method or the solution

• Within the pupil’s conceptual grasp

• Pupils: the devolution takes time

• Teachers: inferring the method or the solution

PROBLEMS ENCOUNTERED

It enables the teacher :

- to see how their pupils apply the mathematical concepts

- to understand which concepts and knowledge pupils are able to apply correctly

- to see what mistakes they make

- to devise learning situations that better reflect the needs of pupils

Teachers learn all of this through observing their pupils’ activity during the research

PROBLEM SOLVING

WHY CARRY OUT RESEARCH IN CLASS?

“IT ISN’T MATHS, IT’S FISH!”

CP (6-7 YEARS)

DEVOLUTION

Long devolution of the task, during which the pupils do lots of drawing and colouring, inventing elaborate systems for transferring the fish from one aquarium to another…

Difficulty in managing the space on the sheet of paper

THE FISH

I have three fish in my aquarium: 1 brown, 1 blue, 1 yellow. To clean the aquarium I need to put all the fish in another aquarium.

Find all the different ways in which they can be caught with the net.

An example…

DEVOLUTION

Firstly, they line the fish up on a large sheet of paper (devolution)

or arrange them in a circle

THE PUPILS’ WORK…

The teacher then suggests a new situation

 miming the fish: physically moving the fish and gluing them onto a sheet of A3 paper

Random

sticking strategy

THE PUPILS’ WORK…

Slowly we see strategies begin to take shape

First layout attempt:

Blue-brown-yellow Brown-yellow-blue

THE PUPILS’ WORK…

Strategy

Glue in order of blue - brown - yellow

brown-yellow-blue

brown-blue-yellow

THE PUPILS’ WORK…

INTERMEDIATE CONCLUSION

First conclusive overview after first year: the pupils enjoyed themselves and joined in the activity

Teachers’ objectives: to not infer the methodology

• Let ignorance “float”

• Put themselves in a position of “ignorance”

Pupils’ objectives: to help them get involved in this kind of task

• Use reasoning and logic

• To be less concerned with the success/failure dichotomy

THE FOLLOWING YEAR…

REMINDERS FROM TEACHER

DISCUSSION WITH THE PUPILS EFFECTS OF THIS DIAGRAM ON

THE PROCESSES

EXTENSION

TEACHER SAID:

1. We explored some options on the board 2. Individual exploration using the materials

3. Individually, record your possible answers (on paper) 4. “Variable didactique”: add 2 hats or an extra top

(Ella, Ruben)

5. Sharing: How many combinations did you find? How do you know that was all?

6. Some people found many, others not... why do you

Dress a doll in 3 t-shirts and 2 trousers and find out how many different outfit combinations there are

think that happened?

THE OUTFITS

FIRST ATTEMPT BY HANDLING THEM:

Short/long sleeves

CONCLUSION

Pupils

• Task devolution takes a very long time

• The extension to the fish exercise using the combinations of different outfits demonstrates reinvestment and reapplication of processes

Teachers

• It is difficult for the teachers to resist leading the pupils towards the solution

Researcher

• Same observations for now to a greater degree

• We are going to focus on teacher’s training The End