# Young Children´s Notions of Probability Reasoning

**By: Ekasatya Aldila Afriansyah**

## Introduction

## Considerable evidence related probabilistic reasoning is linked to cognitive development has shown. Young children move through stages in their ability to make mathematically appropriate judgements in situations. However, the lack understanding of researchers as a natural thinking of each stage suggests that there may not be an accurate description of probabilistic reasoning.

## This framework can be used to inform teaching practice that supports development of effective strategies. In this essay I will try to explain the example of learning strategies from young children in aged four to twelve years which these children had not received any formal instruction in probability as it was not part of their curriculum.

## Main Question

In this essay, I will answer the following question: *What strategies do children utilize for making judgements and reasoning in different types of probability tasks?*

## Answer

Focused from the Europan research in Mathematics Education which has been made by Jenni Way. The research has interviewed 74 children aged four to twelve years from three schools in the New South Wales. Then, the research prepared a series of five tasks constructed in the form of games using various random generators, to be played by individual children.

The research asked the children to make a series choices and decisions regarding probability and to explain their reasons. The questions related to a range of concepts, such as, randomness, sample space, order of likehood, impossibility and certainty, equal likehood, simple conditional probability, proportions, and quantification of chance. Interview transcripts became individual profiles for each child analysed in terms of the strategies identified through the task analysis.

Results were shown by large amount of data collected about the specific tasks and strategies children evoked. Analysis of the children’s responses was identified in three age-related stages of development, with the following steps:

- Stage 1: Non Probabilistic Thinking

- Average age 5 years 8 months (range: 4 years 3 months to 8 years 2 months)
- Minimal understanding of randomness
- Reliance of visual comparison
- Inability to order likehood

- Transition Phase from Non Probabilistic Thinking to Emergent Thinking
- Stage 2: Emergent Probabilistic Thinking

- Average age 9 years 2 months (range: 6 years 11 months to 12 years 2 months)
- Recognition of sample space structure
- Ordering of likehood through visual comparison or estimation of number
- Addition and subtraction strategies used in comparisons
- Concept of equal likehood and impossibility

- Transition Phase from Emergent Thinking to Quantification
- Stage 3: Quantification of Probability

- Average age 9 years 2 months (range: 6 years 11 months to 12 years 2 months)
- Recognition of sample space structure
- Ordering of likehood through visual comparison or estimation of number
- Addition and subtraction strategies used in comparisons
- Concept of equal likehood and impossibility

## Conclusion

Each of the three stages provides some guidance for the design of teaching and learning activities because it presents a sequence of development of concepts and shows us various reasoning of each probability task through children´s thinking. A relevance point which arise from this study are: The concept of more/less likely, most/less likely, and equal likehood are more easily understood than the concepts of impossibility and certainty, children under 6 years may possess some intuitive notions of probability but these are unstable, children around 9 years possess the basic probability concepts, the concepts of one half and the operations of doubling and halving emerged as highly significant mathematical skills, and there were substantial variations in the strategies invented and tested by the children.

## Sources

- Shaugnessy, J.M.,
*Misconceptions of Probability± An experiment with a small/group, activity/based, model building approach to introductory probability at the college level *(1977)*., *Educational Studies in Mathematics 8
- Way, Jenni.,
*The Development of Young Children’s Notion of Probability., *European Research of Mathematics Education III

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