Teaching Probability to Young Children

Many people assume that probability is a mathematical concept that is introduced and taught in junior high and high school, however, after reading and reviewing much research, I now realize that this idea is untrue. Young children seem to have an intuitive understanding of chance and allowing them to explore this in the early grades simply enhances their probabilistic thinking, number sense, and mathematical connections. Principles and Standards emphasizes that activities in the early grades should take the form of answering questions about the likelihood of events, using such vocabulary as more likely or less likely. Children must be able to recognize that although individual events may not be predictable, there exists trends and patterns that can often occur.

When doing my research it became quite clear that problems dealing with probability should be taught through hands-on experiences. It is extremely important that children participate in hands-on activities such as playing with dice, spinners, or coins as a means to investigate, make predictions, and engage in probabilistic thinking. As the Atlantic Canada Mathematical Curriculum Guide points outs, it is also important to use informal experiences that can be built on and expaned during the primary grades. These experiences should involve real-world situations both inside and outside the classroom where math is used. In doing this, mathematical learning becomes relevant to students. Templates for sample spinners and dice cutouts that can be used in the classroom can be printed off the following website:

Probability and Statistics K to 6

In today's world computer simulations can also be very useful in assiting in the teaching of probability. Many websites and computer programs allow students to watch as a spinner spins or a coin flips and random outcomes are produced with the press of a button. I think the use of computers would be a great addition to a lesson on probability because it provies the hands-on experience that is essentail to learning and then also combines it with an animated visual graphic which is very appealing to children. It enables students to investigate more realistic situations than were previously possible. Having the opportunity to complete problems using a computer allows children to get a break from the usual paper and pencil tasks and actually be interested and have fun while learning their math. There are hundreds of interavtive online activites that can be used to assist in the learning of probability, however, it is important to ensure that they provide accurate information and are age appropriate for the students in your classroom. The following are several computer activites that I found online that I thought would be useful when teaching probability:

Interactivite: Experimental Probability (Spinner Game)

Coin Tossing

Illuimations: Adjustable Spinner

Colour Spinner

Racing Game with one Dice

The following are references that I used while creating this blog:


National Council of Teachers of Mathematics

The Atlantic Canada Mathematical Curriculum Guide

Van De Walle, John. and Sandra Folk. Elementary And Middle School Mathematics: Teaching Developmentally. Canada: Pearson Education Inc, 2005

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Children's Understanding of Probability

Understanding how students' think about a particular topic is an important component of instruction because this kind of knowledge is useful to teachers as they plan and implement instruction. It is for this reason that I choose to research information about how children think and comprehend the topic of probability and chance.

There often exists many misconceptions about chance and probability in the minds of young primary children. When reading an article written by Jeffery A. Frykholm, he says that, “children, roughly up to the age of seven, often struggle with concepts of uncertainty and are generally unable to distinguish events that will necessarily occur from those that may or may not occur.” Many times they believe that an event will happen because they are lucky or it is their favorite colour. This can be seen when little children get very excited while playing a game of Snakes and Ladders because they simply do not understand that the outcome of the game is completely random. In order to help deal with such misconceptions, teachers must allow time for children to be explore and experiment with the concept of probability over a long period of time. They need to develop the idea that some events are more, less likely or equally likely to occur. I will get into more detail about ways to teach children probability in a future blog.

Although there does exist some misconceptions about probability, most young children seem to have some type of understanding of the concept. Frykholm says in his article that young children have an intuitive understanding of chance and that this should be developed through explorations in the early grades that will enhance children's probabailistic thinking, number sense, mathmatical connections. The understandings that children bring to school are typically learned from games that they play at home in informal settings, An example of such a game is the childhood rhythm “Eenie, Meenie, Minie Moe” used when choosing a person to be “it”. There seems to be an acceptance of this form of random chance and even young children seem to understand the process. One article that I read describes student's understanding of probability and probabilistic thinking in terms of levels that range from one to four. Level one involves students who use only subjective reasoning and have a narrow way of thinking that is early distracted and misled by irrelevant information. A student who is functioning in this prestructural level would probably reason that the color red has selected because it is their favorite color. This level is often associated with concrete-symbolic thinking that often involves myths and mental imaging. Level two includes students who are in a transitional period that is characterized by naive and inflexible attempts to quantify probabilities. In this unistructural level, children become involved in probability tasks in relevant ways, however usually only one aspect is pursued. Students are beginning to function in concrete-symbolic mode and are able to use mathematical language and symbols to represent their understandings. The third level of thinking involves children who exhibit both the multistructural and relational levels of thinking and uses quantitative reasoning when dealing with probability tasks. Unlike students in level two, children in this level recognize that there are more than one relevant feature in a probability tasks and they can coordinate and quantify thinking about sample space in relation to probability. Students who reach the fourth and final level of thinking are able to make connections between sample space, outcomes, and probability. Using this relational level, they can use valid numerical measures to describe the probabilities of events and conditional events. Children are able to make meaning from abstract ideas of probability by relating them to their own experiences.

In doing research about children's understanding of probability, I found it really hard to find information and I still have some questions that I would liked answered. I feel as though there are many contradicting ideas out there involving this topic and I must do a little more research in order to get a better understanding. Perhaps getting some first hand experience while working with children on probability would help clear up many of my remaining questions.


The following are references that I used while creating this blog:

Van De Walle, John. and Sandra Folk. Elementary And Middle School Mathematics: Teaching Developmentally. Canada: Pearson Education Inc, 2005


Fykholm, Jeffery A. “Eenie, Meenie, Minie, Moe: Building on intuitive notionsof chance.” Teaching Children Mathematics 8.2 (2001): 112 - 118

Graham A. Jones, Cynthia W. Langrall, Carol A. Thornton, and A. Timothy Mogill.
“Student's Probabilistic Thinking in Instruction.” Journal for Research in Mathematics Education 30.5 (1999): 487 - 519

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Definition

I felt the best way to begin my blog about probability was to research and put together a sufficient definition. Probability, also know as chance, is a numerical measure that helps us figure out the likelihood that an event to happen. The probability of the occurrence of an event can be expressed as a fraction, decimal, or percentage and named from 0 to 1. It is characterized along a continuum from impossible to certain. If an event is certain to happen, then the probability of the event is 1. If an event is certain not to happen, then the probability of the event is 0. If it is uncertain whether or not an event will happen, then its probability is some fraction between 0 and 1.

Experimental vs. Theoretical Probability

Experimental Probability is based on the results of an experiment rather than on theoretical analysis. In real life situations, outcomes are sometimes difficult to predict and they may not be equally likely to happen. In situations like this, the relative frequency of an event can be determined by performing an experiment several times. It is important to note that in order for relative frequency to be a good predictor of chance, there has to be a very large number of trails. The relative frequency of an event, which is sometimes referred to as the classical definition of probability, is:

Number of observed occurrences of an event
Total number of trails

It is very important to use the experimental approach when teaching probability in the classroom. Actually conducting an experiment is often a more valuable learning experience than teaching an abstract idea through theoretical analysis. Several reasons why this is true are as follows:
* Conducting an experiment helps to eliminate children having to make gussess about probability and instead actually understand why they got an answer right.
* Participating in experiments help to simulate real-life experiences and allows children to appreciate that this is a valuable way to solve problems in their daily lives.
*It is significantly more intuitive. Often a result makes more sense to a student when they are dealing with a concept hands-on.
* It is much more fun for students to play with hands-on manipulatives than to solely complete paper and pencil questions.

On the other hand, Theoretical Probability is based on the logical analysis of an experiment, not on experimental results. We use our knowledge about the nature of an experiment rather than going through the process of actually conducting it. For example, when flipping a coin we already know that there are only two possible outcomes; that is, heads or tails. In situations such as these, when all possible outcomes of a simple experiment are equally likely to happen, the theoretical probability of the event is:

Number of outcomes in the event
Number of possible outcomes

In real life situations, outcomes are not always as equally likely to happen as it is when flipping a coin. It is because of this and the reasons listed above that many would agree that the experimental approach to teaching probability is often more appropriate and valuable to use in the primary/elementary classroom.

As the Atlantic Canada Mathematics Curriculum Guide states, "the learning environment [in a math classroom] will be one in which students and teachers make regular use of manipulative materials and technology, actively participate in discourse, conjecture, verify reasoning, and share solutions. Conducting experiments and using a hands-on approach to teach and learn probability will foster such an environment for any primary/elementary classroom.

The follwing are references that I used while creating this blog:

Van De Walle, John. and Sandra Folk. Elementary And Middle School Mathematics: Teaching Developmentally. Canada: Pearson Education Inc, 2005

The Atlantic Canada Mathematics Curriculum Guide

Probability, Random Variables, and the Binomial Distribution

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Math Assignment: Probability

This blog has been created for my Education 3940 course to share information and findings about the mathematical topic of probability. I will be posting information regrading this topic that deals with areas such as the definition of probability, probability in real life, how to teach probability to children, sample lesson plans and problems. I hope this information will be beneficial to those who are dealing with this topic in their primary/elementary classrooms.

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