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
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
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
Thanks!
