Reflection

I have now completed my math blog about probability and I feel as through I have a much greater understanding of the topic. When reflecting on why I originally chose to research this idea in the first place, the reason was because I had always been challenged by probability throughout my school career. It was an area of math that I had difficulty with and since I am going to be required to teach probability to my future students in the years to come, I wanted to make sure I knew more about the subject.

In doing my research and reading plenty of material, I found a great deal of valuable information about the wide range of topics that are involved in probability. One of the things that I value the most from doing my research was learning different methods on how to teach probability to children. Coming to the realization that this area of math does not have to be taught strictly through paper and pencil tasks was somewhat of an eye opener for me because this was how I had been taught while in school. Children need to be involved in hands-on experiences that they are able to relate to there own lives if they are to truly have a valuable learning experience. Also, the creation of many new hands-on computer simulations is a great additional resource that can be used in the classroom when teaching probability. From my own personal experiences, I know most children enjoy getting away from their desks and having time to play on the computer. Learning probability through this means will be both fun and enjoyable for children.

Although I learned a lot while researching for this assignment there are still some questions that I would like to answer. The one area that stands out in my mind as feeling a little incomplete is learning about children's understanding of probability. I found it really hard to find information and I feel as though there are many contradicting ideas out there involving this topic. I plan on doing a bit more research in order to get a better understanding. Some other questions that I would still like to find the answers to are:

1. When do you introduce the formula for probability to students?
2. Besides coins, dice or spinners, which are most commonly used when teaching probability, are there any other hands-on manipulative's that can be used to assist children?
3. What is the history of probability and who was the first people to research it?

Although there remains a few areas that I hope to look into further, in general, I feel as through I am now much more prepared to teach this topic to primary/elementary students.

Thanks!

Tree Diagrams

A tree diagram can be used in many disciplines for many different things. When it comes to probability, a tree diagram is used illustrates all the possible outcomes from an experiment (sample space). It can also be used to help determine the probability of individual outcomes within the sample space. It consists of arcs and nodes and each branch of the tree represents a possible outcome of one event. I can personally remember using tree diagrams in school when dealing with probability and found them very helpful because they allow you to better visualize and organize the problem you are working on. Many students will better understand probability and the problem that they are working with if they are able to have a visual representation in front of them. It is for this reason that I feel tree diagrams have a valid place in teaching probability to primary/elementary children. The following are sample probability problems that can be figured out through the use of a tree diagram:

1. Show the sample space for tossing one penny and rolling one die. (H = heads, T = tails)

By following the different paths in the tree diagram, you can arrive at the sample space which is { H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6 }. The probability of each of these outcomes is 1/2 x 1/6 = 1/12.


2. A family has three children. How many outcomes are in the sample space that indicates the sex of the children? Assume that the probability of male (M) and the probability of female (F) are each 1/2.

There are 8 outcomes in the sample space. The probability of each outcome is
1/2 x 1/2 x 1/2 = 1/8.

I also found a web site that provides some great probability problems that involve the use of tree diagrams that students could use for practice. Have a look!
Practice Page

The following are references used while creating this blog:

Lesson Plans: Tree Diagrams

Tiscali.Reference: Tree Diagram

Thanks!

The Not so Random Coin Toss

While searching up some information about chance and probability, I came across this interesting article that gives a different side to the concept of flipping a coin. It states that a coin toss may not be not as fair as once thought. Apparently, the randomness is due to the fact that when a human flips a coin, it lands randomly because of the way in which it was tossed. The article can be found at the following link: The Not so Random Coin Toss. It really makes you think about how fair a coin toss really is.

Thanks!