Module Seven

Textbook Reading

What are the advantages of having students conduct experiments before they attempt to figure out a theoretical probability?

·        It is all about extending the understanding of the concepts. Using objects that the students are not familiar with help the children have an unbiased experiment. The understanding of the experiment part of probability is important as it allows for the children to predict what could happen next, and see if they were correct. Aubrey-do you agree, or did you get a different answer?

List the title and describe the experiment that you explored and discuss the advantages and disadvantages of virtual experiments.

·        Adjustable Spinner

o   In this virtual experiment you are conducting a probability of what color the spinner will land on with a certain number of spins. The advantages are that you can increase the sectors to a 12 different colors and do any number of spins between 1 and 100 to get accurate data collection. This would allow the students to see how the number of colors selected and the number of spins could change the results.  However, the disadvantage is that it is a computer program, and we really don’t know how random the spins really are. I also think that because it is not all that interactive the students could get bored rather quick.

Aubrey, do you think using the computer or “virtual experiment” is good?

A Whale of a Tale

Dice Toss

1.     Ms. Kincaid wanted the students to make predictions about their experiment on the basis of mathematical probability. Discuss preconceptions that students exhibited about tossing dice even after discussing the mathematical probability. Discuss the instructional implications of dealing with these preconceptions.

·        Most of the students were able to already understand probability due to the previous work they had done with coin flip activity. The students were able to come up with all of the possible results that could happen with two dice, but the teacher had to remind them a few times that the total had to include both dice. Some students

2.     Were these students too young to discuss mathematical probability? What evidence did you observe that leads you to believe that students did or did not grasp the difference between mathematical probability and experimental probability? At what age should probability be discussed?

·        No I don’t believe they were too young to discuss mathematical probability, they are 4^th graders and this teacher is allowing them to have an early understanding of what it means to develop probability. The students were able to give the proper definition of both mathematical and experimental probability without help from the teacher. They also understand that because more combinations of dice could make the number 7 that it had a higher chance of being rolled. We should start discussing probability as soon as possible, as the book mentions, even talking about the chance of rain is early stages of probability.

3.     The teacher asked the students, “What can you say about the data we collected as a group?” and “What can you say mathematically?” How did the phrasing of these two questions affect the students’ reasoning?

·        When the question was asked about the data, the first group she went to expressed what they saw on the graph, and how it looked like a “rocket” but once she changed to mathematically what do you see they knew that she wanted the number answer using math vocabulary.

4.     Why did Ms. Kincaid require each group of students to roll the dice thirty-six times? What are the advantages and disadvantages of rolling this number of times?

·        The total number of possible combinations that could be rolled was 36, so you would want the experiment to have at least that many rolls to ensure you get the maximum outcomes for possibilities. However, with the way some students recorded the data or preformed the experiment they had too many rolls for their group. Instead of them restarting they tried to erase the last answers they remembered.

5.     Comment on the collaboration among the students as they conducted the experiment. Give evidence that students either worked together as a group or worked as individuals.

·        It seemed like most all of the groups worked together, they all had input of how they could collect the data, and they all had a job. It was interesting to see how the different groups decided to do the dice rolling, some rotated with one turn at a time while others did all 9 rolls at once. It was an important task to keep count and even when the one group over rolled, they worked together to recall their past rolls and erase the data.

6.     Why do you think Ms. Kincaid assigned roles to each group member? What effect did this practice have on the students? How does assigning roles facilitate collaboration among the group members?

·        Giving each student a job in the group allowed for them to not only work together but to also hold each other accountable. For example the group that rolled to many times, the person that was supposed to be counting got carried away and caused an error in the data. It also ensures that each member is an active part of the group and no one member is taken control of the experiment.

7.     Describe the types of questions that Ms. Kincaid asked the students in the individual groups. How did this questioning further student understanding and learning?

·        The questions Ms. Kincaid asks of the individual groups allows the students to make connections to what they predicted would happen and what actually happened. This allowed the students to gain a deeper understanding of probability and how the number of outcomes relates to the probability that it could show up more often. They were able to relate personal experiences as well to this experiment.

8.     Why did Ms. Kincaid let each group decide how to record the data rather than giving groups a recording sheet that was already organized? When would it be appropriate to give students an organized recording sheet? Discuss the advantages and disadvantages of allowing students to create their own recording plans.

·        This allowed the groups to create the way they thought would best work to organize the results. As Ms. Kincaid mentions, one student’s way was unorganized and she had to go back and reorganize the data so that they could understand what they had collected. Ms. Kincaid showed examples to the students of ways they previously used to collect data, they could have used this as an idea. It would be better for the lower-elementary age to have a recording sheet or the first time the idea is presented so that they students can see how to record data. Allowing them to create their own allows for the students to learn from possible mistakes it also lets them decide which way works best for them. The downfall is the unorganized collection that could result in inaccurate responses or if time is an issue.

Aubrey, I would using this as a lesson on probability, would you? If so, would you alter any part of it?

For Further Consideration…

I will be sure to introduce the ideas of probability early on, since I would like to teach kindergarten, I would ask my students questions about the weather. If it is cloudy, what is the chance of rain today? Introducing this concept early on will allow for the students to understand that probability is about experimenting with the given information and finding out how often it can happen. The experiments in the book seemed like they could be fun beginner lessons to create an understanding and a way to use the natural language of the children (Higgins, 2014).

I am interested in reading how you will ensure a background knowledge.