Textbook Reading
What are the advantages of having students conduct experiments even before they attempt to figure out a theoretical probability?
The advantages of having students conduct experiments before they attempt to figure out theoretical probability is they are able to make their own predictions. They then use their predictions to try and make connections about what might happen.
Go to the Illuminations website and explore one of the virtual experiments. List the title
and describe the experiment that you explored and discuss the advantages and
disadvantages of virtual experiments. (http://illuminations.nctm.org/ and use the search
site: probability and check interactives)
The title of the virtual experiment I explored was Adjustable Spinner. The virtual spinner was actually really cool. It allowed you to pick how big you wanted each part of the spinner. You got to choose how many times you spun the spinner. Each time you spun the spinner it changed both the experimental and the theoretical probability. It also let you change the number of parts on the spinner. I think this is a great tool to use in a classroom when a physical spinner isn't around.
Did you choose a different virtual experiment to explore?
Did you choose a different virtual experiment to explore?
A Whale of a Tale
Dice Toss
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.The students first had to look at the dice and realize that the lowest number was a 1 and the highest was a 6. They then had to realize that they had to add the two dice together so they could never have the answer of 1 when those there is 1 on the dice.
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 do not believe that the students were too young to discuss mathematical probability. They first talk about the different types of probability, this shows that they understand the concept. They were able to explain different things they could come up with and that it the first step of working with probability. I think probability needs to be introduced as young as possible, the earlier the better. At younger ages do things like spinners and different colors or a coin with heads or tails.
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 teacher asked the first question the student answered talking only about the shape that was made. Once the teacher reworded the question they were about to think of and use vocabulary that he knows about probability to explain what was recorded and could tell her what was more likely to happen and why.
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?
Ms. Kincaid required the students to each roll the dice thirty-six times so each group have the same number of changes of getting each answer. The advantages of this is after completing all the rolls the different groups can compare their answers and see that probability is never always the same. Disadvantages are that is a large amount of rolls so they might be in too big of a hurry and mess up on their data.
What do you think is a good amount of times the students should roll the dice?
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.
The students did a good job of working together like the group who rolled the dice too many times they worked together well to go back words and get rid of the data that they didn't need. Each student in the group had their own job to do during this assignment which made it turn out really well.
Do you think the groups could of done something else to make their working together work even better?
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?
I think she assigned roles so the students knew exactly what to do and weren't wasting time figuring out who should do what. Assigning the roles to students helps them to get started on their work right away and keeps the groups from auguring on who is doing what and making sure everyone is doing something.
Describe the types of questions that Ms. Kincaid asked the students in the individual groups. How did this questioning further student understanding and learning?
She used more open ended questions because she wanted to hear the students explain why they did what they did or how their data was showing probability. By being open-ended it made the students have to think before answering.
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.
I think she did this to see how each group thought it would be best to record the data. By doing this she gave the students the ability to brain storm and come up with a way to record as a group, this shows team work. I think it is appropriate to give students a recording sheet if it was their first time ever working with data like this. Advantages are you get to see all the different ways students are understanding data and how to organize it. Disadvantages makes it harder for the students to compare with one another.
For Further Consideration....
Knowing what you now know about probability concepts in elementary school, how will you ensure that your students have a background to be successful with these concepts in middle school?
To make sure my students have a good background in probability I will make sure I do many activities on this subject. This that the students find fun like M&M sorts (colors). While doing things like this I will ask questions that will make them think about the data and why the data is what it is. Or why their data is different them their neighbors. Have the students compare data with each other and make sure they know that data is ALWAYS changing.
I chose one called "Button Train". It was geared toward pre K- 2nd grade, and I thought it was maybe something I could read through and get easily! lol It taught terms like first, next, and last. I could see the importance of the lesson and thought it was good.
ReplyDeleteI had a hard time with this one too. I also had one more in the middle, and that one was really hard to do. I think writing stuff I would never do, or things that I would would do for sure were easier than the others.
I think that was probably a pretty good number. It kept them busy and gave them enough opportunities to get a fair collection of data.
I was really impressed with the way these kids handled the group work. My kids often spend group activities talking and off task. These kids got the job done and worked well together.