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
The students in this video did struggle with making predictions that were based on mathematical probability. Many students guessed that the most rolls would add up to be 7 because 7 had the most combinations.
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?
I do not believe that these students were to young to discuss mathematical probability. The students in the video seemed to grasp the concepts of mathematical probability and understand what it was they just kept wanting to bring up past experience when trying to think mathematically. When the teacher reviewed mathematical probability and experimental probability with the students they were correct in their explanation and seemed to understand the difference. I believe that probability being introduced maybe starting in second grade would not be bad. I do not mean to the full on extent of this exercise but more of a likely/unlikely type of probability exercise.
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 students were asked about "what can you say about the date collected as a group?" it allowed the students to answer with any sort of answer such as the student who made the analogy about the results looking like a rocket ship. When asked "what can you say mathematically?" it narrowed down what the students were supposed to talk about and gave the teacher an insight on what the students learned mathematically from their activity. The students were then able to answer the questions using numbers and not talking about things unrelated to math.
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 dice were rolled 36 times in my opinion because 36 was the number of combinations (sums) that could be made with the two dice. The groups also consisted of 4 students and using 36 rolls allowed for each student to be able to roll the dice 9 times. The advantages of rolling the dice 36 times is that it allows a good amount of rolls to collect data off of. I feel like 36 rolls is a good number and should give a good idea of what number occurs the most. The only disadvantage I can think of is the students loosing count (despite having a counter) and data being swayed.
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.
The students were able to collaborate well in the video to me. The students talked about how they wanted to organize their data and then they conducted their experiment in the manner they wanted to. The groups were able to work well and discuss their ideas. The students also worked as individuals when doing their own job but their jobs worked collaboratively in making the experiment work well.
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?
I think Ms. Kincaid assigned roles to each member so that everyone had to be involved and so that each person would be responsible for something. I think this helped the students because although they were doing their individual jobs it allowed for the group to work effectively together. Assigning roles facilitates collaboration because it makes it where the students have to work together as a group in order for all information to be distributed because they are all doing a different thing.
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?
Ms. Kincaid did a good job when asking students questions because they were direct and allowed for the students to know what information she was wanting to know. She also helped guide them through their questions by talking with them and asking them other questions while discussing what was going on. Ms. Kincaid used a lot of mathematical terminology when speaking with the students as well and wanted them to respond mathematically to questions as well which helped them to understand probability.
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.
I think Ms. Kincaid let each group to record their data their own way as a way to get them to think on their own as well as a way for her to see the different understandings of data collection that her students have. Students were able to show what they knew and also able to see which ways of data collection made more sense in certain situations. I believe that teachers should give students organized recording sheets whenever students are starting out learning about data collection or whenever she wants all students to use one method as a learning tool.
The advantages of allowing students to create their own recording plans is because it allows them to be creative, really think, and allows the teacher to see what their students know and how they use and sort data. A disadvantage of allowing students to organize their data in their own way is the teacher doesn't really have a certain criteria to grade off of and cannot really tell a student whether their method is the correct one because they allowed the students to use their own method of data collection.
For further consideration...
Knowing what you now know about probability concepts in the elementary school, how will you
ensure that your students have the background to be successful with these concepts in middle school?
Knowing what I know now about probability concepts in the elementary school I want to ensure that my students have the background to be successful with these concepts in middle school by making sure that they know what mathematical probability is, experimental probability is, and that they know how to find probability. I want to do activities like the dice that are shown in the video. I also want to do many other activities with probability to make sure students know what it is and how to find it. I would also allow them to record their results in their own ways so I can see how the students are thinking and so that I can work with them if they are having a problem in using the best way of collecting data. I want to make sure that by students have a solid background when working with probability before middle school so that when they get there they can continue to build on concepts they already know.
A Whale of a Tale:
Impossible Unlikely Likely Certain
1. To run to California in a day. 1. I become a surgeon 1. I become a teacher 1. I am a girl 2. I will be 100 next year 2. I do not graduate in May 2. I go to bed by 11pm 2. I have green eyes.
Preconceptions are something that we are going to have to deal with in our classroom. We will have to make sure our students can forget about these when teaching lessons because they can interfere with their learning. What do you think is the best way to teach students that their preconceptions are not always true and that math is different?
ReplyDeleteI did not even think about there being 36 possible outcomes for rolling the dice. I was just thinking that then each student would get a chance to roll. Now that you said that, it makes a lot more sense. When doing probability, the students should draw or roll or spin the number of times possible for it to happen.
Ms. Kincaid gave rolls to each of the students when doing their probability lesson. I thought this was good because then each student was taking part in the activity and given a chance to be the leader of something. Do you think you will assign roles in your class one day or will you have the students assign roles? Will you even have roles in your groups?
I think you have great ideas about teaching probability in elementary school to be successful in middle school. I think it is important for us to do so because probability can be so difficult. What kinds of activities do you think you would do to help the students besides the ones we have discussed in this module?
My favorite one of your sentences was it is impossible to run to California in a day. Just a suggestion though, you should probably put from NC or a state that is far enough away that you could not because some of the neighboring states to California, you probably could run there in a day if you wanted to.
Do you enjoy probability? Do you have any activities you did when you were younger that you remember or particularly liked?
I think a way to avoid preconceptions is to make sure students know definitions of words and that they know that those definitions are what they need to use when using their certain mathematical ways of thinking. What do you think would be a way to avoid preconceptions? I will definitely assign roles in my class as well as in groups. I feel like roles allow for the students to have to be responsible for their certain task but also feel like an important part of the group because without their job the assignment cannot be completed. I believe that you could use activities such as having colors in a bag as probability activities, using a spinner activity, or even a simple heads or tails coin activity. What are some ones you have thought about? Thanks for the suggestion on running to California…I didn’t even think about implying I was in North Carolina. I would say I somewhat enjoy probability. When I was in elementary school the main activity I remember about working with probability was the teacher putting a certain number of colored balls in a bag and we would draw them out as a way of discussing probability.
ReplyDeleteHonestly, I am not 100% sure how I would get rid of preconceptions. I have never really thought about it before. I guess I would teach a concept and see if any preconceptions come up. If they do, I would go back and see how I could relate real world ideas that were correct about the concept to the new concept to try to rid of the preconception.
ReplyDeleteI really like the colors in a bag. Also, you could do any object in a bag. Maybe if you were reading a story, you could put objects or pictures of objects from the story in the bag and relate the story to the mathematical concept.
I remember using a lot of colors in elementary school as well. I do not really remember learning probability has certain and likely and unlikely though as I have seen now a days in schools.
That is a good idea about using characters from a story in probability lessons as a way to integrate. I guess this could be done with vocab words, spelling words, other subjects as well. Glad you mentioned that. Thank you for your responses. Your input always helps me in these modules.
ReplyDeleteVocabulary does help but it must happen within a context for it to make any difference in a student's understanding. It's often best taught within a lesson versus at the beginning. You'll know the words that are important for them to know and can design the lesson so that it naturally will come up in discussion. It is then that you can make a big deal out of what the word means and possibly put it in a math dictionary or create a math word wall.
ReplyDelete