The math question was given to a 4th grade student. The topic is on probability. Here is the question posed to the 4th grader:
The gum ball machine has 100 gum balls; 20 are yellow, 30 are blue, and 50 are red. The gum balls are well mixed inside the machine.
Jenny gets 10 gum balls from this machine. What is your best prediction of the number that will be red?
Student Answer: 5 gum balls
Explain why you chose this number:
Because red has the biggest number 50 and 10 divided by 2 is 5 so 30+20=50 and the rest would be blue and yellow.
The following is the discussion that followed for me:
How is this fourth-grade student's reasoning?
Although I have not had enough experience in a classroom, I am taking an educated guess that the student appears to be creating an equation using all the numbers available to solve the problem. The reasoning is more based on the need to make a math equation.
Do you think that this response is typical or rather advanced for a fourth-grader?
Again, I have not had personal experience with 4th graders in a math class so I am not sure if this is typical or not. As I read and re-read the explanation to the problem, it looks as though the student does understand how to solve the problem but lacks the vocabulary to explain why. When the student said "10 divided by 2 is 5" I saw that as the solution but the student failed to give the reasoning behind how they came to get that equation. I asked my 6th grade daughter to solve this problem and she came up with the correct answer but was unable to give a reason behind the answer. I also asked my soon-to-be 4th grade son and he came up with the correct answer as well. However, he too was unable to give a coherent reason behind his answer. Both of my kids kept saying there are more red gum balls but didn't say there are 2x as many red as other colors. It makes sense in their heads but the reason gets lost in translation. I look at this 4th grade student and think the same thing.
What percent of fourth-graders would you expect to get this item correct?
I would imagine that most, if not all, students would get this correct. (80%-100%) If this lesson is fresh in their head, I would guess that they would quickly look at the information presented and draw their conclusions and get the answer correct.
What percent of you classmates do you think would get it correct?
I think all of us would get this correct! :) 100%. Although, I have to admit that when I stopped and looked at it, I freaked out slightly due to the massive amounts of information swimming around in my head right now! All the recent formulas that I have been learning is causing me to second guess a seemingly easy question. When I have stress or an overload of information, I struggle with obvious answers, so if anyone else in class is on overload, this problem may appear overwhelming at first.
I suppose to a 4th grade student who may be under stress from changes in their life or just unable to concentrate, this problem may appear overwhelming as well. As a teacher, I need to remember that my students will encounter problems in school academically and personal issues that can effect the outcomes of school work.
After spending time re-reading this problem and reading insight from my classmates I have learned that math is so much more involved than just teaching the concepts. Students come to school with several different learning styles and issues that face them daily. As a teacher it is critical to take the time to learn about my students and understand their strengths and weaknesses. Math is math and several paths will lead a person to the correct answer, but to go a step further and explain how you got to the answer will drive home critical thinking in my students, which is critical in itself.
Jenny gets 10 gum balls from this machine. What is your best prediction of the number that will be red?
Student Answer: 5 gum balls
Explain why you chose this number:
Because red has the biggest number 50 and 10 divided by 2 is 5 so 30+20=50 and the rest would be blue and yellow.
The following is the discussion that followed for me:
How is this fourth-grade student's reasoning?
Although I have not had enough experience in a classroom, I am taking an educated guess that the student appears to be creating an equation using all the numbers available to solve the problem. The reasoning is more based on the need to make a math equation.
Do you think that this response is typical or rather advanced for a fourth-grader?
Again, I have not had personal experience with 4th graders in a math class so I am not sure if this is typical or not. As I read and re-read the explanation to the problem, it looks as though the student does understand how to solve the problem but lacks the vocabulary to explain why. When the student said "10 divided by 2 is 5" I saw that as the solution but the student failed to give the reasoning behind how they came to get that equation. I asked my 6th grade daughter to solve this problem and she came up with the correct answer but was unable to give a reason behind the answer. I also asked my soon-to-be 4th grade son and he came up with the correct answer as well. However, he too was unable to give a coherent reason behind his answer. Both of my kids kept saying there are more red gum balls but didn't say there are 2x as many red as other colors. It makes sense in their heads but the reason gets lost in translation. I look at this 4th grade student and think the same thing.
What percent of fourth-graders would you expect to get this item correct?
I would imagine that most, if not all, students would get this correct. (80%-100%) If this lesson is fresh in their head, I would guess that they would quickly look at the information presented and draw their conclusions and get the answer correct.
What percent of you classmates do you think would get it correct?
I think all of us would get this correct! :) 100%. Although, I have to admit that when I stopped and looked at it, I freaked out slightly due to the massive amounts of information swimming around in my head right now! All the recent formulas that I have been learning is causing me to second guess a seemingly easy question. When I have stress or an overload of information, I struggle with obvious answers, so if anyone else in class is on overload, this problem may appear overwhelming at first.
I suppose to a 4th grade student who may be under stress from changes in their life or just unable to concentrate, this problem may appear overwhelming as well. As a teacher, I need to remember that my students will encounter problems in school academically and personal issues that can effect the outcomes of school work.
After spending time re-reading this problem and reading insight from my classmates I have learned that math is so much more involved than just teaching the concepts. Students come to school with several different learning styles and issues that face them daily. As a teacher it is critical to take the time to learn about my students and understand their strengths and weaknesses. Math is math and several paths will lead a person to the correct answer, but to go a step further and explain how you got to the answer will drive home critical thinking in my students, which is critical in itself.
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