Listening & Learning/ Marcy's Dots
The Marcy's Dot article discussed ways in which students answered a question entailing the Dots. Students are given the same problem we were in class- 2 dots, 6 dots, and 12 dots. Students were asked to solve for the 20th step and the article discussed the reasoning students provided. If students simply state their answer, it does not make sense. However, if they write each step or a formula to show how they got the answer to the 20th step, it is more understandable as to how they got the answer. The next NAEP problem given to students was about soldiers on the bus. The answer ended up being 32, and no answers with fractions or decimals were accepted because you can not have part of a bus. The researchers were concerned about the low percentage of students who answered the question correctly because students at the age of 13 should be able to round to the next whole number to fit people on the bus. This article focused a lot on tasks given and how students justify their answers to show some level of understanding. It stressed that although sometimes students do not have correct answer, they are able to justify their reasoning.
Listening and Learning from Student Thinking explained how teachers can gain insight from student errors. Given the opportunity to justify their answer, they may be correct in their reasoning but not in the steps they took to get there. There are skills and strategies for different types of problems that should be looked for when evaluating a student's response. The article suggests having as many tools as necessary available to students so they are able to work through the problems asked with visual aids. The article also says that students should answer questions using more than one strategy not only for their own benefit, but also for the teacher's. Teachers can see whether or not students are making sense of problems or if they are accurately using the strategy. Over time, it is important to track how students use certain strategies and develop more in depth understandings of problems.
In my own classroom, I am sure I will have Marcy's Dots questions and similar questions to the bus. I will ask my students for their reasoning as to how they got the answer they did and they will provide a rationale. Similar questions can also show whether or not they understand rounding up (in situations of the bus problem) and a rationale will help show the extent they understand. I got a lot out of the Listening and Learning article because it gave ideas to use in my classroom as well. It suggested asking students to solve a problem using more than one strategy, and this is something I will do in my classroom. It is something I had to do as a student and it proved to me that sometimes you can make mistakes using one algorithm but you try a different way and get another answer. This pushes students to check their work and their accuracy on each of the strategies they use. They will also be able to justify their answers for these and prove their understanding.
Discussion questions:
1. Why should we use Marcy's Dots with our students?
2. Other than being able to see if they are correct/ incorrect using one strategy, why is it important that students use more than one strategy while solving problems?
Listening and Learning from Student Thinking explained how teachers can gain insight from student errors. Given the opportunity to justify their answer, they may be correct in their reasoning but not in the steps they took to get there. There are skills and strategies for different types of problems that should be looked for when evaluating a student's response. The article suggests having as many tools as necessary available to students so they are able to work through the problems asked with visual aids. The article also says that students should answer questions using more than one strategy not only for their own benefit, but also for the teacher's. Teachers can see whether or not students are making sense of problems or if they are accurately using the strategy. Over time, it is important to track how students use certain strategies and develop more in depth understandings of problems.
In my own classroom, I am sure I will have Marcy's Dots questions and similar questions to the bus. I will ask my students for their reasoning as to how they got the answer they did and they will provide a rationale. Similar questions can also show whether or not they understand rounding up (in situations of the bus problem) and a rationale will help show the extent they understand. I got a lot out of the Listening and Learning article because it gave ideas to use in my classroom as well. It suggested asking students to solve a problem using more than one strategy, and this is something I will do in my classroom. It is something I had to do as a student and it proved to me that sometimes you can make mistakes using one algorithm but you try a different way and get another answer. This pushes students to check their work and their accuracy on each of the strategies they use. They will also be able to justify their answers for these and prove their understanding.
Discussion questions:
1. Why should we use Marcy's Dots with our students?
2. Other than being able to see if they are correct/ incorrect using one strategy, why is it important that students use more than one strategy while solving problems?
Thank you.
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