Article by: Edward J. Davis
Davis' article first held my interest because in the last year I have been in the Education Department we hear time and time again to never put "the students will understand..." in our lesson plan objectives which makes sense. The article refers to "kinds of logical things teachers do during mathematics" as moves. After reading this article it is proof what the students really need to have as objectives when we want to say understand..and it's a little longer than just understand and requires work. Having students be able to state the problem and solution in their own words, give examples, find it hidden in other examples, see connections from other facts and it, use it in multiple ways, foresee the consequences, and state its opposite. Teachers should start with physical characters and then move to symbols as representation. The article mentions having students answer certain questions to demonstrate understanding such as using the formula in another problem. The amount of moves will vary from lesson to lesson and teacher to teacher. Understanding on the two levels will also vary, some lessons the students will hit both levels in one try while others it might take longer.
The figures throughout the article really helped me appreciate and understand the material. I like that each section was broken down into two levels providing examples of how the concept works. It was eye opening and just really put the whole idea into perspective on how to use it. I took away the fact that as teachers it isn't just important for the student to be able to solve the problem but also to understand why they are doing and using what they are using. If the students can explain to us why then they have reached understanding. It is easy to present the information to students and have them plug in what they know and present it without really knowing what they did and why. I like that the article said to ask the questions such as recalling facts or explaining patterns.
Discussion Questions:
1. How can teachers start adding moves into their lesson plans to reach the level two from the figures or full understanding?
2. Has there been any research done on using moves in other subject areas? How does it compare to the work done on moves in mathematics?
Davis' article first held my interest because in the last year I have been in the Education Department we hear time and time again to never put "the students will understand..." in our lesson plan objectives which makes sense. The article refers to "kinds of logical things teachers do during mathematics" as moves. After reading this article it is proof what the students really need to have as objectives when we want to say understand..and it's a little longer than just understand and requires work. Having students be able to state the problem and solution in their own words, give examples, find it hidden in other examples, see connections from other facts and it, use it in multiple ways, foresee the consequences, and state its opposite. Teachers should start with physical characters and then move to symbols as representation. The article mentions having students answer certain questions to demonstrate understanding such as using the formula in another problem. The amount of moves will vary from lesson to lesson and teacher to teacher. Understanding on the two levels will also vary, some lessons the students will hit both levels in one try while others it might take longer.
The figures throughout the article really helped me appreciate and understand the material. I like that each section was broken down into two levels providing examples of how the concept works. It was eye opening and just really put the whole idea into perspective on how to use it. I took away the fact that as teachers it isn't just important for the student to be able to solve the problem but also to understand why they are doing and using what they are using. If the students can explain to us why then they have reached understanding. It is easy to present the information to students and have them plug in what they know and present it without really knowing what they did and why. I like that the article said to ask the questions such as recalling facts or explaining patterns.
Discussion Questions:
1. How can teachers start adding moves into their lesson plans to reach the level two from the figures or full understanding?
2. Has there been any research done on using moves in other subject areas? How does it compare to the work done on moves in mathematics?
Very nice:) Thanks Sarah!
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