I was particularly impressed by Melissa Sharp, a first year second grade teacher in the Englewood Public School District. She was able to get second grade students to think at a higher level. In the video, she stated that she does not accept students simply giving an answer. She wants them to be able to convince her that they have come up with the correct solution or all of the solutions. In essence, she wants every student to develop a deep understanding of the problems they are working on so that they can build on what they learn in future grades. If more teachers develop this philosophy of teaching then I suspect that the retention of ideas learned in a particular grade will increase.
After listening to some of Arthur Powell’s ideas, I can see the importance of getting students to “own a problem”. Getting students to think deeply about a problem is so important, and this can be done by getting them to be engaged in working with a problem. In addition, it is important to have students share ideas. Obviously, this requires students to get used to the idea of working together and discussing problems, but doing this process has value in and of itself. The reason that I feel so strongly about this is because so many of my students are able to solve a problem, but they do not completely understand what the answer means. Sometimes they come up with answers that do not make any sense, and they do not realize why their answers are not realistic. For example, they may come up with answers regarding time and speed that are negative. How is this possible? Thus, it is important to get young students to work with problems that are hands-on so that they develop a deep understanding of what numbers actually mean before moving on to more advanced abstract problems in later grades. For the same reason, it is also important to press students to provide a convincing argument for why their answers are correct. In this way, students are required to think like mathematicians, and if they are able to prove that their solution or solutions are correct then they have obviously developed “ownership” of the problem at hand.
I think Gina Kiczek, a teacher in the Jersey City Public School District, made an important realization, which is that students often do not see things the same way that the teacher does. Often there is a “disconnect” between students and their teacher because the students do not think the same way that the teacher does about a problem. This is why it is very important to give students the opportunity to share their ideas about problems. In the type of learning environment where students are given the opportunity to work together and discuss problems, they can not only develop their own line of thinking, but they can also learn from their peers. This is much more valuable then the outdated teaching model where a teacher is a “sage on a stage” and students simply absorb knowledge from him or her. By giving students the opportunity to work together and discuss what they are thinking, there is a much greater chance that students will develop a deep understanding of a problem and what the answer to a problem means. In essence, this style of teaching allows for more students to develop “ownership” of a problem.
I was particularly impressed by the ice cream lesson. This lesson is a testament to the value of a lesson that allows students to work together and solve problems. The reason that I say this is because the lesson was planned for an eighty minute block period. Based on the video, it appeared that students were engaged in the problems provided to them for the full eighty minute block. This is quite an achievement!
I thought the World Series problem was a good problem to use with older students. It is important to choose topics that fit students’ interests. Many students are obviously interested in the World Series, and thus, when one gives students this type of problem they are more likely to become engaged in what they are assigned to do.
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