I found the first chapter of “Young Mathematicians at Work” to be very interesting. After attempting the sub sandwich problem myself, I was eager to read about how some children would solve it. I found it comforting that almost all of the children drew pictures in order to help aid in their thinking since this was the way I went about trying to solve the same problem. I feel that looking at mathematics as a creative process can bring in different learners as help math appeal to more children. After doing this same problem though, I was able to understand how solving real life problems such as this can help. Like the authors point out, the children know that having all of the subs cut up into 1/8 pieces is unrealistic because the pieces would be too small. Being able to relate problems such as this to real life knowledge can help children think through a problem. I also liked the way that the authors explained how children think and learn. I liked the idea of children learning through the three different landmarks, strategies as schemes, big ideas as structures and models as tools for thought. I realize that the authors believe that each child must move through and understand each of these ideas. I find myself wondering though what will happen if a child struggles with one of the frameworks. Would you as a teacher just simply focus more on that particular framework or could you just focus more on what the child understands and the rest will eventually follow?
I did also like that the second chapter in the same book brought up the idea of community. I have always been an advocate for strong communities in a classroom because I have personally found that I have learned best in a classroom where I am comfortable. I do like that the authors point out that mathematics must be connected and involved in the idea of community. Community is not necessarily just about feelings and rules but it also creates a safe space for discussions. When discussions are had about mathematics, children can learn more from not only each other but from themselves as they explain their thinking out loud.
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Erin, I also really liked the idea of a teacher's role in the classroom community. Not only do we play the role of dictator, keeping everyone in the community on track, but we also play the role of a member, one who converses and problem-solves with our students. Do you think that these two roles would ever be conflicting? Do you think that it will be difficult for us to relinquish our authoritative role and truly relate to the students on their level of understanding and thinking? In my opinion, this seems like it will be a tough task in that it will be difficult to determine when the appropriate time is to take on each role. Or maybe we need to play both roles simultaneously? But is that possible? This chapter offered a lot to think about for the future..
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