I found this week's reading to be very interesting. It was nice to read through "The Value of Mistakes" because something I see teachers doing sometime in rushing in to correct students right away when they are doing school work instead of allowing students time to think through their own mistakes. In case 11 when Dawn was recording student responses to what number they thought would come next on the calendar she recorded all the responses on the board without comment. Then she allowed time for the students to try to reason out their answers without telling them if it was right or wrong. When students have to really think about their answers this forces them to analyze why it is right or wrong and helps them think about whether their answer makes sense or not. The Eggleton article says, "[students] may make similiar mistakes in the future, but they have now had the experience of analyzing the mistake to know why it is incorrect." This really is the goal of the teacher because they will not always be over the students shoulder to correct any errors they might have later in school and life.
I liked the example the article gave of the students with various numbers who were supposed to line up in order. I think this was more useful than on a worksheet where students have a series of numbers they are supposed to order. When used in this interactive way students have to talk to each other and justify their thinking. This means students have to decide if their math makes sense and they are also inadvertently engaging in group work because they work with each other to complete their line.
Case 14 in the DMI text where the students were discussing the importance of zero reminded me of something I watched in field today. Students were working on taking money written in words and turning it into decimal. One of the problems was something like four dollars and two cents. This was the only problem where the amount of cents was under 10 so many students struggled with it, writing $4.2 instead. This prompted a nice discussion in the class about the difference between .2 and .02 which would not have come up if the students had not made the mistake or if the teacher had just quickly corrected the error. Muriel writes in the case, "I wonder how maing sense of zero affects children's understanding of place value. Actually, it's probably more to the point to wonder how not making sense of zero affects children's understanding of place value," (56). While many of the students in my class seem to grasp how zero works, many others still do not fully understand the role of zero as a "placeholder".
I found the idea of the difference between "I don't know it" and "I don't know it yet" to be rather powerful. If you can get your students to the point where they know they can solve any problem if they try long or hard enough then they will probably have a lot more enjoyment and success with math.
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Anne,
ReplyDeleteI think it is so neat that you are seeing some of the things we are reading from the casebooks right in your own field placement! It sounds like your CT took the initiative to build upon a common error she saw across the students (misconception of zero as a place holder) and was able to help the students learn from this mistake. Do you think Eggleton would agree with the way that your CT handled the situation or did she segue into a mini-lesson simply to teach the students the correct way of doing it vs. allowing them to explore and re-think their thought process on their own? Also, I think what you saw transpire within your classroom is also an excellent example of the ways in which we, as teachers, can write efficient math problems that progressively become more challenging. This is a strategy we have discussed and read about frequently in our CGI book and it seems like your CT is doing an excellent job of writing efficient math problems. Because four dollars and 2 cents is much more challenging than a problem such as four dollars and fifty two cents, it seems the students were truly given an opportunity to expand their knowledge into an array of problem types. Do you think this was purposefully done by your CT? Overall, great post! It's always interesting to see what's going on in other people's placements!