Some of the readings this week really made me think about how math was/is/should be taught. In the 5 Practices chapter, the importance of "higher level" tasks was highlighted. These types of demands include focusing on multiple approaches to problem solving, representing problems in various ways (manipulatives, visuals, symbols etc.), and overall- asks students to engage cognitively to explore and understand mathematics. In contrast, lower level tasks include various methods of basic memorization. When I reflect on my own mathematical learning, I feel I spent a significant amount of time simply memorizing. However, I was fortunate enough to grasp the concepts easily-and thus I really didn't struggle with the process of understanding mathematics. However, for those students who would spend time "memorizing" for a math test and then fail a test- this makes sense. Memorizing doesn't teach you anything if you don't know the underlying concepts. How do you get to the underlying concepts? Through higher level tasks!
In my placement, I would classify the classroom structure as following more "higher level" thinking in regards to mathematics. However, students are not yet to a level of mathematical reasoning in which memorization of various facts etc is required. Manipulatives are used as support as well as visual representations. Students also spend considerable time with their peers working through their activities, rather than individually or simply listening to the teacher. These activities as a whole seem to me, to be classified as "high level" rather than "low level" tasks. What do you see as high vs low level tasks in relation to your field placement?
However, after reading the article Children's Understanding of Equality I puzzled over the idea of higher level thinking further. The whole "equal sign" issue really seems to come down the issue of high versus low level tasks. It is ingrained into students' mathematical thinking that an equals sign is "a symbol describing a relationship rather than as a “do it”sign" (Falkner, 1999). As discussed in the article, if teachers are to take the equals sign concept to a "higher level" by changing its position in problems and varying how it is used, the concept is not only more accurately understood, but students are also more prepared and ready to engage in higher level math concepts. It seems to me that many mathematical concepts are likely able to be engaged with at a higher level to yield similar results.
I wonder how the students in my class view an equals sign? Most students are not yet working with addition, and those that are working with addition are at a beginning level and have not been explicitly taught- they've simply been allowed to work on different activities and games to engage with the content. Because the article details students as young as kindergarten having the same misunderstandings even prior to working with equals signs, I'm assuming the students in my placement are the same. This concept is very interesting to me!
I completely agree with you on the memorizing thing. I think it is something that a lot of students our age have been trained to do. It seems to be the easiest way to study and retain information for most subjects. However, you were right about math not being a good subject for memorizing. In math it is crucial for students to understand the concepts before they are able to memorize anything. I think the ideas in the 5 practices chapter were great especially the ones about higher level thinking. I unfortunately do not get to observe much math in my classroom and they are also in kindergarten which means that they not quite into addition and subtraction yet but I do get to see some other various higher level thinking in other subjects.
ReplyDeleteMy CT has the students working together and constantly working on problems that will engage their minds. They are always surpassing what we think they are capable of and I believe that is because of the way my CT has structured their learning.
From what was discussed in the readings, I would describe the math that I'm seeing in my placement as lower-level thinking. The rocket math program that the students do on a daily basis requires them to answer as many addition problems as they can in one minute, with "practice time" given to them each morning to work on memorizing the facts with a partner. Like Jessie and Chelsey mentioned, I also remember doing these types of memorization activities during my elementary and middle school days. I agree that this is not the type of thinking we should be teaching young children to do.
ReplyDeleteIn addition to the rocket math, students in my MT's classroom also have a daily lesson that is presented to them first thing in the morning. They watch a video about the subject and then complete one or two worksheets as a follow up. These worksheets contain more lower-level thinking problems that have one correct answer and generally only one way to reach it. The class does not go over the worksheets after they are completed, so there isn't much scaffolding for the students that are still struggling to understand.