I chose to blog about the Smith article because I felt as though I was somewhat confused. Near the end of the task evaluations, a small disagreement begins about task A which involves students completing a dot pattern without providing any real directions. “The ensuing discussion highlighted the fact that no procedure or pathway was stated or implied for task A, yet the group had included the use of procedure as a hallmark of tasks that were classified as procedures without connections and procedures with connections” (Smith, pg. 347). The argument can be looked at more as higher-level tasks versus lower-level tasks. However, the group decided that this problem could be viewed as simply doing mathematics, which is considered an higher-level demand because it “requires students to explore and understand the nature of mathematical, concepts, processes, and relationships” and a variety of other reasons listed under the Levels of Demands section (Smith, pg. 348). This is confusing to me because no age group was ever listed. As a college graduate, this task is extremely easy and would definitely be classified as lower-level. I believe that this holds true to the higher grades in elementary. However, those in the younger grades would have to draw on their prior knowledge and really have to work to figure out on to solve this problem. Without any real directions or steps laid out for students, it becomes a higher-level task because they are simply not used to it. It is also higher-level for younger age groups because they cannot simply let their new pattern speak for their answer because they are then ask to put their thought into words. I believe explaining mathematical procedures at any age is difficult because we are so used to letting different numbers, patterns, graphs, etc. speak for our thought process.
I believe that it is important for teachers to get together to brainstorm different mathematical activities because everyone has their own creative input. Leveling the different tasks using the Smith classifications can be extremely helpful. However, I believe that in my placement this type of classification can be very difficult because every concept is new to my students. They do not have much of a mathematical background besides counting and basic arithmetic. What do you girls think because I know that my thoughts are everywhere? I think that reading this article a second time just confused me more!
Jessica,
ReplyDeleteLeveling tasks is a great way to decipher which students are doing well and which students are struggling. Having high level tasks and low level tasks prepared for the classroom and students is a great way to determine how students will work well together and what they are going to be learning. Math is a hard subject for many people and as stated in our class yesterday "you either love math, or you hate it." This is true in most cases-- I for one hate math because I am not good at it, nor have I ever been and it is a constant struggle. I believe that as teachers we need to try very hard to make our students like math and make it seem fun because after all, you never can escape math.
Teachers getting together to brainstorm different mathematical activities per grade level is a great thing I think as well. But you are right, with concepts being new to students it is going to be a challenge for them regardless. I think that this is a toss up because you really will need to know your students in order to level the tasks and activities and which ones you give to them. Interesting article!