The problem-solving approach somewhat assumes that all of the students come with the same knowledge base and would be equally receptive to the information/format being given by the teacher. The approach doesn't really give wiggle room for bringing in previous experiences and other frames of knowledge - there's one right way of solving the problem. Period!
2. How do you think your experiences, feelings, and beliefs about math will impact the kind of teacher of math that you will be or the kind of teacher of math that you want to be?
One thing I'm working hard at is to put aside the "it's easy!" frame of mind. I've been fairly fortunate in math to be able to grasp concepts fairly quickly and had great support at home when I didn't understand. Through my experiences as an intern teacher, my brain has been expanding to explain things in different ways and I've been learning more ways to bring in students' interests to try to make sense of what I'm asking them to do. I'd definitely like math to be a fun and interactive part of the day rather than something we "have to do."
3. Not everyone believes in the constructionist-oriented approach to teaching mathematics. Some of their reasons include the following: There is not enough time to let kids discover everything. Basic facts and ideas are better taught through quality explanations. Students should not have to "reinvent the wheel." How would you respond to these arguments?
It's frustrating and unfortunate that teachers are constantly (in some districts even more so than others) under pressure to make sure every student in their class is on the same page and can keep up with the pace to make it to TAKS week. While some think that kids discovering what works for them may be time consuming, it's what works for them! It is of far greater use for them to actually understand what is happening than to have them memorize formulas and be able to pass the test.
4. We sometimes want to jump in and help struggling students by saying things like, "It's easy! Let me help you!" Is this a good idea? What is a better way of helping a student who is having difficulty solving a problem?
Not a good idea! This will only make the student feel worse and be down on themselves; if it's "so easy" then they must be "so stupid." - No!
Helping a student relate a problem to something they enjoy and are familiar with will serve them to not only work on the current material, but also add more problem-solving solutions to their framework of understanding.
5. Reflecting on how tasks were defined in the Van de Walle chapters, how did the tasks presented in the Behrand article to Learning-Disabled students help in their mathematical development? Please give specific examples.
Having the students work together and compare ways of solving the problems seemed to have been a great way for them to either reformulate their own answer or to feel even more strongly about their answer and defend it to the death. It also provided a check that didn't feel like an authority was shooting down their method/answer.
Your "Peak Experience" sounds awesome! I wish my teachers would have left me done that (especially the "no turning in homework"). I remember back in elementary school my teachers would always move me around in the seating placement to sit by students "who needed more peer help, or role-model" by them. So every subject I would help whom ever I sat by with their work and try to represent what a "good student" should look like. However, I still had to turn in my homework everyday. :-(
ReplyDeleteBut it sounds like you had a really great experience with not only the class but also helping your peers.
I am also for students comparing their answers. I feel like they have to understand how not to hurt each others' feelings, but i think its good. I would rather be told I was wrong by friend in privacy than a teacher out in the open.
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