1. How does taking a problem-solving approach to teaching math differ from first teaching children the skills they need to solve problems and then showing children how to use those skills to solve problems?
Problem solving is essential to life, and it just as important in solving math problems. You can be great at math skills, but not know who to mark out extraneous information and determine what a word problem is asking.
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?
I do like math for the most have always been good at it. It will push me to learn how to teach different strategies to those whom math does not come as easily. It will also lead me to push those who do well so that they do not coast.
3. Not everyone believes in the constructivist-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?
These theories have some truth in them, however, learning needs to be active and exploration is an ideal way to go about this. I am a fan of the Montessori method and this has proven successful for many children.
4. We sometimes want to jump in and help strugglng students by saying things like, "It's easy! Let me help you!" Is this good idea? What is a better way of helping a student who is having difficulty solving a problem?
It is better to give them direction with meaningful prompts and strategies. You cannot demean the student for struggling, not should you do the problem for them. What defines a "good idea"? Giving students strategies that they can use in and out of the classroom is the best way to help a student.(ex. catch a man to fish v. teach a man to fish).
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.
The tasks helped to expand the methods and thought process in regards to a certain concept or skill. It shows a practical application important area.
I also want to push my students so that they don't just 'coast' through my class. I only hope that I can manage handling the different levels in my class. I want them to have fun, but expect a challenge everyday as well.
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