Week 2 - Reading Responses

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?
   Taking a problem-solving approach differs from simply teaching children the skills they need to solve problems in a few ways. Problem-solving must begin where the students are and does not rely on a set of memorized rules or procedures. There is no "correct" solution, but students still are required to justify their answers. (p. 33)

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 believe that my math experiences will all positively contribute to my attitude and ability to teach math. I have always enjoyed math as a subject and love problem-solving to determine answers. I find math to be like a game where everyone can use different strategies to win. This fun math mentality will hopefully also be reflected in my teaching style.

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?
    I disagree. While some methods may prove to work best or be quickest for a majority of students, it is important to see our student's as individuals. People have different learning styles and different interests that should be utilized to engage them into the math material. It shouldn't matter too much how a student comes up with an answer, as long as he or she is still accurate and can attempt to explain their thought process.

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?
    NO. It is not necessarily to always jump in and provide a student with help. Students should be given adequate time and perhaps tools to help them solve problems on their own before seeking out help from a peer and then teacher. One idea might be to provide a student with manipulatives, making it easier for him/her to solve the problem with a visual.

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.
    Students were given the opportunity to come up with answers on their own prior to teaching. The teacher could then compile their means of solving the problem to discuss how one problem can be solved multiple ways. It's not a competition.