Response to the Reading

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 problem?

By using a problem-solving approach, you are encouraging students to make connections between math concepts that they ordinarily might not see.  In the chapter, I believe that one of the student samples involved using addition in place of multiplication operations.  When a teacher explicitly tells a student how to think about and look at a problem, the connection between different operations might never be made, and the depth of understanding that such thought and experimentation when problem solving might result in students whose understanding of the concepts is not as well-formed.

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 hope to make my students feel confident in their ability to solve math problems, encouraging them to view their experimentation and incorrect responses as a part of the learning process, and more importantly, as qualities of good problem solving.  I also plan to hold high expectations for my students in order to supply the necessary instruction to ensure that they can meet those expectations with success.

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 agree, that when implemented in name only, the constructivist approach to math education can be a recipe for kids to not really come to any understanding of the basic concepts around which math is based.  For example, subscribing to the philosophy that when supplied with time and materials, students will automatically learn the important math concepts, is not a guarantee that such learning will actually occur.  Rather, in order to be successful when learning in a constructivist math classroom, students need scaffolding and supports.  Additionally, I'm not sure that a teacher who subscribes to a constructivist teaching philosophy really has to completely ignore quality explanations.  The difference in this philosophy lies in from whom those quality explanations come.  Having students draw their own conclusions and make their own connections perhaps is an even stronger method of exposing students to the "basic facts and ideas" of math.

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?

Perhaps the most important reason why providing such "help" is not a good idea lies in the message that such actions communicate to the student.  Requiring a teacher to constantly "come to the rescue" when solving math problems runs the risk of imbuing the child with a sense that they are not competent or skilled in the area.  Additionally, when a teacher solves the problem, who really is doing the learning then?

5. Reflecting on how tasks were defined in the Van de Walle chapters, how did the tasks presented in the Behrand article to LD students help in their mathematical development?  Please give specific examples.

This approach helped students who did not feel comfortable in their own abilities and who did not enjoy the subject area take ownership of their learning and discover previously untapped abilities to critically analyze a problem.  By showing the students that to be at math did not mean that you had to always answer the problem correctly, freed them to truly discover their own abilities.