Math Week 9: Transformations through Reflection

This quarter we have studied so many aspects of mathematical learning.  We have talked about using manipulatives in order to root abstract concepts in concrete ideas and understanding.  Also, we have been involved in the group work process and exploring what it means to have meaningful and effective group work.  We have also interacted with a variety of technological tools to use to assist in mathematical learning such as iPod Touches, computers, and graphing calculators.  Throughout all of this, we have found ways to reach all students by offering multiple entry points for learning math.

It was difficult learning about teaching without having time to see different classrooms.  However, the videos that we watched were beneficial glimpses of good teaching practices and I tried to incorporate various methods of math teaching into the classroom I'm in.  I find that the most difficult part of math is accurately assessment students' abilities.  Some students are very good at showing their work and arithmetic, while others are superior at problem-solving and logical, creative thought.  One test certainly doesn't seem to fit all.  What are other ways of assessing student's math knowledge so that we can cater our teaching to suit their needs?

I have greatly valued the time I have been able to spend with small groups of students and individuals in the classroom.  A couple of times so far, I have had students write on a slip of paper what they would like to work on.  Then, I sorted the students into groups suiting their interests.  Being able to work with these small groups on particular mathematical concepts seems to be greatly benefiting them.  I got one comment from a student who said, "why can't we do math like this all the time?"  I also think that the one-on-one mini-conferences I've had with students has been beneficial for them.  In these cases, I had students write a question to me and in the mini-conference, we went over the answer to that question and any others they had.  When I see the results of the unit assessment next week, I hope to find evidence that the students benefited greatly from both of these learning approaches.

I believe that the integration of math with other subjects is critical for the growth of intellect and morale.  I've seen so many math classrooms (particularly at the middle and high school levels) where math is an isolated subject.  Thus, students either develop the belief that they are good or bad at math; there seems to be no middle ground.  If math was more integrated, we would be able to draw upon our students' skills and interests and connect new learning with background knowledge.  Not only would this significantly increase learning, it would also revive math to be a magical and mysterious subject, rather than a mundane and tedious one.