Chapter 8 - Knowledge, Beliefs, and Mathematical Identities

As Sharon so effectively talked about in her blog, I too am becoming increasingly frustrated with the procedures I find myself and my students stuck in. As I read through Boaler and continue my substituting the feelings of ineffectiveness in how we're teaching and how students are learning are growing. I long now to have a full time position where I can begin to impliment some of these ideas we're discovered through Phoenix Park's approach. And like Sharon, I'm being to realize that I can't wait. Each day that goes by without bringing about change runs the risk of perhaps losing another student, turning them further away from mathematics learning, entrenching them with fictious ideas about the relevance of math in their own lives. We need to start today.

Terri-Lynn raised a very important question during her presentation: How often do you see students handing in answers in which they have no concept of whether or not they are even logical, let alone the correct response? We see it all too often in our classes where students do not (for many reasons) thinking about, analyze, and interpret the answers they have arrived at. I think our methods of extreme pencil and paper tasks without enough investigative work and explorations have often led students to a point in their learning where they haven't been taught the fundamentals of checking the reasonableness of an answer. We overhwlm them with so much classwork assigned from textbooks and extra assignment practice outside of class that it would be too time consuming to go back and check all their answers. Another thought of mine just came up here and it is this: I think we are perhaps assigning too much work for our students to complete. I think that often times our teaching strategies are too time consuming, especially when it comes to having students write off notes from the board, and as a result the majority of the practice, the time when students need to talk math between each other, is often lost in the classroom. That means the majority of the work is then left to be done in isolation usually away from class. The math is then perceived as labouors, monotonous, and routine, instead of something that should be interacitve, interesting, and fun inside class. We really can do more with less.

As we read through this book we realzie the importance of incorporating project work into our math classes. Geeno and MMAP (1998) reported that in this type of work students "develop abilities of collaborative inquiry and of using the concepts and methods of a discipline to solve problems." Given this highly significant piece of research it is quite evident that the inquiry and cleverness we expect from our students is not going ot happen by osmosis, or by us standing in front of them asking them to dictate onto their exercises what we say. We have trained our math student not to be disciplined, but rather dependent on us. While substituting for a math teacher a few weeks ago one of hte classes I had to supervise a junior high test. He had written in the notes that it was ok to provide help to the students during the test, give them hints, etc. A year ago I probably wouldn't have blinked at such a request. That day I couldn't stop blinking. We weren't five minutes into the test and hands were going up all around me. The test was constructed well and had a good range of quesitoning for the class so I didn't perceive there would be much trouble. However, the students sat there like drowning rats desperate for a push, a start in a question. Everything from what the word "prime" means to "how do I draw a numberline to show + 3 multipled by -2 was asked. It was so disappointing to see so many students suffereing through this. I wondered to myself what are we really doing to our students? Why are they failing in their learning so badly? How did they get to the point where independence was non-existent in their math? Is it too late to change the tide? I hope not.