I would have to characterize my initial reaction to the Build A Book class as "You've got to be kidding!" Although I was intrigued by the idea of allowing students to create their own mathematics I kept gravitating back to reality and saying this could never work in my world. Major issues to me included curriculum, county policy, and accountability to students, parents, and even myself.

From the beginning I was concerned that a balanced curriculum might not just happen. Would we expect students to just stumble onto every major idea we need to cover in geometry? How would one justify to principal and parents simply throwing out the county curriculum which is mandated? The contract I sign every year includes the statement "the employee will observe such curriculum and standards and obey such reasonable rules and regulations as may from time to time be put in force." Many people spend untold hours selecting curriculum and texts that are approved by our Board of Education, my employer. Further I was concerned about students receiving the background needed for subsequent course work. If every teacher decides to go off on a tangent and determine by themselves what is important to teach where is the scope and sequence needed to perpetuate a knowledge base vital for insight and mathematical dialogue. Who will decide what is most important for your son or daughter, and will you be willing to trust their judgment without benefit of knowing the criterion on which they base these judgments? Do you want your child's future mathematics entrusted to someone who has no strong basis for predicting the future needs of his/her mathematics? How would you expect them to demonstrate accountability for their decisions? Now I will submit that this is a difficult call for any of us to make, but this is an argument for continuing teacher education. I know without exposure to courses like this one in which we share our thoughts and ideas I would be unable to see my own shortcomings. It is my opinion that curriculum decisions should not be made solo.

Throughout the book I kept thinking this person who is suppose to be so inspiring and caring has so many holes in his story that I found it to be unbelievable at times. Now I realize this is based on an actual class, however I do not understand why Chip just did not include the students' view points in their own words. I was glad to see their comments included in the appendix, but it really bothers me that he wrote from their perspective and then asked for their approval. I'm not sure that they would have the courage to say " That wasn't how I saw it". Particularly after all the publicity they were receiving. Was he afraid of what they might write? I know I have been highly critical of him , furthermore I found his lack of effort, his disorganization and his laziness repugnant. I found it hard to accept that a person who greatly cares about his students would not even take time to learn their names. I perceived his Build a Book class as more a function of his laziness than his ingenuity. He intimated that he did not always know what was going on in the groups because he wasn't involved in their discussions. He also divulged that not only did the kids not regard him as an authority, but he himself questioned his own math abilities and his math background . I think there are times in the classroom when someone needs to be the authority. Surely if there are concepts in which you as the teacher have difficulty then further exploration on your part is needed. I would expect the teacher to take the initiative to discover gaps in his/her own knowledge. It further dismayed me to learn that two of the six classes his taught in this manner failed. That is hardly a resounding endorsement.

Having said all that, however I did find that the book raised some questions that are very provocative. First I would like to acknowledge the growth that apparently occurs when students present their findings to other students. If there was a resounding theme throughout this book it was that the students had grown in confidence and self respect. This is no small accomplishment. They learned to be more tolerant of one another and they learned to present, debate and defend their findings. They were very committed to the mathematics that they had created, and they respected the views of others. I always like to help students boost their confidence level, and I think Chip did a nice job in developing this area. I often have my students do exploratory sets in the classroom or in the lab, but at the end the conjectures have been so directed that it hardly encourages divergent thought. It has been very predictable in most cases. I definitely ascribe to the philosophy that students will learn best if they are self directed and motivated, and if they find the material relevant. I will say in lecture courses which I have taken I go home, go over the notes, and reiterate to myself the concepts. In other words I have to prove these truths to myself, and I know my students have to do this as well. I have struggled for ways to help them in this endeavor.

As a result of reading this book I plan to chose labs that are more open ended and experiments with some not so obvious results. I will definitely plan to have students write more, possibly in the form of a weekly journal. I know I will have them write a reflections paper at the end of each six weeks. It will be difficult for me to give up control. I'm simply being honest. When I am responsible for anything I like to have as much control as possible in determining the outcome. I do feel that the buck stops here; so if I am answering for the job being done I want to feel that I have done as much as possible to insure success. Of course in education that is idealistic at best. There is no insurance of student success; there is however the potential. I think I am redefining how I can help them reach that potential by developing their self confidence. I hope to use some team building approaches that I have learned in leadership classes to help build the type of mathematical community the NCTM standards talk about. l like not having to be the fount of all knowledge; that's a pretty big role to fill. I also admit that I have often scripted my lessons; though I was doing this for clarity and brevity I thought. Upon reflection I realize how stifling this could be to creative thought. I also see how students have relied on me instead of themselves. It does not build confidence to simply replicate a procedure. I dare say we could teach a procedure to a chimpanzee. They do not however posses the ability to reason and make choices based on the reasoning done. I think the integration of technology is helping me to see how more emphasis should be placed on the reasoning and decision making. Certainly the use of the calculator or computer has changed my questioning techniques to emphasize higher order thinking. It is always exciting to me when students see connections that I have not emphasized, and I am always open to learning better ways to communicate with my students. I think I have to work on better ways for them to communicate with me and with each other.

In addition, I think Chip created an environment of trust which allowed exploration without pressure or fear of ridicule. I always pride myself on the rapport that I have with my students, but I know that I can improve in this regard. I would like for them to see me as nurturing and caring not only for their academic life, but for their personal life as well. I will admit that I have been very methodical in my coverage of material. I wanted my students to be well prepared. It is not unusual for me to hear from previous students now in college who share that I helped prepare them well and that they often are tutoring their roommates. This of course feeds my ego, but if in the end I have only taught them procedures and not opened that door to creative thought and self direction then in the long run I have shortchanged them. We will only know this when they reach the work place or a college course which requires this type of thinking. I feel a deep responsibility to prepare my students for their future life.

I know my largest paradigm shift this quarter has been that I need to lead but not show them the way. For all my travailing and spouting out county guidelines and rules my allegiance lies with my students' futures. I think all teachers want to have an exciting and motivating classroom. We simply draw on our own experience to define what is a " good" teacher . The teachers that I related to as "good teachers" where those that explained things clearly, made their expectations known and especially those who cared about me as a person. This is the model from which I have derived my own philosophy. But then this is not 1969, and our students will compete in a completely different environment than I did.

Thank you for a class which shook me up a little. I do not want to become too settled or stagnant. I know there is always more to learn, and always learning is how I want my students to think of me and themselves. It is the model of a life long learner that inspires us.

Side note: My favorite teacher was my high school geometry teacher. I still keep in touch with her today. She always saw something special within me, moreover it was her belief in me that lead me to begin college at the age of 28. Teachers make all the difference! Thank you for reminding me.

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