I was surprised a little about the answers to the questions. I was surprised that so many instructors said that student resistance was a major factor. I had talked in the workshops about my own experience with student resistance, but it seems I opened a floodgate for teachers to say how much it affected them. I was surprised that so many instructors said they wanted to work with manipulatives or graphic representations, but were unwilling to do so because they were uncomfortable working with them themselves. One group developed a recipe which was in essence a plan for a workshop to help them get more comfortable with using manipulatives, and I received two requests after the workshop to come and do some professional development with instructors on the subject. I was surprised that participants wanted to connect math with real life, since I had presented some research findings that showed how difficult it was to do so (for example, an article by Alison Tomlin (2002); I thought it showed the hunger participants felt to make math meaningful to students, and I was delighted, if surprised, to fin it showing up.
Based on the findings from the workshops, I decided that in this manual I would write about implementing those four "best practices" that participants had said they were most interested in: hands-on learning, using real-life problems to teach math, using group work as a teaching technique, and helping learners take control of and responsibility for their own learning. Further, I knew that I wanted to write about overcoming the barriers instructors named to implementing these best practices, rather than simply saying, "Do this, do that." I wanted to lay out the complexities that lay behind those deceptively simple statements of how to improve math instruction. Much of the art of teaching is hidden, not only to people who have nothing to do with education, but also to teachers themselves, to administrators and to students. So much of what we do well is not articulated, and so much of what is difficult to do is also not articulated, so that it seems that we do not do it well because of ignorance, or inattention, rather than the complexity of the factors that influence our work. By laying out the complexities, I hope to make clear the problems that face us in implementing these best practices. Only once the problems are clear can we go about finding solutions.
I knew from the beginning that I wanted to make this manual as practical as possible, and, given the number of people who referred to a lack of time as a barrierto implementing the strategies, the need for activities that could be used in the classroom with little or no further preparation was underscored. I have gathered the material to use with students presented here from many sources—from my own experience, from material developed by other practitioners that I have used myself, and, finally, I have developed ideas suggested at the workshops and from print sources.