I was cleaning out a corner of the attic and came across a box that hadn't been opened in years. Out came papers and notes that instantly brought students back to life. I remembered Roberta, who kept mumbling "I'm dumb at math" as we tried to relearn subtraction with borrowing. I bumped into Roberta several years later- teaching math at a community college! There was Marie, who took one look at fractions and moaned, "Oh no, not those again." She desperately wanted to stop emptying bed pans and become a nurse. I also recalled Miguel, who was doing a little carpentry on the side, but wanted to be a computer programmer. Finally, there was Brian, who dropped out of high school and needed a quick brush up before taking the GED and moving on to the stage. A few years later I would attend his wake after an overdose.

There were more, many more. Each of their lives is woven throughout the journal I kept for my second and third years as a full- time math teacher. I'd already taught math as a part-time teacher during the prior three years. Did I say "part time?" Actually, it was three part-time jobs. I'd made the mistake of taking on a total of 36 hours of teaching at three different programs in the Boston area and with all the preparation I had to do, there was nothing that felt part-time about it. Now I had a full-time job in Cambridge, twelve hours of classes in the morning and twelve in the evening. This was really great! I could bicycle my daughter to school in the morning and pick her up after school. Eat an early dinner with my family and back to class. Friday's were staff meeting days and I was learning what it was like to be part of a learning community. And Friday nights were mine!

Reflection Journal
The idea for a journal came to mind as I reflected on my first year as a full-time math teacher. While working part-time (that is, juggling three part-time teaching jobs), I had been troubled by the lack of real progress by some of my students. As a full-time teacher with paid time devoted to preparation, planning, curriculum, and materials development, I had a better opportunity to reflect on why I was having such limited success in reaching these students. I knew it was because they didn't really understand what was going on with the math. I knew that no one really learns math by memorizing a bunch of rules. In my classes we spent more time developing concepts than on mechanics, and this was working well for most. But it was not working for all, and that just wasn't good enough.

As I started my second year, I decided to document every aspect of one six-hour-a-week math class: planning, implementation, and student interactions. Lesson plans included detailed notes from conceptual underpinnings to the most minute subskills. I summarized how every class progressed. I documented how students, together and individually, engaged in the work- conceptually, operationally, and emotionally.

Looking back, I realized how most of my lesson plans (all typed!) were too ambitious; many objectives and activities rolled over to the next class. I also recalled what it felt like each time I "got it"- each time I understood where and why a student was getting stuck. It usually had to do with my overlooking some piece of the path that led to understanding and mastery. Many students could make the leap over a missing piece, but for others, what seemed like a very small omission turned out to be a chasm. These students weren't going to leap forward without filling in some more of the puzzle.

Owning the Math
Back to the students. Roberta didn't have a good grasp of quantity. Once we figured this out, it helped explain why none of the "operations" meant to manipulate quantities made sense. She needed time to count out the totals, to learn for herself how multiplication worked as a fast way to add and that division could be thought of as either "grouping" or "partitioning" - and how each means something quite different. It also meant that once we tackled the hard work of mastering quantity, she was free to take off and fly. She did and along the way she found great joy in mathematics.

Miguel did fine with fractions-after all, he was measuring wood with a high degree of precision almost every day. But he blocked on algebra. He explained that failing algebra had helped his decision to drop out of high school. So, we started into algebra shortly after he got settled into the class. I brought in a balance beam scale and presented him with a series of projects where he had to balance known and unknown quantities (items in a "black box") on the scale. One day he got so excited it was impossible to contain him -- and who would even try? The idea of what it meant to do "inverse operations" to both sides of the equal sign had burst into his consciousness. And none too soon. He had been troubled with "how is this going to help me pass the GED?" Once he understood basic concepts, he was poised to tear through algebra much faster and with a level of understanding that would stay with him for life.

Marie tried to remember rules about manipulating fractions, but she really didn't know what they represented. In addition to using the many manipulatives we had created, I also tried using capacity measurement to explain fractions-and more! She had measuring spoons, cups, beakers, and test tubes to use, and a load of projects to undertake. Once this aspiring nurse understood the relationship of capacity measurement to medication doses, her frustration was replaced with a burning desire to learn. She wanted to be sure she had mastered every possible aspect of fractions- after all, patients' lives would be at stake.

Practitioner Research
I spent seven years at this program, and the two years I documented teaching and learning made these some of the most rewarding years of my life. Documentation and reflection pushed me to study more of my subject and craft. I needed to fill in my own "gaps" in understanding before I could be more useful to students. I spent hundreds of hours at the library researching math analysis and learning disabilities. This pushed me to enroll in a masters program where my two years of documentation and some additional research led to a new math diagnostic instrument for the Learning Center.

We didn't have a name for this approach to the teaching and learning process back then, but those who pursue their craft through "practitioner research" projects today have my full support and admiration. What a glorious way to live a life and make a living!

Bob Bickerton has been the director of Adult and Community Learning Service at the Massachusetts Department of Education for the past 13 years. He started in ABE 30 years ago and has worked as a teacher, teacher trainer, and program director. He can be reached at 617-338-3850 or by e-mail at: rbickerton@doemass.org