After doing my taxes this past weekend, I realized that I did so without doing any math. I just put numbers into various boxes and trusted the software to do the rest. Perhaps the only math involved was having a sense whether those numbers I was entering seemed reasonable. This made me start to wonder about the math most adults do in their daily lives. How many people use the quadratic formula in their daily lives? Yet, when they learned it, did they learn it in a valuable enough way, that with that new knowledge, they can think in a particular way? How many know that when there are six people dining and you split the bill evenly, leaving a 20% tip, all you have to do is just divide the bill by five and have the sixth person cover the tip? If your student is working on 3-digit by 3-digit subtraction and on a post-test makes many errors, can you tell what directly caused those errors?
I ask that last question because as a school we’ve been examining several math curricula. One of them has an incredible technology component that includes computer based assessments. It’s amazing how quickly you get data back and the teacher doesn’t even have to grade the paper. Easy, right? Upon further reflection though, a child who might still get about half the questions directly involving 3-digit by 3-digit subtraction wrong, the data would simply just indicate that. Without examining the scratch piece of paper, interviewing your student, or observing the child in action, you wouldn’t be able to isolate whether or not the error was a simple fact error, errors with regrouping, inversion, or even adding instead of subtracting. If you were able to isolate what that error was, though, imagine how quickly you could help that child develop.
This month’s issue of the journal, Teaching Children Mathematics, contains a few great articles. One is called, “Action Research Improves Math Instruction,” which features elementary school teachers who, as part of a course they’re taking, embark on a “practitioner-based” research process in their classrooms. One of them, a 3rd grade teacher, looked carefully at 3-digit subtraction, read about the kinds of common errors children make on questions like these and decided to make her students ‘subtraction detectives.’ They had equations that were already solved, some with errors, and they had to practice finding and describing the error. The improvement in her students’ assessments improved greatly. The teacher didn’t know whether this was a ‘best-practice’ but it made solid sense to her and she gave it a try. The article mentions that “Action research addresses specific student needs, targets classroom issues, keeps teachers current, and discourages ineffectual methods.”
This year, our school has been examining several different math curricula with one of its objectives being a common scope and sequence. Today, we had a faculty meeting discussing the pros and cons of the different curricula, and I found the discussion rich and robust. We also asked ourselves some very important questions. We didn’t come up with any immediate answers, but I was really impressed when colleagues disagreed with each other, how the discourse remained passionate, but civil, and everyone made extremely insightful and thoughtful comments. Everyone seemed to be aware of their own biases as they spoke. I wondered, leaving that meeting though, and re-reading this article, if we needed not only to think of a common set of expectations, but if we could also find ways to examine student progress even more carefully and identify where gaps lie, or how their learning can be enriched.
Another article in the same issue called, “Professional Development Delivered Right to Your Door.” It listed the following as Best Practices of Professional Development: Professional Development must be -
- grounded in participant-driven inquiry, reflection, and experimentation;
- collaborative, involving a sharing of knowledge among educators and a focus on teachers’ communities of practice rather than on individual teachers;
- connected to and derived from teachers’ work with their students;
- sustained, ongoing, intensive, and supported by modeling, coaching, and the collective solving of specific problems of practice;
- related to other aspects of school change; and
- engaging, involving teachers in concrete tasks of teaching, assessment, observation, and reflections that illuminate the processes of learning and development (Darling-Hammond and McLaughlin 1995).
Regardless what direction we go in math, I feel like we met all those goals. I think the process was, and will continue to be an ongoing one. I feel very fortunate to work at a school with such caring and passionate teachers.