Saturday, October 4, 2008


I spent this morning in a MathPower training at school, getting introduced to their approach to math intervention with struggling students. Finally, a workshop with people whose philosophy of teaching math is aligned with mine, and whose focus on inquiry-based math and helping students truly understand what they are doing has not been distracted by standardized testing and No Child Left Behind! Read the above link to get an idea of the mission, vision, and history of MathPower, which came out of Bob Moses' Algebra Project and has a focus on strong foundational math skills as well as constructivist teaching in order to best serve urban students. Interestingly, improved standardized-test scores are, as I understand it, one of the outcomes of the program, even though it does not "teach to the test."

Our training today was to introduce us to the math intervention curriculum MathPower is piloting in two Boston Public Schools. The curriculum, First Steps, was developed in Australia (a lot of great math teaching has come out of Australia), and the idea is that students struggling with math often have not mastered concepts as basic as place value, counting, or operations. Their foundation is shaky, so when they are sherpherded along into fractions, decimals, percents, integers, pre-algebra, etc., their math falls apart because the basics are lacking.

First Steps, like other Australian math assessment and instruction tools I have seen, is based on developmental stages in math that, while they may correlate in general to certain ages, are not specifically linked to grade-levels. You may have first graders who are in an advanced developmental stage, while some seventh graders have yet to master more basic concepts. The key is in assessing where students are -- which "key understandings" they have yet to develop -- and then working on those concepts with activities that promote real understanding, not just rote mastery of a procedure.

I took away two big ideas from today.

Number 1:

The First Steps curriculum is designed the way I would design curricula, the way I always talk about curricula, and the way I actually use curricula I am given: like a menu. Instead of a prescribed progression (Day 1, everyone must do this; Day 2, everyone must move on to this, whether the students understood it on Day 1 or not), there are multiple entry points. Different students start at different places and move at different paces, and instructional decisions are made by the teacher. I know, revolutionary. Teachers assess their students, group them flexibly (ie. students are not tracked into "high" or "low" math groups but move from group to group depending on the skills being taught), and teach them what they need to learn. For each Key Understanding, there is a menu of activities to choose from, grouped by age level so that middle school students working on more basic concepts are not being asked to do activities that seem childish.

This is how I have been teaching math for several years: grouping students flexibly, tailoring instruction to meet their needs, and choosing math activities that will teach the concepts they need instead of following the curriculum as it is written. It felt so good to be around other people who advocate teaching in this manner, who think that the idea that a prescribed curriculum can ever meet the needs of all students is insane, and who trust that teachers, once well-trained, can make instructional decisions on their own.

Number 2:

Those of us who teach early-childhood math are in such a good position to think about the teaching of math at all levels. We know how hard it is to break down concepts that to us are like breathing, so that children can start to master them. (For example, the fact that when you count a group of objects, the last number you say tells you how many are in that group, is a developmental step -- not all kids can do it. But it is so obvious to adults, many of us have no idea that it's not obvious to small children, and even less so how to teach it.) This puts us in a position of knowing how to approach more and more sophisticated mathematical tasks with students of any age. We know how to break them down into the smallest steps; we know how to start with the most concrete kinds of problems and move toward the more abstract; we recognize many common misunderstandings students fall into; and we know how to teach in a hands-on way because that's the only way to teach small children. (It's the best way to teach older children as well, but many teachers don't realize that.)

It was fun to get a glimpse of how my years of thinking about and teaching math to first graders have prepared me to think about and teach math to older students as well. Much of what I have had to think about over the years is applicable to students of any age, both in terms of pedagogy and content. Older students often still struggle with the concepts I teach to first and second graders; advanced first and second graders are ready to think about concepts older students are learning. The best ways to teach these ideas (through inquiry and concrete experiences) are the same no matter who you are teaching.

Now wasn't I just blogging about a new career? Math coaching is high on my list.

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