Putting It Together

What do we know from the research I've reviewed?

We know that we need to do better in math education in the United States, particularly in middle and high school. We know that at the classroom level, frequent assessment is useful, particularly when teachers are given help on what they should do for children who aren't performing well. We know that children can help each other learn math if peer tutoring is appropriately structured. We know that tracking children by ability level is likely to widen achievement gaps rather than diminish them. We know that how children think about math problems is important, not just whether they get the right answer. We know that direct instruction can help students learn computational skills and understand math principles. As a corollary, we know that children don't have to discover math principles on their own or work with authentic open-ended problems in order to understanding mathematical concepts. At the same time, there are situations in which discovery activities can be useful. We know that we don't have to make math fun for children to learn it, though a little sugar to help the medicine go down is a good thing. Most importantly, we know that classrooms are not islands and that broad achievement gains require coordinated systems from the state level down to the district- and school-level that align standards, assessment, accountability, instructional leadership, effective management, teacher professional development, and curricula.

These are not trivial or unimportant research findings. There is a lot that we don't know, but what we know already, if put into practice, could be the basis for substantial progress towards the goal of mathematical proficiency for all children.