Who has time to understand it? Just show me how to do it!
This was the theme of a recent presentation by Phil Daro, one of three lead writers of the Common Core for State Standards (CCSS). He shares the following comparison between US and Japanese teachers, “U.S. teachers look at a problem and ask how can I teach my kids to get the answer to this problem? The Japanese teacher asks, what's the mathematics that they're supposed to learn by working this problem? How can I get them to learn that mathematics?”
This international comparison stems in part from the results of the Third International Mathematics and Science Study (TIMSS, 1995) involving a half-million students in 41 countries. With the release of the TIMMS results years ago, we learned that the US ranked 12th in grade 4, 28th in grade 8, and 19th in grade 12, with Singapore, Korea and Japan sharing the top three spots. With CCSS and our 2011 MA State Frameworks we have an opportunity to take a hard look at this information.
At the heart of Daro’s analysis is an understanding of what it means to teach mathematics. Even with new standards being implemented, we can only change the results of such studies if we truly understand what our goal is as educators. As Daro states, the goal is far larger than “answer getting.
”When we focus on answer getting, our instruction becomes narrow. Instruction focuses on teaching strategies and tricks that all lead to the ability to solve problems correctly. In doing so, our students believe that what we value in mathematics education is not necessarily an understanding of mathematics, but knowing how to get correct answers, and recalling the correct procedure for the correct set of problems. A correct answer is important, however, not at the expense of understanding.
In considering a classroom based on understanding mathematics, problems become opportunities to learn mathematics. This is a subtle yet powerful shift. This shift of language and approach – thinking this problem is an opportunity to learn mathematics – opens up all kinds of avenues to explore. At first pass, this leads to the process of lesson planning. What is the best problem to use today, with this class or with this student? Teachers choose tasks not just because they are on the next page, but because they have the power to reveal something important about mathematics and to deepen students’ understanding. With this mind frame, we can move from simply covering the material, to teaching Mathematics.
The next level of exploration is in regards to the students. What questions do I anticipate my students asking? What questions can I ask to guide my student in understanding the Mathematics? How many solutions paths are there and how do they compare? What can my students learn from each other in solving this problem? Classroom dialogue becomes critical in developing a community of learners working towards understanding.
Next steps in instruction are then determined based on how the students respond to the problem – did they arrive where I thought they would in their understanding? Did they uncover an important mathematical generalization that will apply to future related mathematics? In what context will we use this mathematics again? What problem should I choose next to connect and deepen mathematical understanding? And so, the cycle of learning mathematics goes round and round: choosing problems, constructing understanding of important mathematical ideas, connecting and applying this idea to other more complex situations.
As many of us are working diligently to align our curriculum guides and to choose materials that support new state and national goals, it is equally important to remember the opportunity bring about true change. When we present children with an education focused on mathematical understanding, we foster creative problem solvers who are prepared to compete in the rapidly advancing world of the future.
Best,
Sue Looney, Ed. D.
President – LMC