The Task Determines the Tool
Tools are most effective when used for their intended purposes. Or, put differently, the task determines the tool. So, for example, if we hope to loosen a rusty nut, a wrench of appropriate diameter and sufficient heft is the optimal tool to apply to that particular task. One might, in a pinch, try to loosen the nut by careful strikes with a hammer if that is the only tool that one has at hand but the results will probably be less than satisfying and the process awkward at best.
Diana Roscoe, formerly an associate for mathematics with the Delaware Department of Education and now a Math Curriculum Specialist with the University’s Southern Professional Development Center, often talks about “curriculum tools” when discussing published mathematics programs. While I found this a bit awkward at first, I am coming to think that curriculum-as-tool is a particularly apt metaphor especially as we think about how curriculum helps or hinders as we gear up to address the ambitious new Common Core State Standards for mathematics.
The parallels with everyday tools may or may not be so obvious when we turn our attention to “curriculum tools.” So, for example, the task in this case may be broadly defined as employing a curriculum tool to support students in meeting the Common Core State Standards. This task is comprised of at least two distinct components. Most obvious, perhaps, is the need to employ a math curriculum that addresses the mathematical content ascribed to a particular grade level, or, in the case of high school, to the full 9-11 grade band.
More challenging, perhaps, is finding a curricular tool that supports students as they learn to practice the Mathematical Practices described by the authors of the Common Core. These include the opportunity to have students “make sense of problems and persevere in solving them.” This is no small task and requires a curriculum tool that routinely requires that students attempt to solve novel problems. Another of the eight Standards for Mathematical Practice asserts that students should learn to “construct viable arguments and critique the reasoning of others,” again, no mean challenge and one that implies that students be provided the opportunity to reason mathematically day-in and day-out.
So, returning to our metaphor: Finding a curriculum tool that satisfies the Standards for Mathematical Practice might be analogous to recognizing that one needs a wrench rather than a hammer to accomplish a certain task; finding a tool that also addresses the indicated content – a tool that is both “focused” and “coherent” to use the language of the Common Core – may require that we select the correct diameter wrench from within our curriculum tool kit. If we are successful in selecting an appropriate curriculum tool, then we will help turn students toward the Common Core State Standards including the Mathematical Practices. If we fail to do so, then we may find them having a wrenching experience and moving in the wrong direction!