So, What Counts as Mathematics?

Does taking math matter if students can’t use it?

During my time working at Apple, my tasks (in simplified form) were to:

  1. Analyze information
  2. Model this information as mathematics
  3. Write code to mimic the mathematical models

As it happens, steps 1 and 2 of this process are paramount to a student’s ability to use mathematics after they leave the classroom (whether or not they work in technology). The Common Core Standards for Mathematical Practice reinforce the importance of analyzing information and modeling it with mathematics; in particular, standard four—Model with Mathematics—calls it out specifically.

Students who collaborate to analyze, model, and explain a math problem can better understand the material.

Yet, I contend that in too many of today’s math classrooms, analyzing information and modeling with mathematics are considered afterthoughts as students and teachers focus on abstract representations and the algorithms used to manipulate these representations.  I don’t blame teachers for focusing on this piece of the mathematics whole; after all, it’s the piece that dominates high-stakes testing. But should this count as the most significant portion of mathematics? Hell no!

If we’re going to make certain that our students leave school with mathematics that assists them in their future, then we need to change what counts as mathematics. In the past, state standards that have spoken to the “habits of mind” we expect students to learn while in our classes were given short shrift. Why? Because they’re very difficult and expensive to measure. Therefore, the exams that mattered to students, parents, and teachers focused exclusively on the content standards where multiple-choice questions were adequate. Unfortunately, this has further entrenched curricula and instructional practices that limit students’ abilities to use math in their futures.

Can the next generation of assessments help? I believe they will. Both of the federally funded consortia that are developing future assessments have committed to authentic assessment using performance tasks. For instance, one of the funded consortia, the Partnership for Assessment of Readiness for College and Careers (PARCC) application, stated: “PARCC assessments will include sophisticated items and performance tasks to measure critical thinking, strategic problem solving, research and writing.” Additionally, PARCC committed to: “Performance task(s) that require conceptual understanding, procedural fluency, and application of mathematical tools and reasoning.”

I have a healthy dose of skepticism as to whether this can be accomplished in a manner that is rigorous enough to change math instruction. But it’s our best hope, as far as I can tell, in changing what counts as mathematics and helping students in their lives after they leave our classrooms. PARCC begins pilot testing 2011/2012 and will be implemented for the 2014/2015 school year. Let’s keep our fingers crossed.

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