The core standards, increasingly adopted around the country (though sometimes with modification), are not bad, although not nearly as gutsy as the Project 2061 Benchmarks and Standards for science. Besides the lists of skills and examples in the content standards, they include a separate list of “mathematical practices”:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
I like these. It’s a good list. And the core-standards document gives them prominence by listing them first—before the content—on pages 6–8, with a paragraph for each one. Of course, the document is almost 100 pages long, and most of it contains lists of expectations for each grade level and, at high school, for each major topic. So it would be lamentably easy, given the sheer weight of pages, to ignore these and teach to the longer lists.
The document’s authors do at least try, however. From page 8:
Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction.
Good! But how? They go on to say that there is a danger of becoming too procedure-bound, and that expectations that begin with “understand” are particularly ripe for making these connections. Unfortunately, this lexicographical rule doesn’t quite fly. For example, in stats:
Making Inferences and Justifying Conclusions
• Understand and evaluate random processes underlying statistical experiments
• Make inferences and justify conclusions from sample surveys, experiments and observational studies
Well, heck! I bet that I could connect a lot of those “practice” standards to justifying conclusions from experiments—more easily and durably than with the admittedly important random processes underlying statistical experiments. (And do they really mean “statistical experiments?”)
So: there is work to be done in figuring out where our aspirations for students’ mathematical practice belong, perhaps beginning with how to connect them to content. I’m sure confused.
And at the risk of being all soap-boxy, don’t you care more about the items in that list than you do about any particular set of math content skills? If you have those 8 items under your belt, aren’t you better equipped to face the world than if you can, say, integrate by partial fractions? I sure think so; and if I care that much about them, and kids work to get better grades, dammit, I should assess on these “mathematical practice” standards!
But how? Stay tuned. Somebody will figure it out.