More Math of Least Resistance
I'm not a math teacher, but I played one in a middle school, not long ago. I found myself unexpectedly teaching 7th grade math in 2005, necessitated by increased enrollment and contractual obligations to keep class sizes uniform. The parents of my math students were surprised too, when the teacher who'd been directing school bands in their community for decades suddenly became their child's math instructor.
I also taught 7th grade math in the 1980s--before "highly qualified teacher," when the presumption was that anyone could teach anything to kids in junior high. Thus, I can speak with some authority about the differences across a 20-year span of math curricula. In fact--I would argue that, as a non-math major, not wed to particular curricular/instructional models, I could analyze strengths and weaknesses in the two math education programs as unbiased full participant.
(This is, of course, precisely the argument that free-market eduwonks use when promoting the idea that Teach for America corps alumnae will eventually become policy experts: I wasn't part of any establishment math education "blob"--so my two years of first-hand experience let me examine math instruction up close without having a political or pedagogical axe to grind.)
Figuring out how to be a good math teacher was an intriguing scholarly quest. Our curriculum, the Connected Mathematics Project (CMP), was relatively new in my school and a revelation for me, considering I took my last formal university math class in the early 70s. Although I can immodestly say that I got sterling grades in math, from kindergarten through college, I hated it. I learned more about the mathematical ideas that lay under memorized procedures and algorithms in one year of teaching 7th grade math using CMP than in all my formal math coursework, combined.
CMP was also a fundamental departure from our 1980s Scott Foresman curriculum, which followed the familiar "worked examples" pattern: Teacher demonstrates how to solve the problem, with multiple examples. Kids solve lots of similar problems, using the same algorithm. Lather, rinse, repeat--the math of least resistance.
It was fun, 20 years later, to watch my students' intellectual light bulbs flip on using the real-life math applications in the CMP units--Oh! That's why you multiply ratios! That's why negative times negative is positive! At the end of the year my 7th graders understood core algebraic ideas--linear functions, for example--better than I did when taking actual 9th grade algebra. The goofy 12-year old boys in my class thrived on the minds-on applications of math--tennis ball drops, stretching and shrinking paper triangles, and flipping chips from positive to negative.
One of the girls in my class was a transfer from the local Catholic elementary school. On the first day of class, she brought a note from her 6th grade teacher: "Meet Alyssa, the best math student at St. ____'s. Over her entire 6th grade year, Alyssa's average in math never dropped below 99%!"
Alyssa was a very personable and confident young lady, but she struggled mightily with the concept of testing mathematical hypotheses and processes. Nearly every lesson--and, contrary to what many people think, there is very specific instruction embedded in CMP lessons--ended with Alyssa wailing "Please just show me how to do this!" Fairly often, I did. There's no proscription against demonstrating conventional algorithms--another fallacy--and many lessons include drill and repetition, to increase fluency with established methods of calculation.
Still--for students like Alyssa, the idea that she might have to devise her own means of solving a math-based conundrum, including checking her answer, was deeply unsettling. I thought about Alyssa when I heard Marilyn Schlack's tale of the high-achieving math students who couldn't apply their skills to real-life challenges with building wind turbines.
After handing me the note from her 6th grade teacher, Alyssa confided that she wanted to be a math teacher some day. By the end of the year, she was probably planning a new career--but I'm still not sure that a lifetime of getting As in math is the best platform for launching a career as a math teacher.
Research does not show conclusively which professional credentials demonstrate whether math teachers are effective in the classroom. It does not show what college math content and coursework are most essential for teachers. Nor does it show what kinds of preservice, professional-development, or alternative education programs best prepare them to teach.
Not so reassuring. Key point: taking more advanced math courses does not improve the effectiveness of educators, especially those who work with lower-grades students. Acing AP calculus does not help a prospective teacher explain re-grouping in two-digit subtraction to her second graders, in ways that are useful and stick to their brains.
It makes me wonder about the disconnect between math proficiency--being good at math--and pedagogical content knowledge: the ability to help kids conceptualize mathematical ideas and apply them to real problems. These are the real issues in ratcheting up math proficiency in America. Not Algebra for All, or fussing over the reliability and validity of NAEP scores.
Back, once again, to basics: curriculum and instruction.