Last week I attended an open forum, conducted by the PTSO, to hear about Wayzata High School's integrated math program. My son is a freshman at Wayzata, who is taking the "regular" integrated track, based on the Core Plus Mathematics Project (CPMP) from Western Michigan University. Wayzata also offers an accelerated or honors track, with the self-esteem neutral moniker of "X" track. In addition, Wayzata offers several other upper-level math courses, including calculus concepts (for those who complete the regular track), Adavanced Placement calculus (for those who complete the X track), Advanced Placement statistics, discrete mathematics, and intro to linear algebra and differential equations. For those who are hungry for more, actual college math is available via the PSEO program, notably the University of Minnesota Talented Youth Mathematics Program (UMTYMP, whimsically known as "UM-tee-ump").
The bulk of the meeting was led by Thomas Kilkelly, head of the math department. Kilkelly seems like a humble guy, but he helpfully started the forum by recounting the highlights of his curriculum vitae. I say helpful because knowing that Kilkelly is apparently one of the top math educators in the country (certainly in the state of Minnesota) put the evening and Wayzata High School's math program in context.
Kilkelly is a mathematician with a teaching degree, rather than a teacher with a few math credits. He also has a couple of years experience at 3M as a chemical engineer, a job he left when he realized how much he wanted to teach math. Since then, he has led the school's Math League teams to championship levels, traveled to Russia to exchange teaching techniques, and grew his department from ten to the current twenty-seven teachers just to meet the student demand for more math classes.
There were roughly forty parents in attendance at the forum, some of whom were engineers and others accomplished in math either in college or in their current jobs. Some are clearly grooming their kids for not only college, but to follow previous Wayzata alums to some of the top science and engineering schools in the country. A show of hands revealed that a sizable majority had concerns about the third-year honors math, known as "3X" at Wayzata.
What is integrated math?
There was some confusion by parents over just what is integrated math. Two things distinguish the integrated math curriculum: topics (algebra, trigonometry, geometry, statistics, etc.) that are revisited repeatedly ("spiraled") over four years, with more advanced material covered at each visit, and applications of mathematics to solve real-world problems (what we used to call "word problems").
There are strengths and weaknesses to this approach. For example, full mastery in any of the topics is not attained until graduation, but students are exposed to all of them early on. Due to the heavy emphasis on application, students rarely wonder, "Why would I want to know this in the real world?" Traditional math students may be better at solving equations but have a harder time figuring out how to solve a real-life problem from physics or finance.
The issue that I have always had with integrated math relates to how social studies are "integrated" into the math curriculum. When a political agenda finds its way into the word problems, is it real-world education or indoctrination? This also can be an issue in other subject areas, to varying degrees.
Curriculum and instruction
Kilkelly cautioned parents to understand the distinction between curriculum and pedagogy (or instruction). Most of the parents seemed to accept, if skeptically, the K-12 integrated math curricula used in the district, but had a tougher time with teaching that seems to skew too far toward constructivism and away from instructivism.
A simple definition of constructivism is where the teacher assigns students a set of problems without presenting the classic algorithm and examples, and leaves them to figure out how to solve the problems. A simple definition of instructivism (also known as direct instruction) is where the teacher, well, teaches a concept with examples, then assigns a set or problems based on the instruction.
Many of the 3X parents in attendance complained that their students were not getting enough instruction; in fact, they are already anticipating that their students will be behind the curve, so to speak, next year in the 4X class.
There is a debate about the use of calculators in lower grades, but the use of graphing calculators at the high school level seems to have enabled a much higher level of math learning than was possible in the era of graph paper and slide rules (although graph paper, slide rules, and brains were enough to get us to the moon and back several times). Kilkelly asserted that the use of these devices dovetails into the integrated curricula by enabling students to focus on applications and problem solving skills, rather than spending that time counting squares on graph paper.
The proof is in the pudding
There was some discussion about the survey of Wayzata graduates enrolled in colleges and universities, which asked about their college-level math experiences. I summarized the results of this survey on this blog, in "Integrated math: unloved, but is it working?" The study revealed that while integrated math was not popular among Wayzata grads, most reported good grades in their freshman math classes. There was also some discussion about a large group of freshmen from Wayzata (and other high schools) at Winona State University who were routed to a remedial math course after taking an incoming placement exam.
Integrated math is still controversial, but most parents aren't going to start a blog when their kids hit kindergarten and be activists for math education until they're in high school (ahem); they just want what's best for their child. The bottom line for parents seems to be to do what my fellow parents are doing: pay attention to your child's coursework and homework, and be an active partner with the teachers in your child's performance. Learn as much as you can about your child's curriculum and how older siblings of your child's peers are faring in their freshman math courses.
Longer term, if you are concerned enough about our country's leadership in science, technology, finance, economics, and other math-related areas, please participate in your district's curriculum review cycle, and engage your school board and the state (which sets academic standards) about math curriculum.
Further parent-oriented information about math instruction:
NYC HOLD National (Honest Open Logical Decisions on Mathematics Education Reform)
Where's the Math?
If you have had any contact with secondary math education (especially in the Wayzata Public Schools), as a student, parent, teacher, administrator, or post-secondary math department faculty, I and my readers would appreciate your comments in the comments section.