Volume 8, Number 52 - March 19, 2009
brought to you online by Pinedale Online
In December, Sublette County School District No. 1 (SCSD#1) board chairman Jim Malkowski and board member Mark Pape met with recent Pinedale High School (PHS) graduates.
The graduates were a cross-section of the school’s top academic echelon.
One concern voiced by the alumni was their difficulty with college math. A few of them were relegated to remedial math classes upon their admission. Those classes were not cheap and they did not count as college credit.
For students who were accustomed to scholastic excellence, remediation was distressing.
“Our information to them was, ‘You guys kind of got caught in the crossfire,’” Malkowski said.
That crossfire is part of a nationwide battle over math curricula.
For the better part of the 1980s, education researchers from the University of California, Berkeley, and Michigan State worked to develop a math curriculum based on exploratory learning, inspiration and deduction instead of rote learning or “drill and kill.”
This new curriculum stresses problem-centered group learning that is less about dry memorization than it is about conceptual applications of mathematics.
For example: In the “traditional” curriculum, quadratic equations are taught as part of the scientific study of mathematics. While learning how to solve quadratic equations, a student may have no idea what it would be used for in a real-world application.
With the “constructionist” curriculum, a student would learn quadratic equations when they are needed to solve a real-world based problem. These new programs were called the Connected Math Program (CMP) for middle school and the Interactive Mathematics Program (IMP) for high school.
By the mid 1990s, the wave of CMP and IMP had replaced traditional mathematic curriculums across the country.
A decade later, many of those same districts have reverted back to traditional math while others remain embroiled in the debate over the fundamentals of mathematic curricula.
There are several elementary school varieties of progressive math, but they all supplant “drill and kill” with problem-centered group learning. The idea is to germinate a fond connection between student and subject instead of a hammering it into a resentful tedium.
Unfortunately some of the programs so distanced themselves from rote learning, parents began to notice their fourth-graders were unfamiliar with basic multiplication tables. Others reported fifth-graders who could not make change or do long division.
The outrage over their students’ lackluster math skills coalesced into parental groups that opposed the constructionist curriculum.
The very look of the new math was foreign. Students used completely different systems to multiply multi-digit numbers. Their long division techniques were different as well.
Further up the ladder, middle school students weren’t taking pre-algebra or algebra. High school math classes became a hierarchy of IMP instead of algebra, geometry, algebra II and trigonometry.
Traditionalist parent groups began publishing academic horror stories such as a tenth-grade, straight-A IMP math student who tested at second-grade levels in some math functions and at seventh-grade levels for others.
In some districts ACT and SAT math scores dropped, while others reported a majority of graduates who required remedial math in their first year of college.
Those results contrasted the 1999 accolades from Assistant Education Secretary Kent McGuire who designated IMP “exemplary” for the program’s outstanding quality and effectiveness.
And regardless of opposition from traditionalist parent groups, the constructionist math movement marched on.
In 2003, it arrived at SCSD#1.
At the time, Laurie Latta’s youngest son Keegan was in eighth grade. After conducting online research Latta and other parents concluded IMP did not work.
“That’s not to say there weren’t elements that were helpful,” she said. “Kids should have real-world math experience.”
Instead of choosing one curriculum over the other, Latta’s group proposed a compromise where elements of IMP and CMP were taught in conjunction with traditional math. But the district rejected the proposal.
Instead, it instituted a full complement of IMP and CMP courses.
“It was a real negative experience for (Keegan) and his contemporaries,” Latta said explaining that many students took online traditional math courses.
Latta said her son went from winning state math awards as an eighth-grader to taking remedial math as a college freshman.
Although Latta admits Keegan’s gift wasn’t in mathematics, she said the real tragedy was his feeling of disenfranchisement that sapped his enthusiasm for the subject.
And that lack of enthusiasm manifests in students who are more mathematically minded.
Tesa Manning graduated from PHS in 2007. At the University of Wyoming (UW) solid test scores put her in sophomore-level math. But as an Ag Business major she says some of her math skills are lacking.
“When I got down to college, I felt really behind compared to kids from other high schools,” she said. “I didn’t have the basic math skills that other kids had.”
In her business calculus class, she said her peers were better prepared with fundamental calculus skills while she struggled to keep up.
Manning also made the common complaint that the vocabulary of IMP is much different than traditional math.
Keegan Latta and Manning’s experiences aren’t unique. Many share the struggle between the constructionist curriculum of high school and the traditional instruction of college.
Make no mistake, the district’s PAWS scores rank it in the top 10 percent in the state.
In Measures of Academic Performance (MAP) test scores, SCSD#1 consistently shows elevated levels of mathematic proficiency.
This fall, the ninth through 12th grades scored well above the national average in algebra.
So why do above-average students from above-average schools struggle to keep up in college math?
The reason could be a clash of systems.
SCSD#1 Superintendent Doris Woodbury says one challenge confronting students is the difference in the structures. IMP utilizes group learning where students collaborate in small teams to solve problems. Traditional math is based on the individual who is often sitting in a class of 50 or more.
Another structural difference is the approach to mathematics as a topic. IMP teaches math in a context of “this is why you do it,” as opposed to the traditional approach of “this is how you do it.”
Woodbury says the transition to the traditional structure can be difficult.
That difficulty has prompted the district to offer a choice of math curricula at PHS. This academic year marks the first year both IMP and traditional math programs are offered.
Because college entrance exams and college curriculums are based on traditional mathematics, Woodbury said high school students wishing to attend college should consider taking the traditional courses.
But she has other concerns.
While SCSD#1 has a large percentage of students who are proficient in the PAWS test (therefore putting the district in the top 10 percent), the district has a disproportionately low number of students scoring in the advanced range.
Those low numbers have the district’s math instructors developing integrated courses that incorporate “drill and kill” with problem-centered instruction.
“IMP has done a good job,” Woodbury said. “But it hasn’t done everything we want our math program to do. Our high-end kids are not achieving what they are capable of.”
But that doesn’t mean she’s willing to discard IMP. She said the district’s math instructors are enrolling their children in both courses.
And she said there is no need to pit powerful learning and powerful instruction against preparedness for the college system.
“You don’t want to ignore the algorithm, but that’s not all you want to teach,” she said, explaining her fondest concept is a “marriage of tradition and IMP.”
One or the other
A popular anti-constructionist math Web site says IMP/CMP dies at the onset of school choice. In other words, students and parents inevitably choose traditional math over other options.
And it’s possible the future of IMP may find the same demise at the PHS.
“I don’t know how long we would support two programs,” Woodbury said. But she also doesn’t want to let the issue become obscured by polarization. She says the two sides are so diametrically opposed it is difficult to find a consensus. Instead districts adopt a “one or the other” mentality.
As hard is it might be, the integration of both system’s strengths might be the most effective politically and mathematically.
Just as parents cringe at the idea of their children being mathematically improficient, students cower at the idea of military-style learning drills that teach despondency to math more than the math itself.
Unfortunately, the choices are less clear-cut than that.
And while the battle between traditionalists and constructionists continues, SCSD#1 students have an opportunity to choose a mathematic pathway that will lead them on the journey to their future.
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