NORTHWEST
EDUCATION
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Portland, Oregon—“No, you do not!” warns Renee Anderson with a look of mock shock. Algebra’s about variables, double-negatives, equations, and abstract thinking—but in Anderson’s class, algebra is also high drama.
Sometimes Anderson bobs her head north, south, east, and west. Sometimes, she stomps her foot. And sometimes, the Grant High School algebra teacher squeals, “Yes, yes, yes!” And that’s just in the first five minutes of the period.
“Get out of here!” Anderson gently shoves a student back to work.
It is mid-October and the 30-year veteran math teacher is dead serious—although she doesn’t show it—as she moves to improve her ninth-grade students’ algebraic skills, starting with pre-algebra lessons in the first weeks of the first semester.
Today’s lesson is decidedly low tech: an exercise in Base 2. Anderson tells the class to fold a rectangular piece of paper in half. Keep folding and keep counting. Nothing fancier than a palm-sized calculator is required.
Anderson’s students are part of a new “Algebra for All” initiative in Portland Public Schools. For the second year, all freshmen in the 47,000-student district are required to take algebra or a higher mathematics class. There are some exceptions for special education students and English language learners, but still 92 percent of high school freshmen took algebra or geometry, advanced algebra, and even calculus last year.
This is despite the fact that not all Portland freshmen come to high school prepared for the rigors of algebra. According to Andy Clark, the district’s K-12 math coordinator, roughly half of Portland’s ninth-graders are not ready for Algebra I without help.
Those statistics—and the fact that one-third of Portland’s eighth-graders don’t meet the state’s mathematics benchmarks—have meant that high school math teachers have had to develop new strategies and classes to help struggling students make the leap to Algebra for All. The approaches vary at Portland’s 10 comprehensive high schools and three alternative schools, but they fall roughly into three models:
Tutorials occur during the school year and are used in schools where the number of struggling students is relatively small. Again, students are identified by their math teachers. Once or twice a week, these students get extra help from a math teacher. The tutorial teacher tracks the students to see how they perform throughout the year.
At Grant High School, roughly 20 percent of ninth-graders will follow the first model—taking a combination of “algebra readiness” (or pre-algebra) and algebra during their freshman year. Sophomore year, these students take the second half of Algebra I and geometry. By their junior year, these students should be “caught up,” having earned 2.5 math credits—two of which will count toward graduation.
“Angels, can you please go to Google? Yes, baby.”
Like her colleague Renee Anderson, Grant High School math teacher Pardis Navi has an easygoing but firm relationship with her students.
“Do I have to repeat myself 18 times?” Navi asks.
Today, each student sits in front of a laptop. They’re beginning a study of “distributive property.” Navi’s directing her freshmen to a Web site that uses what she calls “cool animation” and interactive work.
Navi and Anderson are part of the team that brainstormed Grant High’s algebra program. Principal Toni Hunter gave teachers a common “free” period so they could work together on the program. Hunter, who’s been at Grant for nine years, is a strong advocate of professional development for teachers. She knew her math teachers would need time to collaborate: “Common planning time within the day is important if you want teachers to teach differently,” she notes.
Hunter’s philosophy works. Grant math teachers came up with new approaches to teaching Algebra I, introducing the algebra mandate a year before the rest of Portland’s high schools. Grant was a good place to start Algebra for All: It is the city’s largest high school with 1,831 students, half of whom come from outside the neighborhood. Students are predominantly white, but one-fifth of the student population is African American and almost one-fifth qualify for free or reduced-price lunches.
Hunter was one of a group of Portland principals who spurred the adoption of the Algebra for All program, urging the district five years ago to toughen math standards. She says she was seeing too many students stuck in basic math courses. And Hunter, an African American, was also troubled by the fact that students of color rarely made it to calculus. “The other reason is my belief that kids will rise to the occasion of high expectations,” explains Hunter.
With Hunter’s blessing, the Grant math team meets throughout the year, as well as in the summer to look at instructional practices. Both Anderson and Navi say they were willing to change the way they taught algebra to bridge that math gap with all their struggling students.
“We had to reinvent the wheel while we drove the car,” laughs Navi.
Before the algebra requirement, Navi says kids took algebra based on what their peer group did. That meant algebra became the track for upper middle-class students, but not for others.
National math scores show higher math proficiency rates for elementary students than for middle and high school students (see Region at a Glance). Progress in this content area breaks down as students encounter the abstract thinking and language of algebra.
“It just gets a lot harder,” says Margaret Calvert, high school math curriculum specialist for Portland Public Schools. “Algebra is a leap. Algebraic thinking can be a stumbling block. Algebra is the sifter.”
These facts and observations motivate the Algebra for All movement across the nation. Studies show that algebra appears to be a “gatekeeper” course: Students who master Algebra I go on to higher level math and science courses, and they’re more likely to go on to college, too. In many cases, poor and minority students are “sifted” out of higher education and good jobs in a technological society more and more dependent on advanced math skills.
After one year of Portland’s stricter math requirements, Calvert says she’s “cautiously optimistic” because more freshmen earned a “C” or higher in math than in previous years, even though more students are taking a higher level of mathematics. And, these improved results cut across ethnic lines. Portland Public Schools’ data show the number of freshmen with a “C” or higher grade in Algebra I increased for Hispanic, African American, Asian, and American Indian students as well as for white students in 2004-2005. For many of those subgroups, the number of freshmen enrolled in courses above Algebra I has also increased.
At Grant High, for example, more students of color and students eligible for free or reduced-price lunch are not only taking advanced algebra but are completing it with at least a “C.”
While struggling students at Grant tend to follow the “double block” model of two math periods a day, their counterparts at Franklin High School also get a double dose of the subject, but with a twist. Their second period of math is an elective numeracy class.
In Julie Rierson’s classes, roughly one-quarter of the students also take numeracy. Some kids, Rierson says, couldn’t pass algebra without this extra period. At Franklin High School, where one-third of the students qualify for free or reduced-price lunch, special education students also take algebra. In Rierson’s algebra class, six out of 22 students are special education.
In late September—when school has only been in session for several weeks—Rierson wants to be sure her students understand negative numbers. On the overhead, there’s an algebraic equation: P = - 7; Q = -2; so what does P - Q = ? The answer is -5, but many of her students think it’s -9.
Rierson patiently explains a “parenthesis” method to help her freshmen see double negatives more clearly and avoid confusion. Today, she has them for 78 minutes and most of this time will be spent in the classroom. Students have been working in groups, and today is presentation day. Rierson previously assigned a “real-case scenario,” where two competing shirt-making companies (U.S. Shirts and Hot Shirts) sell their products for different prices. The budding mathematicians practice tables, graphs, comparisons, and problem solving:
“Can you tell me in this problem what your independent variable is?” Rierson asks.
Rierson admits she initially doubted the algebra mandate would work. She had taught math for 14 years and worried that large numbers of students would fail the course. But she’s seen that adding support for these struggling students helps them succeed. Rierson says her kids are “getting it” and they’re retaining what they’ve learned. She calls the course she teaches very solid math, but says it does lack some of the abstraction of traditional algebra. However, Rierson thinks that’s a plus. “I actually think it is good to have less breadth and more depth,” she says. “In math education we try to do too much with the kids and as a result they do not master much of anything. Although, in some aspects the algebra is watered down compared to what we took when we were in high school, I think that the students (at Franklin) are getting more depth and understanding.”
Rierson says her math team used inservice days and discussion time to develop their program. There was no definitive training. She believes Algebra for All is very doable, but it takes a lot of time and support for it to work. In the financially strapped Portland Public Schools, she’s concerned that support will be cut rather than increased.
While most Portland math teachers agree Algebra for All makes sense, many also say advanced algebra doesn’t make sense for every student: Those who pass Algebra I will not necessarily be able to do the more advanced work because it is far more abstract. As Renee Anderson puts it, “Not everyone’s mind works that way.”
Anderson thinks Portland Public Schools will need to offer more options for third-year math in addition to advanced algebra. But according to Andy Clark, the district is looking at the third year as a level that can definitely lead students straight to a four-year college.
The district will decide on third-year options by the end of the current school year. That means the 2005-2006 Portland Public School students will likely be the first class that will have to fulfill a three-year math requirement in order to graduate.
To see how the future might pan out, Portland could look to school districts in California, Chicago, Illinois, and Texas. Closer to home, there’s the experience of Jefferson County (Idaho) School District #251, which is now in its sixth year of Algebra for All. It’s a small, rural school district with one high school.
Unlike Portland, the Algebra for All movement begins in middle school in the eighth grade. Students can then take geometry in ninth grade, which is also a middle school level in Rigby. By the time these students move on to Rigby High School as 10th-grade sophomores, 90 percent of them will take Algebra II.
However, not all the students are prepared for that leap, according to Rigby High School’s Pat Waddell, a presidential award-winning math teacher. “Our math department is still struggling with students who come to us having taken Algebra I in the eighth grade and geometry in the ninth grade,” she says. And while middle school math scores in District #251 have improved in recent years, Waddell estimates that only one-quarter of her students are really ready for advanced algebra. She doesn’t think any more students come prepared for the advanced work than before the Algebra for All movement started in her district.
Waddell, who’s in her 27th year of teaching, says many of her students lack basic math skills and haven’t gained a firm grasp on many of the concepts that lead to algebra.
“We at the high school level are frustrated by the lack of foundation our students have when we try to progress through Algebra II topics,” said Waddell in an e-mail interview. “We also have tossed around the idea that Algebra I for eighth-graders may be too soon for the average student and wonder if there is a maturity that must occur for students to really master the algebra concepts at that early age. It seems they understand it enough to progress through the course, but not to remember it at a foundational level for Algebra II.”
At Rigby High School, they’re trying to fill the gaps as they work with students at the Algebra II level. To do that, teachers turned their Algebra II course into a three-trimester course. Waddell says teachers are spending a great deal of time simply reviewing and re-teaching Algebra I concepts and processes. For the lowest performing math students, Rigby has added one remedial algebra class. Waddell thinks the school will probably have to add another remedial class. There is also ongoing communication between the high school and middle school math teachers.
Waddell calls Algebra for All a “double-edged sword.” More kids are taking higher math now, but that also means kids who never would have climbed this high mathematically are now trying to do so. “We realize that we have students taking Algebra II at our school [who] would not be taking it under the old structure, but we have wondered as a department if there isn’t a compromise out there somewhere. Are we expecting too much of our struggling students? Can every child grasp abstract ideas necessary for retention and utilization of algebra?”
Waddell adds that each year, Algebra for All brings new questions and new struggles. Even in year six of the stricter math requirements, her math department still struggles to find the best ways to move students through advanced algebra. 
Original URL: http://www.nwrel.org/nwedu/11-02/open/
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