Saturday, December 29, 2007

Elementary Mathematics being made more demanding

If the teachers can teach it

Joanne Tegethoff teaches algebra. Never mind that her students carry Disney princess and Thomas the Tank Engine backpacks and have the alphabet taped on their desks. The Montgomery County first-graders one recent afternoon were learning to write "number sentences" to help Lucy Ladybug. "Lucy wakes up and puts five spots on her back," Tegethoff told the class. "Then she gets confused. She wants 10 spots. What's missing?" Tegethoff used to teach what she called "very boring math," using worksheets of addition and subtraction problems. Now her lessons delve into algebraic thinking. By the third grade, Viers Mill Elementary students are solving equations with letter variables.

Long considered a high school staple, introductory algebra is fast becoming a standard course in middle school for college-bound students. That trend is putting new pressure on such schools as Viers Mill to insert the building blocks of algebra into math lessons in the earliest grades. Disappointing U.S. scores on international math tests have added to the urgency of a movement that is rippling into kindergarten. At stake, some politicians say, is the country's ability to produce enough scientists and engineers to compete in the global economy.

But education experts say students aren't the only ones who need more rigorous instruction. Too many elementary school teachers, they say, lack the know-how to teach math effectively. "You can't teach what you don't know, and your students won't love the subject unless you love the subject," Kenneth I. Gross, a University of Vermont mathematics and education professor, recently told a group of college mathematicians at a conference hosted by the U.S. Education Department and the National Science Foundation. "All of mathematics depends on what kids do in the elementary grades. If you don't do it right, you're doing remedial work all the way up to college. Arithmetic, algebra and geometry are intertwined."

Gross and others say many elementary and middle school teachers -- generalists relied on to teach reading, science and social studies and even to make sure a child's coat is zipped -- are drawn to teaching by a love of children and literacy. Most had little exposure to high-level math in college and are more at home with words than numbers. "Many of them fear math," said Vickie Inge, math outreach director with the University of Virginia's School of Continuing and Professional Studies. "Many of them had trouble with math themselves."

Educators, mathematicians and business leaders are working to bridge the knowledge gap. At an increasing number of schools, including Viers Mill, teachers work with a coach who helps boost their math knowledge, plan lessons and examine student work. The National Math & Science Initiative, funded by ExxonMobil, and the National Science Foundation are granting universities and school systems millions of dollars for programs to produce better math and science teachers.

In February, a panel of educators and mathematicians appointed by President Bush is slated to recommend ways schools can produce more algebra-savvy students. The panel will lay out skills students need to have starting in third grade to master algebra down the road. It will also recommend ways to improve teacher preparation.

Test scores released this month reignited concerns about math education in the United States. The Program for International Student Assessment found that 15-year-olds in the United States trailed peers from 23 industrialized countries in math. What's more, Michigan State University professor William Schmidt found that U.S. teachers scored at the bottom of the pack on an algebra test in a recent study of middle school math teachers from six countries. Teachers in Korea and Taiwan, where students earn high marks on international tests, had the best scores. "The U.S. performance was weak," Schmidt said. He found that U.S. and Mexican teachers had taken far less advanced undergraduate math courses than peers in Taiwan and Korea. He also found math knowledge isn't enough. Teachers also need strong training in instructional techniques.

In Virginia, George Mason University, the University of Virginia, Virginia Tech and three other universities have teamed with local K-12 systems to improve math teaching through a master's degree program in math and educational leadership for elementary and middle school teachers. The program, begun in 2002, has about 60 graduates, who have returned to their schools and become a resource for colleagues.

Virginia Commonwealth University math professor William E. Haver, who is involved in the partnership, said elementary teachers need to know far more than the standard curriculum. With a depth of knowledge, teachers can help children understand relationships between numbers and solve problems in different ways. Without it, teachers often rely on memorization and aren't well-equipped to help struggling students. "Elementary math isn't elementary," Haver said. "There are a lot of deep ideas there. Usually, if a child doesn't get the right answer, there's a fair amount of good thinking along the way, but it got astray at some point. If you can pinpoint that problem, you're better off."

Gross runs the Vermont Mathematics Initiative, a graduate program that has trained more than 160 elementary teachers in math leadership. He drew an analogy to elementary reading instruction. "Would you want a teacher who has read 'Dick and Jane'?" he asked. "Or would you want a teacher who has read Shakespeare and the masters and has a fondness for reading?" Results in Vermont are promising. In schools with the math leaders, students are earning better math test scores than peers in similar schools. Achievement of students from poor families has also risen.

Judy Schneider, a 25-year teacher who is a math specialist at Widewater Elementary School in Stafford County, is midway through the Virginia program. She helps teachers understand math and reach students through dynamic lessons. Recently, she helped a fifth-grade teacher who was preparing to teach a lesson on fractions but didn't understand the material. Math wasn't always Schneider's strong suit, but after taking courses in algebra, geometry and statistics, she is able to help colleagues improve. "I was such a bad math student as a child, all the way through high school and even into college," she said. "Math was something I struggled with, and all of a sudden algebra makes sense to me. I want it to make sense for the kids."

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Grading Disparities Peeve Parents

With No Baseline Among Districts, Some Say Students Suffer

Marcy Newberger grew up in Montgomery County and attended Churchill High School. Then she moved to Fairfax County and had children, who attended McLean High School. Both were fine schools in good systems, with one irritating difference. Simply put, Fairfax high schools set a higher bar for grades than those in Montgomery. To earn an A in Fairfax, it takes a score of 94 to 100. In Montgomery, it takes a score of 90 or higher. Standards for grading in the two counties, including bonus point calculations, are so out of sync that it appears possible for a Fairfax student to earn a 3.5 grade-point average for the same work that gets a Montgomery student a 4.6 GPA.

Parents nationwide are increasingly frustrated with wild variations in grading systems that, they say, are costing their children thousands of dollars in merit-based scholarships and leaving them disadvantaged in college admissions.

Sensitivity to grading is particularly acute in Fairfax and Montgomery -- large, affluent counties that send more students to college each year than other local school systems. But grading disparities also have enraged students and parents elsewhere. In Simsbury, Conn., parents stumbled onto SAT survey data that showed that teachers in their state were unusually tough graders. Just 29 percent of SAT test takers in Connecticut reported A averages, compared with 40 percent in California, 42 percent in Florida and 49 percent in Texas. "There are no effective standards," said Robert Hartranft, a retired nuclear engineer from Simsbury who has scrutinized the issue. "Local grades and local GPAs are a crazy quilt of numerical values and systems."

Fairfax and Montgomery school officials reject the idea that grading discrepancies hurt students. Betsy Brown, Montgomery's director of curriculum and instruction, said colleges know grading systems vary and "work to even out what may be uneven across school systems and differences between private and public schools." Fairfax schools spokesman Paul Regnier said the county's students have done well in college admissions. He said people who want to change grading rules assume that college admissions officials "are inept and can be fooled. We believe it is a bad assumption."

Robert J. Massa, vice president for enrollment at Dickinson College, said his school and others do not depend only on GPAs in awarding merit scholarships. "Parents need to chill out about grades," he said.

But demographer Sara Pacque-Margolis, a Fairfax parent who with Newberger is surveying 60 colleges on this issue, said policies at Indiana University, Purdue University and the University of Miami show that Fairfax penalizes its students by failing to give the same grade-point bonuses as Montgomery for high-level courses. For example, Montgomery awards a bonus point for Advanced Placement and International Baccalaureate grades; Fairfax gives an extra half-point for AP and IB. Pacqu‚-Margolis said guidelines for merit scholarships at the three universities are based on a minimum SAT or ACT score and GPAs taken from high school transcripts, often inflated by bonus points. She said her son, an Indiana undergraduate, would have received thousands of dollars more in merit-based scholarships over four years if Fairfax had used Montgomery's bonus-point system.

While suburban parents suggest more reliance on the SAT and other national tests, advocates for low-income urban and rural students are calling for the opposite -- more emphasis on classroom grades, in which students from poor families are at less of a disadvantage.

The issue is complex and confusing, with little research to back either side. Governments are spending millions of dollars on analysis of standardized tests, but officials rarely provide much detailed information on grades, even though grades have more of an effect on students' lives. A failing grade on a report card can force a student to repeat a class and jeopardize college admissions, whereas a bad state test score usually has no effect.

In recent years, it has often been parents, not school officials, who have researched grading policies and called for changes. Newberger, a former teacher, and Pacqu‚-Margolis are gathering information they hope will convince Fairfax school officials that county students are hurt by rules that say 94 to 100 percent is an A (90 to 100 is an A in the Maryland suburbs, the District, Arlington and Falls Church). They also complain of bewildering differences in the way local schools award extra points for honors and college-level courses.

Often, teachers find ways to give as many A's as they like, no matter what their school's grading policy is. "Any teacher can make up an assessment on which many students or none will get 90 or 94," grading expert Ken O'Connor said. He has written a book for the Educational Testing Service that says grading standards should be made clearer and that practices such as grading on the curve or on attendance should be eliminated.

Hartranft said he has detected grade variations by year, by region (with New England tougher than the rest of the country) and by subject (with good math and science grades hardest to get). Scholars Philip M. Sadler of Harvard University and Robert H. Tai of the University of Virginia say their data show that high school science grades would be fairer and more consistent if schools added half a grade point for an honors course and one point for AP courses.

According to Hartranft's research, teachers in the Washington area grade harder on average than teachers in the Sunbelt, but are somewhat more generous than those in Connecticut. Among SAT test takers in the Class of 2007 asked about their grades, 38 percent in Maryland, 37 percent in Virginia and 30 percent in the District said they had A-plus, A or A-minus averages. The survey included students from public and private schools. D.C. students who reported A-minus averages had an average combined score of 1127 on the SAT math and reading sections. Maryland's A-minus students had a 1098 combined score and Virginia's a 1095. Connecticut's A-minus students had an 1146, while those in Texas had a 1039. Such data suggest that an A-minus is worth more in some places than others.

A College Board spokeswoman cautioned that the data need more analysis because Hartranft is comparing states with different SAT test-taking rates. Experts also note that the data rely on student recollections of grades, not transcripts.

Some scholars and college officials recommend giving more consideration to grades, despite variations. Researchers Saul Geiser and Maria Veronica Santelices, in a June report for the Center for Studies in Higher Education at the University of California at Berkeley, concluded that high school grades -- like all measures of student achievement -- have flaws but are better predictors of performance in college than standardized test scores. The researchers, looking at the academic records of almost 80,000 U.C. students, said grades have another advantage: They are "much less closely correlated with student socioeconomic characteristics than standardized tests." A college that emphasized grades in admissions would be more likely to find low-income minorities who would do well in college, they said.

"High-school grades provide a fairer, more equitable and ultimately more meaningful basis for admissions decision-making and, despite their reputation for 'unreliability,' remain the best available indicator with which to hazard predictions of student success in college," Geiser and Santelices wrote.

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