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The math scores at Einstein Academy didn’t add up. Kids aced math in the younger grades at the South Park school, a respected charter with enviable test scores.
Yet when they hit algebra, their scores plummeted. Three years ago, just 9 percent of eighth graders in its sister middle school were proficient in algebra on state tests — even kids who seemed to be math whizzes before.
Instead of jumping on algebra and assuming that something was amiss in eighth grade, Einstein stepped back and examined its whole math curriculum from kindergarten up.
What it found was surprising. The problem started much earlier than eighth grade, back when kids were acing math. Einstein’s students were developing too many shortcuts and not enough understanding. While that had worked in the short term, it ultimately shortchanged kids.
To tackle the problem, Einstein revamped its whole approach to teaching math last year. Its algebra scores have already jumped, a case study for hundreds of other San Diego County schools struggling with the same problem.
Algebra suffers from a bad reputation for baffling kids, but mathematicians say it is actually the logic of mathematics laid bare. It explores how numbers relate to each other, using letters to stand for unknown numbers in equations like 2×2 + 3 = y.
“It’s a foreign language,” said Zalman Usiskin, director of the University of Chicago School Mathematics Project. “Arithmetic is all around kids. You go into a store and the price is a decimal. Your newspaper has sports scores. But you go to algebra and immediately kids ask, ‘What is this? Why do I need it?’”
Algebra has dogged schools for decades. The San Diego Unified School District sees its math scores drop as kids grow older, falling most steeply in eighth and ninth grade, right around when algebra is taught. While 71 percent of its fourth graders meet state math goals, only 17 percent of its 11th graders do.
The problem stretches far beyond San Diego. U.S. schools lag behind other industrialized countries in eighth grade math. That worries educators because algebra primes kids for careers in math, science, technology and engineering. Math experts say the problem has many tentacles, from an overly broad, thin curriculum to elementary educators uneasy with math themselves.
What teachers at Einstein realized was that children could calculate like the dickens because they used tricks they’d been taught. Mathematicians call them algorithms: a neat series of steps that lead to solving a problem. For instance, when dividing a number by a fraction, a teacher might remind students, “Don’t ask why — invert and multiply.” But kids didn’t understand what they were doing.
“The beauty of an algorithm is it lets you get through a computation without thinking,” said E. Paul Goldenberg, a math scholar who helped develop the new curriculum that Einstein ultimately chose. Not having to think can be useful if you have to crunch numbers, he said. “But for learning, you don’t want to hide the thinking.”
At Einstein, the problem became clear when teachers gave fifth graders a simple test. They told them to put down their pencils and estimate answers to simple questions, different ones than they were used to.
Elementary principal Jeannette Vaughn was stunned. Kids who had breezed through math struggled to estimate how much 9/10 plus 35/36 was without writing it out. Word problems stumped them too, a worrisome sign that the students didn’t know how to apply math to real situations. The kids were so wedded to formulas that they couldn’t step back and reason through a problem without them.
“If I said, ‘Here’s how you add fractions,’ sure, they could do it,” said Emily Small, who teaches sixth grade math at the school. “But fast forward and give them a word problem based on fractions, and they couldn’t.”
Mathematicians call it a lack of number sense, an intuitive feel for numbers and how they relate to each other. So when algebra rolled around and forced Einstein’s kids to think abstractly, many were overwhelmed. For a school that prides itself on encouraging kids to ask questions and learn different languages — part of its rigorous International Baccalaureate curriculum — it was startling to realize that math had been rote.
“We want kids who design the 18th generation of the iPhone,” said David Sciarretta, principal of the middle school. “You don’t get that from teaching kids, ‘Don’t ask why, invert and multiply.’”
Sixth graders furrowed their eyebrows and tapped pencils as they scrutinized the problem: How many feet of fencing would be needed to surround a flowerbed and how much it would cost at $8.75 per yard? Small pressed them to give her more than the answer.
“Three feet fit in a yard,” one boy began to explain to the class. But instead of pushing right away for the answer, Small stopped him to tease out his reasoning for the whole class.
“Pause,” Small said, holding a hand up. “Three feet do fit in one yard. Why is he saying that?”
To get kids thinking more deeply about math, Einstein started using new math textbooks this year. Instead of teaching students a new algorithm and drilling them on it in problem after problem, it poses open questions that can be solved multiple ways. That forces kids to figure out what strategies fit a problem, instead of just mechanically following steps.
For example, teacher Peter Kramer recently asked his fifth graders to estimate how many books were in his classroom. One boy reasoned that since every kid had a handbook and a German dictionary, he could double the number of kids, then add how many books were on the shelves. Kramer and the kids debated: Was it a good estimate? Was there a better way?
“They used to get a page with 40 problems of the same kind. Only the numbers changed. You’d just repeat it,” Kramer remembered. “Now there are fewer problems — but they really have to think.”
Einstein also started doing a problem of the day, one like the question Kramer posed. The idea was to let kids throw their brain at a problem, with no single way to solve it.
Scott Kelley noticed this year that his young son was bringing home unusual worksheets from the first grade. They almost looked like Sudoku puzzles, grids of numbers and blanks that he had to deduce. His son, who grew bored with math in kindergarten, loves digging into the new puzzles. Kelley is a microbiology professor, but it can challenge him, too.
“Sometimes as a parent, you’re like, ‘How do you figure this problem out?’” Kelley said.
Einstein isn’t the only school taking algebra on earlier. San Diego Unified is also changing its elementary school curriculum to ease younger kids into algebraic reasoning. Thousands of teachers have been trained in the new methods, which link algebra to every grade.
And the work isn’t over at Einstein. Even after its scores surged last year, it still had twice as many students who fell short on state algebra tests than succeeded. But teachers like Small are confident that with a new zeal for attacking problems, the kids will keep pushing ahead.
“Math really isn’t about filling out a form that has a bunch of problems on it,” said Ivan Alba, a math consultant who worked with Einstein. “It’s about putting people on the moon.”