A study led by Jennifer Kaminski, research scientist at The Ohio State University’s Center for Cognitive Science, found that abstract math concepts do not become more relevant or easier to learn when educators incorporate examples from the real world. In fact, such examples may hinder student understanding.

“College students who learned a mathematical concept with concrete examples couldn’t apply that knowledge to new situations,” says Kaminski. Getting back to the train example, “The danger [is] that many students only learn how to solve the problem with the trains. If students are later given a problem using the same mathematical principles, but about rising water levels instead of trains, that knowledge just doesn’t seem to transfer.”

Concrete examples can still be used to help test that math concepts were learned. However, results from the Ohio State study demonstrate that students are best prepared to apply math concepts to a variety of situations when abstract symbols, such as variables, are presented instead.

Despite opposition from California’s School Superintendent, Gov. Arnold Schwarzenegger and the State Board of Education endorsed a plan to require Algebra 1 testing for all eighth-graders beginning in 2011. Opposition groups sued, questioning whether the state had enough money or trained staff to comply with the state’s decision.

Judge Shelleyanne Chang issued a preliminary injunction, ruling that the State Board of Education acted outside its jurisdiction and without public input. She added that the plaintiffs would likely win if the lawsuit went to trial. The state Board of Education intends to appeal.

While about half of California’s eighth-graders take algebra, only about a quarter score proficient or above on standardized tests. The rate is even lower for minority and poor students.

Using a simple blackboard format, each video walks the viewer through example problems. Available math topics include basic arithmetic, pre-algebra, algebra, geometry, trigonometry, pre-calculus, calculus, probability, and differential equations.

Khan has also created videos on physics, SAT preparation, finance, and the credit crisis.  The SAT videos address all 432 problems in “The Official SAT Study Guide” by the College Board.

The Harvard- and MIT-educated Khan, an investment professional by day, started making math videos at night to help family and friends.  Word of his technique spread and now thousands of viewers from around the world depend on Khan’s one-man tutoring show.

According to Claremont Graduate University education professor and former school superintendent Barbara DeHart, “Recent studies have found that ninth-graders are dropping out of school because of pressures related to NCLB. The push for eighth-grade algebra proficiency is a big part of that pressure.”

With just half of California’s eighth-graders taking full algebra at this time, only about 23 percent score as proficient or above on standardized tests. The success rate is even lower for minority and poor students.

While some eighth-graders are ready for the algebra curriculum, thousands lack the solid foundation needed for algebraic problem solving. According to a Brown Center on Education Policy report [pdf], “One hundred twenty thousand students are misplaced in their eighth-grade math classes.” Students who don’t know how to multiply and divide are not learning algebra while, at the same time, well-prepared kids are being held back.

In a RAND study titled Mathematical Proficiency for All Students [pdf] a panel of researchers, mathematicians, and educators explain that,”Without proficiency in algebra, students cannot access a full range of educational and career options, and they have limited chances of success. Failure to learn algebra is widespread, and the consequences of this failure are that far too many students are disenfranchised.” The report recommends further research on how policy decisions can shape student learning and improve equity.

Algebra 1 should be taught to all students, but only once they have the basic skills required for algebraic proficiency. Before mandating that all students take Algebra 1 at a younger age, the Board of Education has a clear responsibility to provide every student with the basic foundation needed to succeed.