By Frank Wells
Fewer topics and greater depth are among the goals of the newly adopted Common Core State Math Standards (CCSMS), which California will begin implementing in the 2014-15 school year. The new standards pare down topics, realign content to and across different grade levels, and eliminate redundancies that hinder students from building on what they’ve learned before.
Emphasizing focus, coherence and rigor, the new standards modify what were already widely regarded as some of the strongest standards in the nation, so that students are better prepared for college or careers.
The new standards’ focus on depth is a welcome step for many. Critics of current practices say U.S. math courses cover too much with too little understanding. While U.S. students fared quite well in the Trends in International Mathematics and Science Study (TIMSS), those nations that performed better actually covered fewer topics. The U.S. fourth grade curriculum omits only 17 percent of the TIMSS topics, while Hong Kong students cover only half.
The U.S. eighth grade curriculum addressed 30 topics, the Japanese, only 10. Some experts argue that fewer topics lead to better mastery of content and therefore higher test scores. The new standards attempt to offer students that path to mastery and better understanding.
UC Berkeley professor emeritus of mathematics Hung-Hsi Wu has written and presented extensively on the subject. He argues that states have already had a de facto curriculum dictated largely by textbooks that share the same basic content — content that is often defective. An example is asking students to solve difficult problems and make extensive computations with fractions without once telling students what a fraction is. Content that doesn’t really build on itself, along with an erroneous “earlier is necessarily better and more rigorous” philosophy, has placed students at a disadvantage and made math needlessly discouraging.
To illustrate a difference between current practice and the new Common Core, Wu compares two approaches to adding fractions. Currently, students are taught a formulaic procedure — find the lowest common denominator, multiply, fiddle with the fractions in some comprehensive way and then calculate — bypassing any sense of actually combining things (learned when adding whole numbers) or understanding the connection between adding fractions to whole numbers.
The Common Core approach to the same problem puts the emphasis on making sense of the computation. Students learn to place fractions on a number line, learn that addition means finding the total combined length of the segments representing the numbers in question, learn to find a common (not necessarily lowest) denominator, and finally see that addition is combining things after all. As a result, adding fractions is no longer a topic that has too many students searching for the classroom exits long before the bell rings.
Adding fractions isn’t the only source of student frustration under current practices. In an effort to correct what some view as another obstacle to student engagement and progress in math, one of the biggest changes to California’s math curriculum was the elimination of California’s 15-year-old Algebra I requirement for eighth-graders. In January the California State Board of Education voted unanimously to drop the requirement, leaving some students the option of an alternative path for that would still include some algebra but that would not be more transitional than the current requirement.
While some argue that the move lowers standards and rigor, others point to the high failure rate among students who may not have been quite ready and who need additional foundations before attempting a complete algebra course. Algebra may still be offered to eighth-graders deemed ready, and it will remain a requirement for high school graduation.
State Superintendent of Public Instruction Tom Torlakson praised the move. “The Common Core — and common sense — calls for a student’s progress in mathematics to be based on their readiness to advance, not a timeline or a mandate from Sacramento,” Torlakson said. “Making this change now will help our schools make the transition to Common Core, and marks another step in our push to provide students the practical, real-world skills they need.”
Wu agrees with the board’s move. “There has been a prevailing and erroneous belief that earlier is basically better and more rigorous,” he says, “and some have tried to discredit new standards because they don’t do algebra in grade 8. But the new standards actually make algebra learnable in grade 8 for the first time in decades by using part of grade 8 to provide students with the geometric knowledge needed for learning algebra.”
CTA members can and should begin preparing now for the coming changes to the math curriculum and to the related assessments. Department and grade level meetings should include discussions of the new standards. Additional resources are available at www.cta.org/cderesources, commoncoretools.me and www.cta.org/ipd. Sample assessment questions are available at sampleitems.smarterbalanced.org.