Why aren’t American students proficient in mathematics? Teens graduate from high school unprepared for college math and with a strong antipathy to the subject. Most graduates require extensive remediation. There is a dearth of K-12 math skills across the nation.
Why is the United States, long a global education leader, suffering a national breakdown in mathematics? The reason is simple: Schools don’t teach children enough math.
Beginning in the 1980s, most school districts adopted or experimented with a “reform” approach to K-12 mathematics, also known as “standards-based,” “student-centered,” “inquiry based” and “discovery based.” Critics call it “fuzzy math.”
The national Common Core State Standards initiative is unfortunately leading many districts to adopt more of these kinds of materials.
Fuzzy Math, Fuzzy Teaching
Reform-based curricula downplay or avoid “traditional” procedures, focusing instead on less-effective strategies. They emphasize probability, data, and statistics, while de-emphasizing multiplication facts, long division, fractions, the number line, and algebra. But content isn’t the only weakness in reform math. The teaching method is problematic, too.
Direct instruction is a teaching method that entails teacher instruction, examples, and explanations. There are individual and group practice, special projects and discussions, but the emphasis is on teacher-directed activity. There is structure, a logical progression of skills, an emphasis on correct answers and efficient processes, memorization, and “practicing to mastery,” with constant refreshers on previously learned skills. Most parents and professional tutors use direct instruction as their primary teaching method.
Reform math, however, is typically delivered via constructivism, a method of learning where students “construct” or “discover” their own strategies and knowledge. The teacher is a “guide on the side,” not a “sage on the stage.” Constructivism prefers “discovery” over teacher instruction; estimation over exact answers; group work over individual work; explorations and supposed “real-world applications” over procedural knowledge and practicing; and the use of calculators and other technologies over proficiency with paper-and-pencil computation.
In constructivist classrooms, children are to learn math by drawing pictures, counting on fingers, playing games, acting, coloring, writing about their thinking, and taking all day to get practically nowhere. There are few definitions, explanations, or examples. Memorization and practicing are derided as”drill and kill,” an old-school philosophy that supposedly hinders understanding and critical thinking.
Techniques for Failure
Constructivists insist “traditional” math lacks conceptual understanding and that children are bored by “rote memorization.” Discovery learning, they claim, provides “deep” thinking and context, gets students to “think mathematically” and makes math accessible. Children supposedly explore, create, make connections, communicate, collaborate, and become “math literate,” all while having fun.
This sounds great, except that proficiency won’t come this way. Math proficiency depends on a logical progression of skills. Fluency is key. Accuracy is critical. Skills build on skills, and practice is essential.
Reform math proponents call their method “best practices” (as if calling it that makes it so). After years of such classes, however, students rely on calculators and classmates. They lack procedural fluency, basic arithmetic skills, and number sense. They count on fingers and add instead of multiplying. They’re perplexed by long division. Fractions are a mystery. They don’t know the standard or “traditional” algorithms and terminology much of the world uses. They’re stuck with methods that are non-standard, not useful long-term, inefficient, inexact, and often incorrect.
Reform math also can damage children emotionally. Constructivists expect students to struggle. In their mind, if children learned efficiently, the lesson failed. Therefore, children who learn an efficient method at home can be reprimanded for using it or teaching it to classmates. They’re not allowed to deny themselves or their classmates the chance to struggle and fail.
But children are concrete thinkers. They want instructions, guidance, and things that make sense. Having to constantly struggle in front of classmates can be devastating. “I don’t get it” can turn into “I hate math,” which can turn into “I hate school,” then “I hate me” or “I don’t want to go to school today,” which can turn into illness, dropping out, or behavioral or emotional problems. What’s really an instructional failure can become an emotional problem for children, to where they literally panic over simple math.
Undeterred by Failure
Their panic won’t move committed reformers. I’ve heard adults call children “the low group,” “unmotivated,” “selfish,” “dummies,” “typical teens,” “lazy,” “problems,” “bad apples” or students of “low cognitive ability.” In 2010, just 41.7 percent of Spokane’s 10th graders passed a simple state math test that required just 56.9 percent to pass. Local administrators dismissed what was obviously their failure with: “That number is irrelevant.”
My daughter commented: “Saying that kids need to learn in groups and need to struggle is ridiculous and cruel to kids… If you’re going to be an astronaut, if you’re going to be a lawyer, or change the world, school is where it starts. And you’re crushed before you even get half-way in the door.”
All over the world, students enjoy math and excel in it. American children don’t have a “math-is-too-hard” gene. They’re stuck in classes where they’re expected to “discover” complex mathematical procedures and work constantly in groups, trying to teach each other thousands of years of math. Most could develop solid math skills. The reason they don’t is because they aren’t taught enough math.
Laurie Rogers ([email protected]) is author of “Betrayed: How the Education Establishment Has Betrayed America and What You Can Do about It.” Visit her blog at http://betrayed-whyeducationisfailing.blogspot.com.
Image by Woodley Wonderworks.