by Laurie H. Rogers
How do you divide one number by a different number? I was taught to do it using long division. Long division is considered to be a "traditional" algorithm (or methodology). It looks like this:
Our children, however, aren't being taught long division (or aren't being taught it to mastery). They've been taught various "reform math" approaches, like this one:
This reform approach is alleged to increase understanding of division, supposedly showing students WHAT division is. Reformers claim that traditional long division isn't "intuitive" and that children struggle to learn it. (Never mind that an entire country was built on long division, that children around the world learn long division, that homeschoolers and private schools tend to teach long division, and that long division is a more-efficient method. People who are pro-reform math do not like long division and generally won't teach it).
What's the big deal about that? Sure, the reform method is clunky, eking its way to the answer rather than getting there efficiently. So what? The field of public education appears to love it, so why not teach it to the children and not worry about it? Here's why.
The reform method doesn't work well with larger numbers. It isn't efficient. It doesn't include decimals. It adds too many steps, allowing for more possibility of error. It's difficult to later switch students from that to the more-efficient algorithm. And – most important – the reform method often leads to wrong answers. Despite what reformers seem to think – a correct answer is the entire point of a mathematics calculation. Math is a tool that we use to get a job done.
Not long ago, I was explaining this reform approach to some college folks. A young math professor was listening in, nodding his head and saying, "Uh, huh. Uh huh," in that encouraging way people do when they're in agreement. "You don't sound shocked," I said to him. And he wasn't. He praised the reform approach and appeared to prefer it. I was surprised, but I thought perhaps he wasn't familiar with its complications; he claimed to be seeing it for the first time. So, I asked him to do a problem for me.
Dividing 396.3 by 16 is simple for those who were taught long division. However, for those using the reform approach, the decimal poses a problem. Using long division, this is how the problem is done:
Long division efficiently provides a complete answer to the problem. On the white board that day, however, the young math professor used the reform method. His answer: 247 remainder 9. Whoops.
I pointed out the inadequacy of his answer, so he wrote more at the top of his work. His new answer was this:
I also commented on this new answer, so he kept writing. His next answer was this:
Not only was this additional information confusing, it was still incorrect. Later, he fixed his initial subtraction error (43 – 32 = 11, not 9), but didn't complete the problem. His final answer was this:
Someone in the room (not me) wrote a huge question mark next to his work.
Math advocates will not be surprised to know that this person never budged on his assessment of which approach was better. He stubbornly maintained that the reform approach is easier, leads to more understanding, and should be the method taught to small children. He said the traditional approach is not "intuitive," that children can't learn it, and that division should be done with calculators anyway.
We stared at his garbled work on the board. When I asked him – politely, I swear – how the reform approach is "simpler," he responded defensively: "I'm not the enemy." Every time I reminded him that his answer was not complete, he would say, "I'm not advocating for this. I've just seen this for the first time today." But then he would continue to advocate for it. He never wavered in his support for the method, despite his incorrect work and unfinished solutions. It was stunning. But this is reform math, and this is typical of reformers.
Division isn't the only problem in reform math. I tutor students who come to me not understanding negatives and positives because – instead of being taught the number line – they were taught reform methods such as the building model and the balloon model (going up is positive, and going down is negative). Where in these models is zero? Where is the concept of infinity? Where are fractions and decimals? The number line contains all of it, but reformers purposefully avoid using the most-efficient methods such as the number line. Who loses? The children.
Many children also haven't been properly taught fractions, they don't know how to convert from fractions to decimals to percentages, they don't know basic formulas such as the Pythagorean Theorem, the point-slope formula or the quadratic formula. They don't know speed/distance/time ratios. Many don't even know their basic multiplication facts, how to read an analog clock or a ruler, or how many days are in each month (which is critical to calculating calendar time).
Young children do NOT need to know why an algorithm works. They need to know the most efficient ways to get correct answers. Young children should NOT be forced to struggle and get things wrong initially. It causes them to become frustrated and to lose heart – whereupon reformers blame them for not being motivated. Who could possibly be motivated when faced with garbage like this?
Math is a tool to get a job done – unless, as my daughter noted wryly – 4th graders are beginning a PhD in number theory.
The dearth of basic skills is bad enough, but graduates also continue to struggle. Without long division, how do they divide a polynomial? Many math programs have deleted it from the curriculum. Not necessary, they say. Long division, not necessary. Basic math facts, not necessary. Fractions, not necessary. What's important to reformers are fuzzy concepts for which they can't be held accountable: "Deeper conceptual understanding," "critical thinking," "collaboration," "real-world application," and "self-discovery." When you see those terms in your child's math program, grab your babies and run.
This is what the children in many public systems face – stupid approaches from clueless people. Simple problems are made to be clunky, inefficient, and incomprehensible. These approaches will damage their futures forever. You would think that 30 years of absolute failure would have killed off reform math, but the fervor of reformers for fuzzy math is nearly cult-like, and their opposition to the efficiency and effectiveness of traditional math borders on hysteria. Reformers have no real support for their approach, no scientifically collected data to support it as being better than traditional math, but they will not let go of it, claiming that reform math would work if teachers would just do it properly.
Sadly for the children, reform math is now seeing a resurgence, due to the federal imposition of the Common Core initiatives. Many pro-reform-math decision-makers are using the Common Core to implement more reform math. It boggles the mind.
I stood next to this professor, listening to him claim something akin to "the moon is made of green cheese and pigs fly." His process was inefficient and nearly incomprehensible, and his answers were incorrect, yet he preferred it. His face had the same blank look I've seen before on reformers – stubborn and closed, in denial of what was right there in front of him, and obvious to everyone else.
I gave up trying to talk with him. I know from experience that the indoctrinated will not listen. Weak outcomes, angry parents, frustrated community members, a nationwide mathematical Dark Ages, and millions of suffering children will not break through their certainty. Alas, this professor is not the only math professional to have accepted the Kool-Aid. Spokane Falls Community College is now approaching some of its remedial classes using reform approaches, and there are others.
The traditional approaches to mathematics were developed by brilliant adults over thousands of years. It's astonishing that all of that work is being tossed out for methods that are proved to be flawed – in proper studies and in student outcomes. It's alarming that a dogmatic commitment to reform math appears to be worming its way into departments of mathematics.
Without intervention, there soon will come a day when few Americans will know any math at all. At that point, American dependency on foreign professionals will be complete. What will happen then to our children?
Laurie H. Rogers has a bachelor's degree in mass communication and a master's in interpersonal communication, emphasizing the evaluation of argumentation and logic. In 2001, she founded Safer Child, Inc., a nonprofit child advocacy information resource. In 2007, she narrowed her advocacy to public education, and in 2010, she founded Focus on the Squareâ¢, a nonprofit organization dedicated to improving American K-12 education.
Laurie is the author of the blog "Betrayed," located at http://betrayed-whyeducationisfailing.blogspot.com/. Her book Betrayed: How the Education Establishment Has Betrayed America and What You Can Do about It (Rowman & Littlefield Education, 2011) is now available from Amazon and Barnes & Noble. She and colleagues in Spokane, WA, have begun a new informational Web site called Partnership for Kids, located at http://partnershipforkids.org/
Besides serving on the executive committee for Where's the Math?, Laurie has a background in finance, journalism and child advocacy. She has volunteered in schools – tutoring children in literacy and math, and teaching chess, argumentation and knitting. She lives in Spokane with her husband, daughter and two cats.
Contact Laurie Rogers at [email protected].