To read newspaper coverage of the new standards, you'd think they were raising the bar for math proficiency, not lowering it. "More is expected of the students," one article declares. "While they still have to memorize or have fluency in key math functions and do the math with speed and accuracy, they will have to demonstrate a deeper understanding of key concepts before moving on."

But what does this mean in practice? Another recent article explains, "This curriculum puts an emphasis on critical thinking, rather than memorization, and collaborative learning." In other words, instead of simply teaching multiplication tables, schools are adopting "an 'inquiry method' of learning, in which children are supposed to discover the knowledge for themselves." An educator quoted in the article admits that this approach could be frustrating for students: "Yes. Solving a problem is not easy. Learning is not easy."

With 100 pages of explicit instruction about what should be taught and when, one would expect the Common Core Standards to make problem-solving easier. Instead, one father quoted in the aforementioned article complains, "For the first time, I have three children who are struggling in math." Why?

Let's look first at the 97 pages of what are called "Content Standards." Many of these standards require that students to be able to explain why a particular procedure works. It's not enough for a student to be able to divide one fraction by another. He or she must also "use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9, because 3/4 of 8/9 is 2/3."

It's an odd pedagogical agenda, based on a belief that conceptual understanding must come before practical skills can be mastered. As this thinking goes, students must be able to explain the "why" of a procedure. Otherwise, solving a math problem becomes a "mere calculation" and the student is viewed as not having true understanding.

This approach not only complicates the simplest of math problems; it also leads to delays. Under the Common Core Standards, students will not learn traditional methods of adding and subtracting double and triple digit numbers until fourth grade. (Currently, most schools teach these skills two years earlier.) The standard method for two and three digit multiplication is delayed until fifth grade; the standard method for long division until sixth. In the meantime, the students learn alternative strategies that are far less efficient, but that presumably help them "understand" the conceptual underpinnings.

This brings us now to the final three pages of the 100-page document, called "Standards for Mathematical Practice." While this discussion is short, the points it includes are often the focus of webinars and seminars on the new Common Core methods: