# Common Core and the Common Denominator

In the last 50 years, there has been a boatload of research—that’s the technical term, by the way—confirming what most of us know intuitively: there is a definite connection between time and learning, with a higher quantity of the former generally leading to an increased amount of the latter. (For a brief review of the research, see the paper I put together a couple of years ago.) In fact, this direct association was first articulated, at least in a published paper, by the educational psychologist, John Carroll. Trying to distill the many theories of learning into a single framework, he ended up deciding that the dynamic revolved around time. He proposed a simple formula to describe the relationship:

**Degree of Learning = f(time actually spent/time needed)**

It seems commonsensical—albeit a bit artificial—to frame learning in this way. If it would take you two hours to learn the quadratic equation, for example, but you spend only one hour learning it, you’re not going to learn it in full. Or, put another way, the closer the numerator of time spent is to the denominator of time needed (i.e., a ratio of “1”), the higher your degree of learning.

And when you play out the implications of this formula in the real world, you can see pretty quickly the fallacy of having a set amount of time for learning (i.e., the standard school day and year) for a wide range of students who differ so much in the time they need for learning. Indeed, writ large, this framework helps explain the achievement gap. There are many complicated factors for the its persistence, of course, but surely one of them is the simple fact that children from disadvantaged backgrounds or those with special needs or those whose first language is not English need more time to learn the same amount as students who have no such impediments. Their denominator is significantly higher, so their numerator should likewise be higher in order to achieve to the same level. Instead, what happens is that these children who are further behind to start spend no more time learning and, consequently, their degree of learning is less.

I must say that this simple ratio filled my head as my colleagues, David Goldberg (of NCTL) and Tiffany Miller (of the Center for American Progress), and I wrote a paper (which we released last week at an event in Washington) on the need for more learning time to meet the higher expectations of the Common Core State Standards. In this case, the “degree of learning” has been raised—one expert estimated, for example, that expected learning in Common Core is one to two grades ahead of those in many current state standards in math—and so this automatically means that the time needed to learn more must increase in kind. And, in turn, in order that students’ time-needed-to-time-spent ratio approach 1, then the time spent needs to increase, as well. The need for more learning time could hardly be more obvious.

Now, the audience at the release event was one of policymakers and thought leaders and so musing on these kinds of academic constructs did not really hold a place, but at the release event, Carmel Martin, Executive Vice President for Policy at the Center for American Progress, who introduced the event, said as much when she observed “The Common Core is asking a lot more of our students and teachers and the question is whether the current 180-day 6.5-hour day is enough to meet those demands.” Paul Reville, former Secretary of Education for Massachusetts, was even more explicit about the underlying concept of a time-needed-to-time spent ratio: “It is high time that we hold learning constant and let the time in school vary.”