An interesting story at Education News:

A study recently published in The Journal of Neuroscience finds that a strong grasp of basic mathematical skills can serve as a good predictor of student success on the Preliminary Scholastic Aptitude Test. The PSAT is an exam designed to gauge student preparedness for the SAT and is typically administered to kids in ninth and tenth grade.

To reach these conclusions, Daniel Ansari, Associate Professor in Western’s Department of Psychology and a principal investigator at the Brain and Mind Institute, used functional magnetic resonance imaging machines to monitor the brain activity of high school seniors. The MRI highlighted certain areas being utilized by students who were doing simple math exercise, and activity in those regions correlated strongly with their PSAT scores.

Now, how does the Common Core Math Standards help this?

With the Common Core State Standards teachers are moved to the role of a facilitator. Barry Garelick wrote late last year that not only will the Common Core Math Standards actually complicate math for kids.

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.

I’d be interested as these are implemented if we see a rise in kids needing math tutoring away from school.

Scott McLeod says

Hi Shane,

Would you agree that no one cares what graduates know, they care what graduates can do with what they know? Deeper conceptual understanding of why and how something works – not rote recall – is necessary to take knowledge and skills and apply them to new contexts, problems, etc. In other words, you have to know stuff to think critically about it but mere factual and procedural knowledge (which dominate 80%-85% of day-to-day instruction) are insufficient in and of themselves. This higher-level thinking is the intended focus of the Core (and the PISA assessments, and …) and it’s being driven largely by concerns of employers and policymakers that in a hypercompetitive global information economy, graduates don’t know how to think critically and collaborate and problem solve and do all of that other higher-order thinking stuff that justifies an expensive Western worker.

Thoughts on this?

Shane Vander Hart says

Why does it have to be either or?

Scott McLeod says

It doesn’t. I think that’s what both I and the Common Core are saying. Pay attention to foundational knowledge and skills but ALSO pay more attention to higher-level thinking concerns. The Core doesn’t diminish the former (although it does get rid of the exhaustive content laundry list); it’s a plea for the latter…

Shane Vander Hart says

Unfortunately that’s not what I’m hearing from the trenches.

Scott McLeod says

I think there is a lot of confusion about the Core. I do know many educators who see this as an EITHER/OR, not an AND. We’ve got lots of work to do on this front… 🙁

Bridgette Wagoner says

I think there are two different perspectives in the trenches. What the Common Core illustrates is a shift in math pedagogy that has been happening since the late 1980’s. Fundamentally, the debate has been about whether we should teach “traditional” math that is heavy on algorithm — no doubt the math Scott, you and I were each taught — or whether we should teach inquiry based math that seeks to develop conceptual understanding before introducing algorithms. Like most two-sided arguments, the right answer is some iteration that balances the two. There are many districts that made the shift to inquiry based (or balanced approaches) long before the publication of the Common Core. I taught in a school that made the shift 15 years ago. The district I’m currently in made the shift 5 years ago. There is a steep learning curve for teachers, students, and parents, but our teachers who have been in this “new” system for five years now would tell you that balance is supported by the Common Core — and that balance is what’s best for kids.

Robin Mebus says

Hi Shane! I certainly don’t want to oversimplify this conversation because there is nothing simple about anything in education at this juncture in time. However, I would invite you or any of the experts you quote to come to my school district and let my 1st and 2nd graders explain to you all that they “know” about numbers and how they work. I watched my school board as well as my high school principal sit open mouthed as they explained all the ways their numbers work together and how many ways they can create numbers and make them work. The problem with old school math is that we got used to teachers just “telling” us what we needed to know. The vast majority of students just “carried the one” without realizing that they were really carrying a TEN. Oh ya,…that makes more sense. No longer can we afford to have a student say “just tell me what I’m supposed to do”…we need them to inquire, to question, to wonder and to most importantly…”BUILD knowledge on what they already know”. In order to do that, they have to “KNOW” something. We were taught to mimic. By allowing young children to explore, build off their own foundation and stay engaged (another huge missing link when I sat at my desk and was told where to put that number), we are offering them an opportunity to develop a thinking strategy that serves them well beyond the world of mathematics. Sure there are times when we just need to show kids or tell kids a piece of the puzzle but for too long we have done that with the whole puzzle and they do not have the option to see anything but the finished picture.