Several years ago, Grumpy Old Teacher (GOT) took a MOOC provided by Stanford University’s Jo Boaler in which she presented ideas about better maths teaching in schools. That’s not a typo, Dr. Boaler is British and they pronounce the subject with an ‘s’ on the end.

GOT is a math teacher and one of the lessons has stuck with him; the one in which Dr. Boaler described a public high school classroom where students were learning by discovery. Observers and visitors could hear the excited buzz pouring out of the room as they came to find out what was happening.

There was only one problem. Parents and others who said, “This is not how I learned math and so no one else should either!”

Sigh.

It wouldn’t help, GOT supposes, to tell you that this is what the Common Core developers have in mind. By now, the phrase ‘Common Core’ is a ringing bell that causes everyone to drool in response, usually a response that involves a lot of growling, snarling, barking, and snapping at the nearest flesh-bearing human.

But the American approach is one that is over a hundred years old, one that Charles Elliot, president of Harvard University, specified. Thereafter, American high school students studied mathematics branch by branch, year after year, as distinct and separated bodies of knowledge, rather than as an integrated academic discipline.

The world did not follow. The international approach to maths (the ‘s’ intentionally applied to the word) is the integrated approach. Each year, students study all branches of mathematics as they acquire knowledge and skill.

A state deciding to reorganize math courses is not radical or new. It is different and that is all it takes for the snarling, growling, and snapping to begin.

“How are the advanced students supposed to take advanced courses?”

First, students are not as advanced as everyone thinks. If you take a hard look at math curriculum under the Common Core (and yes, most of America still follows it however the individual state attempted to rebrand it), you see that students redo most of Algebra 1 in Algebra 2 because …. we really need a drum roll here … Common Core shoved Algebra 2 into Algebra 1.

What happened to Algebra 1? It got shoved into Pre-Algebra, the course most students skip over as they are accelerated into Algebra 1 in middle school.

When ninth grade Algebra 2 students show up in GOT’s classroom, most of them are in desperate need of remediation. They missed a lot because they were plopped into Algebra 1 in seventh grade! No wonder these students tell GOT they never understood what everyone assumes they know.

What about Geometry? Ninth grade students taking that class were also skipped over Pre-Algebra. They found a way through the Algebra 2 disguised as Algebra 1 course, but they never learned how to write linear equations, determine the slope of a graphed line, Pythagorean Theorem, simplifying radicals (square roots), or basic transformations.

And yet students and teachers are faced with a demanding curriculum that assumes that these Geometry students arrive in high school with that knowledge that they were never taught!

Part One.

“First, [math] students are not as advanced as everyone thinks.”

BINGO!

Students are accelerated way too early in math as it is usually determined by the end of 6th grade (age 11). Top math students have no better understanding of number sense or application, they simply attend daily, pay better attention, follow orders of operation better, faster brain development, and were lucky enough to have no learning disabilities. I have talked to countess students who all say something to the effect of, “I didn’t really get math until 10th grade.” Skipping pre-algebra is a bad trade-off that allows them to take calculus by grade 12. Scope and sequence of math instruction should be “semestered” allowing for a more sensible progression; grades 7 through 12 would allow for 12 specialized math classes. This would also provide weaker math students with numerous fresh academic starts, maintaining hope for success as brain development improves.

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