Saturday, May 30, 2015

This Is How The Common Core Adherents *Want* Us To Teach Math In The US

From Canada's National Post:
Canadian students’ math skills have been on a decade-long decline because rote learning was replaced by discovery-based methods that promoted multiple strategies and estimations, according to a new report that calls for a return to tradition.

“You know what’s the worst kind of instruction? The kind of instruction that makes kids feel stupid.

And that’s what a lot of that discovery stuff does; their working memory gets overloaded, they’re confused. That’s bad instruction,” said Anna Stokke, an associate professor in the University of Winnipeg’s department of mathematics and statistics, who wrote the C.D. Howe Institute report.

The report draws on results from national and provincial tests as well as an OECD assessment performed every three years in more than 60 countries that measures how well 15-year-olds can apply skills in reading, math and science to real life situations.

Canada fell out of the top 10 countries for math in 2012...

The report puts a good deal of the blame on discovery or experimental learning approaches that encourage students to explore different ways to solve math problems instead of using a single standard algorithm and often promote concrete tools such as drawing pictures, or using blocks or tiles to represent math concepts. The idea is students will gain a deeper understanding of math and be better equipped to apply it to a variety of situations.

What really happens, though, says the report, is students’ working memories get overwhelmed if they don’t know their times tables and can’t quickly put a standard algorithm to work to solve a more complex problem, both features of what’s known as “direct instruction.” Key operations, such as addition and subtraction of fractions, are overly delayed until the middle school years, just as students need that facility to tackle algebra.

Such concepts should be introduced earlier, says the report. And while it stops short of throwing discovery learning out completely, it says the curriculum balance should be tilted in favour of direct instructional methods, recommending an 80/20 split as a rule of thumb.
Yes, yes, yes!

Remember when so-called Whole Language was pushed in the 90's, and it was hyped as the latest and greatest thing out of New Zealand?  Are we always a day late and a dollar short in education in this country?


Auntie Ann said...


pseudotsuga said...

I am surprised they figured this out...better late than never,I guess.
But yes--this is exactly the problem with my daughter's elementary school math: if she doesn't know her times tables or the quick algorithm to do a problem, then she can't just do the problem. The focus becomes meta-mathematics rather than solving problems.

maxutils said...

You know how much I hate Common Core, and the new math program it has befot … which, literally drops my son1-2 grade levels back and virtually eliminates geometry. I've taken to calling it 'retard' math. Not because of the stdens but because, literally, the math program has been slowed down, or retarded. But, fortunately, thanks to whole language, most people don't know it actually has a non offensive meaning … so when I go to back to school night, and ask my son's mathteacher "How's your retarded math program going?" I will be both factually correct, and stilkl furious that the district's math teaches didn't stand up against it's implementation, and it will be super fun to watch the teacher attempt to wiggle out of the question … (you have been warned. :) )

That said, though … your fascination with algorithms and rote methodology also alarms me … less so, but still. To me, there are three levels of math teaching: rote, socratic, and discovery. In my opinion -- rote is the preferred tactic only when there is no better way. Discover a times table? Probably not, although if they have to fill out one to understand where it came from, sure. Long division? Absolutely. To teach the reasoning to third graders would be an impossibility. Discovery learning is great --IF you have a really good activity that is sufficiently guided that the students are virtually guaranteed not to fail. I know you don't teach geometry or calculus, but there are at least a few group/discovery tings that work really well there. Your pre-cal/alg 2 …not so much. But then, there's a middle ground: the Socratic method. It's great to learn the algorithm, or just the rule that will work …but it's even better if the students know whwere it came from and why it works. And if you ask quest ions, and don't put people on the spot, and make sure they know you're not going to make them look stupid for not being able to answer a question that they reasonably have no way of knowing? Magic happens. It takes patience, but if you structure your questions from broad intent to narrow rule, and wait for them to think? The smarter kids usually get in quickest; but you don't always call on them. Just hang out. And everynow and then, one of the less intelligent ones will stun you with the answer, or something new …and I guarantee, that student's day was just made. So it's balance.

The problem with Common Core, like with whole Language, is that it's all or nothing. Getting the student involved more is really important. But having them read stuff and saying "It's fine … I'm sure they'll learn grammar on their own" is just lazy … Frankly, I haven't seen that in the CC materials for math --what I have seen is a substantial reduction in what we expect them to know --which, I thought, was the opposite of the intent.

Ellen K said...

I remember Whole Language far too well. My youngest son and his peers were victims. With similar IQ's, family background and encouragement in the three years between my oldest son and my youngest, reading programs embraced Whole Language and doomed far too many kids to puzzle out shapes of words over truly decoding them. Instead of phonics and spelling tests, they had jolly romps with word shapes. My son, a dyslexic, was already struggling in kindergarten. He could not see the difference between sit, sat, and set. Yet he could ascertain the "shape" of the word aquarium. We tried outside tutors, reading at home and countless fixes to no avail. Finally, in third grade with high stakes testing on the offing, the school got concerned. They tried to force feed various reading solutions which changed with each teacher and aide. My son, a very affable, verbal and pleasant kid became sullen and resentful as his failures were blamed on lack of effort while every afternoon was full of tutoring. He lingered in the special ed classes for reading and math until his sophomore year. He graduated under the recommended plan (albeit without foreign language) but not without learning to hate school. And he was not alone. This was 2002 when special ed students began to skyrocket in numbers. Most of those students were sent to SpEd for reading problems. Any wonder why? What's ironic is as an adult this son-who has struggled with personal issues-has become the best compensated and more reliable of my three kids. And for all those parents of SpEd kids who think their kids will thrive in college, think again. My son was "counseled" by his SpEd college liaison and she put him in all the wrong classes, chewing through the money we had saved. He may go back to college someday-but he will do it on his terms and timetable.