Basic algebra involving fractions and decimals stumped a group of City University of New York freshmen - suggesting city schools aren't preparing them, a CUNY report shows.
"These results are shocking," said City College Prof. Stanley Ocken, who co-wrote the report on CUNY kids' skills. "They show that a disturbing proportion of New York City high school graduates lack basic skills."
Welcome to the fight Professor Stanley.
P.S. You really should get out more!
Indeed! Welcome.
ReplyDeleteI've tested a sample of our 7th and 8th grade kids with a very basic addition test...
Single digits only, using digits 3 to 9. Mastery is defined as no more than 1 error and 6 secs per answer.
Under this rule only 40% of my kids have 'mastered' single digit addition.
Even more shocking, 15% gave up (28 problem set) without finishing. It was "too hard"
I devised a similar test for double digit addition with 9 seconds average time to answer and found 40% 'mastered' with 20% giving up.
BTW: These are Investigations kids. Hmmmmmm
Don't blame Stanley. He has been a national leader in this fight for a long time. I love his writings on the subject.
ReplyDeleteIt would be interesting to see how this article came about in the first place. Unfortunately, the general reaction to this article is "duh!", as if this is supposed to something new.
Maybe this kind of article needs to be done every so often for those new to the problem, but I'm not sure how much it will help. It would be better to actually see all of the problems and results.
"Only a third could convert a fraction into a decimal."
Of course this isn't algebra, but I would blame the journalists. It just makes me (once again) second guess everything I read in the paper. It's the Murray Gell-Mann Amnesia effect.
So the question is how do you get schools to enforce mastery of the basics when they really don't want to do that? Even EveryDay math wants kids to master these basics. Their problem is that they tell schools and teachers that the spiral will take care of it. Schools know that this doesn't happen. Teachers see kids who are bright enough to master the material, but don't. We're talking about K-6 skills that can be mastered at school with no expectations of help at home.
ReplyDeleteWhy isn't it happening?
As best that I can tell, many of our lower school teachers really believe in some sort of natural learning process; that kids will learn when they are ready. The kids are then gone and they never see the results of their (in-)actions. When they get to fifth grade, teachers might see students who are capable, but they don't have the time to remediate all of the problems.
Don't K-6 schools ever have meetings where they talk about how to ensure mastery of the basics? I'm not talking about doing long division by hand. Are schools incapable of solving this problem, do they not think that it's a problem, or does everyone pass the buck?
"I devised a similar test for double digit addition with 9 seconds average time to answer and found 40% 'mastered' with 20% giving up."
ReplyDeleteI love this!
What would the reaction be at your school(s) if you tried to get the lower grades to meet this simple criteria? Is there any process for you to bring this up?
Schools are now jumping on the "balance" bandwagon, but is it just talk? Are they willing to calibrate what that means? If they don't do this sort of test, then what is their justification? What is their justification for passing kids to the next grade when they can't meet some minimal performance standard? Do they think they are doing these kids a favor? Do they assume that they have done all that they can for these kids? Do they have trouble with reality?
In my district, teachers are explicitly told *not* to teach the basics to mastery. They are *not* to provide any but the most superficial practice in learning the number facts, because all students are to use calculators for tests. It is in the curriculum that students do not need to know the math facts any more, and "rote" learning is not to be a focus of instructional time.
ReplyDeleteSome teachers do it anyway, some provide it as homework, and many parents buy workbooks or practice materials for their kids at the gorcery store. A few go to Kumon -- not many, due to cost (Kumon is cheap but most of our families are well below the poverty line even with several adults working).
Teachers that I talk to are unhappy about the situation -- most can see that kids *do* need some automaticity in the math facts (a fifth grade class I was in yesterday was doing a patterning activity and writing the rule for the pattern, and several kids could not see regular patterns that involved adding or subtracting by 2,3 or 5 -- they had to laboriously draw pictures for each step of each pattern).
So I suspect the reasons schools don't emphasize the basics may vary from place to place. We don't use Everyday Math (too expensive) but our curriculum is similar to EM expectations except it does NOT call for mastery of the math facts *or* learning either standard or non-standard algorithms "by heart."
I also noted, shades of Paul B's anecdote, that most could not do single-digit addition (of up to 4 digits) without a calculator. I showed several how to do it by "counting up" (got answer faster than with a calculator) and they were amazed that it was in fact easier. These were ones with some number sense but not automatic knowledge of addition facts.
First off, I just have to say that too much generalizing leads to over simplification which tends to pinch off thinking. Statements like 'schools do xyz' or teachers 'are abc' are way off the mark. Schools aren't monoliths and teachers aren't a bunch of lemmings marching to the same drum.
ReplyDeleteThe reasons for lack of mastery are pervasive, wide spread, and not immediately obvious. In my district, for example, there are certainly lemmings but there are also courageous, independent thinkers who buck the system every day to do what they think is right for their kids.
In this specific example of addition (not an anecdote) I can tell you that I was way off the reservation when administering this test and I'll be way off the reservation in my remediation. I can also relate (because I checked) that the elementary school these kids came from (which is in my building) has teachers that DO go for mastery (also off the reservation). In fact, their 'test' for mastery is more rigourous than mine. Their criteria is 100 problems, with 1 error in 5 minutes, 3 seconds per problem.
So you might be perplexed as to why their kids get to 7th grade and can't do it anymore. Simple. It's not the same kids. We have >30% turnover in student body every year. In any given year, the kids I get in 7th grade are comprised of something like a third that have been with us since Kindergarten. This cohort is predominantly on or above grade level.
The balance are a mixed bag; in and out of our district, in and out of our state, and in and out of the mainland. I have kids whose cumulative records (grade 7) contain 12 different schools. We have kids in families with 4 siblings and the cumulative record shows 5 different surnames (mom and 4 dads). It's problematic to look at achievement data at too high a level because in some data slices for our system you could easily 'prove' that our kids are getting dumber every year. You'd be wrong!
The truth lies in the weeds more often than not and decision makers, at all levels from building to White House, have a tendency to look at aggregated 'achievement' data that makes the weeds look like the greens at Augusta.
This is precisely why top down, centralized control of anything is doomed to failure. The devil's in the details and the confluence of mandated standards, high stakes testing, misguided curricula, teacher quality disparities, chicken management, and child mobility provide the fertile ground for healthy weeds.
I'm not trying to defend the status quo. There are plenty of hacks to pick away at but a true and lasting solution to these things has to acknowledge the breadth and depth of the problem, then attack it comprehensively. Anything less runs the risk of creating one more silver bullet in an already bristling magazine.
"...has to acknowledge the breadth and depth of the problem, then attack it comprehensively."
ReplyDeleteComprehensively could be interpreted in different ways. I look for solutions that are not top-down (comprehensive?). I look for a mechanism or a process. One of those is school choice. Another is state standards, but I'm not too hopeful on that front. We discuss pedagogy, content and skills on KTM, but I expect that has more effect on parents than schools.
I'm not looking for the big solution. I'm looking for getting individual kids out right now. It's easier, and they will show the way.
THANKS FOR GETTING THIS UP!!!!
ReplyDeleteAnother item languishing on my to-do list.
Stanley Ocken's been part of the math wars forever, hasn't he?
Wasn't he part of the original NY City Hold group?