Algebra for all: A dumbing-down of U.S. math classes that hurt the most elite students
Jacob Vigdor, a professor of public policy and economics at Duke University, wrote an interesting essay earlier this year challenging the conventional wisdom about school discipline. It led to a lot of discussion here on the blog
I suspect we will see a lot discussion around his latest report about U.S. math instruction. In a report for the American Enterprise Institute, Vigdor explains what has gone amiss with American math education.
In a recent essay based on his research — “Does Your Job Really Require Algebra ?“ — Vigdor writes:
Unfortunately, the misguided transformation of algebra into a course for the masses has proven to be a cure worse than the disease. The transformation has resulted in a less rigorous course. Introductory textbooks have slimmed down considerably over the past century, omitting some subjects entirely. The primary victims of this dumbing-down are the elite students themselves.
Among the most recent cohorts of college graduates, the proportion of male students majoring in math-intensive subjects has continued to hover in the 20 percent range. If we compare this to the historical 30 percent rate of two generations ago, we lose about 100,000 mathematicians, scientists and engineers every year — enough to replace every American employee of both Microsoft and Google and still have tens of thousands to spare.
Among the questions in his report: Can we really think of an algebra course offered to every eighth grade student as the intellectual equivalent of a course that was offered only to the top quarter of students, typically in tenth grade or later, sixty years ago? (His answer is “no.”)
A highlight from the report:
The new-math movement may have succeeded in raising the bar, but students reacted by giving up rather than attempting to clear it. The implementation of new math in the 1950s associates with the marked decline in math-intensive majors: the birth cohorts of the late 1940s and early 1950s would have been exposed to this curriculum during their primary or secondary years.
Given that the substitution of rigor for practicality appears to have turned students off to math, it stands to reason that substitution in the reverse direction would undo the effect. And indeed, the wane of the new-math movement in the late 1960s and early 1970s helps to explain the resurgence of interest in math-intensive majors — the only such episode observed over a period of seventy-five years — among cohorts born in the late 1950s to early 1960s.
The resurgence was short-lived. From the 1962 birth cohort onward, the proportion of college graduates completing math-intensive majors dropped steadily. As we move forward from the 1962 birth cohort, we encounter students who spent a more significant proportion of their primary and secondary years in the 1980s, a decade when American policymakers focused increasingly on improving the performance of average students while not worrying much about those at the top.
Here is the AIE summary of Vigdor’s report, but try to read the full report:
Too Much Too Soon for Too Many: Accelerating students in algebra and other advanced math courses does not always improve their math performance. In the Charlotte-Mecklenburg Schools, students who took algebra early scored thirteen percentile points lower on a standardized end-of-course test than students who took algebra on a regular schedule, and accelerated students were less likely to pass an end-of-course test in geometry.
Dumbing Down Classes Hurts Strong Students: Attempts to close the achievement gap by reducing the rigor of math education have meant fewer top performers are equipped to pursue math careers; the past thirty years have witnessed a twenty-point increase in aveage math SAT scores but a 25 percent drop in the proportion of college students who major in math-intensive subjects.
Different Students Need Different Courses: American students are not all the same, and a rational strategy to improve math performance must begin with a willingness to meet different students’ needs rather than a single-minded focus on having all students taking the same classes.
The report’s conclusions include:
- For several decades, the United States has counteracted its decline in math in part by importing highly talented immigrants. American immigration policy prioritizes family reunification over skills, in direct contrast with peer nations such as Australia and Canada. Any attempt at immigration reform should address this issue.
- Curricular fads such as Singapore math hold promise in many circles but may not be readily adaptable to American cultural and educational settings. Experimentation is warranted, but we must be mindful that the net effect of our past curricular tinkering has been negative.
- Pursuing equity in curriculum must harm some students, and evidence suggests that some past reforms have managed to harm all of them. American students are heterogeneous, and a rational strategy to improve math performance must begin with that premise.
–From Maureen Downey, for the AJC Get Schooled blog
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85 comments Add your comment
Chuntter
August 20th, 2012
4:02 pm
LUCKILY for us, RACE-BAITER Bernie is CONSTANTLY on hand to DEMONSTRATE the IDIOCY of expecting EACH and every reader to add SOMETHING INTELLIGENT to the debate—BEYOND smears and what he CHILDISHLY thinks passes for mature discourse …
… in the creepy world Bernie has CREATED for himself living in his MOTHER’S BASEMENT !
Teacher, Too
August 20th, 2012
4:02 pm
Thanks, Devil’s Ad… I forgot about the parentheses. That’s what happens when you’ve been an English teacher for 23 years- you forget about the little things that cause mistakes to occur.
Devil's Advocate
August 20th, 2012
4:23 pm
No problem!
HoneyFern School
August 20th, 2012
4:27 pm
Please excuse my dear Aunt Sally….
Parentheses, exponents, multiply, divide, add, subtract.
Mountain Man
August 20th, 2012
4:28 pm
I had to go back and look it up again – MY Dear Aunt Sally is not totally right – addition and subtraction are equal, just as multiplication and division are equal. The correct answer is 7.
Mountain Man
August 20th, 2012
4:29 pm
My head hurts now – would everyone please put parentheses so there is no question about what comes first!
HoneyFern School
August 20th, 2012
4:30 pm
1. Limping dreadfully, King Phillip came over from great Spain.
Life, domain, kingdom, phyllum, class, order, family, species.
2. My very elegant mother just served us nachos (or “nine pizzas” for those raised before the 90s)
Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune (Pluto)
Homework time…just a few mnemonics to help…
HoneyFern School
August 20th, 2012
4:31 pm
For math, complete the first part (parentheses and exponents), then move left to right for the others.
Hillbilly D
August 20th, 2012
4:33 pm
I think there is an object lesson in the problem that’s been discussed:
Solve: 6-1×0+2/2
In my opinion, that lesson is that lots of us knew how to do it at one time but most us haven’t needed to know that for a long time, so we’ve forgotten. However, most of us who forgot, do know how to look it up and find out how to solve it. That’s the true lesson, knowing how to find what you need to know.
A friend of mine, who is a Tech grad, said he once had a professor who said that you don’t need to know all the formulas, etc, you just need to know where to find them, if you do need them. A lot of wisdom in that, I think.
Ashley
August 20th, 2012
5:13 pm
I entered high school in 1972 as a 9th grader , my choices in math were General Math, Pre-Algebra, or Algebra 1. I had already taken Algebra1 as an 8th grader, so Geometry was my next course of action. What I’m getting at is only a select few 8th graders took Algebra in 1971. Forward the clock 40 years later and we are still having a discussion about Algebra and when it should be taught, somewhere in the back of my mind I’m thinking that if I took Algebra in the 8th grade it shouldn’t be a stretch for students to take it before they reached high school . General math should always be on the table, but isn’t education about enriching the mine and getting the very best from said student, what harm does it do to take advance math in middle school? I really don’t see a downside , we shouldn’t be in the business of dumbing students down just the opposite.
Devil's Advocate
August 20th, 2012
5:13 pm
Hillbilly D,
Google ftw! Students today don’t know how good they’ve got it. I remember the days of getting info out of outdated encyclopedias and even print journals (outdated by today’s standards unless you were doing a report on a current event) to write reports.
Pride and Joy
August 20th, 2012
5:21 pm
Hillbilly D, I loved your comment that “All those years ago when I was in school, my algebra teacher told us that “algebra is nothing more than finding the unknown”.
That’s how I tutored my cousin in algebra. I explained it to like this — Remember second grade math? 2 + ____ = 4 as in “two plus blank equals four?”
She could do the math and correctly answered the question. I told her she’d just “done algebra”.
The same equation could be written as “2+X=4″.
Finding the unknown — exactly or — just fill in the blank.
Old Physics Teacher
August 20th, 2012
5:33 pm
I couldn’t find the math question on Facebook, BUT the answer is “multiple answers.” All of the answers presented are equally correct because parentheses AREN’T EXPLICIT. Work it on a calculator/computer as shown. The calculator will show “1,” as the calculator uses order of operations as the problem develops: 6-1 = 5. The next process is “times zero.” The calculator now shows “0.” +2/2, which equals one. And everyone knows “zero plus one = 1.” Anyone writing this type of problem is just asking for trouble AND IS ATTEMPTING TO SCREW YOU UP AND PROVE WHAT A SMART PERSON THEY ARE. You can elect to get in an argument with them, or ignore their smartness and go your own way.
Old Physics Teacher
August 20th, 2012
5:50 pm
Now that I got that out of my system, the author of the article is spot-on. Yes, I use algebra each and every day. I’m a science teacher. I used to be a business manager. I NEVER USED ANY MATH HIGHER THAN PRE-ALGEBRA. Most of the comments on here about algebra use, doesn’t concern algebra. It’s simple business math – percentages, percent profit, mark-up, margin, and others. That’s not algebra. Algebra is:”Matt has two times what Martha has. Martha has 3 times plus 15% of George… etc, etc, etc.” Two or more variables are in transition. All numbers and one variable means pre-algebra at best. Percentages is a business math class and not even taught by the math department as they are few and far between and need to teach real algebra, geometry, trig, and if your county is large enough – calculus.
This idioticy of “You need a good education to get a good job,” because guys with good educations make a lot of money is a stupid as:
Football players make big, BIG money. “Everyone needs to play football so they can make a lot of money.” If someone (politicians or teachers) said this, they’d be run out of town on a rail because only a very few people are large enough, fast enough, and have the attributes of professional footbal players. No one ever mentions that the more people who have a trait or apptitude for a job, the lower that job pays. No one pays somebody a lot of money for something that is easy ; see janitor, dishwasher.
On the other hand smart people generally get paid quite well. If they don’t, they move on and put themselves on the open market and get businesses to bid for them. That’s because they’re smart — not educated!
Jerry Eads
August 20th, 2012
6:41 pm
“Dumbing down” has been going on a long time. I recently for fun re-read Robert A. Heinlein’s 1958 “Have Space Suit – Will Travel” in which he repeatedly jabs at the lack of rigor of an off-the-beaten-path high school. (I could cite a bunch of history but this was more fun.)
Jabs aside, there are a number of reasons for the “dumbing down” of algebra. Certainly the HUGE push to offer it in middle school had its impact.
But let’s not forget my beaten unfortunately still not to death and no I won’t stop minimum competency program which, of course, REQUIRES ALGEBRA TESTING.
Granted, relatively few kids take it and roughly 70% of the kids fail it, or at least did three years ago (the latest data on the state website – really? it takes 3 years to put that together?), but if you’re going to beat teachers and principals and superintendents with a stick and on top of that keep stealing resources – including class days through furloughs, these folks are simply responding to what YOU demanded – pass rates on a test.
In the absence of adequate resources, there just aren’t many ways to increase pass rates except to focus on those who MIGHT pass it if the teacher spends all his or her time with them and not the “smart kids” who will pass the test anyway – or the less able or motivated ones who likely won’t pass it no matter what.
And why do we have minimum competency testing? We have “STANDARDS” which are (again) just dandy for fitting car doors to fenders but not for fitting kids to algebra. Schools shouldn’t be factories, and kids aren’t one size fits all. You want better math performance? Elect state representatives who will change the law so John Barge can get rid of minimum competency testing so teachers can at long last go back to teaching everyone to the best of their capacity.
Devil's Advocate
August 20th, 2012
6:45 pm
Old Physics Teacher,
Not trying to be “smart” but every calculator functions based on algorithms programmed by human beings. They are not flawless or the authority on math operations. Based on your statement that the calculator applies the order of operations as the problem develops, that implies grouping is occurring from left to right without considering the entire statement. The only way a problem can “develop” as you put it is based on sequential input from the user.
6-1×0+2/2
is different than
((((6-1)×0)+2)/2)
The latter would be the grouping if the calculator took the expression “as it develops” because it would be working from left to right and basically ignoring the order of operations (starting from the inner most parenthesis and working outwards, ultimately left to right).
If you are using Windows 7, you can launch your calculator and put it in Programming mode then enter the statement and it will give you 7 because it takes the entire statement and applies the order of operations as you would do it on paper following mathematical principles. Other modes may give other answers depending on if the calculation algorithm updates each operation as given (which a lot of basic calculators do). The calculator’s algorithm is likely taking the first operation it sees, generating an answer, then feeding it to the next operation until complete. The order of operations does not apply in this case because each operation is being evaluated as given. The second example I provided shows this as a full statement.
Take the calculator out of the scenario and solve based on mathematical principles.
Hillbilly D
August 20th, 2012
6:48 pm
That’s because they’re smart — not educated!
That’s an important distinction. Some folks are smart; some folks are educated; some folks are both and some folks are neither.
Ole Guy
August 20th, 2012
7:22 pm
Let’s do away, if we may, with the tired ole justifications for studying algebra, trig, or any of the mysterious disciplines which the education community, in all their wisdom, seems intent on dumbing down, to the point of oblivian, anything which posses the least difficulty for these young folks who have never known true challenge; have never known the joys of victory in overcoming anything but the simplest of goals. Similarly, let’s stop trying to find applications in our daily lives where algebra may have actual applicability.
The simplest, yet most-impelling reason for studing these things lies in mans’ most-basic need…Maslow spells this out quite well: THE NEED TO BE OF SOME USE. While we are quick to complain over jobless rates, unemployment, and the “woe is me” attitudes many have developed, we tend to ignore a few basic facts about this economy: 1) there ARE jobs out there’ maybe not a lot of jobs, but they are there 2) these jobs, the good ones which have the propensity to ultimatly demand anything near a living wage, REQUIRE EDUCATION.
And that, children…boys and girls…is the best reason to take algebra; to challenge yourselves beyond your self-imposed comfort zones. Don’t stop at algebra, nor at those “stepping stone” disciplines. Keeping yourselves, and maybe, someday, you will have a job which you can be proud of; one which just may allow you to reach Maslow’s level of self-fullfillment; I believe he refered to it as self-actualization. Your alternative is to face the very real prospect of a bleak, drab life.
Is that a good-enough reason to study algebra?
Ashley
August 20th, 2012
8:02 pm
@Ole Guy 7:22……Amen!
Bernie
August 20th, 2012
10:02 pm
MiltonMan @ 1:35 pm – Sounds like a personal issue to ME! Try being BLACK MAN in a White world then come and share you problems with ME!
YALLOweMe
August 20th, 2012
10:36 pm
Most people on this board aren’t qualified to talk about algebra.
Ed Johnson
August 20th, 2012
10:39 pm
“Some people are way better with words than numbers. The human brain is just wired differently for some folks.”
It’s called “variation,” and Mother Nature is a wonderful, awe-inspiring master at producing it!
But then we come along and flub it by calling it “diversity.”
Pride and Joy
August 21st, 2012
1:45 pm
HOney Fern School, love your devices…I think you forgot the g in great spain. YOu wrote “1. Limping dreadfully, King Phillip came over from great Spain.
Life, domain, kingdom, phyllum, class, order, family, species
G is for genus and then species, perhaps?
Pride and Joy
August 21st, 2012
2:55 pm
Bernie, black or white, you’re still a man. Try being a woman fora while. Try doing anything in a burqa.
HS Math Teacher
August 21st, 2012
2:57 pm
Isn’t it nice when research catches up with common sense? However, no one at the helm of our educational ship is listening. They know more than us peons in the field.
Pride and Joy
August 21st, 2012
3:32 pm
To Ole Guy — here’s one reason that hasn’t been mentioned: math and algebra teach a person to think logically and problem solve.
I was in a meeting one day and my manager was upset over a travel schedule. He couldn’t get all the right trainers and employees together and have them all trained before the deadline. I sat in a room of eight trying to work it out. I figured it out, logically and a calmly, just like math.
Math and algebra teach us to think about all the variables in a problem and to solve them logically.
Old Physics Teacher
August 21st, 2012
5:12 pm
Devil’s Advocate,You’ve probably gone on the the next topic, but I thought I’d answer anyway.
No, I don’t think you’re trying to be smart. I agree with everything you say. However, it is poor item design to ask that specific question. Why would anyone multiply by zero? The only possible answer would be to try to “trick” the examinee into missing the question. According to my course in item design many, many, many years ago when the earth was without form or void, you should simply ask the question to the student, “What are the rules for mathematical operation as to which type of calculation should be used in what order?” Or as my instructor put it bluntly, “Ask what you want to know! Don’t try to be cute! Just ask the %$#$# question!” This guy didn’t. If I was asked the question, I would have simply turned the exam back in and asked the instructor to put in parentheses and I would be glad to do the calculation.
And speaking of doing this in programming mode, you would never write code like this anyway. You would put explicit parentheses in the calculation due to the constraints of the problem you were performing based on the potential variables of the specific problem. You would NEVER ask a calculating machine (computer/software program, or calculator) to multiply by zero. You already know what the result would be and would skip that variable and continue on. As you know, every extraneous line of code raises the possibility of human error creeping in.
It was obvious the “item writer” was being “cute” trying to show he/she knew more than everybody else about the Please Excuse My Dear Aunt Sally. As Robert Heinlein once said, “These type of people should be beaten until they apologize.”
Old Physics Teacher
August 21st, 2012
5:17 pm
Pride and Joy,
Did you realize that even if “the boss” couldn’t figure out the answer, he still was the boss and made more money than you? He didn’t know how to do the math AND HE WAS STILL THE BOSS. He had you figure it out. Obviously, some one decided that skill wasn’t necessary for his job. And as he had you to do that, he didn’t need to?
I’m not trying to make fun of you, HONEST! I have a lot of respect for people who do math. I’M ONE OF YOU. I’m not quite sure my superintendent can chew chewing gum and walk at the same time, but the BOE hired him knowing his limitations. Just saying that everybody doesn’t need to know algebra!
@Math Teachers
August 21st, 2012
8:57 pm
Can anyone tell me exactly what the difference between Math I / II / III and CC Coordinate Algebra / Analytic Geometry / Advanced Algebra is?
I know that some math teachers on this blog keep saying that CC is integrated, just as Math I/II/III was. How is it different?
Thank you.
A Parent
Ole Guy
August 21st, 2012
10:56 pm
Pride…you are absolutely correct. At the “fear” of appearing ole fashioned and out of touch with the the problems and issues (ostensibly) “unique” to the current gen, the primary point I am trying to convey is simply this: There is (or should be) no law which dictates that everything we are obliged to assimilate within the educational process has to be fun nor completely understood as to the reason we expend our energies in mastering. If, through the process of exploring new-found challenges (academic or otherwise), we find joy in fun and new forms of mental discipline, well and good. The entire arguement here seems to center on the notion that before one takes the time to tackle “new stuff”, one must have a good reason to do so. While this may seem like a “nice” concept, the harsh reality remains: LIFE’S CHALLENGES…THE ONES WORTHWHILE…ARE A SINK OR SWIM PROPOSITION. You either hack it, or pack it/you either get accostomed to facing, head-on, life’s tough challenges, or…you lose. It’s that simple.
Your arguement, while justified and right on target, is, to be perfectly frank and honest, is preaching to the choir. If the kid can :dig” this reasoning…great!
N. GA Teacher
August 22nd, 2012
12:01 am
As a math teacher, I see mostly dead-on comments here. Public school state depts. STILL refuse to accept that putting all 9th, 10th, 11th graders, etc. into the same math classes is incorrect. They are so caught up in the current Chicken Little “U.S. math knowledge level is falling” that good educational theory and common sense has left the building. Some 9th graders can handle very advanced math, even precalculus, while many 11th graders can’t add or subtract without a calculator, or do fractions or pecentages (the latter stuns my adult nonteacher baby boom friends but welcome to reality). Math teaching is a fulfiilling career; what is NOT fulfilling is not serving our students properly by treating them as square pegs to be driven through round holes. The leaders of state education offices must rethink what a “diploma” means and realize each child’s potential instead of desperately scrambling to eke out homogeneous, mass-market diplomas that say every kid has kid has 4 credits (notice I did NOT say “mastered” or “earned”) in math, science, English, etc. I cannot tell you how much better off we would be with a much more flexible curriculum that developed kid’s strengths instead of numbed them to a “common core”.
HS Math Teacher
August 22nd, 2012
7:37 am
@Math Teachers (above): Simply put, there’s not a lot of difference between the Math I, II, III, IV, and what I thought was going to be separate (”discreet” … used loosely – as the State calls it) units. There’s still some blending of Algebra, Statistics, and Geometry. The GPS Geometry, for example, is indeed mostly Geometry, but about 35% of it is Algebra, Probability & Statistics.
Pride and Joy
August 22nd, 2012
4:39 pm
To Old Physics teacher, you wrote ” He didn’t know how to do the math AND HE WAS STILL THE BOSS. He had you figure it out. Obviously, some one decided that skill wasn’t necessary for his job. And as he had you to do that, he didn’t need to?”
It wasn’t math I used, it was logical reasoning, reasoning that is learned from practicing math.
I am certain my manager could have thought of the answer himself if he’d wanted to but it was an urgent time and he needed an answer fast — or else we would have had our budget cut and would have lost our jobs. So he did what I would have done — he quickly assembled his staff of people he hand-selected to work for him, knowing that “two heads are better than one.”
He wasn’t, as you might have inferred, lazy and dumb and overpaid and delegated to a subordinate what he could have done himself. He is brilliant and honest and he’s one of the best persons I’ve ever worked for and because of him and the flexibility and encouragement he gave me, I am successful now. I owe him a lot of gratitude. I’m sorry I gave you the wrong impression.
Pride and Joy
August 22nd, 2012
4:49 pm
Old Physics Teacher — you said “Just saying that everybody doesn’t need to know algebra!”
I respectfully disagree. I use algebra in everyday life. I also use the effects of algebra in everday life — by that I mean logical reasoning, something that is practiced in algebra.
Specifically,
Identify all the variables in a problem.
Assemble all the variables in a logical sequence.
Then solve the problem.
I use the benefits of algebra when doing mundane chores such as determining car pool schedules, consignment sale budgets, determining weight loss factors and organizing my family’s budget. You know, mom stuff. Stuff we do everyday.
I can always tell which moms know math and which moms have little math experience by ordinary things such as fundraisers for the PTA.
Those who are educated and experienced in math make excellent PTA leaders. Those who don’t often derail a process.
Let me give you an example.
At a consigment sale one mom didn’t want us to charge non-member customers a $5 entry fee to shop the sale early citing it would only bring in an extra $400 per sale. What she didn’t understand is that $400 was pure profit. We would have had to sell tens of thousands of dollars in merchandise to get $400 in profit. I used algebra to show her and others just how much merchandise we would have had to sell in order to realize a $400 profit.
An everyday situation that I used basic algebra to solve.
Algebra is for everyone.
Your wife uses it everyday. You just don’t realize it.
HoneyFern School
August 23rd, 2012
7:57 am
Pride and Joy, yup. Skipped genus. Threw everything off!!!
Thanks.