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
1776
August 20th, 2012
12:13 pm
Lowering academic standards (for those who cannot make them) is a very poor course of action. This would apply to college admissions as well.
Attentive Parent/Invisible Serfs Collar
August 20th, 2012
12:23 pm
The actual Common Core implementation via career pathways for all, student achievement measured by SEL criteria, Positive School Climate, 21st century skills of the 4 C’s, learning communities that make social interaction the main point of high school, etc will make the dumbing down of Algebra for All and the GPS one curriculum for all with the difference being timing look mild.
What education would look like if you wanted to destroy the US’s future is an apt description.
And college gets redefined via Lumina’s Diploma Qualifications Protocol which USG adopted in November 2011.
How did you think they were planning on increasing those high school and college graduation rates?
Suck that content right out except for essential knowledge on issues like Climate Change where the intent is to manipulate the students politically for years.
“Just enough content knowledge” to be aware and alarmed.
Holly Jones
August 20th, 2012
12:26 pm
My husband is a consultant and his field requires very advanced computer skills (I don’t even pretend to know exactly what he does). The majority of the staff on his current project comes from India primarily because there aren’t enough Americans with the necessary math and computer skills.
In addition to the lack of math skills, there in another issue- lack of motivation. Mu husband has given seminars at Georgia Tech about how to interview for an internship with his company and 95% of the attendees are students from India and Asia. His comment to me after a spending a Saturday on campus doing these seminars was, “I guess the American kids didn’t think it was worth getting out of bed on a Saturday to find out how to get hired.” Not only have we lost our academic edge, we’ve lost the drive to be the best. The Indians that are new to the country, in my husband’s experience, will work much longer hours than Americans will. The interesting thing is that the longer employees from India are here, the less they work. They start to work “American” hours.
mountain man
August 20th, 2012
12:27 pm
Perhaps they need three levels of diploma – meets minimum standards, meets average standards, and meets honors standards.
Sort of like they have in college – you get a regular diploma if you complete the requirements. You add honors if you graduate with honors.
mountain man
August 20th, 2012
12:29 pm
Why are we worrying about advanced math when some graduates cannot read, write , and do simple arithmetic.
RJ
August 20th, 2012
12:34 pm
“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.”
I doubt that you’ll find any teacher that won’t say “duh” to this statement, yet we continue to have a one size fits all mentality in education.
mathmom
August 20th, 2012
12:34 pm
As a secondary math teacher, I can tell you that most math teachers already knew this…but it’s even worse than what is written in this article. NCLB meant that not only the elite students but almost all students were ignored as teachers tried to help the lowest performers cope with what quickly became a dumbed down curriculum…except here in Georgia. Here, we implemented a very demanding curriculum with the GPS and expected the lowest level students to perform at what used to be a fairly advanced level. We discovered quickly that the curriculum had to be dumbed down even more, and then even more, and… Our upper level students have been the biggest losers. Now the entire nation will be learning that lesson with the Common Core. It’s so sad.
Dumbing it down
August 20th, 2012
12:44 pm
Seems to me that the Democrats are constantly trying to dumb down education to make things more equal between people. More of the equal outcomes nonsense. This is NOT the way to go.
Another Math Teacher
August 20th, 2012
12:45 pm
mountain man: “Why are we worrying about advanced math when some graduates cannot read, write , and do simple arithmetic.”
Because the lower end kids can make a difference for themselves. The higher end kids can make a difference for everyone.
Bernie
August 20th, 2012
12:56 pm
Very interesting report and statistics presented. However, We are faced with (2) Two National Political Parties, namely The Republicans and Tea Party and their many supporters. Who have essentially, VOWED and with Great Intent to DISMANTLE and ABOLISH The U.S. DEPARTMENT OF EDUCATION.
That mindset in correlation with this report presents, a VERY STARK reality that the thinking of PEOPLE of this NATION do not care and are not seriously interested
in raising the MATH & SCIENCE achievement SKILLS of AMERICA’s CHILDREN. PERIOD!
Whereas, in other NATIONS around the WORLD with a majority of them with the poorest and uneducated populations. Are investing MORE and more of their National resources to improve the MATH & SCIENCE achievement SKILLS of Their CHILDREN.
One could easily determine there is something seriously WRONG and OFFENSIVE, in the thinking of these (2) NATIONAL Parties.
Especially, when it comes to America’s CHILDREN’S EDUCATION needs and requirements.
Ernest
August 20th, 2012
12:56 pm
I’m not sure of the overall discussion point but my opinion of offering Algebra to the masses in the eighth grade was a subtle attempt to find ‘diamonds in the rough’ for a possible STEM career. It was also an attempt to expose more children (especially women and minorities who were sometimes tracked into other areas such as humanities and vo-tech) to math to help them with logical reasoning and thinking. I see this as a good intention that has had some repercussions.
I’m a STEM grad and can admit I’m ‘wired’ different than many of my friends (mostly liberal arts backgrounds). We look at problems and solutions differently. I personally think this type of diversity is necessary.
I also want to agree with Holly’s comment above regarding her husband’s observations. We are the land of opportunity for many first generation immigrants however with each subsequent generation, there is more assimilation to our culture. In my observation, once there are 2-4 generations removed from the initial person that came to this country, many adopt the US culture. I believe there was a study on this also.
wanttohaveinput
August 20th, 2012
1:15 pm
No child left behind dumbed down education so the lower students and the kids that didn’t want to be there were not “left behind”. As a result, the high performing students were instead “left behind”.
Tony
August 20th, 2012
1:16 pm
Nearly every other country in the world requires students to complete the equivalent of algebra one by the end of eighth grade. In our country, we have been too quick to make excuses for why our children should not have to take algebra. Instead, we should all be holding our children to higher expectations and pushing them to do their best in all academic areas. The dumbing down that has occurred is more the result of parents’ low expectations than actual abilities of students.
Howard Finkelstein
August 20th, 2012
1:16 pm
Once we dilute the common standard enough the all these precious “little cargos” can then be deemed to be a “little genius.”
The only fair solution is to penalize those who appear to be more intelligent than the norm and subject them to a forced lobotomy.
William Casey
August 20th, 2012
1:16 pm
I understand the argument here but would frame it a little differently. Recent policies have hurt the “good” students rather than the “elite.” Elite guys are taking AP courses as soon as possible. Elite students can learn basic algebra on their own.
Math Optimist
August 20th, 2012
1:20 pm
People often throw out the concept of math being dumbed-down , but
the reality is that rigorous math courses have been pushed-down on
younger students.Most seventh grade students were not exposed to
finding the slope thirty years ago. Is the issue that not enough college
students have the sufficient background in math, or that many
businesses don’t want to pay for the expertise in math. Many experienced
engineers have been let go not because of their work ethic,or lack of
expertise,but because of financial pressures. About 59% of the
students taking the AP Calculus exam (national figures 2012)
passed with a score of three or higher. Many students are
progressing well in math. More optimism, and less student
bashing is needed to meet the challenges of the future.
Pride and Joy
August 20th, 2012
1:28 pm
We don’t have to make algebra dumber for all. We simply need to offer regular placement and advanced algebra to meet both needs.
YES we need algebra. Yes, I use algebra in my job. Yes, I use algebra in my life every week.
I sold my kids’ clothes at a consignment sale and used algebra. I wanted to earn $500. The commissions paid to the consigor are 30%. If I want to earn $500 at the sale, how much total revenue do I need to sell in order to earn $500?
That’s algebra in everyday life.
If I need to save $2,500 to pay for a vacation at the beach during Spring Break, how much money should I save from my bi-monthly paycheck ? That’s algebra in everyday life.
Telling students they don’t need to learn algebra is a lie perpetuated by those who either want to keep the poor people poor or for those who don’t understand basic algebra themselves.
Attentive Parent/Invisible Serfs Collar
August 20th, 2012
1:29 pm
Howard-the forced lobotomy is being subjected to a chorus of “Are You an IB Learner?” for years at a time.
One of the reasons the Fulton Super gave me the black as coal, I wish you were dead stare, after I asked questions at a parent forum was because I pointed out that the IB Middle Years Programme was largely affective and not academic.
He didn’t like the fact that I knew that apparently. Now we know he sees that as a feature not a bug of his Charlotte-Meck vision of “excellence.”
Which would be the John Goodlad definition. I wonder if the same end goals are involved?
I know it is the end goals of the Dumbed Down Common Core implemnentation because I have those documents. Downloaded, hard copied, and locked away.
Note to Common Core architects: What you say out of the country about Common Core is not hard to access.
bu2
August 20th, 2012
1:29 pm
You need to look beyond education for reasons for the change in STEM majors. Try the moon shot. For those too young to remember, there was a big push for engineering and science majors and there was a tremendous excitement in the 60s. There was also fear with the nuclear competition with the USSR (I remember having fallout drills in school, not just fire drills). Then we made the last moon landing, had Watergate and the withdrawal from Vietnam and Jimmy Carter’s presidency of limits. It was a different mindset for those born 62 and later. On top of that, there was the dramatic decline in the car and other old industries and many engineers had a hard time finding a job in the late 70s and early 80s (ie that 62 and later cohort would have seen that going into college). And rather than being celebrated, Hollywood made fun of “nerds.”
You need to look at social trends to explain the changes. And yes, many Americans don’t want to work as hard as the foreigners at our colleges and universities. I had a nephew say all the Americans dropped out of Electrical Engineering because of the competition with the foreigners who were often older and more mature and disciplined.
MiltonMan
August 20th, 2012
1:30 pm
I have interacted with employees in many Asian countries who are fluent in mathematical concepts to the point they could tell you square & cube roots of numbers down to 4 or 5 decimal points without any external aid like a calculator. I quickly found out that their native countries look upon engineers/scientists like we look upon rock stars/movie stars/sports stars. The USA still label these uber-mathematicians as “nerds”.
Canard
August 20th, 2012
1:33 pm
“The majority of the staff on his current project comes from India primarily because there aren’t enough Americans with the necessary math and computer skills.”
Peter Cappelli at Wharton, among others, has debunked this myth. There are plenty of qualified Americans; they just aren’t willing to work for the salaries being offered. Instead of raising compensation levels, however, employers simply outsource work or bring in H-1B’s to do it on the cheap.
MiltonMan
August 20th, 2012
1:35 pm
“Very interesting report and statistics presented. However, We are faced with (2) Two National Political Parties, namely The Republicans and Tea Party and their many supporters. Who have essentially, VOWED and with Great Intent to DISMANTLE and ABOLISH The U.S. DEPARTMENT OF EDUCATION.”
Pal, the DOE has been a failure. What exactly has the DOE done to ensure that we produce more engineers/scientists??? I was prodded to become a high school STEM teacher a couple of years back BUT only if I obtained a “teachers certificate” at my own expense. Laughable considering that I have more education than 90% of teachers in high school
jd
August 20th, 2012
1:35 pm
Once upon a time, a scientist could write theory one day, and great literature the next. A liberal arts education meant you had the awareness of knowledge, its origins, and the biases that tainted any judgements. Now, we give you a diploma from a college, for mastering the skill of cooking.
Can you write, no.
Can you derive values from data with missing information, no.
Can you identify a pattern of behavior from various data points, no.
But, I can cook an omelet!
bu2
August 20th, 2012
1:39 pm
@math optomist
Speeding up instead of dumbing down could serve to discourage interest in math. I know my elementary student is doing things we didn’t do until junior high. I don’t know what HS math looks like now, but everything else is being advanced into earlier years.
The educators really need to work with development specialists to figure out if what they are trying to teach is right for the children’s minds at those ages. There are huge gaps in the capabilities of 7th graders vs. 8th graders and 8th vs. 9th, let alone the gaps at earlier ages.
HoneyFern School
August 20th, 2012
1:43 pm
Agree with William Casey re: “elite” v. “good” students.
“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.”
Should be applied to ALL subjects, yes? Or are students only different in math (stupid, rhetorical question to which we all know the answer). If we offer students what they need when they need it and not too soon (e.g., accelerating all students to take algebra in 6th grade when the brain is physiologically not capable of abstract thought OR waiting until first grade to teach full sentences), and then take the time to make curriculum relevant, rigorous and engaging, we would not have this pickle at any level (high or low).
Once again, though, we have to change our views of what education should be first. This is usually where the train jumps the tracks and we implement a half-hearted reform that has people scratching their heads over why it was not successful.
NONPC
August 20th, 2012
2:04 pm
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?
Not only “no”. but HELL NO.
I graduated in 1979. I had algebra in both 8th grade and 10th grade.
My 8th grade algebra was in a class where the best and brightest of the grade were automatically placed. We learned Algebra in a class of peers. Then, in 10th grade, we had Algebra as prep for college. Only the kids who were going to college took this course.
We did it with less money in higher student per teacher ratios than exist now. It worked because the smart kids were not stuck in a class with the less-bright kids. Jacob Vigdor is absolutely spot on.
NONPC
August 20th, 2012
2:07 pm
p.s. This was a GEORGIA High School BEFORE the Department of Education was established. The Dept of Education BROUGHT STANDARDS DOWN in many schools in Georgia.
There is no magic in the DOE.
Hillbilly D
August 20th, 2012
2:13 pm
All those years ago when I was in school, my algebra teacher told us that “algebra is nothing more than finding the unknown”.
Once Again
August 20th, 2012
2:14 pm
I thought dumbing down the masses was the entire point of government education. Why is anyone surprised at this conclusion?
Halftrack
August 20th, 2012
2:17 pm
Here we go again. Why do those in charge, want equal outcomes of students? Not all students have the same talents. I wanted to do music but can’t keep time and rests co-ordinated. No one complains about my not being a decent musician. Curriculum opportunities should be made for the average student and grade level. Algebra I was offered to me at the freshman level at high school. We had been educated prior to this for starting there. We do not give critical thinking enough value in our teaching today. The current leaders have not had critical thinking in their backgrounds, therefore, we get poor results. Equal outcomes should not be the goal of our required educational process; only an equal opportunity to various fields of study.
bootney farnsworth
August 20th, 2012
2:19 pm
way back in the day, I took classes called math for non math majors. 10 years earlier it was called practical math. somewhere along the way the concept of appropriate math for appropriate studies got lost.
Mountain Man
August 20th, 2012
2:19 pm
“Because the lower end kids can make a difference for themselves. The higher end kids can make a difference for everyone.”
So you increase the education rigor and make MORE kids drop out?
People are talking about foreign students being so much better than American students: what percentage of THEIR total student population “graduates” from the equivalent of our high school? I think you will find it is a lot lower than ours, because they are relegated to “occupational training” after the eighth grade if they are not the “best and the brightest”.
Mountain Man
August 20th, 2012
2:22 pm
Not even Algebra:
This just came up on Facebook:
Solve: 6-1×0+2/2
Answers were all over the map and most were wrong. My favorite was the person that explained it using 1 x 0 = 1
Pluto
August 20th, 2012
2:39 pm
This would go hand and glove with the way our elitist ruling class treats those who excel in society except that it’s harder to rob the good students of their intellectual property so they just frustrate them with educational mumbo jumbo.
AdoringFan
August 20th, 2012
2:54 pm
@Mountain Man
7?
6 – (1×0) + (2/2)=
6 – 0 + 1= 7
I was taught to multiply/divide first, and then add/subtract from left to right. Is this still how it’s done?
AlreadySheared
August 20th, 2012
2:54 pm
@Math Optimist
I agree that some math topics are being pushed down from the college level into the hs curriculum.
Counting (combinatorics for the braying ingnoramous jacka$$es out there), probability. and statistics are topics I studied for the first time as a sophomore and junior math major; now they are introduced, although without nearly as much rigor, in hs. This, to me, is questionable.
Mountain Man
August 20th, 2012
2:54 pm
“The majority of the staff on his current project comes from India primarily because there aren’t enough Americans with the necessary math and computer skills.”
Just like Steve Jobs moved all the IPAD manufacturing to China because he couldn’t find thousands of “engineers” here. What he couldn’t find was minimally educated workers willing to work for $10 per day in the US.
Chris
August 20th, 2012
2:55 pm
I went to Walton and graduated in 2002. I just took a look at the curriculum today. Great to see some advanced class options available today that didn’t exist when I was around. Chinese. Pre-engineering classes. Programming. Forensics. Nice.
But the math classes seem complex now with the CCGPS stuff. Freshman year offers Algebra, Algebra Enriched, Accelerated Algebra, or non CCGPS Accelerated Math 2?? Complexity continues throughout the four years. The only classes I still recognize are AP Calculus and AP Statistics.
When did this mess of math happen? I guess it’s a good thing if everyone including the smartest kids are appropriately challenged though.
Mountain Man
August 20th, 2012
2:57 pm
AdoringFan – Right you are. I couldn’t remember the mnemonic “My Dear Aunt Sally” until my wife reminded me, but I did know there was something called order of operations and looked it up on wikipedia.
Multiply, Divide, then add, then subtract. My dear aunt sally.
Mountain Man
August 20th, 2012
3:00 pm
So now we have higher standards in high school, but we still give out diplomas to students who cannot read, write, or do simple arithmetic, so the High School Diploma is STILL worthless, whether you take algebra or not.
Judge Smails
August 20th, 2012
3:01 pm
Never took algebra. I knock down $150K with my ability to communicate effectively. Some people are way better with words than numbers. The human brain is just wired differently for some folks.
Inman Park Boy
August 20th, 2012
3:05 pm
Arde we really ready to admit that not all students have the same capabilities? Are we really ready to admit that all chidlren do not need algebra, or physics, or chemistry? Are we really ready to admit that students strong in Language Arts and history but weak in math and science have been shortchanged by the SAT and college admissions officers? Are we?
Jan
August 20th, 2012
3:08 pm
@AdoringFan…. Yep. You used the order of operation rules. The answer is 7.
Devil's Advocate
August 20th, 2012
3:12 pm
Just remember, privatizing education means students will lead the world in math and science! The simple fact that a private business is writing a teacher’s check means that students and their families will become motivated.
Fred
August 20th, 2012
3:18 pm
My daughter just started Tech after graduating from a Gwinnett high school. She was a part of that accelerated integrated math program and it was very rigorous. She and her peers in the class actually ran out of advanced math in the 11th grade and “settled” for a Calc II BC class to satisfy the math requirements for graduation. For those that *want* to, the options are there.
The bigger issue is that we as taxpayers don’t want to fund what it would cost to provide the varying levels of classes. As NONPC said, when I was in school we had levels 1, 2 and 3 with 1 being basically remedial type work, 2 being basic math, and 3 being advanced algebra I, trig, algebra II, calc. That required 3 different tracks and set of teachers, books, etc. We had more students per class then but a significant difference is our parents were engaged with what we were doing in school. They may not have understood but they were interested. Far too many parents today just plain don’t care.
Hillbilly D
August 20th, 2012
3:23 pm
Just like Steve Jobs moved all the IPAD manufacturing to China because he couldn’t find thousands of “engineers” here. What he couldn’t find was minimally educated workers willing to work for $10 per day in the US.
Amen to that.
Some people are way better with words than numbers. The human brain is just wired differently for some folks.
I think some people have trouble accepting that. We’d never deem somebody as ignorant/stupid/lazy if they can’t play basketball like Michael Jordan, throw a baseball like Nolan Ryan, play guitar like Chet Atkins, or write like Mark Twain but many people have no problem trying to fit all kids in the same slot. Everybody needs a good, basic education (the 3 R’s), after that, there comes a certain point were talent and ability needs to serve as a guide.
As an example, I have a mechanical mind. Things like that come easy to me. On the other hand, if somebody even mentioned science, in school, my eyes glazed over (and often still do). Many people think otherwise but a mechanical mind and a scientific mind, are two different things, though there is some overlap. That applies to a wide variety of topics.
Teacher, Too
August 20th, 2012
3:36 pm
Well, the answer to the math problem depends on if the entire numerator is divided by 2, or just the 2 in the numerator is divided by 2. I read the problem as the entire numerator is divided by the denominator “2″.
Mountain Man
August 20th, 2012
3:52 pm
Whoops, I think I screwed up. If you apply add before subtract (Aunt Sally), you get five. I guess I ain’t as smart as I thought I was!
Devil's Advocate
August 20th, 2012
3:58 pm
Teacher Too,
Solve: 6-1×0+2/2
The “entire numerator” is 2 if you want to recognize a fraction which you really shouldn’t because that’s just adding unnecessary complexity to the problem. Following the order of operations does not allow for different answers or interpretations. Multiplication and Division are equal and come before Addition and Subtraction which are also equal.
Multiply, divide, then add/subtract:
6-1×0+2/2
6 – 0 + 2/2
6 – 0 + 1
6 + 1
7
Divide, multiply, then add/subtract:
6-1×0+2/2
6 – 1 x 0 + 1
6 – 0 + 1
6 + 1
7
If the problem were written as (6-1×0+2)/2 then you would solve for your “numerator” first and divide it by 2.
Fred
August 20th, 2012
3:59 pm
@Mountain Man – you were right the first time. MDAS – Multiply, Divide, Add, Subtract (although we were taught that multiply & divide were equal and add & subtract were equal and it didn’t really matter the order as long as you did all the m/d actions before the a/s actions).
6-1×0+2/2 The implied parenthesis created by the hierarchy makes the equivalent equation 6-(1×0)+(2/2) or 6-0+1=7.
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.