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

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.