Would US Education Be Better If We Replaced Algebra Requirements With Stats & Logic?
from the reshuffling dept
By now you may have heard about the NY Times article from over the weekend in which political science professor Andrew Hacker makes the somewhat contrarian suggestion that the US education system would function much better if we ditched algebra requirements. The whole article is worth reading, but the basic gist of it is that many people who end up dropping out of school do so in part because of trouble they have in getting past basic algebra. It’s a key stumbling block.
California’s two university systems, for instance, consider applications only from students who have taken three years of mathematics and in that way exclude many applicants who might excel in fields like art or history. Community college students face an equally prohibitive mathematics wall. A study of two-year schools found that fewer than a quarter of their entrants passed the algebra classes they were required to take.
“There are students taking these courses three, four, five times,” says Barbara Bonham of Appalachian State University. While some ultimately pass, she adds, “many drop out.”
Another dropout statistic should cause equal chagrin. Of all who embark on higher education, only 58 percent end up with bachelor’s degrees. The main impediment to graduation: freshman math. The City University of New York, where I have taught since 1971, found that 57 percent of its students didn’t pass its mandated algebra course. The depressing conclusion of a faculty report: “failing math at all levels affects retention more than any other academic factor.” A national sample of transcripts found mathematics had twice as many F’s and D’s compared as other subjects.
I will admit that my initial reaction to this article was to scoff and think that it’s ridiculous. Understanding basic algebra, to me, seems fundamental to understand a variety of other important things — including some forms of logic and statistics. So, I wondered how dropping algebra as a requirement might make those already lacking fields even worse.
However, Hacker’s piece actually suggests something of a solution: potentially replacing algebra with a form of statistics, which is rarely a required course.
Instead of investing so much of our academic energy in a subject that blocks further attainment for much of our population, I propose that we start thinking about alternatives. Thus mathematics teachers at every level could create exciting courses in what I call “citizen statistics.” This would not be a backdoor version of algebra, as in the Advanced Placement syllabus. Nor would it focus on equations used by scholars when they write for one another. Instead, it would familiarize students with the kinds of numbers that describe and delineate our personal and public lives.
It could, for example, teach students how the Consumer Price Index is computed, what is included and how each item in the index is weighted – and include discussion about which items should be included and what weights they should be given.
I will admit to being unsure how such a class will work without a basic underpinning in algebra. However, conceptually, what Hacker is saying makes sense. Focusing on the formulaic side of algebra isn’t particularly practical for many people. I could see how classes that focus on practical mathematical skills around statistics and logic, could actually be a lot more useful. And while he says these don’t need to be “backdoor” algebra classes, I’m not so sure that’s a bad thing. Having people understand the basics of algebra by putting them in realistic situations they understand, and showing how to apply such things in a useful manner doesn’t seem like such a bad idea…
Filed Under: algebra, drop outs, education, logic, math, statistics
Comments on “Would US Education Be Better If We Replaced Algebra Requirements With Stats & Logic?”
Nah, you don’t want to do that. Then they would figure out that the 1% really isn’t 1%, and that all the internet whiners still add up to a very small percentage of the public.
Then you would be out of business.
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And people like you is why the article has a point.
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*are
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Hey, I thought people who watched Fox News weren’t smart enough to use the internet.
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No, that would be CNN’s viewers.
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Both, actually. This one’s a mutant.
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[citation needed]
I call it mathematics applied to real world. You don’t need to know how to solve polynomial equations. But it is very useful to know how much interest you’ll be paying in a financed acquisition. Basically the same rationale but once applied to a daily life issue it’s both much more interesting and easier to understand. Need advanced math, go learn at the University or in a specific course.
Most schools around the world simply don’t have useful knowledge in their curriculum.
I was thinking about math these days, and the real problem is language, math is a language and even though it is used to describe real world things the language to describe that is completely outside the normal everyday language.
Fixing that could reduce the barrier that people encounter when having to relearn a completely new language.
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Maybe instead of changing the laws of math as we know it, we should focus on its real life applications.
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Maths is easier to understand when applied to real life situations. I had a similar experience learning spreadsheets – at school they seemed irrelevant, in work they’re essential.
But there is a problem. We learn things more easily when we are younger; and real life scenarios are a bit thin on the ground for your average 5 year old. So the scenarios used for teaching algebra needs to relate to the imaginations of the students. Where teachers can’t adapt, the children will have more problems.
What if we started too late?
What if the problem lies in high school? What if we just didn’t prepare students well enough?
Re: What if we started too late?
The problem lies way before that even. It starts with the when the importance of grades is instilled in the child as opposed to the attainment and application of knowledge. It starts with training as children and becomes a vicious cycle that repeats over and over in a downward spiral.
Re: What if we started too late?
I agree, it starts earlier. We should teach algebra in elementary school.
Re: Re: What if we started too late?
I learned algebra in 5th grade…in a public school…that was only 30 years ago…jeez louise.
Re: Re: Re: What if we started too late?
You learned algebra as soon as you were able to add numbers together.
Most people don’t realize it.
23+45=?
Just replace ? with x and you get…
23+45=x
solve for x
Granted, that’s incredibly simple, but that’s the point.
Algebra is just using numbers of what you know to solve for what you don’t.
Now, Geometry on the other hand…
Yeah, I wasn’t any good at that math.
Re: So full of fail.
If you are thinking of Algebra as a high school or college subject then you have already failed quite spectacularly.
Algebra is basically your first baby steps past what you would have been taught in a one room schoolhouse from Little House on the Prairie. It is not “advanced” by any means. The fact that we are speaking of it as such points to a grave and fundamental failing in our society.
It’s the first baby steps in dealing with any of the mathematics that is necessary for running the modern world.
The idea that we should give up on it just because it’s perceived as hard (mainly due to pervasive anti-intellectualism) simply boggles the mind.
Re: Re: So full of fail.
Exactly. You can teach algebra to a grade-school child by using a simple analogy of a balance scale:
You can teach it that way to a student with an understanding of basic arithmetic, and they’ll “get it” almost immediately. The problem isn’t algebra, it’s that we don’t have a good way of teaching it right now.
Opposite direction
We need to go in the exact opposite direction. We need to shift our focus away from the importance of grades and degrees and more toward mastery of important concepts (like Algebra) and stop dumbing down the curriculum just so that more people can pass.
Re: Opposite direction
We need to go in the exact opposite direction. We need to shift our focus away from the importance of grades and degrees and more toward mastery of important concepts (like Algebra) and stop dumbing down the curriculum just so that more people can pass.
We need to get rid of the shitty teachers who are there just to collect a paycheck and fill the schools with teachers that have a passion for the subject they are teaching and a love of sharing that passion with their students.
I did exceptionally well in Pre-Algebra in 7th grade, and it was all due to my teacher and Algebra in 8th grade. I never had a math teacher since that came close to the passion she showed for math, though some were notable.
There are so many teachers out there that hate their job and suck at it, and they make up the teacher unions…which is why it is so difficult to get rid of them. Instead, we should switch to a performance model for teachers, not based on grades, but based on how their students succeed. We need to get rid of the one size fits all way of teaching we use now…it doesn’t work…and allow students to determine what they are good at, teach them the basics, and then allow them to master what they are good at. What bothered me most about school was the redundancies; I took 10 years of math in middle school, high school, and college, and the second three years was basically a repeat of the first 3, and the third three was a repeat of both. I was still good at Algebra the third time, but the students that failed in middle school were still failing college Algebra. I learned a lot more math in college: Discrete Mathematics, Logic, Statistics, Combinatorics, etc., but I still had to get past the elementary maths that were repeats of what I had before.
A career in Computer Science and Electrical Engineering needs Algebra, but a career in Psychology or American History does not. Teach the basic math everyone needs and then move on.
Real world skills
While we’re at it, we can also start teaching critical thinking in elementary school – and keep reinforcing it through high school. Financial literacy in middle or high school. These are real world skills necessary for modern life that are sorely lacking.
Re: Real world skills
Critical thinking is too much of a threat to religion. The conservatives who run the Texas Board of Education which influences the content of textbooks that are used around the country will not allow such “liberal” skills as critical thinking to interfere with the Lord’s education.
Re: Re: Real world skills
I see it didn’t take long to turn this into a religious discussion. If non-religious people took critical thinking, they might see that much of what they are told in the science books has never been proven either. Wouldn’t want that would we?
Re: Re: Re: Real world skills
There are ways where religion can live with critical thinking (or at least that’s the way I’ve been taught during my pre-bachelor course of Teology). In fact, when a person thinks critically, they have another weapon to reinforce their faith and believes, if they choose so.
Unless you want to have “fanatics”. They do not need that.
Re: Re: Re: Real world skills
they might see that much of what they are told in the science books has never been proven either.
Really? Name for me one general scientific idea that is in science textbooks and taught to students prior to college that hasn’t been proven?
Re: Re: Re:2 Real world skills
Evolution. The missing link…..is still missing.
Re: Re: Re:3 Real world skills
I’m well familiar with evolutionary biology and I have no idea what you mean by “missing link” – care to explain?
Yes, evolution is proven. There are many completely separate lines of evidence. There’s the fossil record. There’s geographic distribution of species. And in the last 30 years, we have an entirely new line of evidence in genetics. There are experiments showing evolution in microscopic life – one clear example is antibiotic resistance in bacteria.
Evolution is a theory in the scientific sense. So is gravity. Sure, there are some disagreements among scientists on some of the specific methods of how evolution works – but evolution has more lines of supporting evidence than many other things even you would take for granted.
Re: Re: Re:4 Real world skills
The fossil record does not show any missing links. Every time a new fossil is found, it is deemed a new species. We do not have one species as it “evolved” over time. If we do, please cite it for me.
We have skeletons of early man that turn out to be apes. We have DNA in dinosaurs that should should not have survived 65+ million years. Unless of course, the dinosaurs aren’t that old.
We age rock layers by the fossils found in them and we age fossils by the rock layer they were found in. Pretty circular logic.
Re: Re: Re:5 Real world skills
“The fossil record does not show any missing links. Every time a new fossil is found, it is deemed a new species. We do not have one species as it “evolved” over time. If we do, please cite it for me.”
This is in fact logical if you have a clue as to how evolution works. You can even see it now in the world. Some species are hugely succesfull, while others aren’t. The ones which are successfull are much more likely to turn into a fossil than those rare species which are less well adapted. And that’s where you have to look for your missing link, which you won’t find, because the chances of those fossilizing are slim. Furthermore evolution is a punctuated equilibrium, evolution speeds up enormously if large changes in environment take place, which means these ‘missing links’ aren’t around for a long time, making the chance of them fossilizing even smaller. Furthermore, this ‘missing link’ thing is an unsolvable problem since creationists will just keep asking for more, no matter how many gaps you fill, all they see is two new gaps before and after the ‘missing link’ you’ve just found.
“We have skeletons of early man that turn out to be apes. We have DNA in dinosaurs that should should not have survived 65+ million years. Unless of course, the dinosaurs aren’t that old.”
Who determines when a hominid becomes a human instead of an ape? Exactly, it’s just a formality. And your dinosaur DNA turned out to be human. Contamination.
“We age rock layers by the fossils found in them and we age fossils by the rock layer they were found in. Pretty circular logic.”
Ahahahaha XD How funny. You obviously don’t know what you’re talking about. The ages of rock layers can only be determined using radioactive isotopes (Uranium or Potassium-Argon dating). What you’re talking about here are biomarkers, which have been determined to be abundant during a certain period in time and can therefore be used to determine a rock was from that specific period of time. But this in no way provides an age, it simply places the rock formation in a certain era. You can only attach an AGE to your formation if the age of the layers belonging to that era has been determined using an exact dating method. So why not just do the exact method for all the tiem? 1. The public doesn’t want to pay for it. 2. Not all rocks are suitable 3. Biomarkers are faster and easier. A proper geologist knows this.
Re: Re: Re:6 Real world skills
Furthermore, this ‘missing link’ thing is an unsolvable problem since creationists will just keep asking for more, no matter how many gaps you fill, all they see is two new gaps before and after the ‘missing link’ you’ve just found.
I love how a lack of evidence is somehow a creationists problem when evolutionists always demand evidence of God. I also like how you use a lack of evidence as evidence itself. Wonder how that would work in a criminal trial?
Re: Re: Re:7 Real world skills
No one needs proof of God. Believers believe regardless, hence the name; non-believers understand that you cannot prove a negative, which is the point of many parody dogmas, such as the orbiting Martian tea pot or pink unicorns or the Flying Spaghetti Monster.
Incidentally, belief in God is not mutually exclusive with understanding evolution. Only a small subset of people believe that Earth is only 6000 years old, and they are contemptibly wrong.
I also like how you use a lack of evidence as evidence itself. Wonder how that would work in a criminal trial?
No, you see, that’s not what he did. He made a statement illustrating that no matter how much evidence is uncovered (and there is more every day), there will always be people who reject that evidence as insufficient. There is a Socratic acceptance of the limits of your own knowledge, and then there is ignorance.
(I apologize in advance to the Monster Cabling and Beverage Corporation for including mention of their intellectual property.)
(I further apologize, because I knowingly conflated two separate companies, but can’t be bothered to look up their actual names.)
Re: Re: Re:8 Real world skills
The problem is, he didn’t show any evidence, only used the usual faith based trick of trust us, there is evidence. There are no missing links, just more theories as to why there are no missing links. Evolution is faith just like believe in God is faith. Problem is, Christians admit their faith, evolutionists deny it.
Re: Re: Re:9 Real world skills
Ah, the tu quoque defense. Go back to Talk Origins.
I do like how you admit that not only are faith based arguments tricks, but that they are also usual.
Re: Re: Re:5 Real world skills
“The fossil record does not show any missing links. Every time a new fossil is found, it is deemed a new species. We do not have one species as it “evolved” over time. If we do, please cite it for me.”
This is in fact logical if you have a clue as to how evolution works. You can even see it now in the world. Some species are hugely succesfull, while others aren’t. The ones which are successfull are much more likely to turn into a fossil than those rare species which are less well adapted. And that’s where you have to look for your missing link, which you won’t find, because the chances of those fossilizing are slim. Furthermore evolution is a punctuated equilibrium, evolution speeds up enormously if large changes in environment take place, which means these ‘missing links’ aren’t around for a long time, making the chance of them fossilizing even smaller. Furthermore, this ‘missing link’ thing is an unsolvable problem since creationists will just keep asking for more, no matter how many gaps you fill, all they see is two new gaps before and after the ‘missing link’ you’ve just found.
“We have skeletons of early man that turn out to be apes. We have DNA in dinosaurs that should should not have survived 65+ million years. Unless of course, the dinosaurs aren’t that old.”
Who determines when a hominid becomes a human instead of an ape? Exactly, it’s just a formality. And your dinosaur DNA turned out to be human. Contamination.
“We age rock layers by the fossils found in them and we age fossils by the rock layer they were found in. Pretty circular logic.”
Ahahahaha XD How funny. You obviously don’t know what you’re talking about. The ages of rock layers can only be determined using radioactive isotopes (Uranium or Potassium-Argon dating). What you’re talking about here are biomarkers, which have been determined to be abundant during a certain period in time and can therefore be used to determine a rock was from that specific period of time. But this in no way provides an age, it simply places the rock formation in a certain era. You can only attach an AGE to your formation if the age of the layers belonging to that era has been determined using an exact dating method. So why not just do the exact method for all the tiem? 1. The public doesn’t want to pay for it. 2. Not all rocks are suitable 3. Biomarkers are faster and easier. A proper geologist knows this.
Re: Re: Re:6 Real world skills
Urgh… Double posted… Sorry…
Re: Re: Re:5 Real world skills
The fossil record does not show any missing links. Every time a new fossil is found, it is deemed a new species. We do not have one species as it “evolved” over time. If we do, please cite it for me.
This statement makes it clear that you fundamentally misunderstand evolution.
Of course the fossil record does not show “missing links” – which you still have not given a definition of. The fossil record shows individual snapshots at a certain time. Think of them as a single frame of a movie – one frame will not show movement, but put them all together and the movement is quite clear.
You seem hung up on an arbitrary label of a species. It is exactly that, and arbitrary label. What we have are constant lines of descedents that branch out from a single organism. Hominids did not evolve from chimpanzees – both chimpanzees and hominids descended from a common ancestor (somewhere between 5 and 7 million years ago).
We age rock layers by the fossils found in them and we age fossils by the rock layer they were found in. Pretty circular logic.
Keep on showing your ignorance. Please look up radiometric dating (that is, dating using radioactive isotopes). This is well understood, verifiable physics. Here’s a link: http://en.wikipedia.org/wiki/Radiometric_dating – Now, once you have identified fossils between layers that have been dated, you can make inferences as to the age of those fossils, and you may be able to use those same fossils elsewhere to confirm other rock layers. But there is no circular logic here.
Now, you spent a lot of time arguing against fossil evidence. Would you care to try arguing against any of the other lines of evidence supporting evolution, which in and of themselves would be all the proof we needed even without fossils?
Re: Re: Re: Real world skills
Evangelicals are explicitly hostile to critical thinking. They are also intolerant of alternate viewpoints. It’s pretty hard to route around that. There’s really no debate and no potential to “live and let live”.
They are also by their very nature meddlers. This has led to mixed results over the long haul.
Any serious educational reform is going to be blocked a significant (if not majority) part of the population.
Re: Re: Re: Real world skills
Actually we would want that. The whole point of science is to build our knowledge via testable predictions. Anyone taking critical thinking who then set out to try and prove, or even better disprove theories would be furthering science.
Re: Re: Re: Real world skills
You’re referencing a false dilemma. It’s not either you believe in God or you believe in science.
I don’t “believe” in God or science. I take everything with a healthy dose of skepticism because the pattern of human knowledge (according to however much we can trust historical accounts) is that every time humans collectively think we know the truth about something, like the model of an atom, someone comes along in 30 or 100 years and blows the old model out of the water. We laugh at ancient texts talking about the four humours and superstitious beliefs, but our own current beliefs are going to be mocked by people in a 100 years because they’ll have grown up learning how absurd some of the things we’ve been taught are.
Science can’t prove or disprove the existence of something that by definition isn’t empirically observable (like God) and religion can’t reliably explain natural phenomena because it is by definition supernatural.
So the science books should teach the science that will one day be out-dated and the religious books should be taught in the church of your choice (and left out of education unless you choose to attend a private, religious school) and in 100 years, our grandchildren can laugh at how absurd our religious and scientific beliefs were.
make math relevant
One thing that always bugged me about middle and high school math classes is how math was presented in a sterile “here’s another equation” kind of way with no relationship to the practical uses. At best you’d have two page “enrichment” section at the end of the chapter that briefly mentioned real world applications. It seems like it would be much more engaging to first present a relevant real-world problem, then introduce the math to solve it. This is at least partly what the article is getting at.
For example you need the concepts taught in algebra to properly understand compounding interest, which is something that should be relevant anybody who makes money. But is the curriculum motivated by financial examples? Not in my experience.
(Disclaimer: speaking as someone who uses trigonometry and linear algebra on a daily basis for 3D graphics programming; and last took a high school math class about 15 years ago).
Re: make math relevant
You just described a basic physics course and a basic business class, either of which would teach math more effectively than dry algebra.
A big part of algebra *is* logic
Look, I’m someone who started learning algebra in the 5th grade, so maybe I shouldn’t be talking, but the gist of the algebra taught at the basic level is the concept of placeholders and how to manipulate them. If that’s the part that supposedly post-secondary students are having issues with, how are they going to fare any better with logic and statistics?
Maybe logic and statistics have a better chance of having principles stick. If so, go for it.
Practical Application is Key
I learned algebra and trigonometry and calculus and differential equations through real life examples. I was able to get a second major in math because a high school teacher of mine took the time to sit down with a below average math student and explain the real world implications of the stuff he was teaching. It’s a lesson I carry with me today.
Too often education isn’t used to empower, it’s used to exclude. I wouldn’t be surprised if many leaders of higher education see math as a “weed out” course to eliminate students that don’t match their vision of a student.
A fine idea, but...
I’m a high school math teacher, and I’m all in favor of trying different approaches (including Andrew Hacker’s ideas) to help people learn math, but I’m not convinced that the primary issue is one of dry-boring-algebra vs. real-world-exciting-statistics. The fact is that all mathematics requires developing skills in quantitative reasoning, and quantitative reasoning is difficult (more so for some than for others). A course in “citizen statistics”, even one that includes a lot of interesting real-world applications, is still going to require learning to reason effectively with numbers; I would argue that it will also require some fluency with fundamental algebra concepts like variables, interpreting graphical data, etc.
So by all means, let’s continue to come up with different ways to help people learn math. But the bottom line is that learning math is hard work and the hard work part’s not going to go away, even with better courses.
Re: A fine idea, but...
What you need is a budget to make your class interesting to modern students. What you do is hugely important, but because its a platform for so much more, and not relevant in the vacuum you are forced to teach it in.
Everyone who makes a real salary deals with math all day long and this is important. How is that art history prodigy going to properly appraise a painting last sold 400 years ago without understanding how money,interest and currency fluctuations work?
Re: Re: A fine idea, but...
What we need is to revert to corporal punishment for troublemakers and those who choose to not pay attention in class.
We also need to get rid of “no student left behind”.
Finally, we need to start kicking Parents in the ass for not pushing and caring about their kids’ futures.
Right now we’re living in an “entitlement” society rather than a “work to earn” society. The government likes it that way as it makes us better sheeple.
We the people need to stand up to our government and kick their ass to rolling back these fundamentally wrong educational changes.
Scare the bejesus out of littly Timmy and Sally, make them sweat and work and learn. Put them in the corner with the dunce cap on when they fail to do so. Send em to the principal’s office for corporal punishment when they act out. Remove the troublemakers from the classrooms so that the remaining majority can actually learn. The troublemakers are then their parents responsibility to find another school that will accept them.
Each child may be *entitled* to an education, they are not *entitled* to disrupt any other child’s education.
They are not *entitled* to be bullies.
They are not *entitled* to receive grades without earning them.
Re: Re: Re: A fine idea, but...
Yes, fear, shame and pain are such effective educational tools…
Re: Re: Re:2 A fine idea, but...
Yes, they are. Glad you agree.
🙂
Yes I caught your sarcasm, but in this case it wasn’t warranted.
Watch the placements of the United States as compared to other countries. As soon as we started to backslide on punishment and put forward making everyone a winner, we started to go down, and will continue to go down until we reverse those changes.
I was also one where classes came easy, couldn’t remember dates for crap, but concepts and ideas were oh so easy.
But I also had an education system the enforced it’s rules and parents who supported the educators if corporal punishment was necessary. Started off early enough it really becomes unnecessary in later years, just the threat of it hanging over little Bobby is enough.
But go ahead and live in your little make-believe world where entitling everyone to everything without working for it, see where that world stands in 10 to 15 years if it still exists.
Re: Re: Re:3 A fine idea, but...
Part of the problem as I see it is that we teach children to focus on the wrong things. The focus on comparing us to others is a perfect example of this. GPA and class rank doesn’t mean jack. What’s really important to focus on is actually BETTERING YOURSELF by actually LEARNING something useful and being able to APPLY that knowledge. Instead we teach them what is important is to get good grades and a high class rank so it people will THINK you are educated. So grades become the focus not the knowledge. We’ve stopped teaching people to think for themselves and start dumbing down the system so that more kids pass and the world will think our population is better educated than it is and kids learn to advance in this system by regurgitation or information to that they don’t have any clue about much less why it is important and useful just to satisfy the test and get the grade.
Re: Re: Re:3 A fine idea, but...
You are really big on false dichotomies here. Entitlement, lack of work, and making everyone a winner are not the natural result of removing fear, shame, and pain from education. They’re just bad ideas. My childrens’ education, for example, has not had any of the things mentioned above, and they’re doing great.
Re: Re: Re:2 A fine idea, but...
Coddling works great, too! So many kids expect to get $70k salary a year after completing their liberal arts degree (‘Oh Timmy, you’re so smart’). Then reality hits them and they are out asking for handouts (student loan forgiveness) just like the corporations they despise.
Re: Re: Re:2 A fine idea, but...
Fear, shame and pain… and an almost fanatical devotion to the pope!
Re: Re: Re: A fine idea, but...
Corporal punishment is not needed. It won’t change the fact that there are ppl with natural inclination towards human sciences or biological that will have a hard time with math. Regardless of punishment.
As for the troublemakers or bullies, I was considered some sort of troublemaker because I always learned stuff fast, specially math, physics and chemistry so I got bored and stopped paying attention and started doing other stuff. Also, I used to get extremely upset with history classes because I simply couldn’t memorize dates. I made it on history tests out of pure luck except when I had a teacher that wanted us to know about history in context, not dates. Then my grades went sky high.
You can’t lump all students together because they have different inclinations. But if you must lump them together then at least make it so the classes are about stuff that is applied in real life and develops their criticism, their thinking process. Statistic might not be the best course of action here and exams certainly aren’t the best way to evaluate but your ideas are not the way to go.
Re: Re: Re:2 A fine idea, but...
We need to institute corporal punishment for Congress.
Re: Re: Re:3 A fine idea, but...
Corporal punishment is for those that *can* be rehabilitated, like children.
Congress needs capital punishment.
Re: Re: Re:2 A fine idea, but...
No, corporal punishment won’t make subjects any easier.
What they may do is prevent people from surrendering.
You can push people to better than they think they can be. You can also inspire them. Inspiration is much harder of course.
You simply don’t let people fail. You don’t let them slack off. This should come from the parents but not everyone has the benefit of that.
Re: A fine idea, but...
Why is the belief so widespread that reasoning with numbers is more important than reasoning with language and ideas? My own view is just the opposite.
Re: Re: A fine idea, but...
So lawyers! Lawyers running the world. How is that working out?
Re: Re: A fine idea, but...
Why is the belief so widespread that reasoning with numbers is more important than reasoning with language and ideas?
I don’t remember ever hearing that, either here or somewhere else. Do you see it a lot?
Re: Re: A fine idea, but...
2 is 2 regardless of any other ‘knowledge’ so it’s not too difficult to learn and use logic related to the fact that 2 is two, however To can be too or two and each can have multiple meanings depending on the context and the intent of the ‘user’….
Logic with numbers…. easy
Logic with words…. Semantics = Some Antics….
my intuition tells me...
It’s easy for me to scoff at this; I’m good at math. But…
The author makes a strong case that math is a major hurdle for students, but he does not make much of a case at all that algebra is not valuable. He simply says there’s no case that it is (“nor is it clear”, “there’s no evidence”, “I haven’t found a compelling answer”).
One sentence caught my eye: “Certification programs for veterinary technicians require algebra, although none of the graduates I’ve met have ever used it in diagnosing or treating their patients.”
They’ve never used it? How do they know? One consequence of mathematical training I’ve seen is that it sharpens intuition. Maybe I’m confusing correlation with causation, but people who have studied a lot of math seem able to see the solutions to problems without writing out the equations. They can’t explain how they do it, it’s just there.
So let’s do an experiment. Let’s test students with real-world mathematical problems, e.g.:
An elephant stands on a platform supported by a beam. If you need a beam four inches thick to support an elephant six feet tall, how thick a beam do you need to support a ten-foot elephant?
A pizzeria takes telephone orders. Taking one order takes one minute. During peak hours, the telephone is silent for an average of two minutes between orders. How many orders are lost during peak hours because the phone’s busy?
Which gets heatstroke faster, a large short-haired dog, or a small long-haired dog?
We’ll test three groups: students who have passed algebra, students who have flunked algebra, and students who have taken “citizen statistics” classes instead. Now let’s have a show of hands, who can tell me why I’m using three groups instead of two?…
Re: my intuition tells me...
What terrible questions.
An elephant stands on a platform supported by a beam. If you need a beam four inches thick to support an elephant six feet tall, how thick a beam do you need to support a ten-foot elephant? This ignores the cube-square law and is not as simple as multiplying the beam’s thickness by 1 2/3.
A pizzeria takes telephone orders. Taking one order takes one minute. During peak hours, the telephone is silent for an average of two minutes between orders. How many orders are lost during peak hours because the phone’s busy? Not enough information, such as call volume and the number of employees, phones, & phone lines. Additionally, telephone calls (despite having what you can call an average call time and average idle time) follow a poisson distribution. Given the right information, and using an Erlang-C formula to figure this out would yield a result much different from expectations from just doing the math on the averages you supplied.
Incidentally, the answer uses a statistical model, not an algebraic model.
Which gets heatstroke faster, a large short-haired dog, or a small long-haired dog?Hopefully the small one, but this has way too many unstated factors to be answered successfully.
Re: Re: my intuition tells me...
Re: Re: Re: my intuition tells me...
Your comment’s broken…
Re: Re: Re:2 my intuition tells me...
You just couldn’t see it because it a ninja and everyone knows you can’t see ninjas.
Re: Re: my intuition tells me...
1) “This ignores the cube-square law and is not as simple as multiplying the beam’s thickness by 1 2/3.”
You’re saying the question is bad because you can think of an answer that’s wrong?
2) “Not enough information, such as call volume and the number of employees, phones, & phone lines.”
Sorry, I thought “one phone, answered whenever it rings” was easy enough to read in. Call volume? Well, how are you going to measure that?
“Additionally, telephone calls (despite having what you can call an average call time and average idle time) follow a poisson distribution.”
Did someone say they didn’t?
“Given the right information, and using an Erlang-C formula to figure this out would yield a result much different from expectations from just doing the math on the averages you supplied.”
So your answer is that there is insufficient information?
3)“This has way too many unstated factors to be answered successfully.”
Yeah, that one was kind of open-ended. I should have marked it “discussion” or something.
Re: Re: Re: my intuition tells me...
You’re saying the question is bad because you can think of an answer that’s wrong?
Personally, I would like to know what you mean to measure by these questions. You presented them as though they’re intended to be correctly answerable by someone with a basic grasp of math and numbers (but didn’t say that). However, they’re all at least a little more complex than that. Not to mention that some of them require some knowledge you would never get learning math. So what are these questions meant to do?
Re: Re: Re:2 my intuition tells me...
I personally think that math questions were INTENDED for creating a “real life” situation in which you should apply the math to solve a problem. Sad thing is, the ones I grew up with (and most of my Fellow Americans) have nothing to do with real life situations. However, that does not mean we need to purge the education system of Algebra. We just need to prove to our young there really is a use.
Great examples are doing the math for keeping a patient on an I.V. medicated properly; or for the more common use….ballencing your checkbook.
Also, the New York Times article is bunk because Statistics has a lot of the same elements of Algebra and you need Algebra skills to do statistics.
Re: Re: Re: my intuition tells me...
You’re saying the question is bad because you can think of an answer that’s wrong?
I’m saying all the questions were bad because they all make assumptions and don’t provide enough information to answer them purely algebraically.
The elephant problem is an engineering question dealing with a structure’s ability to support a weight. While weight is related to height, weight cannot be extrapolated from height with the given information. Try doing this math with the information stated: http://www.engineeringtoolbox.com/stress-strain-d_950.html
You may as well have asked: An average desk has a height of 29 inches to accommodate most people. If a person is two inches taller than average, how long is the desk?
So your answer is that there is insufficient information?
I’m saying that the answer yielded is a probability function. You proposed that you were giving real world examples of algebraic problems.
In your example, the math is that the phone rings once every three minutes, followed by one minute of order taking and two minutes of silence. So 20 calls are answered and no calls are missed (per hour, which is the only answer I can give since you failed to state how long peak hours were). That’s the answer to your problem as stated, all other variables notwithstanding.
Please don’t write textbooks.
Re: Re: Re:2 my intuition tells me...
I’ll give you three different answers for the elephant problem:
? First answer: We need to get a licensed Professional Engineer (Structural) in here. Pronto.
? Second answer: The 10ft elephant almost certainly masses less than 8 times the 6ft elephant. Meanwhile, we know that a conservative engineer put a 10 times safety factor into that 4in beam. So that damn 4in beam will hold the bigger elephant as long as that elephant is fully insured.
? Third answer: We just spent the last week in class doing moments of inertia for square beams, Young’s modulus, and bending. The problem does not give us the width of the beam, therefore we know for a fact that the beam is not going to twist and lay over. Further, we can see that beam is not going to shear off at its supports. There’s only one possible failure mode to consider for this quiz.
It all depends on context.
Re: Re: Re: my intuition tells me...
After reading your problems, and your replies to comments about them, I think we should mark your problems as examples of sloppy thinking.
You might be able to solve problems just fine, but creating a good math problem is a different skill – with one exception.
If you can’t write a good math problem, you will never be excellent at math.
Thanks for trying, though, and don’t forget to enter again!
Re: Re: Re:2 my intuition tells me...
Are you sure you didn’t just read others’ comments and decide to jump on the wagon?
As for your implication that I’ll never be excellent at math, well, I haven’t won a Fields Medal, but I did figure out an 11-state minimal-time solution to the Firing Squad Problem (without looking up anyone else’s solutions(*)). It took me about two weeks, which is less time than it originally took the community, but then I had the advantage of having studied parts of quantum field theory which didn’t exist in the 60’s.
Also, I would bet everything I have that my math (general) SAT scaled score was not lower than yours.
(*) If you haven’t heard of it and want to try it, don’t go to wikipedia.
Re: Re: my intuition tells me...
depends on the breed of the dog, short snout dogs, bulmastiffs, bulldogs, pugs ect… heat faster then other types,
Re: my intuition tells me...
To answer your questions
An elephant stands on a platform supported by a beam. If you need a beam four inches thick to support an elephant six feet tall, how thick a beam do you need to support a ten-foot elephant?
A 10 foot elephant isn’t just 66% heavier. So I couldn’t tell you unless you give me weights and how much weight the damn beams support. Trying to solve with your current information is how engineers kill people on accident.
A pizzeria takes telephone orders. Taking one order takes one minute. During peak hours, the telephone is silent for an average of two minutes between orders. How many orders are lost during peak hours because the phone’s busy?
Enough to justify getting a second line.
Which gets heatstroke faster, a large short-haired dog, or a small long-haired dog?
Which one is better at regulating body heat? More factors than just hair are involved here. Even if you wanted to just go with “hairier = hotter”, you still need no math. What the hell was the point of this question?
Congratulations, you posted 3 questions that are supposed to be answered with math that were better answered with logic and rubbing two brain cells together.
Re: my intuition tells me...
Watch out… the bending strength of a beam goes with thickness cubed 🙂
Re: Re: my intuition tells me...
Rats, you’re right. I meant to say “column”, and even then I was thinking of something like stone(*). A platform suspended by a cable would have been even better, but I was trying not to be too wordy.
(*) Or tortoises, but that’s a different story.
only if someone is allowed to earn from copyrighting it!
Personally, I think another solution here would be to strenthen the school science requirements and start teaching it earlier as they do in Russia, China, Japan, and some other countries. Teaching something like algebra at an earlier age (in former Soviet Union algebra was being taught starting at grade 4 (10-yr olds)) would be far more beneficial. Younger minds seem to be able to conceptually understand things much bettert than hormone-ravaged teenagers.
I can’t help but see this as further ‘dumbing down’ a part of the education system because something is difficult and takes work.
America's Democracy becoming Idiocracy
So it’s *too* hard, let’s drop it?
I’m sorry, what?
The basis for most modern thinking is in Algebra, not statistics.
Here we go again, dumbing up Americans just so we don’t leave anyone behind…
Fucking idiots…
Re: America's Democracy becoming Idiocracy
Actually algebra has nothing to do with modern thinking. It’s a mix of contribution with a lot of Arab and Greek help. You don’t need Algebra to be able to think and form coherent and rational lines of thought and that’s part of the point of the article. Algebra is, however, very good at developing many aspects of this “modern thinking”. Statistics can contribute much more as it needs abstract thinking and it encompasses the rationale needed for Algebra. People have an incredibly hard time with abstract stuff.
What’s dumbing down Americans is precisely giving too much emphasis in determined areas and forgetting the rest. Along with presenting no real application nor an interesting way to learn.
Re: America's Democracy becoming Idiocracy
Actually logic is a great way to introduce algebra. For anyone who has ever dealt with complex truth trees, you are aware that logic looks a lot like algebra.
Would the New York Times be better if it quit trollbaiting?
I disagree: ? The New York Times article is trollbait.
Have fun with your discussion here. Remember to laugh a lot… It’s the internetz.
Algebra IS stats and logic. Replacing the classes doesn’t get past the issue that those kids are having troubles learning a very simple concept, the foundation of pretty much all hard sciences. Blame the teachers or the kids, not the class.
Re: Re:
Algebra IS stats and logic.
Logic maybe (though that’s stretching it IMO) but what does algebra have to do with statistics?
Re: Re: Re:
Wow…I remember taking relatively low level stats courses in grad school and the professor would write these long equations on the board and go through the algebraic transformations to show us, for example, how a weighted least squares transformation worked.
I know that’s pretty basic stuff statistics-wise, but even then (18 years ago) many students struggled to follow along with the algebra. They typically didn’t do very well in the class.
I guess my point is: How does one really understand the statistics if one doesn’t understand the math (algebra, trig, calc, whatever) behind it?
Re: Re: Re: Double Wow
I took an introductory stats course in undergrad and it wall to wall algebra. I can’t see how anyone could cope with a stats class without being way past algebra. You don’t just need it, you need it to be 2nd nature.
When I was a student, I struggled with math classes. I jumbled numbers and could barely understand some of the equations. I was even forced to repeat a class at one point.
I don’t want to make excuses for myself, and I do not want to blame the teachers or the cirruculum. A good portion of what I learned has application in every day life. And I use it not only for work, but figuring out my basic expenses, my taxes, and everything else I need to be a functioning member of society.
And I can admit that some of the classes that I had to take had other portions that were not needed for me all the time. But if I can understand how they are important – and argueably would be vital if we were not in a consumer based disposable society where we don’t build anything ourselves.
But that being said, I feel that we may be lowering the bar too much.
Several studies point out that owning smartphones and other technology that make life easier, is also dumbing us down since we no longer need to study and practice what we learn to retain it. It is always just a few clicks away online, or “there is an app for that”.
You can see youtube clips of students embarassing themselves, confusing the dates of the civil war with world war 1 or 2? Not being able to name a country that begins with the letters E (Europe is not a country) or U (They couldn’t even think of the USA?).
If taking some of the more esoteric math classes and replacing them with statistics and logic work out for the best, I can see the value in that. But basic math should not go the way of the dodo. Because eventually that battery wears down, the computer can’t connect, and when you need it most, there wont be an app for that.
Re: Re:
You can see youtube clips of students embarassing themselves, confusing the dates of the civil war with world war 1 or 2?
I am a complete disaster when it comes to remember dates. But I can remember what happened and why it happened from previous historical facts. Dates are not important (you don’t need to have them in your memory). The historical facts, context and aftermath in the long term is what is important. I had ONE history teacher that actually understood that. Never had trouble in her exams.
There are people that complain they don’t get the same opportunities, but when you try to teach them the basic skills to improve their situation, they complain that it is too hard and want to make it easier. My message to you is that you get what you ask for. If you don’t want to put the time into some basic math, fine, but than you also can’t complain when you don’t get the same opportunities as someone who did put the time in. It’s like Thomas Edison said, “Opportunity is missed by most people because it is dressed in overalls and looks like work.”
curriculum*
arguably*
embarrassing*
Wasn’t paying attention, and wrote it out in notepad.
It is hard to imagine that anyone who had trouble passing freshman algebra would fare any better in stats. Get past mean, median and mode into things like skew and kurtosis and a lot of people will be lost.
Re: hard to imagine &c
My sister, a theatre major, repeatedly attempted to pass college algebra and failed every attempt. But she was able to earn an A in statistics & probability. She is exactly the kind of student Hacker is talking about. Her struggles with math delayed her graduation by several years (and scored the university several hundred bonus dollars).
Re: Re: hard to imagine &c
Personally, I had a tougher time with stats that algebra. It may be due to the fact that my Farsi was better than my instructor’s English. However, I think many people find that below the surface, statistics is really tough.
Fundamentally we need to emphasize math by teaching it earlier and paying effective instructors a shitload more than we do.
Re: Re: Re: hard to imagine &c
However, I think many people find that below the surface, statistics is really tough.
Statistics, or probability? The latter always seemed harder to me, but I’m not sure most people know the difference.
Re: Re: Re: hard to imagine &c
As a teacher of Statistics, I can tell you that there are so many KINDS of Statistics being taught that it boggles the mind.
In the university where I teach there is “Business Statistics”, “Psychology Statistics”, “Biology Statistics”, “Social Studies Statistics”, and several others.
In the actual Statistics Department we get literally dozens of graduate students a month who have passed one or the other of these “Statistics” classes only to have to come to us to actually do anything competent when it comes to writing their graduate papers or their Thesis or Dissertation.
They are totally in the dark with what their own departments have told them was “Statistics”. Many of them actually meet with total disaster because they don’t even KNOW that they should consult a real Statistician.
Maths Teachers
What we need is to pay Maths teachers enough for them to drive in and out od the school gates in BMWs – maybe even Ferraris – that way you will get the pupils’ attention.
At present the people they are most likely to see with expensive cars (in somne neighbourhoods) are drug dealers
When people cannot solve:
1+1+1+1+1+1+1+1×0 = ?
It doesn’t matter how “real world” you make your math class.
Re: Re:
When people cannot solve:
1+1+1+1+1+1+1+1×0 = ?
It doesn’t matter how “real world” you make your math class.
Well, what do you think the answer is? Would you be surprised that it’s not zero? Would that just prove your point further? 😉
Re: Re: Re:
I guess I should have put “PS – It’s not 0”. 7.
Re: Re: Re: Re:
If you learned logic it would be 1.
Re: Re: Re: Re:
Or 42.
Re: Re: Re: Re:
I guess I should have put “PS – It’s not 0”.
That’s OK, it was a good point either way. I’m sure you would get at least three answers if you asked that question of a general audience in the US, not even counting “I don’t know”.
Re: Re: Re:
” Well, what do you think the answer is? Would you be surprised that it’s not zero? Would that just prove your point further? 😉 “
LOL … Nice one. Sadly, mention PEMDAS to most adults and they look at you like your speaking a foreign language. I am curious as to what answer the AC came up with for the basic problem he/she posted.
Re: Re: Re: Re:
What is PEMDAS? I bet you don’t know what BUAWIOFO is. Before using an acronym, write it out fully once. I don’t know what you mean by AC, either. You are speaking a foreign language. One that is in your own mind. Oh, Anonymous Coward. But there are a lot of those around. If you had said OP I would have known what you are talking about immediately, though.
Re: Re: Re:2 Re:
What is PEMDAS?
Please Excuse My Dear Aunt Sally (which doesn’t make much sense, but makes it easier to remember.)
Parenthesis, Exponents, Multiplication and Divison, Addition and Subtraction.
Everywhere else in the world, it is BEDMAS/BIDMAS/BODMAS. Brackets, Exponents/Indices/Orders, Division and Multiplication, Addition and Subtraction.
I’ll admit that I haven’t had a chance to read the article in full yet, but learning math isn’t always about what’s on the surface. Math is the universal language and rigorous math is invaluable to society, but one of the skills that most people can take away from math is the analytical skill required to be successful in some topics like algebra.
x + 1 = 10, therefore x = 10 – 1 = 9, should probably be thaught to everybody.
(x + y)^2 = x^2 + 2xy + y^2, probably not.
Re: Re:
” x + 1 = 10, therefore x = 10 – 1 = 9, should probably be thaught to everybody.
(x + y)^2 = x^2 + 2xy + y^2, probably not. “
Why not ?
Just curious.
Re: Re: Re:
I may have communicated poorly. I mean, during high school, everything should be taught to everyone, probably (this is the stage of “throw everything and see what sticks”), so my argument was more like, we shouldn’t expect everyone to learn it.
Knowing what algebra looks like, at least, and to solve basic stuff (I need to fit N cabinets in a X x Y space, or whatever), but most people aren’t going to go around life messing with polynomials or square roots most of the time unless it’s in their job description.
As one who has had difficulty with public education, the issue isn’t Algebra itself, but the way it is taught. In fact, the way we learn math is wrong from the second students enter the first grade.
When the current approach is taught incorrectly at an early age, it’s tremendously difficult for people to unlearn it by the time they reach high school.
More importantly is the fact it’s called “Algebra”, and not mathematics. If schools want to teach students correctly, they’ll need to actually provide examples of how such mathematics are applied to the real world, not just shove two semesters of equations at them.
The real solution is to balance both Algebra and statistics and apply them reasonably with real-world examples.
Dontcha Know
No. We would be better of if BOTH were taught – along with a few other real-value courses (such as how to be a good parent) in place of thouchy-feely fluff courses. I’m amazed at the number of “communication” majors who have read fewer books than than their inches in height.
Self defeating
Many states school systems have become accustom to getting some of their funding from the lottery. Thus it follows that if you start teaching stats and logic in school there will be less money for the schools. The lottery after all is a tax on those that don’t understand math. 😉
"Using" algebra is a red herring
The very act of learning mathematics changes your brain. It makes you think differently. You become a different person for having learned math, whether or not you use it in your daily life.
No way
If we substituted logic and stats for algebra it would destroy our political system.
From a political science teacher?
A political science teacher wanting to teach people about statistics and economics? This would be many a congress critter’s nightmare.
If you include programming/logic, I don’t see the issue. This would have more real-world applications.
Disclaimer, I like maths, especially geometry and algebra, I never had any issues with it. I just don’t think algebra is for everyone, as long as they can handle themselves.
I found algebra annoying in school
I was amazing at geometry and
Calculus was totally pointless
I would have loved Stats, Logic, and Finance classes
I dropped out of highschool mostly from the 8am Calculus class and the substandard reading list, I was tearing through Shakespeare, Milton, and Dostoevsky while English class was stuck reading the Great Gatsby…
luckily I clawed my way into Fortune 100 Technology Company
and no I didnt go to college or carry any stupid student debt
An elephant stands on a platform supported by a beam. If you need a beam four inches thick to support an elephant six feet tall, how thick a beam do you need to support a ten-foot elephant?
what material is the beam made out of ? its compression and flexibility are completely variable. steel? bamboo? titanium? oak? mahogany? koa?
A pizzeria takes telephone orders. Taking one order takes one minute. During peak hours, the telephone is silent for an average of two minutes between orders. How many orders are lost during peak hours because the phone’s busy?
when a pizza place is busy usually the phone monkey has to help make pizza’s too. How fast does the oven bake the pizzas is really what your asking…
Which gets heatstroke faster, a large short-haired dog, or a small long-haired dog?
neither if they live in the arctic, but their poor paws will freeze.
I haven’t read the comments or anything beyond the Techdirt portion of the article but honestly as a person who has learned math up to Non-linear differential equations and a full set of logic courses for CS and a couple differently focused statistics… I would say this is concept is a constructive one that would have almost relatively immediate effect on US society.
For people who are not interested in pursuing further mathematics study, there are two main points to be made. First, Algebra is increasingly less useful in the common uses of daily life. Remember, balancing a checkbook was something that was commonly dreaded. It is not that algebra cannot be applied, it is that it is not worthwhile to apply when you can simply Google the necessary formula rather than derive and understand where the derivation came from.
The second point I want to make is that for many people (I make this statement with my personal experience in successful and popular* tutoring) mathematics lessons, the usefulness and understanding of the subject matter a large number of people are content with occurs when at the point they are applying the mathematics in the next course. At this point the usefulness and understanding of that course is in question until the next course and so on. So for people who have no interest in pursuing mathematics beyond algebra, it is would be fair to call this pointless for that group.
In contrast logic and statistics would be more useful in daily life. These branches of mathematics can be applied to more areas of life even including social aspects and politics**. For instance with an understanding of statistics, advertiser’s life is significantly more difficult(at present unless the majority of a target audience has this skill, this group is commonly written off as an insignificant minority). Whether the subject matter is medicine or laundry detergent, the interactions of corporations with consumers relies heavily on the (inappropriate) use of statistics and logic. Without an understanding in these areas, the consumer is a severe disadvantage.
*Popular is relative, it is in context to tutoring after all. Having a person bring their friend along next time because it is helpful I assume suggests it was at least not unpopular.
**Unbiased, a common practice among all politics are statements formed to sound like logical truth, but cannot be proven true by any formal logic. This is a common method to trick people into thinking an action will definitively provide the result they desire, when there is no formal logic that would suggest this.
What age are you lot doing algebra? UK starts are age 11 with it.. If explained properly its easy as ABC. if explained badly its a nightmare. Get some teacher training in and bin the bad maths teachers, of which we have all had more than our fair share.
Teachers
You know something. I don’t think I’ve ever seen a NY Times article about education my father, happens to have just retired from teaching. I asked him why we have Algebra and he simply told me everyone from nurses, chemical engineers (his major before teaching chemistry) bankers, police, programmers, and anyone who needs to add two to two.
Algebraic calculations are the fundamentals of 2+2=4. The problem isn’t the teachers (though sometimes you get that one person waiting to retire) entirely; I have found that the published school books make it more confusing for students than it needs to be.
The point is, we actually use Algebra on a daily basis. Anyone who has ever ballenced their checkbook, has used algebra. Anyone who has ever saved a life in the ER, has used Algebra. We use algebra for calculating business finances. If you want Statistics (far more confusing I might add), you will be wanting to predict futures in the stock and commodities markets.
Yes Teach Algebra
Having taught algebra to 7th and 8th graders, I think a move to teaching “basic math” (counting fingers and toes with calculators) is a BAD IDEA. Algebra teaches abstract thinking (What if x is any number?) and problem solving (What knowledge do I need? What do I know? What is missing? How are these related? How can I solve for the answer?) These skills along with a sense of number proportion and logical order are invaluable to success in modern life and work.
A few years ago, my state devised a basic math test for graduation, a tenth grade level test. A well regarded local suburban high school was one of the initial testing sites. At that time, algebra was not required for graduation. The scores were so bad that the school dumped eleven high school basic math courses and added algebra for all students. When I read the titles of the courses, I was aghast. Basically the titles reflected grade school math skill.
What you mean by practical math and what a high school will teach as practical math, when the bar of expectations is lowered, are light years apart.
applicable comic
http://xkcd.com/1050/
Horrible teaching
As a parent, I discovered that the teachers no longer understand basic mathematics. Because they were not properly taught mathematics. What they are taught was “New Math”.
What is “New Math”? While I was helping my daughter with her math homework I was horrified to find out that “New Math” meant they’d removed multiplication and division from the basics. Multiplication was “just adding together that many times” and division had become “just guess and see how close you can get”!
How can anyone handle Algebra when they don’t understand basic mathematics?
So, instead of actually teaching mathematics let’s do away with Algebra?
This is sick!
It’s about time these damned schooltards stopped stealing algebra.
My high school AP math teacher took a semester off from usual stuff and spent it teach us how to calculate probabilities. For trig he brought in a surveyor’s transit and we went around figuring out the heights and volumes of buildings. Only math I really remember (and I was pretty good at it) and use. Don’t think I’ve even seen a quadratic equation since.
Statistics vs Algebra
How on earth do you understand statistics without algebra?
Algebra is a prerequisite for statistics.
Re: Statistics vs Algebra
You don’t tell them you are teaching them algebra, that’s how. Without considering the teacher’s skill, the abstract, ‘Why am I doing this?’, is an intimidating and deterring part of algebra as a final step in the math courses. A large part of it is also adjusting for how many people are. Wherever it comes from, just saying ‘algebra’ can make some people resistant, like telling them something is healthy for you. And simply, arguments of ‘You (will) use it for everything’, while a student is not using it currently, is undermining to the teacher. If a statement conflicts with persons experience (while it may be true even if they don’t see it), they question the statement and the person who made the statement.
Re: The Limits of Mathematics (to: Richard, #95)
Quite right, Richard! I would go further. The quality of applied math courses, such as statistics, tends to vary with the amount of pure math underneath. For example, if you want to understand correlations and regression analysis rigorously, you need multi-variable calculus (compute the error function, root-mean-square, and then take the partial derivatives of error with respect to each coefficient). Applied math, in the absence of mathematics fundamentals will simply become more formulaic. Now, of course, “baby stat” is graded on the curve, so a lot of people can get their “gentleman’s C,” and get out. Because it is a terminal course, the instructor can afford to be magnanimous. By contrast, easy A’s in College Algebra deliver unqualified people to the Calculus course, so the department head encourages the instructor to flunk some people.
Look at it this way, when I was in secondary school, they tried to teach me to play a musical instrument, an Alto Recorder, but when I turned out to be very bad at it, after two weeks instruction (I simply couldn’t learn the fingerings for the lower notes), I was allowed to go back to things I was good at, and no hard feelings. No dunce cap, or anything like that. There are things which people could reasonably take in lieu of mathematics (Foreign languages, etc.).
I don’t know what the situation is in England, but in America, colleges are full of people do not have any particular talents, and who want to be employed by large corporations. Such people generally do not have the inclination to be risk-taking entrepreneurs. They therefore take Business Administration. The Business Administration major is built around accounting knowledge. Accountants, especially if they are going to be cost-accountants, need to know a certain amount of Operations Research, so the Business Administration major requires a “lite” calculus course, that is, three hours a week of lectures for a year. However, big businesses use computers to centralize nearly all quantitative information. Only a handful of people get to set prices, or determine inventory levels. The opportunities to become an independent businessman are best in those businesses where quantitative information is least important, and big businessmen cannot compete so well. Restaurants, for example. Food tends to spoil, and if you treat it as inventory, that tends to work out in practice to serving the customer bad food. There is a case to be made for diverting some of the future businessmen into some kind of non-quantitative curriculum, such as foreign languages.
Nobody understands stats almost surely ;-)
Having taught Intro Stats for a good many years, let me assure you that being good at algebra, or being able to solve a line integral are not sufficient to make heads or tails out of statistics. However, not having the capacity for some abstract reasoning required by algebra is an extreme impediment to actually understanding statistics.
Most people do not and cannot understand statistics. That includes almost everyone in academia as well, and I am pretty sure political scientists who can actually understand what a significance test means can be counted on the toes on a cat’s paw. They cannot and will not come to grips with Stats because understanding it would lead to an honest evaluation of the importance of their work.
I am sorry, I just don’t get the notion that one can somehow understand understand anything that requires quantitative and abstract reasoning without not being intimidated by simple mechanics. That doesn’t mean never ever using a calculator. That means being able to do simple things like solving a single equation with a single unknown.
I recently wrote:
I agree, in general schools need a more open nature. To be blunt, I don’t agree with schools as they are, nor when I had to deal with them. After 5th grade it all became to obvious that they wanted me to learn nothing, just to recite whatever garbage they demanded of me and class mates. Keep your kids away from that machine.
This wouldn’t change much, because the U.S. education system would find a way to teach logic and stats in ways that make them also appear completely useless. The education system itself needs to change management practices and incentive systems (the way that all incentives are handled, not just for students). It’s backwards and foolishly designed, and that is why there are problems.
Firstly: Math is not equivalent to logic or general thinking skills.
1+1=2 is only true insofar as it reflects real objects in the real world, but even then, if you continue the reasoning through to its logical conclusion it becomes irrational (see: Pi). You cannot study any abstracted combination of algebraic terms to learn anything whatsoever about the real world. Mathematical science describes (parts of) reality, but because it only does so contingently the applied math in any field is so limited that it can almost always be learned on the job, even in the most math heavy professions.
Secondly: Not one of the many arguments here defending math has used a mathematical argument to defend math or required any math to grasp. All arguments, however, require at least a basic grasp of logic to decipher and appraise.
People, general, suck at logic and reasoning. As proof of this I present the number of people who firmly believe that you can learn to reason properly by learning any amount of algebra.
I have serious problems with Dr Hacker’s assessment of the situation. I have spent the last 15 years teaching College Algebra, Calculus and other math courses at several universities.
The students that Dr Hacker claims we are not serving because they can’t get past the math requirement of algebra do not have a problem with algebra per se…they have a problem with arithmetic. In most cases the reason they cannot pass a basic algebra course is because they cannot add, subtract, multiply, or divide. I argue that a person incapable of doing these 4 basic operations should not be attending a four-year university at all much less expect to
obtain a bachelor’s degree while still being unable to perform a basic life skill. Offering them a (practical) statistics course instead of algebra will do nothing to solve the problem. For one, many colleges and universities are already happy to accept a statistics course in place of an algebra course when judging core curriculum completion and moreover a blanket change might make it harder to address the issue of whether a student lacks a grasp on simple arithmetic.
Offering these students a basic arithmetic class to shore up their math skills is a good step but they should not be receiving college credit (and completion of their college math requirement) for learning material every middle school student should have mastered.
Now Dr Hacker might well argue that we should have some mechanism in place to support the types of students who have either had an inadequate education (through no fault of their own) or made choices in the past that prevented them from learning the material. But I argue that such a system is already in place. Local community colleges offer courses like these…if a student knows they do not have the prerequisite skills for a college level math course they can enroll in a class at their local community college and gain the needed skills. Often times a community college is much better situated to teach these skills than a 4-year university.
Another issue I have with his article is his use of statistics. Mainly…he should stick to political science because his statistics ability stinks. Near the beginning of his opinion he states that at CUNY 57% of their students “didn’t pass their mandated freshman math course.”
Hacker seems to take this statement as saying that 57% of all students who take CUNY’s freshman math course failed it. (Or at least he gives a wink and a nod in this general direction with how he wrote his article.) However, this is not what the statement says…it says that 57% of its student body never passed its freshman math course. There are many reasons why this could occur – given my experience the most prevalent reason is because many students enroll at college with either advanced placement credits or IB credits which satisfy the mathematics core curriculum. These students don’t need to take CUNY’s freshman math course so of course they have never passed it either. I have never taught a math course where the historic failure rate was anywhere close to 57%.. I doubt the failure rate for CUNY’s freshman math course is anywhere close to 57% either.
Many of the same arguments Dr Hacker makes for eliminating algebra from the core curriculum requirement at most universities also works for other subjects such as English or even political science. Students who fail their freshman English or political science course tend to do worse on their other courses than those who do well in English or political science. A student’s grades in any one of their freshman courses is usually a (slightly biased) estimator of their success or failure in the rest of their college career. The fact that many students who fail freshman math go on to drop out is not surprising…it would also not be surprising to find out that most students who fail their freshman English or political science course also go on to drop out.
Why would any intelligent person care what a professor of a pseudo science (pol-sci) opines about a real science?
Algebra needs context
I couldn’t understand algebra for 10 years. I couldn’t make any sense of it, I didn’t know what I was doing with it and none of the algebra teachers I ever had ever bothered to try and explain practical applications for what I was doing. Then, one year, I took physics 101 when I finally made the grade for financial aid and went back to school.
Physics used a lot of basic algebra, but put into context of things I could actually visualize in my head. Algebra was no longer strange magic tricks with numbers, it was letters and numbers that represented physical forces I was familiar with.
If I had been taught algebra in context of what those formulas were for, as opposed to random numbers and letters I was required to do magic tricks with, I don’t think I would have had nearly as much trouble with the subject.
I actually enjoy math now. I got a B in Honors pre-cal last year and I don’t even need the class for my major.
Re: Algebra needs context
Interesting. I was the exact opposite in school. I did great in algebra (and just about every other type of math).
But, I did poor in physics. I had no spatial common sense. Wind blowing due east at 15 mph and bird flying due north at 20 mph would end up going straight up at mach 3. (It wasn’t until I got to quantum mechanics were things became more pure math based that I got good grades in physics).
One size doesn’t fit all. The trick is recognizing a poor student based on effort, raw intelligence and those who perceive things differently.
I gotta ask...
I graduated HS 25 years ago. I’m in a technology-heavy job (software development). Do you know how many times in the past 25 years I’ve had to use the Quadratic Equation?
Yeah.
Motivation is the Key
I’d say that to a good degree I’m one those people this professor was talking about.
Way back when (late 50’s, early 60’s) my problem wasn’t algebra. Even at that age I understood the need for algebra in every day use, so learning it wasn’t hard at all.
It was geometry and higher math I failed miserably at (biology and chemistry too for that matter). I just couldn’t see the relevancy of it to myself, as at the time I couldn’t see myself working in a field that needed it (I didn’t have a clue as to what I wanted to do). Nobody, including my Dad, was able to give a compelling reason why it did matter. In a nutshell, at that time my motivation to learn advanced math was entirely lacking and the ‘powers-that-be’ were singularly lousy and/or uninterested in explaining the need for it.
It wasn’t until I was about 19 that I finally realized what I was both good at and interested in pursuing as a career, which was electronics and computer science. Once I figured that out I was motivated and advanced math somehow became very easy to learn.
What I’m pointing at here is that replacing algebra is not really the answer. Motivation is the key, and teachers/student advisers etc weren’t all that particularly good at motivating and explaining why those subjects were important back when I was a kid. I suspect that is mostly still true today.
Heh, especially bad at explaining it to a lackluster going nowhere high school student and pig-headed plus clueless teenager, i.e. me. 😉
About REAL Statistics
As a teacher of Statistics, I can tell you that there are so many KINDS of Statistics being taught that it boggles the mind.
In the university where I teach there is “Business Statistics”, “Psychology Statistics”, “Biology Statistics”, “Social Studies Statistics”, and several others.
In the actual Statistics Department we get literally dozens of graduate students a month who have passed one or the other of these “Statistics” classes only to have to come to us to actually do anything competent when it comes to writing their graduate papers or their Thesis or Dissertation.
They are totally in the dark with what their own departments have told them was “Statistics”. Many of them actually meet with total disaster because they don’t even KNOW that they should consult a real Statistician.
Be careful what you TAKE when you TAKE something CALLED “Statistics”.
Be careful what you TEACH when you TEACH something CALLED “Statistics”.
Algebra is a hellish subject for people who have both dyslexia and dyscalculia.
I have no trouble with logic “in the wild” and it’s nowhere near as difficult as algebra when working with it formally, although still a struggle to interpret, especially the brackets (using different coloured pens for each pair of brackets is really helpful if anyone out there with dyslexia is studying formal deductive logic, or anything with multiple brackets and struggling to keep visual track of these tricky little symbols).
Re: Re:
I hate to be the bearer of bad news, but you also have sexlexia.
On the bright side I hear it’s a very sexy learning disability.
The problem is that the only sort of citizens statistics class I see easy enough to pass college algaebra failures involves teaching only one statistics rule; that 95% of statistics are made up on the spot. Armed with only this knowledge they would be forced into either politics or copyright research think tanks. So admittedly this would increase the potential posts for techdirt, but jeez Mike think of the rest of us.
Dropping algebra
Let’s take it a small step further: if you pay for the courses, you get a degree. Of course, I am biased, I have
a math degree, but at the same time, if you eliminate math, why not eliminate going to class and listening to a dull lecture? Just pay the tuition and spend the rest of your time in college being an “artist”, giving you fame without pain.
Education and Math
I recall in the 1960s resemting deeply the study of log tables as the teacher himself could not answer a question on utility of same. Years later, in the midst of a demanding career to create reimbursement forumulas for medical providers that required heavy data bashing I longed for a revisit to college logic classes and a regret that there had been no courses (at that time) in statistics. Of course this work needs to be revisited and targeted. My guess is that a “pared down” (which requires the BEST thinking) version of logic and statistics would serve today’s high school population very well. Check the HBO series “The Wire” and see how sets of probability get taught via dice games. It IS time for outside the box thinking and drilling down on what is the essence of, for most, esoteric disciplines. Yes, how DO you best teach critical thinking…. there is no more important time than now to teach this.
Why can’t people understand that to do well in math, you got to work hard on it, just like how you need to work hard to master just about anything.
No wonder why our PISA scores in math are so low.
Algebra, practical, or not?
What teachers need to do is explain WHY and HOW the process of algebra works. The instructor I had 21 years ago passed me with a C- just so he could get rid me.
The instructors I’ve had in college have not explained anything, they just sit and proctor your tests for $3,000.00 I expect more than that! And if you are a mathematics instructor but cant break things down into laments term please…don’t teach!
Algebra is plain theory with no tangible facts to support it as far as I can tell. Give me hard facts I’ll give accurate answers. Please yes replace algebra with statistics
Algebra, practical, or not?
And if you are a mathematics instructor but cant break things down into laments term please…don’t teach!
“Layman’s terms”
Algebra is plain theory with no tangible facts to support it as far as I can tell.
It’s abstract math, why are you expecting facts to be involved? Are you saying you want to learn the proofs for everything? I promise that wouldn’t make you like math better because the proofs for some simple things you take for granted, like addition, are not simple. 🙂 The professor doesn’t have time to take you through all the proofs – that’s saved for advanced degree programs.
my intuition tells me...
re: the elephant question.
So, you have a 4 inch thick beam supporting the 6 ft tall elephant and want to determine the thickness of a beam needed to support a 10 ft tall elephant. The load on the beam is determined by the weight of the elephant. In the absence of the actual weights of the elephants, we must assume that the weights are proportional to the VOLUMES of the elephants. Since, we do not know that one elephant is proportionally trimmer than the other (elephant diet perhaps??), we can assume that the volumes are proportional to the cube (third power) of the ratio of the heights. Therefore, the thickness of the beam can be estimated:
4(10/6)^3 = 18.52 inches.
Without math I would have problem understand 3d graphics and VFX or animation. All things like derivatives or vectors are useful here.
I was bad at math in school because I didnt understand why I need vectors. At least I did understood about derivatives because in that year I tried to be better at math, ended up from F or C to B at end of year.
But in computer graphics it’s not about remembering formulas or able to calculate without using calculator, but about logic. There’s so many things to remember or even figure out if you didnt see tutorial how to do something, you need to understand what you’re doing. So both math, logic and also some programming needed.