I think there’s a lot of overlap in thinking style between a good mathematician and a good programmer. Both require the ability to look at a problem, categorize the problem set, and come up with a series of steps that lead from the problem to a solution. A CS graduate with a lot of math and physics would probably indicate a person with good problem solving skills and curiosity about how the world works, which is the same skills you need to be a good programmer.
Well, that’s what I’ve been saying. And, though you may disagree with me, you seem to serve as an instance of my point that it doesn’t work to try to force math education (or anything else) onto someone who has no interest in learning it, and those those who do later on find such desire sparked will be able to learn it much more effectively then.
Should we dump spelling too? As a person who suffers from dysgraphia that would have made all that painful spelling drills go away. Learning is hard and many times you don’t understand why they are teaching you something.
But just because you don’t like a subject or have difficulties with it doesn’t justify removing it due to some vague fear of damaging a persons psychological feelings about the subject.
Or do you have any empirical evidence that elementary algebra is hindering math education, evidence not editorial rants.
Or as the linked story in the OP infers, should we just graduate people who can’t write or do basic math? What is the value of the diploma if it is just handed out so that people don’t feel bad?
I have a degree in Mathematics. I love algebra. So, yeah, I am completely biased.
The way algebra helps me is not just in my job (which, as a computer type, it does) but in my everyday life.
You see, algebra constantly builds upon itself. To me, it is a pure extension of addition. It is a language onto itself with rules and structure. Each thing you learn in algebra is a tool. Every time you are presented with a new problem, you need to look at the tools you have and see which ones are the best for solving it. Sometimes, you can even use different tools than someone else and still come to the right logical answer.
Life is the same. Each day, I learn new things. I see the world in a new way. Each thing I learn is a tool that I can use in my everyday life. Being able to mentally find the right tool and apply it is what makes me so successful. This applies to everything from finances to shopping to cleaning.
The ability to be able to come up with an algorithm to do something or a solution to a complex problem is based on my math skills.
I said above, I believe, that a few skills are worth jamming in against childish resistance, and most aren’t, and that literacy and basic numeracy fall in the former category.
Yes, but what is accomplished? Everyone keeps proposing curricular standards based on fantastic goals without assessing whether they actually accomplish those goals! For all the compulsory math education/torture we’re engaged in, it’s still the case that the students who are interested get something out of it and those who aren’t don’t. Why not let the latter off the hook, free to come back if they change their minds? If you take a survey of the general populace’s experiences in math class, large numbers will have nothing positive to say in the way of either interest or knowledge that stuck.
I am not proposing deriving anyone of the opportunity to learn anything. I would march against the removal of math classes. I only want the removal of compulsion. I would want math, beyond basic numeracy, treated the same way piano or football is.
Er, I never claimed elementary algebra was hindering math education. I don’t even know what that would mean. I claimed that not everyone needed to be trained in math beyond basic numeracy, and that algebra is right on the border of that cut-off.
You have given no evidence, outside of your distaste and difficulty with the subject, that stopping at elementary algebra is the place to stop.
I would argue that your low bar for education is already optional, you are free to drop out after grade school which would meet your limited goal of education.
College students are hardly prepared to decide what courses will help them in life, giving those same choices to the whims of a child in middle school would be disastrous.
We need the vast majority of the population to be educated in many fields, letting them opt out because it is not “what they like” will do nothing to improve our competitiveness in the world market.
The lack of math skills directly impacts my ability to higher useful workers, the inability to understand basic computer functions without memorizing steps is one manifestation of that issue.
The concepts behind elementary algebra, which is what is compulsory are critical to our society in the modern world. The fact that people don’t remember where they learned that a problem isn’t solvable or to find the solution set in real life doesn’t mean they didn’t learn those base concepts in Algebra class.
In other words, the issue isn’t whether algebra is necessary, but how much algebra is necessary.
In the sense that elementary algebra is a language, it’s necessary because so many other subjects are awkward if not impossible to learn without a working knowledge of the language of algebra.
I am reminded of the claim, which I think was originally cited by Stephen Hawking in his book A Brief History of Time, that (at least according to one editor), that for every equation in a book about science for the general reader, readership would be halved. If true, this indicates that something is seriously amiss, if someone with the intellectual curiosity to pick up a book on science isn’t able to handle a few equations, which, to someone who’s fluent in the language of algebra, can convey an understanding of what’s going on more precisely and concisely than paragraphs of verbiage.
(On reflection, this business about manual arithmetic drills is a hijack from the point of this thread, but having already typed it…)
Well, we might ask if the tests are testing the skills we actually care about. For example, if what is tripping the students up is not the algebraic reasoning, but that they are very slow at or keep making glitches in multiplying digit-strings by hand, not through inability to memorize the algorithm but sluggishness or sloppiness executing it, this is perhaps not a problem that should concern us terribly, and which would be perfectly well resolved with access to a calculator.*
Again, we might, instead of saying “Boy, there’s something wrong with this student; they need to shore up their math skills”, say “Boy, there’s something wrong with this math test; it’s not effectively assessing the skills we care about.”
[*: “But how will they know when their calculator is wrong?”, some say. Well, not by always double-checking all the calculator’s work by hand, of course. I don’t do that; nobody does. It obviates the point of the calculator (or slide rule or abacus). They will need an intuition for what makes for a grossly implausible result, same as they would need for manual arithmetic. “Yes, of course. And how will they develop such an intuition, except by having been made to drill on performing such calculations by hand?”. Hey, they could develop the same intuition by repeated performance of such calculations by calculator on top of basic conceptual understanding, same as all those legions of adults who’ve never calculated a logarithm or sine by hand are forced to resort to for sanity-checking those calculations.
For all the talk that manual arithmetic builds intuition in some special way, I see people spit out the same kinds of grossly implausible results from mistakes in manual arithmetic as they might have from a calculator instead. Of course, the student needs to understand conceptually whatever they are doing; it’s no good having them blindly multiply decimal-strings on a calculator if they have no idea what multiplication means and some sense of how it distributes over addition and interfaces with decimal notation and so on. They just don’t particularly need to do long multiplications by hand ever in their life; it may not be a skill worth fine-honing.
It’s not that drilling is incapable of achieving some positive benefits through accelerated familiarity, but we need to ask exactly what the benefits are that we hope to achieve, and whether different kinds of practice might achieve those benefits more effectively.]
My goal is not limited education; my goal is voluntary education.
Having the ability to drop out after grade school is not helpful. I don’t want a system that’s all or nothing. À la carte, rather than prix fixe. I want students to be able to pursue the material they are interested in pursuing, while not being burdened, beyond the most basic necessities, with slogging through the material they are not interested in pursuing. I think there’s a high bar for “Material it is worth forcing everyone to be trained in, against their own wishes”, which has to in particular be assessed relative to the amount of effort such training takes and the results such training accomplishes, and very little clears this bar.
Again, and again, we come back to the question: Ok, we’ve made it all compulsory, every subject under the sun. What has that compulsion achieved? Are there not legions of adults who made it through the compulsion without anything for it but a transcript and perhaps resentment?
People learn things readily when they have interest in learning them (either intrinsically or as a means to some other goal for which it is prerequisite), and not so much otherwise. I’m sure you could force anyone to pick anything up eventually, even if they are utterly uninterested, but there’s an opportunity cost; the time spent on such a gargantuan effort is time which could have been put to better use for both the teacher and the reluctant student (the former more engagingly interacting with students who are there in voluntary transaction, the latter pursuing those skills which they do desire). Horses and drinking water and such…
It is a reality that there are people who go through the system and pick up no significant math skills past some point. If there were a means to predict those people and let them off the hook early, why not do so?
Yes, I agree with this.
And I agree with this as well. This level of algebra is, I would say, worth jamming in involuntarily, as a skill not unlike literacy.
Correct. Can we be honest with ourselves to ask without historical bias if we get by with less force-fed Algebra? How about 1 semester “Intro to the Power of Algebra.” The kids that want to continue can take the full 2 years of Algebra I and Algebra II.
There is zero evidence that the people who don’t use it get anything out of it. I’ve heard a lot of fuzzy platitudes but zero proof.
“But there is value in forcing kids sit through Algebra I & II class!”
Not for the students that aren’t motivated in it. They will use every coping mechanism possible (mnemonics, cramming, etc) just to get a passing grade.
Consider 2 different curriculum scenarios:
year 1, semester 1 – Algebra I
year 1, semester 2 – Algebra I (continued)
year 2, semester 1 – Algebra II
year 2, semester 2 – Algebra II (continued)
or…
year 1, semester 1 – “Intro to Power of Algebra”
year 1, semester 2 – Media Studies (understanding deceptive marketing)
year 2, semester 1 – Linguistics (understanding building blocks of world languages)
year 2, semester 2 – Statistics & Probability
We have zero evidence that the traditional 2 years of force-fed Algebra creates outcomes superior to the hypothetical curriculum. Sure, some of us have some warm fuzzy intuitions that it must be so be that’s not real proof.
A lot of people just aren’t retaining/using algebra. See:
Primary school teachers fail to pass basic maths exam
Example question:
Q: The mean height of a group of four people is 2m. One more person joins the group and then the mean height is 1·9m. What is the height of the new person?
A: 1.5 metres
Answered correctly by 22 teachers (14%)
As I’m not privy to the content that you intend for “Intro to the Power of Algebra”, perhaps I misunderstand you. But I’m not the slightest bit sure how someone can be expected to learn any non-trivial amount of statistics and probability without knowledge of high school-level algebra (to say nothing of what modicum of mathematical maturity that confers). I don’t know if it’s possible for me to describe how utterly horrible my semester of statistics was, after having only remedial algebra (and before catching the math bug). If you’re going further than, say, defining various summary measures, you’ll need more than arithmetic.
If someone can deduce from the fact that there were three cats on the couch, and now there’s one cat on the couch, then two cats must have left the couch, then that person can learn algebra. The solution is finding better ways to motivate, not throwing in the towel entirely.
Then design it into more of a survey course: “Basic Statistics, Probability, Discrete Math, Number Theory”
…or… (gasp!) skip it entirely and the student can substitute another worthy academic subject to sink his teeth into. Possibly better for him; possibly better for society too.
That’s not algebra. That’s arithmetic… 3 minus 1 equals 2. You can make some superficial text substitutions to make it look more like algebra, “3 - 1 = ?” or “3 - 1 = x ; so what is x?”
So sure, if you water down algebra by relabeling “arithmetic” as the “New Algebra”, amazing progress can happen. 
Traditional algebra is more like, “2 typists can type 5 pages in 1 hour. How many typists needed to finish 100 pages in 4 hours?”
Those kinds of quantitative reasoning questions are deceptively difficult for many folks. (See Guardian news article for example of 86% of teachers failing that type of question.)
And we’ve tried for 100+ years. I’m not against rote memorization forced on kids for some topics. The technique works very well for arithmetic and the skills stick for life. It’s not been proven to work for algebra. (Again, see Guardian story above. Similar stories of teachers flunking math tests in Florida and New York.)
Even this, I would want to call arithmetic, in the same fashion…
“Typing efficiency is (5 pages per 1 hour) per 2 typists. If you divide this into 100 pages per 4 hours, how many typists do you get?”
I am going to ignore your hyperbolic straw man there but…
Wouldn’t the correct path be to encourage kids to learn vs. tossing out core subjects?
And I am sure they resented having to bathe, clean their room and mow the lawn.
All your claims are pure conjecture, you have given no evidence that most don’t get anything out of algebra.
Algebra is logic. When you learn algebra you are learning how to solve logical problems.
What is wrong with teaching someone to the terminus of their ability? Why should we stop short just because a tiny number of individuals will carry a chip on their shoulder for the rest of their life?
If they don’t learn because they don’t care look at the education system for flunk the kids.
The problem to a dropout problem is not to lower the bar. Sure you need to account for learning disabilities or low abilities in all the subject but making it optional doesn’t do anybody any good.
Or are you shooting for the old, invalid “boosting self-esteem” idea? Because in several recent studies it has been shown to lower subsequent academic performance. Of course someone who has made it to higher math would know that when you have a lot of studies on both sides of a topic that typically means it is noise and the correlation doesn’t exist…but that would require more than arithmetic.
Kids will choose what ever is easiest and what will give them the most time for xbox or what allows them to hang out with their friends.
So Sally wants to hang with Jill who doesn’t like math, so like Jill she “opts out” of math in middle school at age 11. Now if she wants to go into a STEM field (which we really need) she will have to take remedial classes. Do you know how much harder it is to learn math as an adult?
Why should we limit their education attainment so they aren’t “bitter” and once again, where are your cites that this would be better and why stop there at this arbitrary point or are you saying if they don’t like long division they can opt out there too?
This is a valuable skill that they will undoubtedly use for the rest of their lives.
I’m in processing geophysics (the processing of seismic geophysical signals), and our company also takes this stance.
The VP who implemented that hiring strategy always that it was easier to teach a mathematician geophysics than a geophysicist mathematics. So far, he’s been proven correct. Our top employees have degrees in mathematics, ‘normal’ physics, and engineering, rather than geophysics or geology, and nobody in the industry questions our results (though they often balk at the price - we think you should pay for high quality).
If we let kids take only what they wanted to take, we could get rid off all of our science, math, and history teachers. We’d be overrun with art, music and PE teachers. Part of running a school system is preparing the next generation to take over, and, soory kids, learning about algebra andhow the U.S. was founded, and what DNA is (among many other things) is necessary.
Obligatory link to my second favorite comic of all time (after Calvin & Hobbes)
The typist question is arithmetic. 100 pages in 4 hours is 25 pages an hour. To get that rate you need 10 typists (5 sets of 5 pages by 5 sets of 2 typists).
The algebra question is more like this.
If you know that n typists type m pages per hour, what is the formula for number of typists to do x pages in y hours?
Then the answer is ((x / y) / m ) * n which is equal to xn / ym
Now you can program your Excel spreadsheet to solve this for you.
This kind of ability helps with all kinds of everyday activities. Sure, you can do without it, but a common sense approach leads to being taken advantage of by the people who know the math and the psychology to trick you.