## The case against algebra II

There’s an interesting debate described in this essay, Wrong Answer: the case against Algebra II, by Nicholson Baker (hat tip Nicholas Evangelos) around the requirement of algebra II to go to college. I’ll do my best to summarize the positions briefly. I’m making some of the pro-side up since it wasn’t well-articulated in the article.

On the pro-algebra side, we have the argument that learning algebra II promotes abstract thinking. It’s the first time you go from thinking about ratios of integers to ratios of polynomial functions, and where you consider the geometric properties of these generalized fractions. It is a convenient litmus test for even more abstraction: sure, it’s kind of abstract, but on the other hand you can also for the most part draw pictures of what’s going on, to keep things concrete. In that sense you might see it as a launching pad for the world of truly abstract geometric concepts.

Plus, doing well in algebra II is a signal for doing well in college and in later life. Plus, if we remove it as a requirement we might as well admit we’re dumbing down college: we’re giving the message that you can be a college graduate even if you can’t do math beyond adding fractions. And if that’s what college means, why have college? What happened to standards? And how is this preparing our young people to be competitive on a national or international scale?

On the anti-algebra side, we see a lot of empathy for struggling and suffering students. We see that raising so-called standards only gives them more suffering but no more understanding or clarity. And although we’re not sure if that’s because the subject is taught badly or because the subject is inherently unappealing or unattainable, it’s clear that wishful thinking won’t close this gap.

Plus, of course doing well in algebra II is a signal for doing well in college, it’s a *freaking prerequisite* for going to college. We might as well have embroidery as a prerequisite and then be impressed by all the beautiful piano stool covers that result. Finally, the standards aren’t going up just because we’re training a new generation in how to game a standardized test in an abstract rote-memorization skill of formulas and rules. It’s more like learning student’s capacity for drudgery.

OK, so now I’m going to make comments.

While it’s certainly true that, in the best of situations, the content of algebra II promotes abstract and logical thinking, it’s easy for me to believe, based on my very small experience in the matter that, it’s much more often taught poorly, and the students are expected to memorize formulas and rules. This makes it easier to test but doesn’t add to anyone’s love for math, including people who actually love math.

Speaking of my experience, it’s an important issue. Keep in mind that asking the population of mathematicians what they think of removing a high school class is asking for trouble. This is a group of people who pretty much across the board didn’t have any problems whatsoever with the class in question and sailed through it, possibly with a teacher dedicated to teaching honors students. They likely can’t remember much about their experience, and if they can it probably wasn’t bad.

Plus, removing a math requirement, any math requirement, will seem to a mathematician like an indictment of their field as not as important as it used to be to the world, which is always a bad thing. In other words, even if someone’s job isn’t directly on the line with this issue of algebra II, which it undoubtedly is for thousands of math teachers and college teachers, then even so it’s got a slippery slope feel, and pretty soon we’re going to have math departments shrinking over this.

In other words, it shouldn’t surprised anyone that we have defensive and unsympathetic mathematicians on one side who cannot understand the arguments of the empathizers on the other hand.

Of course, it’s always a difficult decision to remove a requirement. It’s much easier to make the case for a new one than to take one away, except of course for the students who have to work for the ensuing credentials.

And another thing, not so long ago we’d hear people say that women don’t need education at all, or that peasants don’t need to know how to read. Saying that a basic math course should become and elective kind of smells like that too if you want to get histrionic about things.

For myself, I’m willing to get rid of all of it, all the math classes ever taught, at least as a thought experiment, and then put shit back that we think actually adds value. So I still think we all need to know our multiplication tables and basic arithmetic, and even basic algebra so we can deal with an unknown or two. But from then on it’s all up in the air. Abstract reasoning is great, but it can be done in context just as well as in geometry class.

And, coming as I now do from data science, I don’t see why statistics is never taught in high school (at least in mine it wasn’t, please correct me if I’m wrong). It seems pretty clear we can chuck trigonometry out the window, and focus on getting the average high school student up to the point of scientific literacy that she can read a paper in a medical journal and understand what the experiment was and what the results mean. Or at the very least be able to read media reports of the studies and have some sense of statistical significance. That’d be a pretty cool goal, to get people to be able to read the newspaper.

So sure, get rid of algebra II, but don’t stop there. Think about what is actually useful and interesting and mathematical and see if we can’t improve things beyond just removing one crappy class.

Ironically, Algebra 2 is where they teach a lot of probablity and statistics! See e.g. the NY algebra 2 standards at

http://www.p12.nysed.gov/ciai/mst/math/standards/a2trig.html

I think that’s because algebra 2 has tended to be the “catch-all” course where all mathematics that’s not calculus and not geometry winds up. Also, there’s now a statistics AP; it started in 1997 and now 150,000 kids a year take it (against 260,000 for calc AB and 94,000 for calc BC.) The high school district I live in in Madison offers a stats AP course and I assume lots of others do, too.

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100% agree with your final comment–Statistics is covered very briefly in the HS curriculum in my experience. I’d say it’s become much more relevant over the last 30 years not only to the average person reading a newspaper or participating in a democracy as well as to specialists, as statistical analysis has become a bigger and bigger part of many areas of both science and math. Learning the intricacies of Trig, OTOH, doesn’t really have much practical application to the former pool, and is going to be part of pre-calc requirements for the latter pool.

Interesting trivia–statistics is completely absent from Singapore Math, because the puritanical Singaporians believe teaching statistics will encourage gambling.

On the earlier discussion, I’m on the “keep it” side for several reasons. First, I’m a direct result of having focused in Math in school, but then used those conceptual abstraction skills in a non-math field. Second, if it’s hard, my knee jerk response is “quick fucking whining–if it were that easy it wouldn’t need a fucking course now would it, so shut up and actually study the shit.”

My $0.02.

FoW

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We had statistics in my high school (in CA about a decade ago). I think the math track was Algebra 1 -> Geometry -> Algebra 2 or Statistics -> Pre-Calc (A2 was a pre-req) or Statistics -> Calculus (pre-calc was a pre-req). Technically we were only required to take three years of math, but four was recommended if you wanted to go to college, and you could start further down the track if you were an advanced student (and there were special sections of Geo and A2 for advanced students). So if you weren’t on the Calc track, then you probably ended up taking statistics at some point. It doesn’t address whether A2 is a good college pre-req or not… but most students ended up taking stats, which I think is a good thing (ironically, the most advanced students didn’t take stats in this system).

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This is an interesting and important topic; just some disjointed thoughts here:

(1) Many embedded in math education have this dualistic view of plug and chug vs. thinking. The implication is that plugging and chugging is done without thinking. I think this is (mostly) a fallacy, and they need to rethink a bit what is really going on here.

(2) Throwing out Algebra II because most people won’t use it is a classic “flaw of averages” fallacy. The fact is, most 15 year-olds don’t know whether they will end up in a career where having Algebra II is useful. If the default is to leave Algebra II of a student’s course plan, then there will be a significant number of people who would end up in a STEM career but will either be disadvantaged because of this choice or will end up in a non-STEM career entirely. We need to compare the burden of a non-STEM student taking Algebra II against the loss of STEM careers to really do the efficiency calculation.

(3) On statistics being part of Algebra II, my experience is that while statistics is often on the lesson plan, it is for the end of the course, and many teachers sacrifice the statistics to catch up and prepare for the standardized exams, most of which have virtually nothing on probability and statistics.

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My only memory of algebra II was that the (summer school) teacher’s voice was impossible to focus on. I read the textbook instead of listening. I don’t think that’s enough to have an opinion.

I do have an opinion on first year college math.

For many students freshman calculus is the *only* math they take. Is calculus really the one math course people should take, if they are only taking one? How much could they ever possibly use calculus? I mean, these aren’t physics students (who do need it).

Linear algebra isn’t any harder than calculus, and has more easy applications. Wouldn’t it be a better choice for student’s that only take one math course.

Ralph Hartley

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On the other hand, I think that a poorly taught Linear Algebra class has all the same disadvantages as a poorly taught Algebra II class. (David Jones’s point below is relevant here.) I’ve known science people who got turned off of math when they got to linear algebra.

Linear algebra is more about building up abstract power tools, where as the basic concepts in calculus are more concrete. (And people taking physics at the same time get to see it in action.)

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You are describing my math and science education. I entered college a physicist with multivariable calc, took said “poorly taught linear algebra class” and ended up a history major (and PhD)… Luckily since then i have left academia, and am now fallen back into my quantitative ways in financial research, though disadvantaged by the decade and a half off, for sure.

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I remember Algebra II being my least favorite math class in High School. Actually, I think it was my least favorite math class ever.

I think the problem is that whenever you have a math class that “promotes abstract thinking”, you really need an awesome teacher to make the students both appreciate and enjoy the content. This is especially true for a course like Algebra II that doesn’t introduce a truly revolutionary concept in the way that Algebra I and Calculus do.

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David, I would go you one further: Algebra II was my least favorite CLASS ever. That woman was a horrible, horrible teacher, and the material SUCKED. I would go so far as to say that it turned me off of math completely. I was advanced in jr. high and took geometry freshman year, qualified for mu alpha theta, then took algebra II sophomore year. I quit taking math. I even eased off of the science, because I did not want to have to encounter any more of that horrible crap. I took algebra over in college, because I had felt so insecure about it from then on, and aced it. I went on to tutor the class. And I’ve done tons of advanced stat and economics over the years – I got a masters degree in it.

And hating (and sucking at) Algebra II was wildly unpredictive about my college abilities. Phi beta kappa, summa cum laude, several advanced degrees, bla bla bla. All it did was make me certain that I hated math and never wanted to try to do anything with it ever again.

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One of the goals of an educational system is to identify those with the talent to become scientists and engineers and to train these people, because having such people is good for society. If these people are not to be identified a priori (for example, as the sons of physics professors and rich people) then it becomes necessary to expose everyone to a substantial amount of mathematics, science, whatever is relevant, in order to find those with the talent/interest and also to begin to nurture their talents/interests. From such a perspective it is essential to teach algebra in high school because in practice very few 18 years olds who know no algebra will later be able to contribute productively as scientists or engineers (the one or two counterexamples I have encountered in many years of teaching future engineers came up through machine shops and were possessed of the native tendency to work very hard and to play and tinker).

Said all that, for the vast majority of students there are probably more useful things to know than algebra (and the same could be said for calculus at the university level). Nonetheless, the problem is that one does not know beforehand who are the students who need to know it or will want to know it.

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I did remarkably well in Algebra II and remarkably mediocre in later life, but I’m only one data point.

Math is the only HS subject in which I consistently got “you’re better than most people at this” feedback. So I made the mistake of majoring in math. Maybe this isn’t the post to be commenting on and I need to consult Aunt Pythia, I don’t know.

Bobito tells us “One of the goals of an educational system is to identify those with the talent to become scientists and engineers and to train these people, because having such people is good for society.” Maybe, although I’m skeptical. Maybe if the system got the signaling right, but even then, it begs uncomfortable questions. If the goal is to identify and further refine the proverbial “best of both worlds” student who has both native talent (which I was successfully trained to think of as a form of unearned unfair advantage) and work ethic, then at some point the “prospects” have to be taken aside, maybe out of earshot of the General Population (school sociology is a microcosm of prison sociology, right?) and read the riot act. In my own case (current age 48) the problem seems to be more a failure of counseling than of teaching.

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2nd year algebra for everyone started from mistaking causation for causality. About 25 years ago I was shown studies finding a strong correlation between success in Alg II and success in university. From this our district (Detroit) decided every one should take a second year of algebra. I believed then, and still do that the correlation stemmed from the abilities of the students taking the second year and not the year itself. The result was a less rigorous course.

In response to the musings at the end of the blog I would suggest taking a look at the Core Plus Math Project. The authors of this curriculum tried to answer the question: If I only had 1 (or 2 or 3 etc) year to teach maths (I like the English way, I also liked being un maestro dela mathematica in my bilingual school) in high school was should I teach ? The result was a series of units teaching algebra, geometry, prob and stat, and graph theory.

,

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Agree in spades that algebra II should be chucked in favor of stats, for the good and sufficient reason that it actually has some real world applicability (the computations are also a lot easier to perform than they were 30-plus years ago, a not-insignificant consideration when you consider the work divide between high school and college.) The flip side is, word problems. No one wants to grade on reading comprehension when they’re actually testing for math.

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I disagree that we should remove everything and then add back only what we think adds value. The problem, as you know, is that no one can agree on what values we should have. Everyone who uses math has a use for

somesubpart, and in addition it is impossible to quantify (or even discern) the abstract benefits of a student learning algebra versus calculus versus statistics versus geometry versus number theory. People clearly need to think hard about what are therealmathematical subjects of which these traditional curricular units are combinations (for example, the concept of abstract arithmetic, or the translation from intuition to formalism, or just plain computation, as distinguished from techniques for solving specific equations or memorizing specific vaues of special functions or familiarity with certain idiomatic word problems like “two trains are approaching…”). Then we can decide what value is added by one subject versus another. But nothing will come of pitting algebra against statistics in the arena of educational politics.They may not want to, but it’s more important for applications. Real-life occurrences of statistics for the general public tend not to come in straight-up formulas.

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It’s finals day and my future depends on passing the “abstract thinking” requirement. We’ll be asked questions about bizarre paintings. Despite months of fretting, whining, anxiety, and late night memorization, my teachers and I know that I just don’t get it. No “abstract thinking” and there will be no college for me. I just hope that they lower the bar enough for me to randomly score more than half of my classmates who are just as lost as I am. Not being all that good at construction or trades, failure leaves fast food work or debt collection – along with public assistance.

The merit badges promoted by MOOC providers are looking better every day….

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I use Algebra II/Trig on a daily basis. Most people who work in the physical sciences and many of the engineering disciplines do. I would call that real-world applicability.

But, there’s a more basic point. Let me rewrite what you said:

Education is not about learning particular things. It’s about learning how to think in different ways, made concrete by studying a particular thing. I don’t use

MacbethorHamletfor anything, but in studying it, I learned about the dramatic form and experienced some beautiful English at a time when I actually had the time to appreciate it. It taught me how to experience the world differently.There’s some merit to judging algebra II on its usefulness, but (a) you clearly don’t have a broad perspective for “real world applicability,” and (b) that’s not the only metric one should use to judge a high school course.

The flip side is, word problems. No one wants to grade on reading comprehension when they’re actually testing for math.

The biggest problem I’ve seen in college-age undergrads is their inability to take concepts used in math class and apply them to things outside of math class. Math serves as a precise language to describe real-world behavior, but doing so requires practice.

Word problems practice this link between math and the real world. This is true both for prob/stat and for algebra II/trig. In my opinion, testing pure math comprehension is important, but equally important is testing whether one can apply it to the real world. More word problems, please.

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(I definitely agree with you on the whole, but just had to drop in and say:)

Trigonometry?! But you need that for shop class!

Shop classes actually might be an interesting example of the effect of slackening requirements; at least at my school they were perpetually losing funding because not required -> less government funding -> worse classes -> fewer people care about them -> less resistance to budget cuts -> less government funding and so on.

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Algebra is sooooooo middle-class, you know?

I mean, that’s the real problem here — class distinctions.

And nobody wants to talk about — class distinctions.

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Just in case you thought I was joking — I am not!

Ruby Payne is someone that takes seriously the cognitive divide between classes.

http://www.ahaprocess.com/

Google her. It is the cognitive divide that makes Algebra sooooo middle-class.

And I saw it at work all the time — po’folks unable to navigate middle-class reality. All of it cognitive.

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The question should not be “why algebra?” but “what algebra?” The concepts of variable, parameter, linearity, proportionality to name a few are important thinking tools and should be required of all college grads let alone high school graduates. In the same respect concepts from statistics particularly sample variability are essential knowledge for an informed citizenry. Unfortunately, but for good reason, most people think of algebra as pushing symbols around on a paper. This is the way it is taught because it is easier that way both to teach and grade. Symbolic algebra problems were originally devised to test a student’s understanding of underlying concepts but devolved into skill exercises, skills most people will never use. Original problems that test concepts are hard to devise and once used can not be used again since once a question is published and a solution worked out the next time it is used it will just be an exercise in pattern matching for most students.

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I’ve always been really suspicious of the “it trains abstract thinking” argument (which sometimes is called “training students how to think” or simply “it makes them smarter). Is that something that’s actually been studied, and proven? How the heck would you prove that, anyway, with all the controversy over the validity of iq tests? And how do you prove that studying math is really the *best* way of training abstract thinking- more so than, say, philosophy, which is hardly ever taught in high school.

Algebra II is an especially wierd class because it’s advanced enough that most people will never use it in their every day life, but it’s basic enough to have almost nothing in common with what real mathematicians do. I’d rather see math taught more like the way we teach art- everyone has to introduced to it a little, and if you’re good at it and you like it, great! Go as far with it as you can! But if not, no big deal, you can still get into college and get a decent job without it.

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The “training students how to think” argument has been a justification of the classical curriculum (i.e., Latin and Greek in high school, Gaelic Wars and Plutarch in college) from the 1800s in this country. It doesn’t matter WHAT is being taught, but BECAUSE it is being taught, it is ALWAYS “training students how to think”.

In other words, the “training students how to think” label is rhetorical, not factual, and used to legitimate what ever the institution happens to be doing currently. Presumably, the same could be said of porno film studies today.

On the other hand, teaching chicken thieves and financial hucksters and shyster lawyers how to think better is NOT always a good idea.

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Great point. I do think it would be nice to quantify that.

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A few remarks:

1) I had statistics at my (admittedly up-scale) high school, but it was also full of rote memorization and repetition. The problem doesn’t appear to be the content, but the way it’s taught.

2) You’d be surprised how many mathematicians know what a joke high school education is, not to mention the math we subject students to in college! Make no mistake: for the majority of US universities, calculus is mandatory and mindless. On the topic of why the derivative of an exponential is again an exponential, a colleague of mine tells her students “don’t ask questions, just accept it.”

3) Many mathematicians are outspoken about what belongs in pre-college education. Paul Lockhart wrote an amazing essay which I’m sure you’re familiar with ridiculing the typical high school’s math program. The theoretical computer scientists know that students would be much better off inventing algorithms in their classes than factoring polynomials. The statisticians know that designing and critiquing experiments is far better than rote memorization. The game theorists know that analyzing games is way more *fun* than graphing rational functions. Graph theorists know how natural graphs are to work with.

The problem is that the people who make decisions about pre-collegiate mathematics education are by and large the people who themselves dislike mathematics!

So of course, let’s get rid of all the stupid courses we make our students sit through and replace them with courses where they actually think.

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“So of course, let’s get rid of all the stupid courses we make our students sit through and replace them with courses where they actually think.”

Sacrilege ! Never happen..

But I digress. What needs to be done is to stop teaching math as an entity unto itself and teach it along with physics and chemistry where it’s used heavily. Physics – after all – is primarilly applied mathmattics.

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Even major scientists can’t get the statistics right.

http://www.economist.com/news/briefing/21588057-scientists-think-science-self-correcting-alarming-degree-it-not-trouble

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my spouse and I are both degreed chemists; she worked in industry and later taught high school; she found that algebra II was a necessary prerequisite for learning chemistry — especially reaction kinetics and stoichiometry; and she avers that the abstract thinking IS important for acquiring and using (chemistry) knowledge

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http://www.wired.com/business/2013/10/free-thinkers/

This article is rather intriguing and is along the lines of what you are proposing in an extreme way. I am not an educator. My doctorate is in molecular biology. The statistics I learned were pretty basic. I believe that critical thinking is the best skill you can teach kids, but math is right up there since we’ve seen economists who can’t do empirical analysis and seen how well that works out macroeconomically.

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One can not learn math from the text book and therefore a parent can not help a student from the classroom text book.

There is a teacher’s edition of the text book that gives the answers from the back of the chapter tests. There is an example text and a text to explain to the instructor the methodology and order to instruct the subject using the classroom text.

If a student does not understand the principles of the math in class there is no hope that they will lean the exceptions (tricky things) on their own.

Our education system produces results for those who match the learning styles used. Those who learn by different learning styles are in trouble.

In short our education system is an initiation that denies advancement for those who take more effort to acquire the secrets to participate in formal education and have a better income in life.

Our goals for educational institutions like all institutions and individuals in society are to be efficient for themselves. We do not view our goals as ones all should have and achieve. The glue of the society and country has broken down and there is only survival by eating others lunch and letting the other starve.

The way it was expressed before as a joke was get the money, legal if you can.

Now it is get the money!

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There are so many courses which require an understanding of Algebra that I cannot endorse the bizarre idea of scraping it.

Statistics on the other hand needs more emphasis. For example, there is a move afoot to substitute the Chained CPI for the usual CPI in calculating COLA, a catchtup for Social Security and many retirement programs. Sadly there are at least 3 on-line calculators available to aid one in assessing the damage inflicted by this draconian move. They give 3 different answers, two of which are incorrect and one of which is “correct” only for the assumptions used (which are at odds with most thinking). Any 1st year statistics student could easily solve the simple problem; viz 1.7% Vs 1.4% growth for a period of say, 20 years. Most citizens cannot even recognize the fact that the 3 calculators are incorrect to one degree or another.

Sadly Congress is making decisions (law) based upon such shabby math.

T. M. Kelemen-Beatty

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Thank you for summarizing the piece!

Algebra II is not an “abstract” idea, at least in terms of the definition of abstract. Functions? Logarithms? Exponential functions? Graphing? Inequalities? These are not “abstract” ideas — these are things we see and use (therefore are concrete in existence, not abstract) in the “real world.” Let alone teaching probability, statistics, even a normal distribution without an exponential function (or even the idea of a function)? Are you kidding me? Good luck!

The Harper’s opinion piece appears to be ridiculously sensationalist — just an indictment of the “idea” of Algebra II using cherrypicked examples and anecdotes galore… without actually using any analytic research (the irony!). Just as easily anyone could indict the “idea” of any subject using anecdotes, and examples from 1930 — that’s the real abstraction.

Sites that list Algebra II topics (which appear quite similar to what I learned a little over 10 years ago in Algebra II):

http://mathforum.org/mathtools/sitemap2/a2/

http://jcflowers1.iweb.bsu.edu/rlo/mathalgtutorial.html

http://www.virtualnerd.com/algebra-2/

Is math not for everybody? Sure. But deleting course “x” from a curriculum is a bit too simplistic of an answer, at least as I have seen argued.

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Algebra II is where the concept of exponentials are introduced. Exponentials are crucial to the understanding of basicconcepts such as growth, and its implications from everything from how interest makes personal indebtedness so onerous/dangerous to the implications of supposedly endless economic growth in a finite world. Exponentials also naturally arise in any system with feedback; what systems in our world don’t have feedback? The understanding of exponentials is foundational for basic scientific literacy. So I’m pretty unimpressed with the arguements against algebra II as a prerequitelt for college. The level of collective intelligence even with our current population of college graduates doesn’t exactly inspire awe….

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At our local high school statistics is available only as an AP course so only the most advanced students are eligible. This year they made pre-calculus a prerequisite for statistics, which is completely baffling.

I teach introductory statistics at the local community college and can easily get any student who has mastered pre-algebra (number lines, simple linear equations, inequalities, order of operations and solving for an unknown) successfully through the course.

Unfortunately, not all community college students have mastered pre-algebra material . . .

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Scrap Alg II and put Civic back in.

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This discussion seems arcane and parochial, like the American “World Series”, to non-US participants. What is Algebra II? Or I, for that matter?

In case it is interesting to hear about another time in another place, In the UK, A-level mathematics (pre-University) in the 1990’s was typically [1] taught in two flavours, one version heavy on calculus and trigonometry and devoid of any statistics and another called mathematics and statistics, which was a more balanced diet. Nearly all of the pupils planning to read a hard sciences degree did the former papers. The latter was seen as a soft option. Many of those also did the Further Maths course, which, as it suggests, was more maths (since you only do four A-levels, typically, half your schoolwork would be maths!), although often of a more stretching and powerful sort, with introductions to a lot more pure and applied maths (various classes of function, number theory, numerical analysis, discrete maths etc,) but little more stats!

As the above suggests, stats was a bit of a cinderella discipline compared to “purer” parts of mathematics. Any statistical knowledge I have is self-taught and fairly limited for it – it would have made undergraduate natural sciences a lot easier. Intriguingly, the mathematics School in Cambridge is divided into two faculties, Pure Maths and Stats (very diverse and abstract) and Applied Maths and Theoretical Physics (very applied and two sides of a coin), so Stats at least gets top billing at degree level and is not shunted off into the experimental data corner of physics!

[1) in an academically selective, fee-paying school environment. I hate to think what publicly funded schools taught….

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Commenting on my experiences from decades ago is not pertinent in the specific, but in general I would offer the following:

A. Our schools are “best fit” to some curve that doesn’t fit most our population, homework presumes a stable homelife, discipline to prioritize work over distraction, lock step prerequisites exclude capable students who have had life changing experiences, etc

B. Latin was taught for years on the basis “it taught you to think”. Still true, where is it?

C. Motivated students have so many more resources available, Wolfram and it’s community as an example, cheap but not free.

I personally did so poorly in high school I would never have been “accepted” if I applied to college. Several years later with a stable personal life I just showed up and started taking individual classes. By second semester I shifted to double allowed course load. In just under 3 years I left with my BS in math.

I applied to the college the same day I filed to graduate.

What was the drive? I had a family to feed, I went to work as a junior engineer same year at twice the money I’d been making.

My point is the sustem actually serves very few, you have to make it work for you or go around the obstructive parts.

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I agree wholeheartedly with statistics and algebra II. I’d even tend to chuck algebra I and Euclidean geometry as mandatory. Of course they are needed as options for those who will be doing college level math, but then your HS curriculum should be going through AP calculus. For others (e.g., lawyers, politicians) they are useless. They are leftovers from when the curriculum was first embedded in stone back around 1900 – they were useful on the farm. But the modern city dweller no longer needs the level of tech capabilities that the farmer did.

Reasoning should be taught through symbolic/math logic. You need to explicitly know the rules for valid reasoning, not just being able to do it.

If high school grads knew the rules for deductive (logic) as well as inductive (statistics) reasoning we’d have a better educated populace, particularly if somewhere along the way they were taught how to detect the techniques sophists use to make false reasoning seem true.

As an aside, back in the 1960s I was involved in an experimental course by a Prof from Salem State in which algebraic techniques were permitted in geometry proofs. I personally though it was a much improved way to teach high school geometry. I have no idea whatever became of it since I then went off to earn more money as an engineer rather than labor as a high school math teacher.

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The use of algebra to prove geometric theorems was introduced by Rene Descartes in his seminal work, Discours Sur La Methode, in 1627. It has the name, Algebraic Geometry.

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Articles like this are quite common, in those sort of publications that also tend to carry articles on the angst of getting your child into a good school.

They always propose dropping some branch of science or math, I imagine because these are the hardest subjects in which to fake erudition. They seem to be somewhat resistant to the techniques that have dumbed-down the essay question for the SAT (though I wouldn’t count on them remaining so.)

As always, the author here elicits our sympathy for the student denied the education he deserves, but I think that if the author were not so narrowly focused on the subject of his disdain, he would discover quite different causes of even greater iniquities of this sort, most having something to do with money, or rather a lack of it.

Editors seem to be eager to publish these articles, perhaps because they incite a firestorm of responses.

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Trigonometric functions provide the primary models for periodic behavior, know as Simple Harmonic Motion. All radio wave communication work features the sine and cosine functions prominently. “Chucking” trigonometry is not such a good idea. It would be much better to “chuck” more obscure topics, such as conic sections.

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For cripes’ sake, I’m 54 years old and planning to go for a degree in English or Library Science. W.T. F. do I need basic or even elementary algebra w/apps??? I’m going through hell right now with basic, this is what children learn in sixth grade and I don’t know it because I was shoved through grade and middle school, nobody wanted to take time to help children who did not do well in math. Now at my age, to pass a COMPASS test, to get into any sort of technical college program, I have to take effing algebra. It’s very confusing, frustrating and upsetting because I have no need whatsoever for this crap, but it’s a school requirement, to teach “critical thinking.” Eff critical thinking. I’m still having trouble with it, even with a tutor. My head just does not work with numbers, let alone all this abstract crap that I will never use again in this life or any other. Extremely frustrating that they’re doing the same thing in tech college; shoving people through a course as fast as possible. You’re expected to learn and study a lesson on your own, then a quick review of it in class the next day and understand it. I took 2 hours with a tutor the other day just for one simple chapter of place values, inequality symbols, and then simplifying. The whole thing gives me a migraine and there’s no sense whatsoever for an English or Library degree to requre algebra.

Rant over. I needed to vent.

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