On occasion, I get objections to the nastiness of this blog: “Why can’t you be nicer?”, and so forth. The answer is that I can’t because I can’t: my blog is fuelled by my disgust and anger at the perversion of mathematics education, and of education in general, and of our entire culture. That’s the way it is. But there is a solution: have someone else be nice for me.
Meet Tom Peachey. I’ve known Tom for about three hundred years, and through that time Tom has been one of the quiet heroes, a dedicated lecturer and tutor. He reads and occasionally comments on this blog. Tom has advocated for more positive stuff, a focus on specific issues of teaching and their solutions. And, since I’m obviously not listening to him, Tom has decided to listen to himself.
Tom has started a new blog:
Teaching Mathematics: What, When and Why
Tom’s first topic post is How to Introduce Algebra? Tom also has a suggestion post, where readers can indicate topics that they would like to see covered, including the possibility of reader contributions.
Please support Tom’s new blog by reading and commenting, particularly while Tom is finding his feet.
Two maths blogs for the price of one – amazing!
Thanks for the intro, Marty.
Well, we’re gonna charge double now.
Marty, come to this side of the pond 🙂 we would have fun
Thanks, Dr. M. I just took a peek and I see there’s good activity there. That’s great.
As it happens, I’m coviding at the moment. I’m not awful, but it’s difficult to find the energy to enter any ponds right now.
Damn, sorry to hear it. Nasty disease, had it twice. Didn’t like it all. Hope you fully recuperate soon. Take off yourself.
What do you think of this?
https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1234&context=hmnj
Why might I care?
He makes some points that click with me, about pedagogy. His main thing is that too many new university teachers (fresh out of Ph.D. pure math programs) want to increase the level of the course and/or turn a calculus course into a real analysis course. But that this is too hard at the time. That they are not realistic about the level of their students. And that they tend to overestimate even their OWN ability to learn, which was dependent on gradual training (no they really were NOT ready for Rudin in 12th grade).
Personally I see it all the time with fresh new instructors. Like they know a lot of math, but have zero savvy about training math. Which is an interpersonal task. And a human project with limited information, time, money, etc.
Maybe you agree. Or don’t agree. But you know a lot about a lot of different things. So…just interested in what you agree/don’t in the article.
Oh…and it’s a fun read. Even if you disagree, think you will enjoy it.
That may be, or once was, an issue in the US. The issue in Australia is the opposite. It seemed well-written, but I’m busy …
I think I agree with you about 95% of the time, but didn’t on this article:
https://www.qedcat.com/misc/136.html
Hacker might be wrong. But he’s not NECESSARILY wrong. Just saying he is nonsense is just one liner dismissal, not arguing. And FWIW, he does a nice job explaining his point and at least teeing up the topic as worth more serious discussion.
FWIW, there was a long time where kids did not need to get through “Algebra 2” to get a HS degree. Like my dad’s generation. Agree, that this is now an expectation for any kid going on to a uni for STEM work. But many kids will study non STEM stuff at uni.
Or (not a horror) never go to uni. And there’s nothing wrong with learning to weld or the like. “Yale or jail” is a fallacy.
I mean…should every kid need to get through calculus? Through Algebra 2? Through ODEs? We obviously need to draw a line somewhere and he is just arguing that not everyone needs huge math STEM skills. I actually wonder how much of this push of math (or even of college in general) is sort of a jobs program for teachers. Yes…I know they are not making money like investment bankers. But if you look at the entire societal spend (private and public) in k-12 and university, it is a MASSIVE INDUSTRY.
Umm….also “because we can show .999… is = 1 is a pretty darned silly point to build your defense of algebra on! I would be much more interested in their ability to do unit analysis in chemistry and physics, to solve simultaneous equations in stoichiometry, or to follow multistep derivations in the natural sciences and engineering. If they have rock solid manipulational skills in moving stuff around the equals sign, working with logs and exponents and trig and the like…that will totally be foundational and NEEDED in their STE(noM!) work. But if they NEVER showed .999….=1, who gives a damn, really? They can go watch a Mathologer/Numberphile/Veritasium/whatever video for shits and giggles if they get a wild hair about that.
Hacker is wrong.
After these couple sentences, one shouldn’t even read further because it is all summed up: “A provocative opinion piece titled “Is algebra necessary?” recently appeared in the New York Times. Written by Andrew Hacker, emeritus professor of political science at Queens College, The City University of New York”.
Some shmuck, who went to learn political science because he couldn’t get two numbers together at school, expressed his subjective, like everything else in political science, opinion on algebra—the topic which he never understood.
Disclaimer: This is my provocative response to a provocative article by Hacker (family name is rather symbolic in this case).
The article by Burkard and Marty cited above states that numeracy is a tricky concept. For me, numeracy is applied mathematics. The term is often used in the context of primary mathematics but my definition is broader. I seem to be in a group of one. However, today I attended a conference on numeracy and I was pleased to hear to a keynote speaker define numeracy as “the use of mathematical knowledge”. Naturally I think that my definition is better, but I don’t feel so isolated anymore.
Terry, I am in the middle, although I think about it slightly different. Mathematics is a language. Language that explains everything around us. Some things we already know how to explain some not yet. As any other language the language of mathematics can describe abstract situations and concepts – fantasies to put it simply. However, before one can write abstract stories one have to master it’s language.
The amount of required math training IS NOT a quantitative issue to resolve. It is a cost/benefit question with the proper weighting of costs (various) and benefits (various) almost necessarily somewhat subjective.
Probably we could advance the argument by listing the costs and benefits and attempting to quantify some of them, making the question at least more understood and semiquantitative. But it’s never gonna be a two simultaneous equation chemistry problem.
You could write a master’s degree on the topic and Hacker did not expound at that length. But he did a great job tee-ing up the issue and asking the important contrarian question. Go Hacker! [And I’m not even endorsing his point, per se. I don’t know what my opinion is, on it. But I think it’s worth thinking about and we shouldn’t have simplistic, “gotta beat the Russians to the moon” style bromides.]
I could kinda care less if he is a political scientist. That’s a very surface-y cheap seats (‘first two sentences told me enough’) criticism. Maybe political science is even relevant, since we are talking about societal decisions on required actions. Heck man, if we ask math teachers how much math kids should learn and English teachers how much English and civics teachers how much civics and Latin teachers how much Latin and etc., they will tend to overprescribe their subject. Just like every CNO thinks we need to spend more on ships. But time, money, and IQ points are limited.
P.s. I was two years accelerated (at my wishes) in math in high school and a year accelerated in math, chemistry, physics and biology. I loved doing all these AP courses and the like. No regrets. But. I remember my guidance counselor (who was not very pushy) telling me that the two courses, I should take that I hadn’t were typing and drafting. And I thought typing was for secretaries (this was the early 80s) and drafting would be hard since I had bad handwriting and was bad at art. But typing has become more and more needed (even in the 80s you could see how it would help you…and two-fingering college papers was just painful). And I ended up doing a couple years in an MEP firm and even with a draftsman to CAD my redlines (this was before everyone had their own computer), it was obvious to me how I had missed a trick by never learning hand drafting.
P.s.s. Peggy Sue actually used time travel to prove her lack of need for algebra. 😉 https://www.youtube.com/watch?v=-3eKzmozvrI
Teeing up what issue? Whether school maths should be more than a little arithmetic? Gee thanks, Hacker. My gratitude knows no bounds.
Anonymous, my reference to political science wasn’t made in order to denigrate Hacker. The comment ment that someone who studied subject, which only by huge stretch of imagination can be called science, trying to be an authority on the topic of algebra. This is an elephant sized problem. Political ‘scientist’ is someone who knows how to read and write and this would be one of the best of them. Some of them only know how to read. How do I know? My bachelor was in two subjects one of them was political science.
Life is full of places where people should analyze the importance of things outside their personal expertise. I’ve never studied ancient Greek. But I can make a cogent argument against the Greek professors of the 1870s who defended it as required. Congressmen are not (generally) fighter pilots. But they still have to decide whether to appropriate funds for next generation fighter planes. Hacker is not setting himself up as a general expert on algebra itself, but on the universal requirement for 3 years of HS math (algebra, geometry, and advanced algebra) for every HS graduate.
Just because we do have a current requirement doesn’t mean we can’t consider to lower (or raise it). It’s a state variable to consider cost benefit of the investment, not path dependent. No hysteresis here. And for that matter it’s not like current requirements are the way we’ve always done things. Minimum math standards for US high school diplomas were lower in the 30s than they are now, not higher.
Does a plumber, welder or the like really need to know logarithms? A mechanical engineer or a metallurgist, sure. Sure they need to know algebra to handle Bernoulli’s equation in their fluid flow classes. (Except you’re going to use it to introduce pre-algebra…ugg!) But every tradesman? Does a historian need second year algebra? A newspaper reporter?
And…maybe even everyone does need to know logs. Again, I’m not even defending Hacket per se, just arguing against the too simplistic rejection of even discussing his ideas. But the question becomes where to draw the line. If everyone needs second year algebra, does everyone also need calculus? ODEs? PDEs? Complex analysis? There has to be a line somewhere.
And he’s not saying NOBODY should study higher algebra. He’s just arguing against it being required for everyone.
P.s. And you were too slagging him for being a poly sci. “…Some shmuck, who went to learn political science because he couldn’t get two numbers together at school…”
I certainly slugged him for providing an ‘expert’ opinion on the area where he hasn’t got any idea, and his writing confirms it. Also, I am not qualified to even remotely evaluate the merit of your argument against Greek professors.
Everyone has to make decisions on things where they have imperfect information. How do you know you don’t “need” Latin, when you are a high school student? What if the Latin teacher says you do? Should you blindly follow the Latinist who says you need Latin, the French teacher who says you need French, the math teacher who says you need math, and even the dairy farmer who says you need milk? All biased to the importance of their business. More, more, more they cry!
But you personally have to make decisions. Let’s say you have a slot and can take French or take Latin. But not both. You have to decide. And with imperfect information. And “experts” each biased to their side. Well…that’s the situation with assigning required subjects in school.
Oh…and it’s not even like the average math teacher is an expert on the importance of math. He’s actually more an expert on the math itself than on the (relative) need for it. And heck, don’t get me started on the pure math f&$#twits who are clueless about applications. I actually think you probably have more understanding of the applications of math (since you have a general engineering background) than these Lie Algebra loverz forced to teach ODEs to engineers.
The average math teacher also doesn’t write pompous op eds for the NY Times.