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Mon Sep 28, 2020, 11:29 AM

Is it time to kill calculus?

Is it time to kill calculus?
Math curricula are designed to shepherd students toward calculus. Some mathematicians think this path is outdated

DANIEL ROCKMORE
SEPTEMBER 26, 2020 6:00PM


(Salon) Many parents relish reliving moments from our childhoods through our children, and doing homework with them is its own kind of madeleine. For Steve Levitt of "Freakonomics" fame ó who is, in his own words, "someone who uses a lot of math in my everyday life" ó a trip down memory lane vis-a-vis math homework became a moment of frustrated incredulity rather than gauzy reverie. "Perhaps the single most important development over the last 50 years has been the rise of data and computers, and yet the curriculum my children were learning seemed to have been air-dropped directly from my own childhood," he told me. "I couldn't see anything different about what they were learning than what I learned, even though the world had transformed completely. And that didn't make sense."

Levitt has made a career of questioning the received dogma. In this case, what he saw was that "A mathematical way of thinking, numeracy, data literacy, is far more important today than it has been; the ability to visualize data, the ability to make sense out of a pile of numbers, has never been more important, but you wouldn't know that from looking at the math curriculum." Data combined with the use of mathematical ideas had transformed the way he and others look at the world. Should data also change the way we teach mathematics?

In most schools, children are grounded in basic arithmetic in elementary school, and then, somewhere between middle school and high school, force-fed the "algebra-geometry-algebra sandwich". The first year of algebra ("Algebra I" ) continues to reinforce basic arithmetic, and then brings in fractions. The familiar starts to give way to the unfamiliar when variables and functions are introduced. That's when "x the unknown" makes its first appearance in word problems and linear equations, which for many marks a first sign of confusion rather than buried epistemological treasure.

Things then take a big turn, and math class time-travels to the days of ancient Greece for lessons in formal geometric proofs ("Geometry" ) that Euclid would have little trouble stepping in to substitute teach. Following that is a yearlong return to algebra ("Algebra II: The Sequel!"
), which given the previous year's partial hiatus from x's and y's and numbers first requires a lengthy review and then finally a return to new functions (exponentials, logarithms, polynomials) that either amuse or irritate you, depending on your taste, predilections, and teacher. .............(more)

https://www.salon.com/2020/09/26/teaching-data-science-instead-of-calculus-high-schools-math-debate/





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Arrow 26 replies Author Time Post
Reply Is it time to kill calculus? (Original post)
marmar Sep 28 OP
Dream Girl Sep 28 #1
Zorro Sep 28 #2
Cirque du So-What Sep 28 #3
lagomorph777 Sep 28 #4
HelpImSurrounded Sep 28 #9
hlthe2b Sep 28 #5
PirateRo Sep 28 #6
HelpImSurrounded Sep 28 #8
Midnightwalk Sep 28 #14
Chainfire Sep 28 #7
Igel Sep 28 #24
HelpImSurrounded Sep 28 #10
CaptainTruth Sep 28 #20
OAITW r.2.0 Sep 28 #11
Jim__ Sep 28 #12
Igel Sep 28 #25
hedda_foil Sep 28 #13
SWBTATTReg Sep 28 #15
Midnightwalk Sep 28 #16
malthaussen Sep 28 #19
genxlib Sep 28 #17
Lucky Luciano Sep 28 #18
CaptainTruth Sep 28 #21
Igel Sep 28 #26
NNadir Sep 28 #22
msongs Sep 28 #23

Response to marmar (Original post)

Mon Sep 28, 2020, 11:31 AM

1. My son would say yes!

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Response to marmar (Original post)

Mon Sep 28, 2020, 11:35 AM

2. Sounds like someone who didn't do well in high school math classes

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Response to marmar (Original post)

Mon Sep 28, 2020, 11:37 AM

3. I gotta admit

that itíd be a real ordeal to come up with a derivative of a polynomial nowadays, but Iím not sorry for having taken four semesters of calculus. Itís proven useful on more than a few occasions over the years, and I still see value in taking calculus to improve problem-solving abilities.

I dread the day when nobody is capable of performing simple 12x12 multiplication without aid of a calculator app.

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Response to marmar (Original post)

Mon Sep 28, 2020, 11:39 AM

4. That's idiocy. Complete lunacy. How does that make any sense in our technological world?

What an asshat.

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Response to lagomorph777 (Reply #4)

Mon Sep 28, 2020, 11:51 AM

9. AGREED!!

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Response to marmar (Original post)

Mon Sep 28, 2020, 11:40 AM

5. I'd be satisfied if they learned (actually learned) algebra and geometry, frankly

Even basic principles are too often lacking among many, even college grads. In patient-delivered health care, statistics, epidemiology, building, contracting, construction, you name it: These are skills that are needed.

From my observations, Hospital ERs, ICU's, and practices would do well to ensure their staff can accurately calculate drug dose, especially in constant rate infusions. Computers go down, pharmacists make mistakes, and disasters require old school skills Guess where algebra comes in.

As to calculus, I enjoyed it. Physics too. Both are at use frequently, though we don't recognize it and are not, ourselves, usually performing the calculations. But the concepts underlie a lot of new technologies.

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Response to marmar (Original post)

Mon Sep 28, 2020, 11:42 AM

6. No, it's time to teach it earlier!

There are bunches of people out there all for teaching less every year. Donít listen to that! With rising automation and increasing need for additional education, calculus is key!

Thereís no removing this or anything else!

Look at the world! People will sell brain machine interfaces, soon! You need a keen education today and even more tomorrow. This isnít a cheap sci-fi movie! This is real world! As it is, kids graduating from school already have obsolete skills. No, thereís no discarding anything!

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Response to PirateRo (Reply #6)

Mon Sep 28, 2020, 11:50 AM

8. * E10

Enough of this +1 stuff, I'm agreeing with this exponentially.

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Response to HelpImSurrounded (Reply #8)

Mon Sep 28, 2020, 12:02 PM

14. +∞

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Response to marmar (Original post)

Mon Sep 28, 2020, 11:45 AM

7. By the time of the end Algebra II

I completely tuned out because my teachers could not tell me how this knowledge would be used in my life. As it turns out, the answer was simple, I have never used more than the most basic algebra. What did turn out to be useful was being forced to take typing and bookkeeping. Since the rise of computers I have been very happy to be able to touch type. A basic knowledge of double entry bookkeeping helped me a lot when I owned my own business.

I have a nephew who went the math route, through a PhD and post grad research, and lives an excellent and fulfilling life in highly specialized engineering, but he is the exception, not the rule.

It seems to me that today we should substitute History and Civics for most higher math classes.

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Response to Chainfire (Reply #7)

Mon Sep 28, 2020, 07:57 PM

24. My students demand certainty.

They need to know they will use something.

I tell them we teach them possibilities and opportunities.

My nephew's friend started college for business. Became a film major. He never thought he'd have a use for his art classes.

I was going to be an engineer. When am I going to need foreign language? I became a double major--science and language.

All that reading and literature? How useless for an engineer. But, oops. My master's is in literature.

Then after a stint of translation as my employment, I now teach high school science.

If you are only taught at age 14 what you know at age 14 you'll need at age 40, you're not going to be taught much beyond literacy and basic numeracy.

A friend loved electricity and electronics when he was in high school. Went on to become an electrical engineer, now a consultant in robotics. So some kids do know. Problem is, you can't really tell the difference between those whose interest fades or doesn't work out and those who do. So you teach possibilities and opportunities.

Civics is a good thing and should be taught. But you know, I have seniors in class who finish a semester dedicated to nothing but civics, and their question is, "When am I ever going to use this?" and "Just tell me what I need to pass the test." Which is the same "I know what's important for *me*."

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Response to marmar (Original post)

Mon Sep 28, 2020, 11:52 AM

10. As if we haven't dumbed down the curriculum enough.

Through my entire time in high school they kept yanking things out and making it easier.

This is why we have Trump - our education curriculum is a shambles.

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Response to HelpImSurrounded (Reply #10)

Mon Sep 28, 2020, 02:13 PM

20. +1 And why we have Trump supporters.

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Response to marmar (Original post)

Mon Sep 28, 2020, 11:55 AM

11. I did OK with math up to and including trigonometry.

But Calculus was a whole nother animal. Solving for a finite answer made sense. Solving for an equation was a bridge too far.

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Response to marmar (Original post)

Mon Sep 28, 2020, 11:57 AM

12. A lot of the article is actually asking a different question.

I read the article quickly so may have missed some of what it's saying.

The main question I took away from the article is, something like, should calculus be a gateway to STEM. I take the article to be saying that it shouldn't be, and I agree with that. A lot of data analysis can be done without any knowledge of calculus, and for at least some analysis that requires calculus, the calculus portion can be handled by pre-packaged programs.

That said, it is absolutely not time to kill calculus.

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Response to Jim__ (Reply #12)

Mon Sep 28, 2020, 08:39 PM

25. I find teaching data analysis to be a rough task.

Even in high school. They learn the algebra, but they have absolutely no idea what's going on and where the algebra comes from.

I draw the line at teaching a course that involves astronomy and telling them all kinds of facts about brightness and luminosity, composition of stars and comets, and having them just memorize that all this comes from spectroscopy. The first year I taught it, I did as I was told. They didn't connect wavelength with electron transitions, brightness with average kinetic energy. If they forgot something, they couldn't reason their way back to it; every fact was an isolate. Now I take a few weeks and pull together their middle school science, their chemistry, any physics they had, and for many--not all--it makes sense. There's still a lot of stipulation, but it's old stipulation. Matter is made of atoms. They move. They have electrons. They know these things. Why not unify it?

Calculus is the same sort of thing. It unifies a lot, just in its basic assumptions and techniques, and once those things are learned a lot of techniques and processes just sort of flow from it.

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Response to marmar (Original post)

Mon Sep 28, 2020, 11:58 AM

13. Fascinating. My HS Junior granddaughter is taking pre-calc/statistics. Seemed odd to me.

Now I get it and I'm super impressed that her school is at the leading edge with this approach. She's really enjoying it too.

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Response to marmar (Original post)

Mon Sep 28, 2020, 12:11 PM

15. No. Some IT programming believe it or not, do rely on some pretty complicated formulas and such,

to which I've had to program into my programming. Now of course this could be downgraded to an required electives course for IT and / or other professionals, vs. others trades/degrees that don't require such specialized mathematical skills, but I suspect that a lot of trades do in fact rely on having a desired skill set of math...after all, the digital world relies on the most basic of numbers, zeroes and ones, but assembling a hodgepodge of nested IFs/THENs/ELSEs all in one requires a little more expertise with numbers...

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Response to marmar (Original post)

Mon Sep 28, 2020, 12:29 PM

16. The answer is more and better

Kids should learn some programming. That swift tutorial from apple seemed really good to me. At least the first set.

Others mentioned adding statistics and I agree. My first exposure was in college with a teacher who was incapable of explaining anything. All he could do is read the class notes out loud in response to any question.

That to me was the biggest hurdle. Many teachers made math so boring Iíd always be off day dreaming. To the point where i was put in remedial class. That was free form, so I did self study and got a year ahead and then got to take the advanced classes that really were fun. I still remember the teacher deriving the quadratic equation by completing the square one class.

I wonder if that is a better approach. Record some really gifted teachers presenting the material and have the live teacher be there to answer questions and get kids to work out problems in class.

There are a lot of things in the early years that are learned through repetition and exercises. My mom taught us while were young riding the subway asking questions and using flash cards. That was low stress. Not exciting but we learned just the same and i was never stressed out about times tables.

A bit of rambling.


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Response to Midnightwalk (Reply #16)

Mon Sep 28, 2020, 02:03 PM

19. I agree the teacher makes a difference.

I've had to take Algebra numerous times in my life, and the only time I did well in it was under a teacher who was really good at explaining things. Math profs seem to be particularly challenged in communications skills, in my experience.

-- Mal

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Response to marmar (Original post)

Mon Sep 28, 2020, 12:41 PM

17. Sure

I look forward to our Chinese overlords.

I mean if we are going to just cede the technology field to them that is where we are headed.

I am an Engineer and did a lot of Calculus. In the 30 years since, I have not actually needed to do the math to directly do my job. But being forced to know the calculus was the pathway to making sure I understood the actual science behind what I do.

Let me put it this way. I would never drive over a bridge designed by someone who did not study calculus as a root to their engineering education.

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Response to marmar (Original post)

Mon Sep 28, 2020, 01:51 PM

18. I am a mathematician...I've been wondering about this too.

Last edited Mon Sep 28, 2020, 06:17 PM - Edit history (1)

Of course, I don't think we should kill calculus. There should still be AP Calculus, but AP Linear Algebra might make a ton of sense given how critical that is to data analysis. I would love to see linear algebra become a thing in high school. Manipulating matrices is huge in this day and age. Being good at linear algebra is paramount to data analysis, probability/stats (covariance matrices, regression, Kalman filters), multivariable calculus, and optimization - not to mention solving simultaneous systems of linear equations which is the first thing people encounter.

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Response to marmar (Original post)

Mon Sep 28, 2020, 02:25 PM

21. We might be able to learn something from Europe on this.


My Italian wife has explained to me how high schools in Italy are specialized. For example, her brother decided he wanted to go into a technical field so he went to a high school that emphasized math & science (he went on to get an engineering degree).

There are other high schools with more of a liberal arts focus, like the one my wife went to (she went on to major in languages & art history).

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Response to CaptainTruth (Reply #21)

Mon Sep 28, 2020, 08:49 PM

26. We're all Puritans.

We are to be taught literacy and basic skills.

And we're all into equity. As we teach more reading, more science, more math, more whatever, it's all to be ramped up. I get it--for an elementary school kid, middle school kid, they need a basic competence in a million things.

But by high school they have likes and dislikes. They may change, so it's not a slam dunk. People choose paths that foreclose what they later think they'd want to do. Bad teacher, infatuation, some fad. Whatever.

Still, the savings in grief and cost by having kids specialize a bit earlier is worth it. CTE, humanities/liberal arts, science, engineering ... Yeah, some kids are shut out of some opportunity they later regret, esp. when specialization happens based on some sort of placement process. But overall, it works better.

The drawback is Snowe's "Two Cultures" sort of problem, but to a large extent that was the result of how one side developed. In the 1800s the two sides were easily bridged, but by the 1950s each side hubristically was claiming sole knowledge of how to properly structure everything, and in a democracy that's just giving most people a choice of tyrants.

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Response to marmar (Original post)

Mon Sep 28, 2020, 02:36 PM

22. Yeah, and the alphabet, the periodic table, thermodyamics,

General chemistry, physics and a whole bunch of other stuff unimportant to journalists and people getting their MBAs

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Response to marmar (Original post)

Mon Sep 28, 2020, 02:36 PM

23. actually the concept of n representing an unknown # is taught in elementary school these days

in my area

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