Guest essay by Eric Worrall
Scientists have written an open letter criticising an effort to de-emphasise advanced mathematics in K-12 courses.
Open Letter on K-12 Mathematics
We write to express our alarm over recent trends in K-12 mathematics education in the United States. All of us have first-hand experience of the role that clear mathematical thinking has played in advancing information technology and American economic competitiveness. We all also share the urgent concern that the benefits of a robust mathematical education, and the career opportunities it opens up, should be shared more widely between students of all backgrounds, regardless of race, gender, and economic status. We fully agree that mathematics education “should not be a gatekeeper but a launchpad.”
However, we are deeply concerned about the unintended consequences of recent well-intentioned approaches to reform mathematics education, particularly the California Mathematics Framework (CMF). Such frameworks aim to reduce achievement gaps by limiting the availability of advanced mathematical courses to middle schoolers and beginning high schoolers. While such reforms superficially seem “successful” at reducing disparities at the high school level, they are merely “kicking the can” to college. While it is possible to succeed in STEM at college without taking advanced courses in high school, it is more challenging. College students who need to spend their early years taking introductory math courses may require more time to graduate. They may need to give up other opportunities and are more likely to struggle academically. Such a reform would disadvantage K-12 public school students in the United States compared with their international and private-school peers. It may lead to a de facto privatization of advanced mathematics K-12 education and disproportionately harm students with fewer resources.
Another deeply worrisome trend is devaluing essential mathematical tools such as calculus and algebra in favor of seemingly more modern “data science.” As STEM professionals and educators we should be sympathetic to this approach, and yet, we reject it wholeheartedly. The ability to gather and analyze massive amounts of data is indeed transforming our society. But “data science” – computer science, statistics, and artificial intelligence- is built on the foundations of algebra, calculus, and logical thinking. While these mathematical fields are centuries old and sometimes more, they are arguably even more critical for today’s grand challenges than in the Sputnik era.
We call on national, state, and local governments to involve college-level STEM educators and STEM professionals in the design of K-12 mathematics and science education curriculum, set the following as explicit goals, and allocate resources to help school districts meet these goals:
1. All students, regardless of background, have access to a math curriculum with precision and rigor, and that would enable them to pursue STEM degrees and careers if they so choose.
2. Far from being deliberately held back, all students should have the opportunity to be nurtured and challenged to fulfill their potential. This is not only for their own benefit but also for society and the nation’s economic competitiveness.
3. There cannot be a “one size fits all” approach to K-12 mathematical education. Students should be offered multiple pathways and timelines to explore mathematics. But one of these pathways should be the option to obtain the fundamental preparation for college-level STEM, including algebra, calculus, and logical reasoning. Students should have the opportunity to take those classes at varying grade levels of middle and high school when they are ready, so that they acquire the tools to explore other STEM options and can build their proficiency in a balanced pacing, avoiding irresponsible compression late in high school.
Mathematical education is a challenging enterprise, and we have the utmost respect for our K-12 colleagues who are doing this hard work. In appreciation of the difficulty, we believe that changes to educational standards should be approached with care, using incremental experimentation building on lessons learned from both the US and abroad and using credible measures of success. In contrast, initiatives like the CMF propose drastic changes based on scant and inconclusive evidence. Subjecting the children of our largest state to such an experiment is the height of irresponsibility.
Finally, K-12 math curriculum development cannot be disconnected from one of its most important end goals: Preparing students for success in college-level STEM education and a STEM career. As educators in public and private institutions, and working professionals in the technology industry, we have a first-hand understanding of the skills needed for this goal. While the US K-12 system has much to improve, the current trends will instead take us further back. Reducing access to advanced mathematics and elevating trendy but shallow courses over foundational skills would cause lasting damage to STEM education in the country and exacerbate inequality by diminishing access to the skills needed for social mobility.
Boaz Barak b@boazbarak.org
Edith Cohen edith@alumni.stanford.edu
Adrian Mims amims@thecalculusproject.org
Jelani Nelson minilek@berkeley.edu
Blog posts (cross-posted): Shtetl-Optimized Windows on Theory
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Ying-Ju Tessa Chen, Assistant Professor, Statistics, University of Dayton
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Jing Li, Professor of Industrial and Systems Engineering, Georgia Tech
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Zhen Liu, Assistant Professor, University of Minnesota
Ivan Loseu, Professor of Mathematics, Yale University; Fellow of the AMS
John Lott, Professor of Mathematics, University of California, Berkeley
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Elena Machkasova, Associate Professor of Computer Science, University of Minnesota Morris
Mauro Maggioni, Bloomberg Distinguished Professor in Mathematics, Applied Mathematics and Statisics, Johns Hopkins University; Popov Prize, Sloan Fellow, Simon Fellow, Fellow of the AMS
Mehrdad Mahdavi, Assistant Professor of Computer Science and Engineering, Penn State University
Konstantin Makarychev, Professor of Computer Science, Northwestern University
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Aneesh Manohar, Distinguished Professor of Physics, University of California, San Diego
Vanel Marc, Algebra Teacher, Southshore Charter Academy; Founder of Sherpa Math Game
David Margulies, Retired Research Staff Member, IBM Research-Almaden Lab
Amelie Marian, Associate Professor of Computer Science, Rutgers University
Ivan Marinovic, Professor of accounting, Graduate School of Business, Stanford University
Brad Marston, Professor of Physics, Brown University; Fellow of the American Physical Society, recipient of a number of awards.
Sergei Maslov, Professor of Bioengineering and Physics, University of Illinois Urbana Champaign; U of Illinois Presidential Award and Medallion, Fellow of APS and AIMBE
Clifford Mass, Professor, Atmospheric Sciences, University of Washington; Ph.D. Atmospheric Sciences, numerical modeler
Samuel Matej, Research Professor of Radiology, University of Pennnsylvania
Norman Matloff, Professor of Computer Science, University of California, Davis
Abraham Matta, Professor and Chair of Computer Science, Boston University
Eric S Maurer, Director of Classical Engagement, Regina Angelorum Academy; 2020 Archdiocese of Boston Excellence in Education Award recipient
Nelson L Max, Distinguished Professor emeritus of Computer Science, University of California, Davis
Alex Mackenzie Phillip May, Postdoctoral scholar, Physics, Stanford University
Barbara R Mayden, 8th Grade Algebra 1 Teacher, Private School in Houston, TX; BA, MA, EdD (expected 2022)
Arya Mazumdar, Associate Professor, Halicioglu Data Science Institute and Department of Computer Science and Engineering, University of California San Diego
Barry C Mazur, Gerharde Gade University Professor, Harvard University; National Medal of Science, Chauvenet Prize, Cole Prize, Veblen Prize
Aaron McCollum, AP Math and Computer Science Teacher, Richmond County School System
Scott A McGregor, Chief Executive Officer (Retired), Broadcom Corporation; Fortune 500 CEO; Founder of the Broadcom Foundation
Stephen E McKeown, Assistant Professor of Mathematical Sciences, University of Texas at Dallas; J.D., Ph.D.
Peter L McMahon, Assistant Professor of Applied and Engineering Physics, Cornell University
Patrick Meade, Professor, C.N. Yang Instiute for Theoretical Physics, Stony Brook University
Dinesh Mehta, Professor of Computer Science, Colorado School of Mines
Raghu Meka, Associate Professor of Computer Science, University of California, Los Angeles
Ray Merewether, Cheif Scientist, retired; 3 sole inventor patents; ~80 coinventor
Diego A Mesa, Assistant Professor of the Practice of Computer Science, Vanderbilt University
Scott D Metzler, Research Professor of Radiology, University of Pennsylvania
David A Meyer, Professor of Mathematics, University of California, San Diego
Peter F Michelson, Professor of Physics, Stanford University
James Mickens, Professor of Computer Science, Harvard University
Risto Miikkulainen, Professor of Computer Science, The University of Texas at Austin; IEEE Fellow
Kenneth D Miller, Professor, Department of Neuroscience, Columbia University; Swartz Prize for Theoretical and Computational Neuroscience
Adrian B Mims Sr., Founder & CEO, The Calculus Project Inc.; Recipient of The 1954 Luminary Award
Yair N Minsky, Einar Hille Professor of Mathematics, Yale University; Fellow of the AMS
Anshuman Mishra, Principal AI Researcher, Numenta
Pratyush Mishra, Cryptographer, Aleo; PhD from UC Berkeley
Umar Mohideen, Professor of Physics, University of California, Riverside; Fellow, American Physical Society
Daniel A Moncayo, Associate Professor of Economics, Brigham Young University Idaho
Andrea Montanari, Professor of Electrical Engineering and Statistics, Stanford University
Niema Moshiri, Assistant Teaching Professor of Computer Science & Engineering, University of California, San Diego
Dana Moshkovitz, Professor of Computer Science, University of Texas at Austin
Michael C Mozer, Professor / Research Scientist, University of Colorado, Boulder / Google
Shankar Mukherji, Assistant Professor of Physics and Cell Biology & Physiology, Washington University in St Louis
David B Mumford, University Professor Emeritus, Brown University; Fields Medal, former President of the International Mathematics Union
Kevin Murphy, Senior Staff Research Scientist, Google Research (Brain Team); PhD
Venkatesh N Murthy, Professor and Director of Center for Brain Science, Harvard University
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Mircea Mustata, Professor of Mathematics, University of Michigan
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Mayur Naik, Professor and Graduate Chair of Computer and Information Science, University of Pennsylvania
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Balasubramanian Narasimhan, Senior Research Scientist, Department of Statistics, Stanford University
Michael Neff, Professor of Computer Science, University of California, Davis
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Hung Ngo, VP of Research, RelationalAI Inc.; Former professor of Computer Science at SUNY Buffalo
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Armita Nourmohammad, Assistant Professor of Physics, University of Washington
Maxim I Novikov, MD, Anesthesiologist, Geisinger Medical Center
Zohar Nussinov, Professor of Physics, Washington University in Saint Louis
Darian O Nwankwo, PhD Candidate, Computer Science, Cornell University
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Vadim Oganesyan, Professor of Physics, The City University of New York
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Alex Olshevsky, Associate Professor of Electrical and Computer Engineering, Boston University
Alexey Onufriev, Professor of Computer Science and Physics, Virginia Tech
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Onyema Osuagwu, Associate Professor, Electrical and Computer Engineering, Morgan State University; Assistant Director, Cybersecurity Assurance and Policy Center
Art Owen, Professor of Statistics, Stanford University; Statistical Society of Canada Gold Medal, Noether Senior Scholar Award, American Statistical Association
Hakan Ozadam, Research Scientist, University of Texas at Austin
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Sonia Paban, Associate Professor of Physics, University of Texas at Austin
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George J Pappas, UPS Foundation Professor of Electrical and Systems Engineering, University of Pennsylvania
Dana Paquin, Professor of Mathematics, Stanford University; California Polytechnic State University; Former Director of the Stanford Math Circle
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Will Perkins, Associate Professor, Mathematics, Statistics, and Computer Science, University of Illinois at Chicago
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Stefano Tessaro, Associate Professor, Paul G. Allen School of Computer Science & Engineering, University of Washington
Ari Trachtenberg, Professor, Electrical and Computer Engineering, Boston University
Hung Tran, Associate Professor of Mathematics, University of Wisconsin, Madison
Son C Tran, Professor of Computer Science, New Mexico State University
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Charalampos Tsourakakis, Assistant Professor of Computer Science, Boston University
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Al Urim, Head of Engineering, Aalto
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I don’t have a problem with schools providing alternatives to advanced math classes. Some otherwise intelligent people just can’t do advanced math, any more than I can write world class poetry or compose a rock song anyone would want to listen to.
But advanced math classes should always be an option. Denying advanced math courses to children with a born talent for math is just as bad as denying artistically gifted students access to musical instruments and art lessons and materials.
Completely agree
Maths is the foundation and should be along with the core Science and English / native language courses
if you cant measure / calculate a volume / work out an area etc then you cant follow recipes, work out how much paint you need or work out how electrical problems of the new erra
then all the data analytics is useless as you wont have computers or anything else
We don’t want people to be able to calculate that unreliables are a waste of money, do we?
Agree, Einstein wasn’t very good at solving differential equations. At first relied on help of his wife, later on help of his fellow scientists. His black hole equation was solved by Karl Schwarzschild, crouching in a WWI trench somewhere on the Russian front.
Despite the difficulties Einstein still proclaimed
” Pure Mathematics is, in its way, the poetry of logical ideas”It’s rather obvious that I’m not Einstein, but to pass Mathematics II at university I had to (successfully, I’m pleased to report) solve the exam’s set Bernoulli’s second order differential equation.If you like a challenge I’m sure you can find an example somewhere on internet if you search hard enough.
Ahha, after a short search I found a generalised solution on youtube here:
https://youtu.be/_WKq3emMPfs
If you are man of maths have a go, needless to say after so many years I wouldn’t have been able to do it again, but watching the video, the long gone dead brain cells came to life, barely.
And that is a simple version, so your next step is to try
d^2y/dx^2 +…. =f(x)y^n
If you ask me to try it the answer would be ‘explitable delitable’
Vuk, all I needed to know about was HOW Bernoulli’s principle applied to lift for an airfoil (plane wing) when I was learning to fly gliders. Ir also explained (without specifically doing so) why some birds can glide forever while others, not so much.
Hi Sara,
Yes indeed it is one of classic physics principles.
Bernoulli family of Swiss mathematicians and scientists in general, did make huge contribution to number of science branches including hydrodynamics, mechanics, ballistics, differential calculus,thermodynamics, gas theory even magnetism.
Their importance is on the level of great 17th and 18th century scientists.
There were more than one Jacob, Johann, Nicholas (about 2 or 3 of each), and a Daniel Bernoulli who worked on magnetism among many other things.
Which one did what I have no idea, but I’m sure google will know.
Thanks! Ever wonder if they had fights over it at the dinner table?
fairly certain of it. I’ve been practicing ‘real’ science for oh, 50 years going or so, and i’ve yet to encounter a dinner party of fellow science types, that isn’t either peppered or marred by a vigorous-to-ridiculous debate of something or another.
IT IS THE WAY we need to be: opinionated, debating, resolute, wiley. Without that, science becomes an gruel of thin platitudes, whitewashed orthodoxy and brittle scaffolding.
There appears to be an error in the video; at about 1:37 the equation produced by dividing by x squared is missing the y factor in the second element.
Hi David, well spotted, looks like error in copying of for the video, After introducing variable z, he got (-1/x)y at around 4’10”.
I’m not tempted to go all the way to the solution.
And if you inquire of a member of the younger set to tell you what 10% of 3 dollars would be, you will undoubtedly be given a blank stare. Or as I was told, “We weren’t taught that”!!!
A lot of time doing math is just a matter of finding the best way.
One time when my wife was struggling to calculate 15% in her head, I told her a trick I use. Instead of trying to multiply by 0.15, take 10%, then take half of that. Add the two sums together.
A lot of math is pattern based, but as they used to tell us, does the answer look reasonable?
Especially if you’re using a slipstick (slide rule).
I’d give you a +10 if I could.
Poor ol’ slide rules.
I till pack mine in my briefcase…
To haul out at times during meeting.
To get that ‘incredulous dinosaur’ stare.
And ALWAYS to get the ‘same answer’ well before the youngsters
Its a joy.
GoatGuy
That is the same shortcut I have been using for decades! It is surprising how many people don’t get how much easier it is that way.
You mean there are people of at least average intelligence that don’t immediately get that on their own? I always thought I do it that way because “I’m not very good at math”.
Or understand or be interested in anything involving numbers. So they’ll be free to manipulate the numbers w/o worrying — nobody will know or care how to challenge them.
UN Agenda 21, education systems around the world must be devalued as educated people have higher carbon footprints (whatever they are) than lower educated people. The Great Reset, only the wealthy elites sill be educated, the rest must have to look up to the elites for guidance on how to live our lives!!! I don’t believe in conspiracy theories per se , Agenda 21 is no conspiracy, conspiracies are undertaken behind closed doors, Agenda 21 is being conducted in full view of everyone, but who wants to read hundreds or thousands of pages other than to get to sleep???
But math is just so inconvenient to the True Believers in any area of science … whether extreme left or extreme right on the political spectrum.
Do you actually know anyone you could describe as “extreme right”?
I mean in terms of a 1950’s definition, not today’s definition, where anyone to the right of Angela Merkel is condemned as “far right”. 😉
Math exams can separate the smart from the not-so-smart quite easily…so are against the very principles of leftists…
And in my little corner of sunny California, some school districts are eliminating both D and F grades, to be more equitable, I hear. What becomes the point of having ‘a stick’ and (A B) a carrot, without the stick part?
Having a fiancee with a ‘failed in school’ child … raised as a hedonist, and taking ‘to the streets’ without any fear of what ‘F’ was going to hold back at home, I can tell you, ‘the stick’ part is beneficial.
Send Dave Chappelle to sort things out.
Taking gender theory and intersectionality into account we need to take a more nuanced approach to the teaching of mathematics thereby ensuring that nobody gets left behind or has feelings of inadequacy. /sarc
As long as we ignore biology then, one male rabbit + one female rabbit = a bunch of asexual Minions! I always wondered where they came from!
(If you don’t know what a Minion is, thing of a Twinkie with an eye (sometimes two).
Meaning of minion in English
minion
noun [ C ]
usually disapproving uk
/ˈmɪn.jən/ us
/ˈmɪn.jən/
a person who is not important and who has to do what another person of higher rank orders them to do:
Originally it meant favoured servant.
https://en.wikipedia.org/wiki/Les_Mignons
But “Minions” are important … until they are are gone.
PS I was alluding to the “Minions” in Despicable Me. But you probably knew that. 😎
Oh, come on, Dnalor50. Intersectionality has its place:

intersectionality
nounA feministsociologicalmethodology of studying the relationships among multiple dimensions and modalities of socialrelationships and subject formations.
This and gender theory should never see the inside of a mathematics class
Nor should it see the inside of any scientific institution… like NASA GISS:

I ‘marvel’ at her unjustified assurance that she understands the Big Picture.
Climate science is the universal hammer, by which every wish of the left will be forced onto the rest of us.
Oh, let her ‘be right’. Then follow up with “and neither CLIMATE nor SOCIAL ‘justice’ are actually JUSTICE by any LAW ON THE BOOKS, because such laws would be either racist or totalitarian”
Right?
Based on equity, all variables are equal to the same value … probably 0 or NaN
The answer to the age-old question of 2+2 is a number that lies on the spectrum from 3 to 5.
I suspect the problem is lack of teachers with good math skills – typical for arts and humanities educated persons – the bulk of teachers.
My high school math results were appalling – requiring a year of evening math classes to remedy in order to get into college.
Eventually I scored in the 99th percentile in my math section of my G-MAT tests for my masters degree.
So I had the innate skills – but poor teachers left me mathematically illiterate on leaving high school.
Subsequently as a technical lecturer I was constantly seeing the exact same illiteracy in adult students who had “passed” High school math.
The inability to read a simple X-Y graph for instance.
A vicious circle ensues – such people go on to arts and humanities and become teachers.
I am not trying to slight teachers – just pointing out a problem.
Dumbing down high school math will exacerbate this problem.
My 8 year old grandson loves maths. His particularly joy is Friday’s “Beat The Teacher”, 100 questions multiplication and division. His regular teacher doesn’t always beat him. But a couple of weeks ago there was a supply teacher to cover for his usual teacher. My grandson beat him/her by over 2 minutes and the teacher got some wrong apparently. I was apalled at such poor basic maths skills in a teacher even one teaching 8 year olds.
As an aside I find the lack of history and geographical knowledge in teachers equally worrying.
“Those that can’t do, become teachers. Those that can’t teach, teach teachers.”
Those who cannot teach become administrators.
Those who can’t teach teachers become politicians.
“As an aside I find the lack of history and geographical knowledge in teachers equally worrying”
Totally agree but I would extend that to too many people in general. You can’t begin to understand the modern world without a decent understanding of history and geography,
Which is why the left is so determined to both bury and re-write history.
Becoming a teacher has nothing to do with subject matter.
Here in Calgary many of the Jnr High School (Grades 7, 8, 9) math teachers did not take math at University. Also, those teachers are in the lower income neighborhoods.
And, the Standard of Living North America enjoys for the most part is due to STEM. IMO, too many of our bright students have ended up being lawyers.
“I suspect the problem is lack of teachers with good math skills – typical for arts and humanities educated persons – the bulk of teachers.”
Your suspicion is both badly reasoned and poorly researched. The problem is very clearly a philosophical approach to modern education that implements a racist, quasi-Marxist method to outcomes whereby so-labeled “People of Color” are assumed less capable than their “White” contemporaries of doing high level mathematics. Or at least that’s the excuse they’re using to suppress accelerated learners. You know . . . like yourself. Moreover, the idea is to suppress individual achievement in favor of communal “equality.”
This isn’t a problem of finding individuals who can teach higher mathematics. It’s a problem that’s directly a function of how progressive liberals view minorities as being of lesser intellect, probably excused within their own minds by the contradiction that communal equality is fairer than individual superiority.
From the CA DOE FAQ on the headline article:
“Research provides evidence that schools and districts that design pathways with access, opportunity, and equity at the center are more successful in preparing all students to be ready for college-level math and science. As a result of the documented negative outcomes on certain student populations found in both tracking and ability grouping, the National Council of Teachers of Mathematics (NCTM) strongly advocates for creating a middle school mathematics that will “dismantle inequitable structures, including tracking teachers as well as the practice of ability grouping and tracking students into qualitatively different courses” (NCTM, 2020).”
https://www.cde.ca.gov/ci/ma/cf/mathfwfaqs.asp
Translating the above loosely: “Our research allows us to conclude that minorities aren’t as intellectually capable as their ‘White’ colleagues, thus we think it best not to trigger within them emotional turmoil by pushing them to be better (since, after all, they don’t have the ability to improve in the first place).”
Absotively posilutely. It’s not about math; it’s about Marxist Race Baiting and the stupidification of American children. So-called “Diversity” is dragging down everyone to the lowest level. If one child can’t learn, then none must learn. Equity is nothing for everybody.
The commies fear achievement; it threatens their totalitarian dream. Can it be that some academics are finally catching this clue?
During the 2008-2012 era of no work for civil engineers, a co-worker got his masters and began substitute teaching. His BS grades from weren’t high enough to qualify for the ‘real’ teacher program so he got his masters in the industrial/ag type teaching (don’t know much about that program). He now has a permanent teaching job & still, on occasion, asks me about some of the math issues.
Back then I thought about doing the same thing. When I looked into the teaching Masters degree at University of Oregon I found that acceptance into the program was not only dependent on the bachelors program grades, it was dependent on a required essay about how necessary/reasonable diversity & inclusion practices are for our society. I thought about faking it, and I even went to one orientation session, but decided to ride out the economy and keep fighting with the bureaucrats.
My point being that teachers are told from the start that performance is not as important as the other crap. Most of them are even required to agree with the concept before they are accepted into the program. So, at the U of O, you will get two types of graduates … those that are on the diversity bandwagon & those that are willing to lie about being on the bandwagon; my hunch is that the U of O is not unique.
I went on to teach adult evening classes – this while running my own business.
I did it because I enjoyed doing it.
But finally I ran out of tolerance for all the bureaucratic (and increasingly “woke”) BS and quit.
In most colleges, those who have failed at pretty much everything else, go into education.
Those who fail in education go into journalism.
The bottom appears to be “communications”
Every child should learn basic arithmetic, how to add, subtract, multiply, and divide, while in elementary school. This is a basic life skill. Getting wrong answers is how we learn to get to the correct answers. Kids aren’t stupid, eventually they figure out they got it wrong and teacher apparently doesn’t know the correct answer either!
We don’t want kids growing up to be mathematically literate. They might question ‘the narrative’, and we can’t have that.
Give ’em “Data Scientology” skills. Then they’ll be able to manipulate any data to fit ‘the narrative’.
Remember, folks: any field with “science” in its name ain’t science, just like any country or party with the word “Democratic” isn’t.
Quite right Ziggy, innumeracy is the best friend of those political manipulators for whom rescue of the planet without the slightest of hesitations is the order of the day, with warm emotions like ‘hope and change’ substituting for carefully crafted benefit/cost for policy. Besides, now that Science itself has been self-declared by a certain Dr. Anthony Fauci to personally reside within himself, any contention over his edict of the week must threaten that grand old traditional means of careful inquiry. And with the stunting of social skills among the masked students as well as recurrent overhanging fear to hobble them, they should prove to be desirably sheepish adherents.
Methinks Fauci is the one scientist proving that “the science is never settled”.
He must be a climate sceptic!
Fauci would have said: “l’État, c’est moi”, if he spoke French.
You mean “torture the data” to fit ‘the narrative’.
I remember back in the ’70’s (maybe in the early 80’s) there was a move to teach kid’s that instead of 2+2=4 that 2+2 probably is 4. (Whoever said that likely oversimplified what he saw was happening, but, maybe not.)
Probably 4. Perhaps 5?
2.4 +2.4 = 4.8
Now round to the nearest integer:
2 + 2 = 5
QED
I don’t remember it anymore, but in high school I learned a formula that proved that 1 = 2. The trick was that when you inserted numbers into the formula, you found that there was a hidden divide by zero in the middle of it.
yes, if X = 2, you cannot divide by (X-2) …
That one stuck with me too. The kids that like that one are ready to move past algebra. The kids that don’t give a crap keep at it or give up.
I remember a couple of variations of that.
It would seem to be the foundational “formula” used in “Climate Science” today.
(I’m thankful that there is WUWT and other sites that can and have spotted the hidden “divide by zero”‘s in the CAGW hype.)
1 apple + 1 apple = 2 apples.
That’s how it used to be taught to young kids.
No “slices” involved.
Perhaps, teaching the “probability” that 2+2=4 was part of beginning of slicing and dicing our kids’ ability to think logically?
Back in 1976 I was a teachers’ aide at a Junior High. One of the teachers I worked with taught 7th and 8th graders remedial reading.
I’ll never forget one section in the workbook.
“There are two things I like about my little brother Billy and two things I don’t like.
The two things I like are that he’s easy to please and that he’s fun to play with.
The two things I don’t like are that he screams and cries a lot and that he breaks everything I let him play with. Just yesterday he broke my favorite model airplane.
The two reading-comprehension questions were “What are the two things he liked?” and “What are the two things he didn’t like?”
(Let’s hit the HIGH button on the Brain Scrabblier one more time!)
PS In that workbook, every time, EVERY time a Dad is mentioned he was ALWAYS in a sleeveless tee-shirt, watching TV and drinking a beer.
If the kid was coming to him for help for something, it was always a girl (not the Mom) that provided the help. (I don’t remember if the copyright was Disney.)
I really have been wondering why kids can’t count to 10 any more, or do simple addition/subtraction problems in their heads. This is sad. Galileo weeps. (Math is the language with which God has written the universe – Galileo Galilei)
I’m sure you’ve had a like experience –
Present your goods to the cashier, total = $17.18
Give the “kid” a twenty dollar bill and a quarter – – – and they stare at you blankly
Good Lord. The future is not bright in that one.
Wait till you do that and you get …
“Do you want your change back or to you want to donate it to …”
I have seen that myself. It is very, very sad.
The result would most likely depend on the cash register being employed.
Give them a $20 and 18 cents, same look.
How many people would know if they got the right change back? If they got back $2 how many would know it is wrong? If they got back $3 how many would know it is wrong?
I worked a hot dog cart 40 years ago. People would show up and order lunch for themselves and 4 others (eg 2 sausage dogs, 2 large regular, one regular, two small drinks, two large drinks, one water, three chips four cookies…)
I would add it up in my head and tell them how much. Only about one in fifteen would (could?) check and make sure I was charging them correctly.
As a California inmate, I totally agree with the sentiments expressed by these educators and scientists.
I had not heard of CMF but I am not surprised by the effort to coddle students with simplified math.
I can envision the debacle that data analysis by “data trained” high school students could soon bring to commerce. Just look at the “insights” that Facebook, Google, Yelp, and others are already foisting on us all.
I think I’ll share with our local school superintendent and see what transpires.
This dumbing down of the curriculum seem to be something of a global trend these days.
Down in NZ a group of pretty respectable scientist wrote a letter to a local magazine objecting to mātauranga Māori (Māori knowledge) being given equal status in the school science curriculum with what had been referred to as “Western” science. See background here https://www.kiwiblog.co.nz/2021/11/guest_article_a_professor_without_honour_in_his_own_country.html
This issue has bubbled on with the Spectator weighing in https://www.spectator.co.uk/article/why-punish-a-scientist-for-defending-science- and now Richard Dorkins and Jerry Coyne, Professor Emeritus in the Department of Ecology and Evolution at The University of Chicago joining in https://pointofordernz.wordpress.com/2021/12/07/richard-dorkins-a-foe-of-creationism-pitches-into-the-nz-furore-over-letter-in-defence-of-science-by-seven-professors/
One suspects it is becoming endemic, we can only hope the push back has soem effect, but one suspects there will be a need for new bodies to represent science.
You guys are party poopers. I say pre-Galileoian Church teachings should also be given equal emphasis, and don’t forget the Aztecs!
Specifically, Inca math was mind blowing (still is).
🙂
In a similar vein, doing math with Roman Numerals is quite a trip.
I thought about how one could go about doing that. “Just no” came to mind.
Using an abacus?????
Adding and subtracting letters.
I think that’s how they teach English these days!
I watched this kind of thing happen to my son. Every single communication from the district was about “eliminating the gap.” Well, there are two ways to do that. One is to magically teach students who are unwilling or unable to learn and the other is to reduce what is taught.
I know this is seen as a “white supremacist” argument by the CNN crowd. I believe I’m for equality. But I’m also pragmatic enough to understand that education is a contract between a family and a school. A student can’t succeed without educational support from both.
Unfortunately, right now, that means there are racial “gaps” that have nothing to do with systemic racism. Maybe it’s single-parent households or other factors. More likely, it’s the cruelty of low expectations.
Whatever the reasons, it’s not a substitute for thinking individual children in minority groups can’t thrive. The “eliminate the gap” group seems like the group that wants to deny individual minority children the chance to succeed.
The most pernicious element of this CRT document referenced by the letter is that individualism is considered a major sign of white supremacy. That’s the kind of thing that makes me think we’re headed back into the dark ages. And that even if a lot of smart people show convincingly that global warming isn’t a current crisis (or even all that warm), it’s too late. We’ve lost the future.
So my son received math and science instruction better suited for children half his age. Not surprisingly, he started disliking school. Nothing is worse than going into a middle-school parent-teacher conference, in October, and having a science teacher tell you, “well, I don’t think he’s going to learn anything in this class this year.” Surely the teaching profession needs some sort of version of the Hippocratic Oath.
You might think this is a poor district or an otherwise challenged district. No, it’s a very wealthy school district in a major university town. It just hasn’t had anything other than Democratic rule in decades.
Joe, it looks like you’re getting into the topic of “the racism of low expectations”. This appears to be the actual result of the current “Woke” movement and it’s various associates. If you even brought up this topic at most public schools you would likely be shouted down and labelled (and maybe investigated by the Justice Department?).
One school board member in Virginia has been releasing personal information on those who have been opposing the liberals. Including home address and phone, information on employers, etc.
I don’t know if this still the case, but I remember reading about minority kids being ridiculed for being good at academics. They were accused of “acting white”.
My family has been helping recent emigres in our community learn English and otherwise help them adapt. Their kids are ridiculed for trying to learn and speak English in school by Hispanic students who have been here longer.
Mark, this true. In the 1970’s one of the three networks did a special on the poor academics of inner city youth. One of the issues holding back many was the peer pressure of not “acting white”.
mkelly
I remember that too. It is likely that those who were ridiculed have gone to be successful engineers, scientists, mathematicians, and business persons. While those that did the ridiculing are now the proponents of CRT.
‘if we give them a fair chance, there is no reason that black kids can’t do just as well as the smart kids’
(or something similar)
One of my regrets in life, I’ve had a few, but then again too few to mention, is having passed my O level at not quite 14, I was told by the maths teacher she couldn’t help me anymore.
I spent the next couple of years sitting at the back of the class reading fiction and helping other kids with their maths.
Bit of a waste of someone who seemed to have a natural ability, but then I was a product of the comprehensive system transitioning to a more liberal attitude to teaching.
I had the same experience in science and maths, I got a low grade in the Scottish 11+ exam and went to the High School rather than the Academy. There my maths and science bloomed thanks to some good teachers. In Physics I sat at the back amusing myself, I was too disruptive when sitting with the rest of the class. The maths teacher used to send me round the school with round robin notices for other teachers. I was too honest/niave to read these notes but I suspect they just said “send him to next on the list”.
On the other hand my hand skills meant I was never going to be one of the joiners, mechanics, metal bashers and brickies who were the usual output from the school, not that these aren’t important skills no longer taught either.
yeah, mine was maths, chemistry and physics. I found the subjects interesting and fairly easy
It’s not like it was rocket science
Never really used them in real life though
Never used in real life???? Fiddlesticks, Redge!!! Balderdash!!
Chemistry? What do you think goes into preparing food? There is massive chemistry in the kitchen, Too little sodium bicarbonate (baking soda) and the cookies will be hard and nasty and your pancakes will be too thin for words.
Not enough salt (sodium chloride) on the fries or the roast beef and it becomes a rather dull chewing exercise, never mind the rest of your food.
I’d bet you think there’s no chemistry in black pepper, right? Try this: Piperine is the primary ingredient that distinguishes black pepper and other related peppers (like white pepper). The chemical makeup of piperine is C17H19NO3, or 17 parts carbon, 19 parts hydrogen, one part nitrogen, and three parts oxygen. – https://sciencing.com/chemicals-salt-pepper-sugar-8506178.html
I could go on with that, but those are just a few samples for chemistry.
In regard to physics, how do you think the proper pressure for your car’s tires is determined? It’s PHYSICS, Big Guy, because without those volume and pressure calculation to determine the proper volume of air to pump into your tires, you’d still be driving a wooden-wheeled cart.
We “use” or apply physics, math and chemistry every cotton-pickin’ day, whether or not we pay attention to it, and that includes the camera in your phone, the storage in the hard drive of any type of computer whether a desktop or a handheld tablet, etc. That is all PHYSICS and CHEMISTRY, which requires calculating resistances and strength of materials, as well as output, which is MATHEMATICS, and the actual chemicsl (CHEMISTRY) that puts all of that into existence.
Never use any of it???? Poppycock!!! You use it every time you pick up your electronic stuff or turn on the stove or punch the buttons on your microwave.
So you had never had to calculate the value of a tip for service? You’ve never had to calculate what the interest cost on a loan or credit card balance will be? You’ve never had to adjust your speed while going around a corner in your car to maintain traction? You’ve never had to calculate how much water to add to a cleaner concentrate, fertilizer concentrate, or weed killer concentrate? You’ve never built a bird house or picture frame? You’ve never had to estimate what size nail you need to put in the wall to hang a picture from?
No
I have people to do that for me
look ! it’s Reggie from the Archie comic strip
or was it Richie Rich ?
“You’ve never had to adjust your speed while going around a corner in your car to maintain traction?”
People who can’t even spell calculus seem to do just fine with this.
As for the amount of Baking Soda in cookie dough, that’s what recipes are for, n’est-ce pas? In Ca tipping is simple. The tax on the bill is @8%. Just double that, and round up a bit depending on the quality of the service. Even I can do that in my head, no need for the calculator on my cell phone.
Didn’t say they needed to have studied calculus to understand slowing down going around a curve. But they *are* using it, even if they can’t quantify it. Besides that’s more vector algebra than calculus.
Crikey, it was meant as a joke
Same as “It’s not like it’s rocket science” – maths, chemistry and physics – get it?
When I was in school there was a policy of not teaching algebra below 9th grade. I took it in 6th grade. But since I was required to take math in 7th and 8th, I did pre-algebra two more years in a row…
In my home community and others of this deep blue State, I am aware of efforts to do away with ALL high school Advanced Placement courses. To make everyone equal. Is that sarcasm?
In today’s liberal progressive conflict-free education system, everyone gets full Marx.
And these are the same people who want all grading to be just pass and fail.
No fail, just participation trophies.
Communists figured out the best way to reduce “disparity” a long time ago: force everyone to be poor and stupid. It works, and it destroys people and societies.
Ever notice that the people most emphatic about reducing “disparity” are colossal losers? If I were a loser, I’d probably be jealous of all the winners around me too. Jealousy is a common trait of losers. Bridle your envy and start being grateful and you’re halfway to being a winner. Gratitude is a common trait of winners.
The reason the Left hates Jordan Peterson is that he eloquently points that our. link
It is very easy to convince the lazy and stupid that they are victims and that anyone who is successful is an oppressor. Stalin did that:
I missed a category: lazy, stupid, clueless
You’d think cluelessness could be cured by education but it seems to be hard to do.
Cluelessness can only be cured by education, when that is the goal of the educators.
Education is a two-way street. While the one doing the educating must be reasonably versed in the subject being taught, the student must be reasonably motivated to accept the learning offered. Without both, failure is guaranteed.
Dictators do it far better than communists.
Most communist countries have Billionaires (think China) => they aren’t even vaguely communists, more like National Socialists.
None of the countries that claimed to be communist ever was communist.
Communism is an impossible ideal, however 100’s of millions have died trying to reach that ideal.
Yep, the transition to communism always get stuck at either fascism or socialism. Those in the fascist/socialist government bureaucracy simply won’t give up their power. Consider how we are ruled today by a Bureaucratic Hegemony. Think they will *ever* give power back to the people?
“fascism or socialism”
Not wanting to quibble, but Fascism is just one application of Socialism.
It’s actually a bit more complicated than that. In fact the average standards for kids in maths in, say, China are pretty high and getting higher.
Why are the standards falling in the U.S. (and Australia where I live)? Surely the curriculum has something to do with it. But, I sense strength in maths is just not prized as much as it once was. If people just don’t think maths is so important, then kids won’t bother with it.
A young acquaintance of mine who had decided to be an engineer was shocked and discouraged to find that he would have to do mathematics. Time for me to be shocked. How can that be?
As for data science, it is understandable, but completely wrong to imagine a computer will do your mathematics for you. Again, how anyone could be so misled as to believe that for more than a minute is a worry. It speaks to a lack of education amongst the educators. A good statistician is good at mathematics. Can’t have it any other way.
Fat fingering an input is trivially easy to do. Even when using calculators, you need to have enough familiarity with the math to recognize when the result of your calculations simply make no sense.
If he got an Environmental Engineering degree and went to work for a governmental agency he wouldn’t have to utilize any math.
(I was trying to determine capacity in a storm line so I pulled the City storm study. All it said was:
“I ran the program with a 12″ pipe and the result was a water surface above the curb. I ran it again with an 18″ pipe and the water surface more than 12″ below the gutter; this was determined to be acceptable.”)
And this graduate was not even a Environmental 🙂
So, if your acquaintance can memorize it long enuf to get past the tests and they want a govt job, they’re good.
China abandoned Maoist/Marxist communism decades ago and allowed limited private ownership and limited free enterprise which drastically improved their economy and education, but the government remains totalitarian and private enterprise is subservient to the CCP. Scholastic achievement, however, has long been a point of pride among many east Asian cultures, regardless of government.
“Such frameworks aim to reduce achievement gaps”
This is typical lefty thinking, dumb everything down until everyone gets a prize.
But … high school education is way too academic in my view, everybody has to learn to solve quadratic equations, in order to pass exams, then never again to use the skill, unless it is to teach the next generation. The problem is that maths education is under the control of maths teachers, with their vested interests.
The solution to this problem is obvious, it is already known in the adult education sector, in which people who struggle with maths are taught only what they need to know to deal with everyday life. So, teach everyone in school the adult education subset of maths, and make academic maths available as an option.
How will a child know whether he or she wants to be in one of the many fields that requires advanced mathematics if he or she isn’t pushed into understanding the basics of algebra and geometry? This opens the door to chemistry, physics, much of biology as well as engineering and medicine.
One of the important ideas CRT gets completely wrong is that required math should be limited to “real world” concepts, like making sure you are capable of handing out the right change once you’re promoted to cashier at McDonald’s. In other words, second grade should be the end of compulsory math. Just rinse and repeat for the next ten years.
A large percentage of adults never need to understand quadratic equations. But if they’re never forced to try as children, it’s closing off an entire world.
Math curriculum has been carefully designed to expose children to concepts, then enter appropriate tracks, or just stop entirely. Taking that away, which is what CRT proposes, eliminates STEM opportunities for disadvantaged children. That’s what makes CRT so awful – minority adults are only granted opportunity from their benevolent political leaders. The ability to earn opportunity on their own, and thus escape that control, is the greatest danger to the political leaders of urban areas.
Meanwhile, the only children who will become capable of learning those professions will be the ones who have private schooling. CRT eliminates upward mobility, which is exactly what it’s designed to do.
“A large percentage of adults never need to understand quadratic equations.”
I’ve heard the exact same thing about geometry. Yet when you ask tradespeople like carpenters and welders how they tell if something is square they quote you basic geometry. Same thing for someone digging laterals for a septic system except they quote you basic trigonometry. Sadly many of them don’t even know it!
I find myself needing geometry and trig in DIY projects around the house or woodworking all the time. Sometimes I need even more advanced math – stuff I’ve forgotten so I have to look it up, but since I learned it in the past I can remember it fairly easily once I have the reference again. Having to learn it on the fly would be rather difficult.
Ask a carpenter how to calculate the rise and tread of a stair! Or the anangles on a roof truss.
What is K-12 please?
Thanks.
And here I thought that it was a smarter than average K9. 🙂
At least that’s what my dog tells me.
An old prayer
God, please make me the kind of man my dog thinks I am.
Math is great stuff BUT let’s not forget that morality is now taught in English literature class (analysis of Shakespeare, et al), as religions have rapidly declined in the modern era.
Critical thinking is further developped in History class as we unlearn our national myths and try to remember the lessons of 1,000 years of battles between rulers and ruled that have produced our evolving Parliaments. Canadians weren’t born nice – we descend from much blood, some of which we inflicted on our First Nations after they welcomed Loyalist settlers and helped save us from American invasion. At least, we are committed to Reconciliation for those mistakes of our ancestor settlers.
Ditto for Americans unlearning their national myths and reconciling with the bad deeds and broken treaties of their ancestors, starting with their first – Versailles 1783, which ended the American Revolution.
Ditto for every other country.
Most of the sceptical wisdom of WUWT comes from people evaluating incorrect math about complex climate concerns, then evaluating how and why we’re in this mess from knowing past world history and politics. We need to be well rounded thinkers.
I would agree that “We need to be well rounded thinkers.” However, most of the rest of what you wrote strikes me as being a patronizing lecture based on your interpretation of the behavior of the “noble savage.”
One of the ugliest foundations of modern “morality” is the notion that every group was an unthinking monolith. History was written by the conquerors. We know that. And today, it is being rewritten in exactly the same way, only this conquering was much more subtle.
The truth likely lies somewhere between noble savage and brave pioneer. Replacing one myth with another is not critical thinking.
These noble savages were constantly at war with neighboring tribes. Stealing land, women, and later horses, was a source of pride for them.
And the “first people” weren’t the ‘first’ either. That would be the Clovis people, most likely killed off by the native tribes. Perhaps there were even others before them.
I’m sick of these activists being described as “well-intentioned.” They’re not. If you think reducing a disparity by making everybody worse off is a good idea, you’re a communist pure and simple. These clowns think that if you ration mathematics education that somehow poor kids will get more of it. They’ve never once considered the impact of uneducated parents and poor cultures supporting an anti-intellectual lifestyle.
You’re damn right, Captain, you’re damn right!
The question is NOT reducing disparity by moving towards average, but to elevate the worst off, so that the average is also elevated.
Thank you very much for such synthetic and clear statement.
They also believe that the way to reduce income disparity is to use government to take money from those who have succeeded and then to give that money to those who haven’t been successful.
Someone once made the claim that if we took every penny of wealth on the planet and divided up equally amongst everyone. Within 20 years, almost everyone who is wealthy now would be wealthy again, and those who are poor now would be poor again.
Those who are willing to work hard, and those who know how to work smart, will always accumulate wealth. Those who aren’t able to, or willing to do either, will always end up poor.
I’m willing to help those who aren’t able to help themselves, I’m not willing to do anything for those who just want to sit back and complain how they don’t have everything they want.
Robert Heinlein:
“well-intentioned”: if you believe that you’ll believe anything.
I am firmly convinced that if someone had the time and resources they could quantify the loss of math skills in high school graduates by analyzing what percentage of beginning engineering students drop that major choice at the end of the first semester.
A far lower percentage dropped out in 1968 when I started than when my oldest child started in engineering in 2003. I can only surmise that it was because of lower math skills. I was even more dismayed when my youngest started in 2007 in microbiology. At that point they were only recommending algebra for that major, no calculus, probability, or statistics. They told him that if he needed something mathematical done he could get a math major to do it for him. I convinced my son that he needed all of this to be successful in whatever branch of biological science he chose and he has never regretted it. He went on to get his PhD in immunology and is now quite successful in industry – where he has to teach grad student interns and post-doc researchers how to do basic statistical analysis of experimental results.
I am a firm believer that math and music (not singing but the actual math of music, progressions, chords, etc) train the brain to follow logical thinking, which helps in *all* subjects from science to the humanities. It is truly disturbing to see a de-emphasis on this. It’s why the US is falling behind the rest of the world in science, math, and READING skills. Even reading benefits from being able to logically analyze what is being read.
Trying to understand what the author was trying to say is rapidly becoming a lost art.
Literature today is mostly about what the words mean to whoever is reading it, forget context, both textual and cultural. Whatever you feel is right for you and anyone who disagrees is trying to oppress you.
Tim,
When I started college in 1960, the math and physics classes were widely viewed as a method to weed out the engineering and physics majors who didn’t have an innate aptitude for the subjects.
I would include chemistry. In fact our classes were named Engineering Calculus and Engineering Physics. If you had not taken calculus in high school (which my tiny high school didn’t offer) you had to bust your butt in Eng Calc in order to stay up in Eng Physics as they got into things like derivatives. I agree they were weeding out classes.
That sounds very familiar. I walked away with most of the science and math awards at my high school; however, when I got to college I was competing against all the other exceptional students, among whom I was just average. Like you, I wasn’t exposed to calculus in high school, and I had to run to just stay in place. It seemed that my physics classes were always about two weeks ahead of my calculus classes! At least it gave me a preview of what I could expect in calculus in a couple of weeks. 🙂
Yep!
Yes, offering advanced mathematics is needed, what is desperately needed first is emphasis on basic math. Far too many people are coming out of high schools unable to do plain math, or to read and comprehend simple instructions. Our education system has been bludgeoned into the ground by leftist morons who, first, hate America, B. hate capitalism and finally hate themselves. It is to our eternal shame that we have allowed these severely mentally ill people to destroy our educational system.
If I had to pick one it is the hating of the self which does the greatest damage.
If anyone wanted to ‘slam’ anything, it would be what I discovered recently
i.e. That High Fructose Corn Syrup is used to make Formula Baby Milk
Babies up to 24 moths AT LEAST, ideally 30 months+ need their mother’s milk to build a normal and properly functioning brain.
Slam THAT for christsake!!!!
And most it is GM highfootrosebrainrotshyte to boot
Because that is where your science, politics, social skills, personalities & relationships, marriages, birth-rate and ‘most everything that makes proper people and societies has gone
jeez what a mess
mebbe, but based on what you say, more than 99% of people don’t have a normal and properly functioning brain.
You are going to have redefine normal.
As mentioned above, monkeying with mathematics curriculum is becoming a global trend. Look at the description of the mathematics curriculum for the province of Ontario, Canada. The rather wordy description begins with great promise, as it describes “the importance and beauty of mathematics” in everyday life.
However, it goes off the rails at the section titled “Human Rights, Equity, and Inclusive Education in Mathematics.” Uh-oh. A sample:
There is plenty of turgid prose dedicated to systemic barriers, cultural context, intersectionality, and other trends.
I don’t care what your culture or skin color is. 2 + 2 still equals 4.
Students bring abundant cultural knowledges, experiences, and competencies into mathematical learning. It is essential for educators to develop pedagogical practices that value and centre students’ prior learning, experiences, strengths, and interests. Such pedagogical practices are informed by and build on students’ identities, lived experiences, and linguistic resources.
What arrant drivel! Students are kids who know next to nothing – that’s why they are at school, to learn!
no, no, no. Little 7 yr old Jamal won’t accept that 2+2=4 unless you value and centre his(her) prior learning, experiences, strengths, and interests; as based upon little 7 yr old Jamal’s identities, lived experiences, and linguistic resources.
(Little Jamal is screwed.)
“…any more than I can write world class poetry”
Whaaaat????? Oh, this cannot be possible!!!! I was so sure it was Eric Worrall who wrote that famous ditty, the “Philosopher’s Drinking Song”, and now he’s saying “not me, someone else”????
Given good teachers, kids can learn anything even if it’s difficult. Unfortunately, inflicting political correctness on them seems to be more important right now than actually teaching them things they’ll need if they want to get into college.
I’m in the part of California called the Bay Area. It’s home to many of the big high tech companies where salaries are high, especially if you have math and engineering skills. The starting pay for teachers is $30,000 per year in some communities here so the chances of hiring a competent math or science teacher is very low. The teachers that are assigned to teach the math and science classes are not trained in math or science. This fact creates a motivation to dumb down the curriculum. Another factor, that has been in play for many years, is an almost complete segregation of the public/private schools in this region. The white children have left the public schools in very large numbers. In communities where the demographic breakdown, as an example, is a mix of 33% white, 33% Black and 33% latino, you will find single digit percentages of white children still enrolled in the public schools. This trend has been happening for decades now and it is a painful reminder of the failing public school system. The high school graduating math literacy rate for the minority students in public schools is down around 2%.
However, there is hope. Almost all parents, Black, White, Latino + Others are demanding more charter schools. The teachers and administrators along with their school board minions are doing their best to slow the charter school approval process but there is great pressure from parents and long waiting lists pushing the charter school movement ahead. I think the progressive communities in California may be the canary in the coal mine for our dysfunctional K-12 public school systems. If parents can defeat the powerful interests of the democrats and teachers union here, the rest of the nation may follow.
Something doesn’t seem right. I started teaching at Foothill College in the Bay Area in 1971 at $11,000 per year. When I left teaching a decade later to go into industry, I was earning over $30,000 per year. That was back when you could still buy a house for $100,000. It is difficult to believe that the starting salaries for teachers is $30,000 when many, if not most, homes in the Bay Area cost about $1million. Starting salaries for engineers in the Bay Area are over $100,000.
It’s also astounding considering the Bay Area has some of the highest tax rates in the country.
I stand corrected Clyde, good catch. It seems I’m a decade behind on the salary schedule. I looked up the current starting teacher salary here in my community and it’s now $49,500 per year. We’re desperately short of qualified Math and Science teachers. People with these skills are commuting into the high tech centers for much larger salaries.
This is the essence of modern left wing thought.
To make everyone equal, the first thing they do is tear down the successful.
Math leads to understanding the world and that would not be good for propaganda and MUST be taken off the indoctrination table. the sooner the better
There are a lot of comments here about dumbing everyone down … y’all might want to check out the story “Harrison Bergeron” by Kurt Vonnegut. He took extended this idea to a logical but extreme conclusion.
Yes it decreases disparities by bringing the more adept down to the levels of the lesser adept students. It’s like socialisms goal to make everyone equally miserable
There is no satisfaction or achievement in forced equality. It only results in lower outcome. People like water will rise or sink to their own level when free to choose with opportunity.
“However, we are deeply concerned about the unintended consequences of recent well-intentioned approaches to reform mathematics education, particularly the California Mathematics Framework (CMF)”
I question the “well-intentioned” part. Agendas such as AGW would be a much harder sell if more of the population was better educated in math and statistics.
“Some otherwise intelligent people just can’t do advanced math, any more than I can write world class poetry or compose a rock song anyone would want to listen to.”
But “equity”! If “Some otherwise intelligent people just can’t do advanced math”, then nobody should be made to feel bad for being unable to do advanced math. My dad could do calculus in his head. I struggled with it on paper. This made me feel bad. I should not have had to endure such emotional trauma!
The letter is only addressing one of the symptoms of the mathematics desert that is K-12.
The number one issue is the fact that the vast majority of our graduates in early grades education get their certificates without a single numeracy course on their transcript. Even when they take a science course to fulfill a requirement, it is one that is dumbed down to bare concepts without any mathematical engagement.
Many if not most of these “educators” are afraid of math and avoid it like the plague. When they get into the classroom, their fear of math translates into students who avoid math and can’t even add two-digit numbers in their heads. Then we get to see these students in our introductory college STEM courses and find they aren’t even suited to do the college math intro course, let alone a calculus-based physics or chemistry.
K-12 education is handicapping many of our students by not engaging them in the full field of arithmetic by 3rd grade and beginning mastery of the concepts of algebra, geometry and statistics by 6th. Starting in 7th grade they should be doing formal algebra with a strict adherence to the logical application of the lemmas and theorems, continued into 8th grade. By high school, they should be able to start on the introductions to analytical geometry, trigonometry, and calculus, or for those without STEM interests, household math, business math and accounting.
This math curriculum issue is being influenced by the lowest common denominator, a math term as it turns out, catering to the unprepared and unmotivated students bringing all the others down to their level. The worst part is the dire epidemic of low-low-low expectations that handicap motivated and unmotivated students alike.
OK, off my soap-box. I have this rant two or three times per semester when I have corrected very simple math errors from arithmetic to simple algebra too many times from the first week of class to mid-terms.
“Starting in 7th grade they should be doing formal algebra with a strict adherence to the logical application of the lemmas and theorems”
Every pupil should be doing that? Even those who will become plumbers and nurses? How many people avoid becoming doctors because they fail to get qualifications in abstract algebra?
yes. Formal logic and application of a rules based structure will impact their thinking when solving problems on a job site – the algebra may be long forgotten, but the pattern of logic will stick with them.
As I remarked above, I started teaching in 1971. During the decade that I taught, I noticed a decline in the math ability of most of the students, despite largely drawing from upscale Palo Alto high school. By the time I quit teaching, I observed that many students didn’t realize that one could multiply/divide by powers of 10 by just moving the decimal point.
Maths is actually a lot easier than it used to be. When I was a kid, up to the age of 15, all calculations were done with pen, paper and head. We were taught how to use log tables at 15 and my first slide rule began at high school. Kids today have calculators. So, if they are not doing advanced maths – there’s nothing left to keep their interest! There should be more advanced maths, not less.
I’ll bet the schools that deemphasize math are the same as the ones that teach critical race theory.
North American education departments seem to specialize in recent years at finding ways to water down curriculums to facilitate inflated grades and higher high school graduation rates. That way they can give the impression that students are learning more when in fact it’s the opposite. That’s the reason we hear education policy makers tell us the emphasis is on “creativity” and “critical thinking” which can be judged subjectively rather than by standardized skills tests which “progressive” educators vehemently oppose. Why bother to teach basic skills when the grades can be jacked up artificially? The whole concept is full of holes since it’s like trying to build a house from the roof downward or trying to teach basketball without any emphasis on the skills of passing, rebounding, or shooting. Just toss the ball onto the court and hope the kids will acquire the skills as they play.
“ Such frameworks aim to reduce achievement gaps by limiting the availability of advanced mathematical courses to middle schoolers and beginning high schoolers”.
Insanity. Some people are better at math, so remove the programs where they can excel so no one can shine above the others?
Level the playing field by cutting down all the tall poppies.
This article encompasses everything wrong with western society
Pat, looks like Harrison Bergeron is happening as we watch.
Thankfully here in AB we elected a nominally conservative government that got rid of “discovery math” which is just as it sounds, leave kids to work it out for themselves with predictable results.
Also, no memorizing of multiplication tables so every simple problem takes forever.
When I found this out I printed off copies and started drilling my girls, their marks improved substantially
And when their teacher found out he huffed that he would have to do the same with all the kids.
DUH!!!!!!!!!!!
It’s our own fault for allowing such people to gain power
I would replace at least one advanced math class with a required course in economics, the knowledge of which is absolutely necessary for understanding human society. Watching high officials, including those at the Fed, attributing inflation to anything except expansion of the money supply, without pushback from most commentators, shows just how ignorant most people are of this basic phenomenon. Of course, the problem now is that economic science has been corrupted by its proximity to government, just as environmental science has.
“attributing inflation to anything except expansion of the money supply”
The way I learned it, “inflation” did NOT refer to the increase of prices. It meant inflation (increasing in size) of the money supply.
This is one of the few examples of a discussion on WUWT where I actually have firsthand knowledge of the problems involved. I used to be a Math tutor.
The belief that everybody should be taught subjects like Calculus and Trigonometry is just a superstition. Probably 90 percent of people who take high school Math never use it to any great degree in their adult lives. Math in schools is, for many people, and arduous and rather cruel hazing ritual, because they don’t really understand Math.
A lot of people who are perfectly capable of getting degrees in various liberal arts have major trouble understanding Math. One of my first priorities when I was tutoring teenagers was to explain to them that, just because they had trouble with Math, they weren’t therefore unworthy or stupid. What you can do with someone with an I.Q. of 115 is teach him or her to recognize Math problems and then apply by rote the procedures to get the right answers. But most of them don’t really understand what, for example, logarithms are, or how they work.
Compulsory Math is a lot like compulsory Physical Education. There is a large subset of students for whom these subjects are just torture. Just as you need a certain base level of physical strength and co-ordination to succeed in Phys Ed, you need a certain kind of mental acuity to succeed in Math.
Of course, athletic people should be trained to use their gifts. Of course we need engineers and statisticians. It’s just that we should get off the backs of young people who are not athletically or mathematically inclined, at a point in their lives when they are vulnerable to the need to please adults.
Algebra for me was easy and fun. I remember classmates bursting into tears because they couldn’t solve the problems, when all they wanted was to please their parents and teachers.
So what do I think? Administer I.Q. tests to all students and exempt students with I.Q. scores lower than 120 from any obligation to learn high school Math.
Algebra is necessary as a basic subject. Who says that algebra is not useful in life – I’m happy for you, but how do you calculate the interest on the loan, take a mortgage and, trivially speaking, count your salary? I work as a writer and after writing my literary review, I have to count the number of characters in the text. And there is a lot of work from the fact that we are recommended by students to each other and the end of the year I have all in writing. I want to finish by saying that education in mathematic sphere should always be a priority for people.
I take your point, Carol, but I don’t think I’ve made my point with you. Of course most people will need to know things like percentages, or how compound interest works, or, if you’re a carpenter, basic Euclidean geometry. All of these topics are covered in Canada by the end of Grade nine. I’m talking about the more arcane and complex Math systems that teenagers are required to learn in high school.
Whenever anyone complains that high school students are being coddled, I challenge them to get a copy of the final exam in Grade 12 Math and see if they can pass it. I mean really, when was the last time you had to factor a binomial equation or apply a trigonometric identity?
As you are a writer, think of the course requirements for high school students in English literature. I graduated from high school in 1970 (sigh), but I remember what a slog it was to read Macbeth. Even now, it takes me five minutes to read a page from a Shakespeare play, because I can’t read more than ten words without having to consult a key explaining archaic language. ( I really, really dislike Shakespeare, and I have yet to meet a single human being who has actually read a Shakespeare play on his own time, without some kind of reward or goad to motivate him to read it.)
My point is that clever people, like the ones who post on this site, are supremely indifferent to the struggles of people of just average intelligence, and have no problem imposing terrible labours on them when they are young and vulnerable. It does absolutely no good to force teenagers with I.Q. scores of less than 115 to learn the things that people like us can do with so little effort, and in fact considerable pleasure. It is cruelty to them for the sake of enhancing our own vanities.