HORRIFYING STATISTICS: AMERICAN STUDENTS FAILING IN MATH

[@slauge]

I don't think you're alone. I'm European. I recently had a look at a calculus textbook from the 1960's, designed for upper secondary education. I was expecting it to be a bit depressing, since obviously standards would have fallen a lot since then. But I did not expect to feel chills down my spine. "We're done for", I thought to myself as I contemplated just how fall we've fallen. The problems would have been difficult for many current day university students. For all but some rare, talented students, they would have been impossible for current high school students. The entire scope was far more ambitious than the watered down version taught today.

[@acelm8437]

I've always been several years ahead of grade level in math. Does that mean I'm just average then?

[@Ilese-xy8on]

Very well said Mr Cromwell. Society begins in the home, and where there is no love for the child there is no preparation for their advancement.

[@CondorAHLS]

Yeah, I distinctly recall as an elementary school kid, when I was home sick from school, my mom would bring me cheap paperbacks by George Gamow and Isaac Asimov on math and physics. And I retained more from reading these popular books than all of my university & grad school education. 😂

[@Ilese-xy8on]

@CondorAHLS Obviously a very fine and truly loving mother. Best wishes to you and mothers and fathers who truly love their children.

[@julians9763]

Recently I was asked " What happens if the parents are illiterate?" I responded that we are not in the 12 the Century. The parents are the first educators. Society begins at home. Careful home training free from useless waste. This is a right of every child ,not just an elite few.

[@Ilese-xy8on]

@julians9763 Yes, well said Julian. Children's welfare, happiness, health, and wellbeing should surely be the highest priority within the family and society in general. Some people realise that a good education is a way to financial security, to attain positions of power and influence, and possibly freedom from poverty and financial distress. A good parent surely would want that for their child.

[@Chihab-z8o]

It's not just in the US, even in Europe the quantity and quality are decreasing horribly.

[@jimsmith1549]

Retired college math instructor here. I can relate to "I can't fix stupid" !!

[@julians9763]

Sadly I have noticed a number spoilt brats enter University or College without mathematics, and graduate as Tertiary educated idiots.

[@cypherknot]

I teach adults who dropped out and did not get a HS diploma. Math and civics and science illiteracy is rampant. Most can't write ideas coherently. They lack motivation, commitment, and interest enough to keep them working towards their goal, yet they are not 'stupid'. I have not graduated a single student in 4 years! I have become resigned to being disappointed. They come, maybe stay for a while, then quit.

[@julians9763]

You might consider teaching elderly in age care who don't wish to have memory loss. If that is difficult ,teach people who has memory loss due to an injury and beome aware that they don't wish to forget the best skills they had in the past.

[@Mambialasombra]

Here in Florida the Algebra II exam was removed from HS Graduation requirements since 2017

[@citytutoring]

Thank you for letting me know about that! How very sad for our students...

[@Mambialasombra]

@ I don’t want to blame anyone but I think that It is because most of the parents, teachers and government staff don’t take an active role in the education of the new generation, and unfortunately they don’t care or they reject the value of education compared with other social or personal responsibility.

[@dhickey5919]

The United States launched humans to the moon from Florida. How we don't have the best math and physics in this state is beyond me.

[@citytutoring]

@@Mambialasombra Yes, unfortunately this has been my experience. Personally, I have been blessed to deal with very serious parents, but I do work with a lot of colleagues who have shown me literal horror stories about what they experience. Also, at the risk of sounding irresponsible in my assessments, I also do think that many teachers leave a lot to be desired with some of their behaviors. I do not say this in a judgmental way, because I know we all have our struggles, but more of a constructive observation because I am a firm believer that no matter how utterly disrespectful a student can be, and many times they are, they still respond based on the standards you project.

[@Mambialasombra]

@@dhickey5919 I bet it is because teachers are not being incentivized enough, and some times schools put to much responsibilities over some professors (I’ve been witness of that) and they just give the classes but don’t really teach, reasons are more than obvious. But I’m not justifying anyone, just stating it and hoping that we all could do something about it.

[@mgmartin51]

A few years ago, there was a big brouhaha here in New York that the math exam was too hard. There was a high failure rate. I asked my daughter to find me a copy of the exam, and I took it, and scored a 98%. (I lost credit for an arithmetic mistake). I had not prepared for the exam in any way. My point is that the math curriculum when I was in school held up over 4 decades. I remember math being tough, and it was hard work. The tougher my teachers were, the more I learned. But it was enjoyable, and I still love math. Learning is hard, but if it weren't, there wouldn't be any achievement in attaining it.

[@alldayumday2660]

We could change so many lives if we required a discrete math type course on logic early on, starting with the idea of p implies q. This provides a framework for understanding ALL proofs and results in math, and requires no prerequisites (it is the prerequisite). If students understood logic like the back of their hand the way they knew algebraic manipulation (which is also good, don't get me wrong), then they would be unstoppable in any math topic. I hope that a focus on computer science will make logic more common at the early schooling level, it could help us greatly.

[@dhickey5919]

Absolutely agree. So much depends on critical thinking.

[@mpmcd81]

I start my precalculus class with a brief unit that includes the Chicken McNuggets problem (Find the largest number of nuggets you cannot buy with packs of 6 and 11). Modular arithmetic helps and this problem helps students see that if a is congruent to b mod p, then 2a is congruent to 2b mod p. At any rate I then ask them to compare this with the number mn-(m+n) and they see with different relatively prime pack sizes that there is a pattern. We then use a the proof without words to generalize what is happening. This leads to a statement of the Chicken McNuggets theorem. If m and n are relatively prime then the maximum number of nuggets that cannot be bought with packs of m and n nuggets is mn - m - n. Then I ask my students to think about how to solve the same problem for packs of 6 and 9. This leads to an entirely different setup where they realize that there is no way to buy a number that is not a multiple of 3. Why is this important? We have a lot of things where we need to know how theorems work about functions and early calculus concepts. There are a lot of places where it isn’t what we wished in public school, but there are a LOT of places where excellence also happens regularly. Our PAP and AP program takes in students averaging an ACT 17 and spits out students averaging an ACT 27 in May of Junior year 30 months later. Some of these go on to pass AP Calculus, Statistics, and Physics in the same year. On the other hand, 2/3 of our kids are innumerate and cannot be made to care. An algebra 1 teacher in high school is not supposed to be the one teaching kids their multiplication tables.

[@rmpob1]

I went to a High School where Pre-Calc was the highest math offered. A local University would wave some requirements for students of this and other schools, along with Foreign Languages, simply because they were not offered. This was a while back. Thanks for the message you spread.

[@dhickey5919]

I'm glad to hear this coming from an educator. I have more data collected from several years ago. In my college trigonometry class only twelve students out of thirty-five made it far enough to take the final exam. Four of those students failed the final exam. This pattern repeated in precalculus, differential calculus, and integral calculus. No one was particularly alarmed at this rate of failure. It was in fact typical for any year at our college. I went back to determine the percentage of students who were successful, beginning with algebra through vector calculus. Less than 1% of the students made it to the end. Those of us who made it through call it "The 1% Club".

[@citytutoring]

Your experience relates academic natural selection-only the mathematically fittest survive! The lack of alarm at the attrition rate is almost poetic, like everyone just accepts that higher math is a trial by fire. The '1% Club' does feel apt! I often begin a semester with about 45 - 50 enrolled students. By the end of the term, there's about 9/10 left depending on the course. Unfortunately, there are now some colleges that make you pass students, regardless of any evidence of academic ability.

[@walter274]

Yeah I would often have semesters where only 1/4 to 1/3 or so of my students would get a C- or above. I'm no that hard of a teacher. If you pay attention when i teach you'll know what many of the test questions will be, because i say things like this would be a good exam question, and when i'm done, i'll ask are there questions. I tell them i will do this on the first day of class.

[@dhickey5919]

@@walter274 As a nation or even as a society, my wish would be to advance the average student to understanding several topics of calculus. They may not grasp the finest points but should at least see an equation and know what they're looking at.

[@walter274]

@@dhickey5919 I would be happy if high schools made students take 4 years of math instead of 3. If coleges and universities had to do less remediation because the students were better prepared, those remediatial class could become a semester of calculus. That will never happen, because peopple are too greedy. That would require more spending for the school district, which people don't want to pay for. A lot of people just want low taxes.

[@citytutoring]

I was very blessed to have had "remedial" options in my high school. Yes, as far back as the late 20th century, where I went to high school you HAD to have 4 years of Math, and English to even be considered for graduation, and we also had a course that was mandatory called "Strategies" if you were honors or college prep. "Strategies" was a Math course designed to specifically prepare you to take the SAT. It was taught by one of our toughest and "meanest" (I say this in a good way) Math teachers. Of course, discipline problems were also swiftly dealt with. If any student even dared to disrupt a class, they'd first get a verbal warning. If they kept up the nonsense, kicked out of class. Today? Too many of our schools are circuses.

[@BernardoLameiras]

Here in Brazil de situation is desperate. I am in my 40's and decided to go back to college to major in electrical engineering. Just to clyrify, I choose the best private college there is in one of the major cities of the country. It is a very traditional institution here. The young students are struggling with basic algebra. Many of them have never seen a logarithmic function. Many have never seen what a function even is! Much less trigonometric, hyperbolics exponentials, inverses, factorials, etc. Even so classes such algebra I or II are not offered. Instead a class which is a mixture of pre-cauculus and calculus I is tought. Basic derivation rules are a major challenge. Teachers give extra marks, bnous marks and even then many students fail to pass. 3 or 4 times in a row! James Stewart's book on calculus is considered an apotheosis as if nothing else in the subject existed. However, even this book is very little used in actuality. It is too difficult for most students. I always considered myself as having a weak mathematical background, although by seeing these young students nowadays I consider myself lucky.

[@citytutoring]

I believe you. In comparison, and looking back, if you were educated in the 80s and 90s, we look like "geniuses" in comparison to the nonsense in so many places today. Yes, you are right about Stewart's textbook. Even a "practical" textbook like his is very hard for students today to grasp. In my experience, it is not only the short attention spans, but also very serious and deeply troubling foundational problems. They are used to passing each grade even when they get F's, and then they hit the reality that they are not as "wonderful" as they were told by either liars or very incompetent people who should never be around our young people. We can only pray for the best.

[@mpmcd81]

@@BernardoLameiras I agree with most of your observations. Stewart’s book, however, is legendary. It is extremely rigorous for what it needs to be. It is not a real analysis text but leaves students well prepared for that.

[@BonFlanders]

Mathematics specifically in America has largely shifted towards rote memorization and formulaic application, lacking a deeper emphasis on conceptual understanding(ex. "MEMORIZE THE UNIT CIRCLE AND TRIG IDENTITIES, IT'LL SAVE YOU SOME TIME ON THE TEST!"). Meanwhile, competition does exist, as China has officially surpassed the United States in claiming the world's top universities in the field of Physics. While this achievement reflects the country's advancements in education and research, it also highlights other contributing factors, such as its large population and highly competitive academic environment. The rigorous and demanding nature of China's education system, combined with intense competition for admission to elite institutions like Tsinghua University and Nanjing University, has propelled its universities to global prominence. However, Americas education system need not be parallel to that of China, but should be more balanced than it is now, embracing critical and conceptual thinking, and derivations of such formulas that are quintessential to mathematics!

[@PatrickCraig-lh5is]

A David Hilbert quote in poster form adorned the front wall of our college's mathematics "laboratory" (actually a computerized drill-and-kill torture chamber, but that's another story): “Mathematics knows no races or geographical boundaries; for mathematics, the cultural world is one country.”

[@citytutoring]

Indeed! Precisely why Math is beautiful to me and why I began to develop an interest in it as I matured. Math is the language of logic, it is universal and truth is truth everywhere. I always tell my students that Math is, in fact, the great "equalizer", in a good sense of the word, because it humbles us all, but it also gives us that incredible sense of satisfaction and fulfillment that only knowing you are right can give you.

[@schrodingcheshirecat]

I salute you, Sir.

[@pratikmaitra4190]

Great points. I know statistics is not pure maths but what books would you recommend for someone who is interested in Probability,especially for data science. Also what books would be good for Linear algebra, once again with a focus on matrices(data science).

[@walter274]

I was starting to fall asleep when I answered this, so I’m editing and clarifying. Obviously, I'm not Alfred, but I know a bit about this. In my opinion, you can never know too much linear algebra. Stephen Boyd, Lieven Vandenberghe - Introduction to Applied Linear Algebra, is a great place to start, especially if your math background is modest or if you’re rusty. Even if you are doing great mathematically he presents some material in here that you might not have seen or may present material in a contest that is more relevant to you. It doesn’t cover some of the material in a traditional linear algebra book, because of this you’ll also want a traditional linear algebra book. Gilbert Strang - Introduction to Linear Algebra. I own the 3rd edition, I’ve looked at the 5th and 6th, they aren’t interchangeable, but they’ll all get the job done. Strang has a unique way of doing linear algebra, if it works for you, you’ll really get something from the book. David Poole - Linear Algebra A Modern Introduction. I don’t have tremendous experience with this book, but it has the right content. Howard Anton, Chris Rorres - Elementary Linear Algebra Applications. I don’t have tremendous experience with this book, but it has the right content. By right content I mean the traditional linear algebra stuff plus the SVD Sheldon Axler - Linear Algebra Done Right is very well regarded, and the author gives away the newest edition (4th) of the book for free on his webpage. I own the second edition of the book, It's harder than the above linear algebra books, and requires some facility with proof writing. While a cool book, that will certainly give you insight into linear algebra, it won't be as directly applicable to data science You should also get a book or two on linear models. They are work horse tools in statistics, and are a great place reinforce linear algebra concepts. John Fox - Applied Regression Analysis and Generalized Linear Models 2nd or 3rd edition as well as the resources on Fox’s webpage. It’s comprehensive and talks about the geometry and theory behind the linear models. For probability and math stat, I would recommend Jay L. Devore, Kenneth N. Berk, Matthew A. Carlton - Modern Mathematical Statistics With Applications 3rd edition. I own the first edition. This a very accessible probability and mathematical statistics book that has modern topics like logistic regression and Bayesian statistics, but the coverage of Bayesian statistics is not included in the first edition and is not well developed in the second. John Rice - Mathematical Statistics and Data Analysis. I used the 3rd edition for a math stat class in grad school. I looked at the second edition and it’s pretty similar. It has a great balance between probability and statistics. It includes coverage of sampling theory, and non-parametric stat. It’s more in depth than Devore and Birk, but less in depth than the next book… George Casella, Roger L. Berger - Statistical Inference 2nd edition. This was a supplemental book for the class that I used Rice in. It’s been the mainstay book for PhD level math stat courses for over 20 years. It has all of the standard topics, but in more depth. I would hold off on this one. You may not need this level of detail. If you need a basic book Allan Bluman - Elementary Statistics: A Step By Step Approach This is a giant Rabbit hole that you can go down. I own at least 5 linear algebra books, and atleast 5 mathstat books, with a few additional books on probability and on math stat seperately. I also own 5 linear model books.

[@pratikmaitra4190]

@ Thanks a lot.

[@walter274]

@@pratikmaitra4190 You're welcome. I'm good with the math and stat part of data science, but I am weak at the comp sci stuff. If there is anything else you're looking for feel free to ask.

[@citytutoring]

Thank you for your question, and thank you Walter274 for such a detailed response and your assistance with the matter. I will defer to Walter's answer, because I would have made similar recommendations since I am familiar with those titles and they are the closest you will get, as far as I know, to your objective with data science.

[@walter274]

@@citytutoring You're welcome. I'm happy to help people when i can.

[@mohamedwalid-g2u]

May I ask you about george chrystal's algebra and euler's algebra

[@citytutoring]

Oh, I am very much an admirer of Chrystal's Algebra and have solved problems in the book. As for Euler's Algebra, that is another excellent source, although I would recommend it as a supplement given that the way the topics are presented would be quite confusing/challenging to a beginning student today if they are in the United States. Of course, I am passionate about structured logical thinking, but I'm afraid even many teachers would have trouble teaching right out of that book. So, that is why I use it as supplementary material.

[@mohamedwalid-g2u]

So I can put them in the category of dolciani's algebra I mean, Are they rigours?

[@citytutoring]

@mohamedwalid-g2u Absolutely! However, for example in Chrystal, the language might be dated if you are using it to teach students, and some of the notation is very old-fashioned, so if you are using it be sure to adapt it with the modern notation that everyone can understand.

[@mohamedwalid-g2u]

Actually I am student trying to re-learn the subject

[@cypherknot]

Where do your students get the textbooks?

[@citytutoring]

So, because the Dolciani textbooks are very hard to find, we have a master copy and work from that. If that fails, we use the copy available on archive.org. Every year, I do get students who are able to find some version of the book online for sale.

[@kathieharine5982]

Where did shop math or business math go?

[@mpmcd81]

Scripted lessons are of the devil. Why? These students never learned the lines. My kids FAR outperform the script. Seven point ACT gains in six months have happened for many, many students. I refuse to use a script and write my own problems.

[@Briand-ei1gs]

The word nation biblically speaking means race. So without breaking down the numbers demographics they really don't help. Thete are several different " nations"[in america.

[@citytutoring]

Fair enough, but I did mention it affects all the races/nations in America. It is no longer something that only affects one group as was the case years ago.

[@citytutoring]

However, if you want the breakdown by race, here are some government statistics: www.nsf.gov/nsb/sei/edTool/data/highschool-06.html#:~:text=Over%20half%20of%20Asians%2FPacific,the%20proficient%20level%20in%20math. You will see that Asians have scored the highest, followed by Whites (but whites are way lower than what the stats once were, which should be alarming as a sign of the decline of our schools).

[@Briand-ei1gs]

@citytutoring well isn't that due to a lowering of standards. If you try to help someone drowning you both end up drowned.

[@Briand-ei1gs]

@citytutoring The problem is that 50 years when we launched this experiment. When the the other " nations" obviously could not match same results. Wo dishonored truth. Not only that we then turned and blamed the more successful nation for being yhe cause. Now we have a real problem

[@Briand-ei1gs]

@citytutoring I cannot even imagine the hell of being a White teenager with average White IQ who is actually interested in learning having to endure these schools as a minority. Talk about injustice. Most of us our age are putting these children through something most of us had the luxury of not having to endure. It is pur evil and we are guilty. Guilty because we are cowards afraid of being called a word. So we sacrifice our children on the alter of tolerance diversity and political correctness

[@okraalfred]

What are some inspiring words you would give to a high school student?

[@citytutoring]

I would say to any high school student who needs inspiration that the key to success in their personal future is to know that they can only truly be free and successful if they are educated and take in every day as if it was their last race to win! If I, who started out as a failure in math made it to being a mathematician, they can achieve their goals in whatever subject as long as one thing never dies: their passionate curiosity and desire to succeed in all they do, and not accepting "no" as the only definitive answer to their plans.

[@CondorAHLS]

From Lord Beaverbrook’s book “Success” (London: Stanley Paul & Co., 1921), Chapter VI: Education, pp. 61-62: “Read anything and read everything… There are, of course, in addition, certain special branches of education needing teaching which are of particular value to the business life. Foremost among these are mathematics and foreign languages. It is not suggested that a knowledge of the higher mathematics is essential to a successful career; none the less it is true that the type of mind which takes readily to mathematics is the kind which succeeds in the realm of industry and finance.”

[@mpmcd81]

Let me also explain that Dolciani’s books have a very important Achilles heel. They do not often require students to make sense of unfamiliar situations and do not place adequate linguistic demands for justification, proof, explanation, prediction, type tasks. It does very little good for a student to master a procedure if they cannot see where else in mathematics, and even more importantly in life or other intellectual disciplines where the math they are learning will be used. THIS is why students in modern schools do not master or retain the mathematics they have been taught. Whether it is Dolciani, Math Medic, Envision, or some other textbook, there is no guarantee that students will come out competent. What does make students competent is a teacher who expects students to be able to explain problems with statements and reasons- not just for geometric proofs. I will also say that not everything in the Dolciani book necessarily should be taught now. There is no need for sophomores or juniors to learn multiple party tricks. But it IS necessary to start with the properties of the ring of integers and the field of rational, real, and complex numbers and to understand why these number systems are necessary. It is also necessary to teach NUMBER THEORY FUNDAMENTALS.