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Sunday, March 17, 2019

No sign for improving math education soon.

America is in a dreadful state. Has been for awhile. One of the reasons for that was and is the awful state of public education.

There is a LOT of cheating in education. But not the one that comes to mind when one reads the word "cheating". I talk about school-level cheating that leads to COLLEGE students who had a passing grade for college math, and then did this (when taking a physics course).

Didn't spot any issues? Ask in a comment field at the bottom of this post and I will help. And don't forget to send a card to your math teacher(s) saying - you taught me wrong!

These example represent just a tiny sample of what I have seen in my classes for twelve years teaching two-three thousand students. I have some statistics on the matter in a different post. And at the bottom of this post you find some examples of problems every Russian high-school graduate must do.

Question - who do you think is responsible for THAT cheating? Teachers? Principals? 
Government in general?

Ignoring the quality of college education when advocating for free college for everyone is nothing but a publicity stunt.

Once, browsing the Internet, I accidentally stumbled upon a piece from 2018: “We Should Teach Math Like It's a Language”, By Jeannine Diddle Uzzi, the provost and vice president for academic affairs at the University of Southern Maine (
The author makes a case that math needs to be taught in a way similar to teaching Latin. She appeals to a 2011 article, "An Apology for Latin and Math," by high school Latin teacher Cheryl Lowe.
This is where I see the problem.
The approach to study math as a language has been known for decades.
A simple search can show books (not just articles) on the matter published more than 10 years ago.
The methods for teaching math have been known for decades.

And every math teacher who wants to be good at teaching should have read at least elements from Euclid’s “The Elements”.
They would know that mathematics starts from the basis of language, from a “dictionary”, these days a.k.a. definitions.
BTW: this approach is not limited to teaching languages or math, it is a fundamental scientific approach essential for teaching any subject, or at least any STEM one (I use it when I teach my physics courses; BTW, very successfully).
The fact that efficient math teaching strategies have been developed decades ago but math teachers at large still need to be introduced to the very idea of the approach, demonstrates how poor the teacher professional development has been and is – on all levels, K12 and above.
This is the actual issue that needs to be addressed.
But evidently, for decades, it hasn’t.
Hence, I see no indicators that things are going to be much better any soon.
There is a wast amount of research on the state of math education. People use complicated statistical methods to prove their point of view. 
It is a major waste of energy and time and funds. 
Do you want to test the quality of the work of a math teacher? Ask his or her students - why 2 + 2 = 4? I can assure you the majority will not be able to give an answer. Hence the teacher has not done a good job. Q.E.D. ◾▢
This is how districts should approach math teachers. 
1. A math teacher must be able to teach at least 4 consecutive math grades. 
2. If N is the highest grade a teacher teaches, he/she needs to know math for (N+3) grade. 
That simple. 
Don't believe it'll work? Let's bet on it. Make your bet with me, and TRY IT.
Instead of spending millions on "research", NSF needs to invest in rudimentary teacher preparation - en masse.

The first picture in this short opinion piece often comes from my students when we start learning about normal force (in physics there are many situation when we need to apply the Pythagorean theorem). All college students taking a physics course must have taken math before - as a prerequisite. I have taught at least a couple of thousand students, probably more. A huge percentage of them have had very poor math preparation, especially American-born ones.

Lately, more and more people advocate for a utilitarian approach to teaching math - "I have not used never algebra in my life, why did I spend so much on trying to learn it, I hated it, and students hate it, so let's get rid of it!".  Yes, let's teach only things students like - what's that, computer games? watching cartoons or super-hero movies? This trend is far from being new.

First and foremost math and physics teach people HOW TO REASON, they develop intellectual abilities (among many other important things, like advancing the brain development). Currently, American policy is governed by poorly educated people - on BOTH sides! The Republicans depend on whites without college education. And so do the Democrats - they simply cannot win without  minority voters - who have a very low average level of education. Eliminating algebra only makes this worse. For thirty years with all that talk about reforming education, it was just a talk. When will policy makers understand that the low level of American mass education has become the biggest threat to the national security? And not just because of politics. Because of economy, too. Economy needs more and more highly educated professionals. Thirty years ago business leaders and politicians had to make a tough choice. Should they start making heavy investments in education? The answer was - no. That would negatively affected profits. So, they invented H-1B visa. And now America has become addicted to the foreign-born highly educated professionals. Even a slight decrease in those numbers leads to a heavy "withdrawal" - with kicking and screaming from business leaders - we need more educated foreigners! 
Why no one asks - how come that all other countries are fine with having their own native, born and grown up professionals, but America cannot survive without foreigners
And don't say "America is founded by immigrants" - that was hundreds years ago. 

Being open to immigrants and being dependent on them 
- are the two very different things!


In response to "What's the right age to quit maths?" 

Teachers are only as good as the teacher preparation system is. In the U.S. there is no system (!) for teacher preparation. The main reason for that is that education is governed by people who have no deep understanding of what teaching and learning is - politicians and businessmen who think about education only in terms of money and hire superintendents who can satisfy their political agendas. 

Some examples of math every single Russian high-school graduate must be able to do. Of course, not everyone can, but the vast majority of graduates who want to go to a college do. If those skills are expected from school students, what do you think a school teacher must be able to do? And many can, indeed. In Russia. And from those who can do that math, many also can teach how to do it (like yours truly).
Calculate the value of

Simplify this expression

Solve this equation

Find the minimum/maximum of this function

Find the anti-derivative of this function

Calculate the area of a figure limited by these lines:

Find all values of parameter a for which the inequality has no solution

And those are just some common examples. All Russian high-school graduates are expected to solve geometry, chem, and physics problems that in the U.S. correspond to AP or college level STEM knowledge. Those graduates may never use that knowledge in their life, but they sure will use their brain for designing solutions to problems they have not solved before (the main function of intelligence). Fish rots from the head down - we know that. But this is true not just in politics and management. It is a general rule for any human functioning. The more rotten a head (underdeveloped brain) is, that leads to the more degraded actions. And v.v.. Evidently, Russia and China take this rule more seriously than America. Probably, because to this day America could simply buy enough foreign-born highly educated professionals. But what if that time will come to an end? Any long-term strategic thinking on this one? Anyone?

A recent example from a student.
The student has no developed algebraic thinking, demonstrates pre-algebraic thinking, when instead of using variables and algebraic actions the student uses a verbal description of the work done. And this student studies physics at one of the top universities. And he/she is not alone (far from alone) who demonstrates this type of thinking. Graphical thinking (plotting, analyzing graphs) is at an even lower level.
One does not need to waste $$ to "study" how bad math education is, one just needs to get an honest feedback from faculty. The key word is "honest". Evidently, no one in American higher education wants to know the honest picture. But the result is clear -  severe primitivization of education.


  1. You may want to correct your question (forgot the equal sign).
    I hate math education research papers and presentations. Where teachers show all the didactic foundations and statistics and no one understands what the activity was!!! In my experience (not proven with research), the objectives of teaching math at school are three: math as a language, math as a tool for reasoning, math as... History? (Methods that other people have discovered and may be useful, or maybe now are not useful anymore). Of course, there are ways to guide students to discover these methods on their own, not as a recipe.

  2. thank you. math as a language, math as a tool for reasoning, math as history - the components of a math "practitioner", and then + communication, child psychology, managing, acting, just being interesting - the components of a "teaching" person. A good math teacher is a very rich person.