## Monday, July 1, 2019

### Math education – a consumer's view on it.

Math education – what its consumer
I am a consumer of math education.
I teach physics, and that requires that students would be able to do some rudimentary math.
Years ago, I have developed a short set of math questions for students taking a college level elementary physics course. The test was and still is supposed to help students to evaluate how ready they are math-wise; all questions represent examples of some specific mathematical calculations students would actually have to carry out when taking a course. I was not collecting any statistical information from the test; I would offer a test (unlimited time), then I would post the answers, and I would suggest to review the topics related to the questions that gave a student a hard time.

This time I decided to check the statistics. And it shocked me.

Based on this question:
practically all students had taken some advanced level of math. Close to 10 % of them took it a long time ago, more than 4 years, but the rest should not yet forget what they have learned, at least they should still remember the basics.

But based on their answers to some questions, close to 50 % of the students had a very low level of math knowledge.

I pooled out some examples, such that a regular high school student (as I was in the past) should have done without any difficulty.

Here are those examples.

1. calculating a sin-value of an angle in a right-angle triangle.

2. Calculating the area of a trapezoid.

3. 10 % of students do not know how to add fractions (again – college students).
4. A trivial change had thrown off 20 % more students.

5. This simple quadratic equation was too difficult to more than 50 %.

5a.
6. This and the next two questions involve some simple algebraic manipulations (some student - about 10 - did not even try).
6a.

6b.

7. And here 40 % of students could not use a calculator to find the value of the expression.
This is a clear and undeniable proof of a very low quality of math education of a very large population of high school graduates – and we talk here about only those who has gotten into a college.

Unfortunately, as I stated before, there is NO indication of any improvement in the area of math education (hence, in general – STEM education).
Millions of students do not have a good math teacher, but education schools keep offering courses in “school leadership”, universities and government pour funds into a “study” what math 7th grade math teachers need to know.
Here is a hint – a 7th grade math teacher needs to know the 7th grade math plus at least two more grades below and above it.
A good math teacher needs to be able – and has to TEACH – in several grades, at least three, but better four of five. Only then a teacher can have a deep understanding of (a) math he or she teaches, and (b) how it needs to be taught.
But millions of dollars go to some fictitious “study”, or workshops on the latest development in neurology - when the most important goal for ANY department of education should be comprehensive teacher professional development.
It is like your house in on fire but you put all your energy in fixing a falling mailbox.
The dismal state of math education is the direct consequence of the current policy of the NSF in the field of education
What should scare everyone, is that many students who have no required school preparation go to a for-profit college with a very low acceptance threshold, and then drop out because they simply cannot learn at the college level. Or even worse - get a diploma. But that piece of paper does not guarantee any actual solid professional skills.

BTW: all the talk about math anxiety (and it is a lot) is BS.
Yes, it exists – like many other anxieties.
But it has nothing to do with math.
It has everything to do with a bad math teacher who does not know how to teach it effectively but blames his/her poor results on children and makes them feel bad about themselves.
When growing up, children are not afraid of asking questions or making statements adults would consider “stupid”. Children are not afraid that someone would call them “an idiot”. But then they begin a school. And then …
Naturally, some children may be born with a nervous more prone to anxieties than other children. But in that case they may have many
anxieties, and math is just one of those. But there are people who like to write about it for the sake of publicity.