An estimation problem for math teachers

You thought I was going to talk about a problem that math teachers could use, didn't you? Well, maybe math teachers can use this. (note: when I say "teachers" I really mean "learning facilitators")

It all started when I read this valedictorian speech from Erica Goldson. Here is part of it:

"I am now accomplishing that goal. I am graduating. I should look at this as a positive experience, especially being at the top of my class. However, in retrospect, I cannot say that I am any more intelligent than my peers. I can attest that I am only the best at doing what I am told and working the system. Yet, here I stand, and I am supposed to be proud that I have completed this period of indoctrination. I will leave in the fall to go on to the next phase expected of me, in order to receive a paper document that certifies that I am capable of work. But I contest that I am a human being, a thinker, an adventurer - not a worker. A worker is someone who is trapped within repetition - a slave of the system set up before him. But now, I have successfully shown that I was the best slave. I did what I was told to the extreme. While others sat in class and doodled to later become great artists, I sat in class to take notes and become a great test-taker. While others would come to class without their homework done because they were reading about an interest of theirs, I never missed an assignment. While others were creating music and writing lyrics, I decided to do extra credit, even though I never needed it. So, I wonder, why did I even want this position? Sure, I earned it, but what will come of it? When I leave educational institutionalism, will I be successful or forever lost? I have no clue about what I want to do with my life; I have no interests because I saw every subject of study as work, and I excelled at every subject just for the purpose of excelling, not learning. And quite frankly, now I'm scared."

She goes on to talk about how there are some teachers that help students break out of the grade based system and actually encourage learning. I agree. There are some great teachers out there. Also, there are some teachers that aren't quite helpful in this regard. I would like to emphasize that I don't want to attack these teachers. Sometimes they are placed in classes that they aren't really prepared for. Sometimes they are just doing what they were taught. I get that.

Instead, I would like to focus on the really great examples of teachers. They are out there. That is what lead me to a thought. How many great teachers are there? What percent of the math teachers do cool stuff? I am going to estimate this in a fermi-problem type fashion.

Where do I start? I start with things I either know or can guess. As usual, I will do this symbolically first. Here are some questions I can ask myself.

  • How many teachers are there?
  • How many of these teachers are math teachers?
  • How many of these math teachers do really cool stuff to engage students in real learning? (I will label these as "good" math teachers)
  • How many of these math teachers have blogs or some type of online presence (like twitter)?
  • How many of these good math teachers that blog do I know?

Let me break this up into pieces. First, how many math teachers are there (in the U.S.A.)? I am not going to look stuff up - that would not be in the proper spirit of a fermi-problem. I am going to start with stuff I know or that I can guess. Let me declare some variables:

  • Population of the U.S.A. = Nusa
  • Fraction of population of students in grades 6-12 that are in a math class = fmath
  • Average math class size = sc
  • Average number of math classes a math learning facilitator facilitates = ct

Ok, so that should be enough to determine the number of math teachers in the USA. I will call the number of math teachers nmath-t:


Now for the second part. Here are some more variables:

  • Number of good math teachers = ngood-math
  • Fraction of good math teachers that blog = fgood-blog
  • Fraction of good math teachers that blog that I happen to know about = fgbtIk
  • Number of bloggers I know = nbtIk

This leads to the following expression:


Of course, could solve that for the number of good math teachers (learning facilitators):


Number time

Here are my estimates. First, how many good math learning facilitator bloggers do I know? I am going to list some (note: if I leave you out, it is not that I don't think you are awesome. You ARE awesome, I am just forgetful).

That is the first pass of people I could think of. If you are in this list and you DO NOT teach math in grades 6-12, just be quiet. I don't want you to mess up my estimates. But that is 8 bloggers. I bet I only know of like 5% of the whole population of good-math-bloggers.

What about those math people that are good but do not blog? I am going to again randomly guess that 5% of the good math teachers also blog. This gives an estimate of the number of good math teachers as:


How does this compare to the number of math teachers out there? Well, I know the population of the USA is around 300 million. That is just a number I remember. What fraction of students are in grades 6-12? That is approximately for kids ages 11-17. If I estimate that the age distribution is approximately even for people of ages 0-60, then 10% of that population would be of the age to be in a math class. Oh, I know that there are people older than 60 - but I am grouping all of those people in the 60 year old class.

How about an average of 20 students per math class and an average of 4 math classes per teacher. Those are my guess and I am sticking with it. So then - how many math teachers in the USA?


That is a whole bunch of math teachers. Is that too many? Well, that is just 0.1% of the population. I am sure we all know at least one math teacher, right? I don't think that is too high.

Then what fraction of teachers are doing cool stuff? 3200/375,000 = 0.85% - or just about 1%. That seems better than I first thought. So, maybe this is as high has 10%.


More like this

10%? 1%? Sounds like you have found an alternate demonstration of Sturgeon's Law (which is, of course, recursive) from the other side.

You really shouldn't have more than one sig fig in your answers, but ...

Is four classes of 20 students really the typical teaching load in grades 6-12? Seems low to me. 30 million kids in 7 school grades seems OK, however.

In the area I live in, teachers on standard schedules (non-block) teach 5 classes a day, and I would make the average class size 25, since in my local major urban area 30 is more typical.

i hateeeeeeeeeeeeeee thissssssssssssss siteeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee hgbfhgfdfgdrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff

Erica Goldson, you rock. I have Masters Degree in Engineering and feel much as you feel. Math and physics teachers in primary and secondary school did more damage than good really, although I excelled in their subjects. Took me years to unlearn what they have indoctrinated me. I feel so good I've found someone with similar thoughts. So much wrong with teachers and school system.