Some recent writers on mathematics education have been talking about mathematics as a field enjoying ’unearned privilege’ as a ‘gatekeeper’ in our society. The more I think about it, the less sense this makes.

For some writers, the reference may be to standardized testing (SAT, GRE, etc.). Certainly these are gatekeepers. Is this privilege ‘unearned’? I don’t know. That argument is for the College Board and the Educational Testing Service to make. I will argue, however, that the whole practice of judging a person’s fate in life by her or his performance on a single test, even the same test given multiple times, is not a good one (although the question of what such a test does select for is interesting). And this observation holds for any subject matter being tested, not particularly mathematics. So even if this is the ‘gatekeeper’ referred to, it’s not about our subject. And this form of gatekeeping is a matter of practice, of implementation, and not a widespread or deeply-held belief about mathematics. The deeply-held belief is about the nature of testing.

Maybe some writers are talking about textbook mathematics, mathematics as it is taught in a mediocre setting, as a set of rules and procedures. Well, this is not mathematics. This is rules and procedures, more and more imposed on teachers by the requirements of high-stakes state testing. Again, it seems to me that the gatekeeper is the testing, not the subject. And again, this observation is not at all specific to mathematics.

In fact it seems to me that mathematics is less guilty of ’gatekeeping’ than many other academic subjects.

There are many gatekeepers, in any culture. The use of language, both spoken and written, is a much stouter gate than knowledge of mathematics. The reader will shortly see how even one misspelled word can cast doubt on the vallidity [n.b.] of a thought, or even on the intelligence of the writer. We commonly value someone who speaks and writes standard academic English over someone who uses vernacular, or even who has a heavy local accent (and we all have local accents!). Just think of the effect, in a job interview or resume cover letter, of even a single mispronounced word or grammatical solecism. Conversely, we all know well-spoken imposters.

And language is unavoidable. We are constrained to speak in any social situation, and to write in any professional position. This gatekeeper appears unbidden. And often unconscious: we frequently don’t have control over judgments we make on the basis of language.

There are still other gatekeepers. Dress is the most obvious. And some very unfortunate ones: race, class, gender. It is quite human, but at the same time quite de-humanizing, to react unconsciously to people we don’t know by grouping them with others with whom they share external characteristics. Unlike language, these gatekeepers are not routinely addressed by formal education. They are almost always unconscious, hence powerful. And they are clearly ‘unearned’.

Is the privilege of mathematics ‘unearned’? Well, no. I think it is hard earned. Mathematics is the *locus classicus* for addressing logic, the derivation of statements from other statements. And this skill pervades human activity. Further, the better you are at this skill, the more valuable your activity to others. This is why I have argued (in several places) that the teaching of mathematics should be centered on logic, and not on algorithm. The latter, for me, should be a consequence of the former. Even for the 80% of our students (this figure is approximate and variable: see https://nces.ed.gov/programs/raceindicators/indicator_reg.asp) who don’t go into STEM related fields, this legacy of a mathematical education is central.

I have heard arguments about other ‘forms’ of mathematics, sometimes called ‘non-Western’. I would argue that the classification of logic-based mathematics as ’Western’ (or sometimes ‘Greek’) is a misnomer at best, and simplistic at worst.

But let’s not talk about mathematics for a minute. Let’s talk about pizza. Everyone thinks of pizza as Italian, and it is consumed worldwide. But tomatoes originated in America, wheat (probably) in the middle east, basil and pepper in India. The Italians just put it all together.

Similarly, the pieces of what we call “Western” mathematics were lying around for centuries, in different parts of the world. The Greek achievement was a synthesis of these human thoughts. That is, mathematics is ‘Western’ only in the sense that pizza is ‘Italian’. Everyone enjoys pizza. Everyone benefits from logic.

And like pizza, everyone wants mathematics. ‘Western’ mathematics. Algebraic topology. Bessel functions. Lie algebras. Intellectual domains in which a ‘non-Western’ culture had not penetrated, before a cultural influence from the West. I have personally worked on every continent except Antarctica, and everyone wants to learn mathematics the way it has developed ‘in the West’.

But notice that this form of mathematics is now being developed as much in Asia as in Europe. And in fact it always has been. Modern mathematics is ‘Eastern’ as much as it is ‘Western’. And, if Africa and Latin America develop as quickly as we all expect they will, modern mathematics will soon be ‘Southern’ as much as ‘Western’.

What about the other 20%, the students preparing for STEM fields? Let’s leave aside for now the fact that we don’t always know who these students are. Is the status of mathematics ‘unearned’ to this group? Again, no. A knowledge of mathematics is, in fact, an intellectual gatekeeper, or better yet, gateway, into STEM fields. For those who are going to make contributions in these fields, mathematics is vital. And it is growing in importance as the sciences, and even the social sciences, develop.

So yes, it is a gateway for this group. Just as organic chemistry is a gateway for medical school. Do you want to be treated by a doctor who hasn’t studied it?

And do you want to travel over a bridge built by an engineer who hasn’t studied ‘Western’ calculus?

(I thank Paul Goldenberg and Al Cuoco for their help in writing this post.)

Evidence supporting the thrust of what you have to say abounds.

Sometime in the 1990s, the head of our Department reported the results of a longitudinal study that showed the best indicator of a student’s success in tertiary education (regardless of discipline!) was that student’s success/mark in mathematics when matriculating from high school.

I don’t know that you ever really addressed the question. Classroom mathematics is a requirement for progress in school. It is true that there are other requirements, but this is the barrier for which we have developed a culture that some can and some cannot do it. We mathematicians and mathematics teachers are a part of that culture. Pass algebra 2 or do not get a state endorsed high school diploma, pass the ACT math to get into college, bas the basic skills requirement to get out of high school.

Yes we want bridges built by people who understand calculus and more, but the question is do we make that accessible to as broad a population as possible? Or have we reduced the pool of potential engineers by maintaining a racist, classist educational system, which uses math class to discriminate.

I think we agree on the nature of mathematics classes.

My point is that it doesn’t have to be that way. It is not the very nature of mathematics that has shaped our mathematics classrooms. It is the nature of our classrooms, and of our culture of which they are an expression.

This is, I think, a meaningful distinction. Meaningful enough for me to have read the work of some academics, in the name of social justice, in which they argue that it is somehow mathematics itself, and even our cultural attitude towards mathematics itself, that erects the gate.

My point is that there are many stronger gates.

I thinks its pretty good

I found this very interesting.

Having read the entirety of this post, I found that the most important takeaway was the fact that mathematics CAN be revived in the education system. A new way of teaching mathematics to the younger generation would evolve our culture for the better. I am just going to lay down some facts here, Asia has a way better learning system, and I think we should pick upon that.

I agree with you that the teaching of mathematics needs to change. But that has always been the case. As cultures change their educational systems must change as well. I hope, as you do, that this change is ‘evolution’ towards something better, more effective.

Asia? I’m not sure that they are ‘way better’. I’ve worked there a lot, and we have a lot to learn from them. But they also have a lot to learn from us–from the best teaching in America. We see only the problems. But in Asia, and many other parts of the world, Americans are seen as the most creative educators, whose teachers get students to think outside the box. My own work there has centered on sharing with them how we do this.

The strength of the (East) Asian educational systems lies in getting large numbers of students up to a certain level. The strength of the American educational system lies in encouraging independent thinking and inventiveness. It is sometimes difficult for us to see our own strengths.