Some recent writers on mathematics education have been talking about mathematics as a field enjoying \u2019unearned privilege\u2019 as a \u2018gatekeeper\u2019 in our society.\u00a0 The more I think about it, the less sense this makes.<\/p>\n
For some writers, the reference may be to standardized testing (SAT, GRE, etc.).\u00a0 Certainly these are gatekeepers.\u00a0 Is this privilege \u2018unearned\u2019?\u00a0 I don\u2019t know.\u00a0 That argument is for the College Board and the Educational Testing Service to make.\u00a0 I will argue, however, that the whole practice of judging a person\u2019s 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).\u00a0 And this observation holds for any subject matter being tested, not particularly mathematics.\u00a0 So even if this is the \u2018gatekeeper\u2019 referred to, it\u2019s not about our subject.\u00a0 And this form of gatekeeping is a matter of practice, of implementation, and not a widespread or deeply-held belief about mathematics.\u00a0 The deeply-held belief is about the nature of testing.<\/p>\n
Maybe some writers are talking about textbook mathematics, mathematics as it is taught in a mediocre setting, as a set of rules and procedures.\u00a0 Well, this is not mathematics.\u00a0 This is rules and procedures, more and more imposed on teachers by the requirements of high-stakes state testing.\u00a0 Again, it seems to me that the gatekeeper is the testing, not the subject.\u00a0 And again, this observation is not at all specific to mathematics.<\/p>\n
In fact it seems to me that mathematics is less guilty of \u2019gatekeeping\u2019 than many other academic subjects.<\/p>\n
<\/p>\n
There are many gatekeepers, in any culture.\u00a0 The use of language, both spoken and written, is a much stouter gate than knowledge of mathematics.\u00a0 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.\u00a0 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!).\u00a0 Just think of the effect, in a job interview or resume cover letter, of even a single mispronounced word or grammatical solecism.\u00a0 Conversely, we all know well-spoken imposters.<\/p>\n
And language is unavoidable.\u00a0 We are constrained to speak in any social situation, and to write in any professional position.\u00a0 This gatekeeper appears unbidden.\u00a0 And often unconscious: we frequently don\u2019t have control over judgments we make on the basis of language.<\/p>\n
There are still other gatekeepers.\u00a0 Dress is the most obvious.\u00a0 And some very unfortunate ones: race, class, gender.\u00a0 It is quite human, but at the same time quite de-humanizing, to react unconsciously to people we don\u2019t know by grouping them with others with whom they share external characteristics.\u00a0 Unlike language, these gatekeepers are not routinely addressed by formal education.\u00a0 They are almost always unconscious, hence powerful.\u00a0 And they are clearly \u2018unearned\u2019.<\/p>\n
Is the privilege of mathematics \u2018unearned\u2019?\u00a0 Well, no.\u00a0 I think it is hard earned.\u00a0 Mathematics is the locus classicus<\/em> for addressing logic, the derivation of statements from other statements.\u00a0 And this skill pervades human activity.\u00a0 Further, the better you are at this skill, the more valuable your activity to others.\u00a0 This is why I have argued (in several places) that the teaching of mathematics should be centered on logic, and not on algorithm.\u00a0 The latter, for me, should be a consequence of the former. \u00a0Even for the 80% of our students (this figure is approximate and variable: see https:\/\/nces.ed.gov\/programs\/raceindicators\/indicator_reg.asp<\/a>) who don\u2019t go into STEM related fields, this legacy of a mathematical education is central.<\/p>\n I have heard arguments about other \u2018forms\u2019 of mathematics, sometimes called \u2018non-Western\u2019. \u00a0I would argue that the classification of logic-based mathematics as \u2019Western\u2019 (or sometimes \u2018Greek\u2019) is a misnomer at best, and simplistic at worst.<\/p>\n But let\u2019s not talk about mathematics for a minute.\u00a0 Let\u2019s talk about pizza.\u00a0 Everyone thinks of pizza as Italian, and it is consumed worldwide.\u00a0 But tomatoes originated in America, wheat (probably) in the middle east, basil and pepper in India. \u00a0The Italians just put it all together.<\/p>\n Similarly, the pieces of what we call \u201cWestern\u201d mathematics were lying around for centuries, in different parts of the world.\u00a0 The Greek achievement was a synthesis of these human thoughts.\u00a0 That is, mathematics is \u2018Western\u2019 only in the sense that pizza is \u2018Italian\u2019. Everyone enjoys pizza.\u00a0 Everyone benefits from logic.<\/p>\n And like pizza, everyone wants mathematics.\u00a0 \u2018Western\u2019 mathematics.\u00a0 Algebraic topology.\u00a0 Bessel functions.\u00a0 Lie algebras.\u00a0 Intellectual domains in which a \u2018non-Western\u2019 culture had not penetrated, before a cultural influence from the West.\u00a0 I have personally worked on every continent except Antarctica, and everyone wants to learn mathematics the way it has developed \u2018in the West\u2019.<\/p>\n But notice that this form of mathematics is now being developed as much in Asia as in Europe.\u00a0 And in fact it always has been.\u00a0 Modern mathematics is \u2018Eastern\u2019 as much as it is \u2018Western\u2019. And, if Africa and Latin America develop as quickly as we all expect they will, modern mathematics will soon be \u2018Southern\u2019 as much as \u2018Western\u2019.<\/p>\n What about the other 20%, the students preparing for STEM fields?\u00a0 Let\u2019s leave aside for now the fact that we don\u2019t always know who these students are.\u00a0 Is the status of mathematics ‘unearned’ to this group?\u00a0 Again, no.\u00a0 A knowledge of mathematics is, in fact, an intellectual gatekeeper, or better yet, gateway, into STEM fields.\u00a0 For those who are going to make contributions in these fields, mathematics is vital.\u00a0 And it is growing in importance as the sciences, and even the social sciences, develop.<\/p>\n So yes, it is a gateway for this group.\u00a0 Just as organic chemistry is a gateway for medical school.\u00a0 Do you want to be treated by a doctor who hasn\u2019t studied it?<\/p>\n And do you want to travel over a bridge built by an engineer who hasn\u2019t studied \u2018Western\u2019 calculus?<\/p>\n (I thank Paul Goldenberg and Al Cuoco for their help in writing this post.)<\/p>\n <\/p>\n