Math is the new Latin

Charles Ungerleider, Professor Emeritus, The University of British Columbia

[permission to reproduced granted if authorship is acknowledged]

When I was in grade eight, I enrolled in Latin I “because,” my mother said, “you can’t get into university without Latin.” This view was corroborated by the school guidance counsellor and the parents of all my friends. Going to university was not a matter of discussion as far as my parents were concerned.

I was not Ovid’s most avid fan or of Caesar for that matter. In fact, most of my adolescent concentration (which in retrospect strikes me as a contradiction in terms) was on Friday night. Long term planning extended to Saturday night. From my perspective, university was as distant a prospect as landing on Mars and about as likely.

So, the following summer I found myself enrolled in Latin I again, and not for the love of the language. This linguistic purgatory was necessitated by the requirement that I have two years of Latin to qualify for university. I had no idea that when my mother referred to having to take Latin for admission to university it was an indeterminate sentence. Or at least it appeared that way from the vantage point of a 14-year-old. Prayer works, apparently, because I eventually passed Latin II.

Latin is no longer required for admission to university. Its place was usurped by mathematics much like the invasion of Rome by the barbarians. In other words, mathematics has become the arbiter of those worthy of attending university. In British Columbia, for example, a student seeking undergraduate admissions to Arts is required to have taken Pre-Calculus 11 or Foundations of Mathematics 12.

Increasingly, however, mathematics’ vaunted status and utility are being questioned. Among those dubious about mathematics is G.V. Ramanathan, a professor emeritus of . . .wait for it . . . mathematics, statistics, and computer science at the University of Illinois (Chicago). To say Ramanathan is questioning mathematics is a bit of an understatement. He compares the marketing of mathematics to “the marketing of creams to whiten teeth, gels to grow hair and regimens to build a beautiful body.”

In an opinion piece in the Washington Post, Ramanathan asks, “How much math do we really need?” He says we should be asking ourselves that question and the next ten people we encounter – such as “your plumber, your lawyer, your grocer, your mechanic, your physician or even a math teacher.” Ouch!

Ramanathan is just one of the increasing number of academics asking us to think about how much math we really need and, by extension, how much emphasis should be placed on mathematics in school. Andrew Hacker, a professor of political science at Queens College (City University of New York), was interviewed by a New York Times journalist for a 2016 titled “Who Needs Advanced Math? Not Everybody.”

Hacker comes at the issue from a slightly different direction than Ramanathan. He said:

At the very time we should be honing and sharpening quantitative reasoning skills we punch students into algebra, geometry, calculus. The Math People take over and ignore much simpler needs. Arithmetic is super essential — we quantify everything.

Notice that he distinguishes between quantitative reasoning and the topics typically addressed in school - algebra, geometry, calculus. Hacker is not advocating teaching quantitative reasoning as a means of improving critical thinking, but because everything is quantified. Besides, as Ramanathan points out, the claim that courses such as “quantitative reasoning” improve critical thinking is unsubstantiated.

Hacker’s piece in the Times is a teaser for his entertaining book The Math Myth: And Other STEM Delusions. Hacker and mathematician at large of the Mathematical Association of America, James Tanton, debated one another at the [US] National Museum of Mathematics before an audience of mathematicians, an account of which was reported in the New Yorker.

During his presentation Tanton confessed, “I have never used the quadratic formula in my personal life. I don’t think I have ever used it in my research life. But learning the formula wasn’t the point. It was the story of quadratics. And, from that story, I know I can nut my way from most any problem to do with that subject.” He seemed to be making Hacker’s point:

Every other subject is about something. Poetry is about something. Even most modern art is about something. Math is about nothing. It sounds like ‘Seinfeld.’ Math describes much of the world but is all about itself, and it has the most fantastic conundrums. But it is not about the world.

Time in school is limited. There is much more of value to be learned than can be accommodated in that limited time. Ramanathan, Hacker, and others ask us to consider how much of that time should be devoted to mathematics. Is mathematics the new Latin?

Another salvo in the math wars

Charles Ungerleider, Professor Emeritus of Education, The University of British Columbia [permission granted to reproduce if authorship acknowledged]

Ontario Premier Doug Ford’s pledge to eliminate inquiry oriented math (sometimes referred to pejoratively as “discovery math”) is one of the most recent volleys in the mathematics war. Ford’s pledge, made in the heat of an election campaign, politicized a long-simmering argument about the teaching and learning of mathematics.

In 1999 - many scientists, mathematicians, and educators in the US signed an open letter published in the Washington Post. They called into question ten mathematics programs considered exemplary by the U.S. Department of Education. The letter was written in part because parents had beseeched its author, David Klein, to help them do something about the way mathematics was being taught.

In April of the following year Klein wrote an article in the April 2000 issue of the American School Board Journal, accusing the U.S. Department of Education of promoting programs that de-­emphasized arithmetic and algebra. Klein compared mathematics to martial arts and music. “A novice cannot hope to achieve mastery in the martial arts without first learning basic katas or exercises in movement,” argued Klein. “A violinist who has not mastered elementary bowing techniques and vibrato has no hope of evoking the emotions of an audience through sonorous tones and elegant phrasing. Arguably the most hierarchical of human endeavors, mathematics also depends on sequential mastery of basic skills.”

   

Preferring evidence to emotion, my colleagues and I recently reviewed a segment of the vast literature devoted to mathematics that addressed the question “What are effective instructional practices in K-12 mathematics education?” The research we examined* indicates that direct or explicit instruction has a positive impact on mathematics performance and achievement. When teachers provide students with explicit step-by-step instructions about how to use problem solving strategies, paired with extensive practice, learning outcomes are positive across age groups and student populations.

The effectiveness of teacher-facilitated instruction and inquiry-based mathematics is less conclusive. While the effects seem to be positive, they also tend to be small. Some authors suggest that authentic problem solving and facilitated learning may be effective after students have learned foundational concepts and procedures. 

David Robitaille, the Canadian study director for the Third International Mathematics and Science Study, a collaborative effort of forty-two nations, agrees with the critics who say students need to know the basics. “You can’t be comfortable doing mathematics if you have to think about what seven times eight is. And you shouldn’t need to use a calculator to estimate the cost of several purchases at a store.” He argues that students need to develop good “number sense” and a high level of comfort with numbers and how they work. On the other hand, Robitaille says that students do not need to do worksheets of long division with multi-digit dividends and divisors.

Other practices that affect achievement include peer-assisted learning, the use of visuals and manipulatives, and the provision of feedback to teachers and students about their progress. Peer-assisted learning has a consistent positive effect on achievement and performance, but the magnitude of the impact differs across studies. Providing feedback to students also tends to improve mathematics achievement, though the magnitude of the effect also varies. Visuals and manipulatives can be effective, but their effect seems to be limited to specific types of skills (e.g., retention and problem solving) and requires carefully planned and executed instruction.

There is a range of instructional programs for teaching mathematics. The evidence seems to favour those that focus on one specific math content area rather than those that focus on multiple content areas. The instructional techniques found to be effective for students with special needs are much the same as the techniques that have been found to be successful for students without special needs. Direct instruction (explicit instruction) seems to be particularly effective with this population.

I lament the politicization of mathematics instruction or instruction in any subject because it encourages people to choose sides depending upon the personalities involved and the emotions those personalities evoke rather than considering the evidence. When the evidence is ignored it is to the detriment of everyone, but especially students and teachers.

* A list of the references that informed our judgments about effective instructional practices in mathematics is available upon request. Please send an email to On.Education.Canada@gmail.com.