As school re-starts this week, the one thing parents must absolutely do: make sure their children get a proper math education, which public schools increasingly fail to provide. International math test scores from the OECD show a steady decline among 15-year-old Canadian students from 2003 to 2018. Updated data to be published later this year are unlikely to show improvement. Provinces do their own testing, and in 2021-22 Ontario reported only 59 per cent of students in third grade, 47 per cent in sixth, and 52 per cent in ninth met provincial standards in mathematics. In each case, the percentage was down from 2018-19. Dismal as those statistics are, they actually overestimate math proficiency by counting only students who “fully participated” in the assessments.

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If half of Ontario, students are unable to reach provincial standards in math, it is not because the standards are too high. One question from the sample ninth-grade test asks, if the length of a landscaper’s boot is 32cm and the width of the garden is 3.5m, approximately how many boot lengths is the width of the garden: one, nine, 11, or 36? In another, students must compute: if the air temperature drops by four degrees for every 1000m of elevation and the air temperature is 25 degrees at the mountain’s base, at what elevation is the air temperature 17 degrees? These are not difficult questions. The provincial standards in mathematics are shockingly low; that half of students fall below them is appalling.

To explain away the documented deterioration of math education, those responsible have employed two strategies. The first, undertaken by staff at the Toronto District School Board’s math department (among others) has been to denounce standardized tests as a manifestation of racial bias and white privilege. It is a bizarre claim, a clear grasping at straws. The second is to hide the decline of educational quality with grade inflation, which has now reached stratospheric levels. Data covering 651,000 students from Greater Toronto and Hamilton show the proportion of students with averages of 90 per cent or higher nearly doubled from 12.1 per cent in 2018-19 to 22.5 per cent in 2020-21. COVID did many things but making students better at school was not one of them. Over half of students (54.5 per cent) receive averages of 80 per cent or higher. With high grades now meaning close to nothing, universities have trouble deciding whom to admit.

The importance of properly learning math, as opposed to inflating report-card scores, cannot be understated. Mathematics is logical and rational. More than that, elementary mathematics is the basis for understanding the world. “The creation of numbers was the creation of things,” philosopher Thierry of Chartres observed in the 12th century. In his book “One, Two, Three: Absolutely Elementary Mathematics,” David Berlinski elaborates: “A man who is unable to tell whether he is looking at one sheep or two is unable to identify sheep. He is left staring at so much wool on the hoof.” Fortunately, most students today can count to two and are therefore able to identify sheep. How much further their mathematical abilities go, however, is difficult to say.

A good rule of thumb is that most math instruction in the public-school curriculum, at least in Ontario, is three to four grades behind where it should be. Not until the end of sixth grade are students expected to learn how to read negative numbers and compare and order integers, decimal numbers and fractions. It then takes another two years until the curriculum expects students to know how to add and subtract negative numbers. But computing the sum of positive four and negative three is not something that should take students until the end of eighth grade to learn. An eight-year-old child should be able to do it. And summing negative numbers, like counting, is both a basic building block for more difficult mathematics and a valuable skill on its own.

In fact, the entire accounting system on which the modern economy relies is based on summing negative numbers. An accountant whose debits and credits do not sum to zero is bound to be miserable and unlikely to be successful. How can debits and credits sum to zero? Unless they are both zero, it must be that one of them is negative — which is how everyone should feel about the sorry state of mathematics education. Undoubtedly, good teachers and good schools exist but, overall, the public education system is a disaster. Parents who can afford it are therefore well-advised to send their children to private math classes. On public school instruction alone, the current generation of students will graduate as mathematical morons — even if their report cards show 90 per cent averages.

Matthew Lau is a Toronto writer.