“Would you like your children taught to read by a teacher who could read only at the Grade Five level?”

That question (I paraphrased it) comes from Anna Stokke, a University of Winnipeg professor who teaches future teachers how to teach mathematics. In a recent radio interview, Prof. Stokke (pronounced Stockee) said education students training to teach elementary school are often incompetent at mathematics. And this defect is aggravated by a education policy that aims to deny children the opportunity to learn basic math skills such as addition, subtraction, multiplication and division.

Yes, you read that right. The policy is ubiquitous in North America, but its latest manifestation comes from Canada. Under the Western and Northern Canadian Protocol (WNCP) — the clumsy, uninformative moniker tips you off to the fact that its authors are muddle-headed — elementary school children will enter high school and university unable to compute simple subtractions such as 723 – 437 without a calculator; or they will be unable to divide 21/36 by 7/6.

(If you have children aged 10 or more, check out their facility with those simple problems. Here are the answers.

That last one involves the reduction of fractions and division by inversion. Neither technique is mentioned in WNCP.)

Prof. Stokke is one of a half-dozen mathematics professors determined to ensure that children come out of elementary school with math skills equal to life in the Twenty-First Century. The group, which calls itself the Western Initiative for Strengthening Education in Math (WISE Math) hosts a WordPress blog (www.wisemath.org) that fights for decent math education. I leave it up to you to read about their point of view. Stay with me if you want to learn about the flaws in the WNCP.

(Note to readers in Eastern Canada and the United States. Similar policies are threatening your children, so read on. In fact, the resources tab on the WISE Math blog lists several sources that imply that American mathematicians have been attacking this dumb-down trend for the past decade.)

Try to get into the WNCP website, http://www.wncp.ca, and you will be asked for a user name and password. Educating your kids is a secret process, apparently. I got information by searching the British Columbia department of education website. Here’s what I found.

Mathematics learning, according to WNCP, comprises seven sets of skills. I have put in quotes material that seems vague to me.

1. Communication. Children should be able to express their ideas about mathematics.

2. Connections. Children should be able to connect mathematical ideas to other ideas in math, in other disciplines and in everyday life.

3. Mental mathematics and estimation. Students should be able to “demonstrate fluency with mental mathematics and estimation.” (I’ll come back to this vague, ambiguous statement.)

4. Problem solving. “Learning through problem solving should be the focus of mathematics at all grade levels.”

5. Reasoning. Children should learn mathematical reasoning. (Another point that needs examination.)

6. Technology. Children should learn to use calculators and computers.

7. Visualization. “The use of visualization in the study of mathematics provides students with the opportunity to understand mathematical concepts and make connections among them.”

Now, I have no problem with most of this. Sure, we want kids to communicate their ideas, make connections between concepts and solve problems. That’s what we all did in school.

But there is something missing here. Where is the following objective?

8 (my addition). Children should become familiar with the nature of numbers by learning to perform simple calculations such as addition, subtraction, multiplication and division on both whole numbers and fractions.

I realize that that is very specific, but I don’t feel like vagueing it up, even by the simple expedient of adding words like “paradigm”, “focus” and “interface”.

Notice that the only WNCP topic that approaches this objective is number 3, which invokes the concept of estimation. Now, I’ve taken — and even taught — advanced statistics courses, so I know exactly what estimation is. An estimate is an informed guess based on incomplete knowledge. If you want an idea of the income of engineers in Canada, you interview a random sample and compute the average income of those people. That’s an estimate of the average income of all engineers.

But if you make $50,000 a year and pay 30 per cent tax on any income over $10,000, your tax bill is $12,000. That’s a calculation, not an estimate.

Of course what the authors of WNCP want to do is laudable enough: they would like to see children develop an intuitive idea about magnitude and relationships. But they seem to believe that learning the basics (multiplication tables and algorithms for addition, subtraction, multiplication and division) somehow conflicts with the development of intuition.

It doesn’t. The two are not mutually exclusive. The confidence generated by mastering basic skills encourages the growth of mathematical appreciation and competence.

I’ll have more to say about this in a later blog.

Hello, Alan. It’s good to have your very capable mind and voice on board with WISE Math. We have a long road ahead, but it is not a hopeless one, as one can verify by looking at the progress made in the U.S. by the NMAP, whose excellent report is linked and summarised on the WISE Math site. It provides a roadmap forward by indicating both what reform

shouldn’t haveinvolved and what itshould.I expect the textbook manufacturers to wisely dull the edge of WNCP Math by deftly inserting needed concepts that are missing here and there, but a quick trip through the “publisher’s questions” on the WNCP website will demonstrate that the designers of the curriculum have laboured to keep future classroom materials in line, and from what we’re hearing from “the trenches”, provincial trainers are making the party line pretty clear to the teachers they work with. But the “dulled edge” of textbooks tend to be, as you know, a bit too dull. Not all “bonus topics” are taught, especially when there is little time for extras. Texts today are far too busy visually and contain extraneous details and distractions, so teachers and students tend to leave them closed whenever possible. And while textbook writers appear to be considerably more conversant in the subject matter than curriculum designers (judging by the frequency of occurrence of mathematical silliness in their respective professional offerings), the current revision of WNCP appears to have taken place in a hermetically sealed chamber designed to prevent significant influence over the final product by actual subject-matter experts, i.e., mathematicians and others with higher qualifications in the field, such as you and us.

I encourage you to continue cataloguing problems of both omission and commission in the framework documents. It is hard to see what is not there, but I have found it shocking to realise certain things are gone. Still, what is not at all obvious is that the problems in the curriculum itself might be almost manageable (besides the lack of standard algorithms, which absolutely must be fixed) in comparison to the accompanying methodologies being aggressively promoted alongside the curriculum, and for which you will find little direct evidence (and a bit of direct evidence) in the Framework materials. Things like teachers being told not to instill skills through repetitious practice (i.e., drills); and the use of constructivism (student-centered learning) as the primary mode of instruction (see how often the phrase “personal strategies” occurs in the CCF); the replacement of classical deductive exercises with inductive explorations (math as an experimental science); a dogmatic adherence to a false dichotomy between skill and understanding, and an unwavering insistence that skills cannot precede understanding (try teaching a child to count while insisting that understanding must come before allowing the use of skills!).

There are other issues we have not touched, but which may have to be addressed by our initiative. There is a strange drive to turn mathematics classrooms into laboratories for social engineering projects — this might not be visible to the general public but it is shockingly up front and center when one converses with those in the inner-circle of curriculum development. And the whole matter of how mathematical learning is assessed, which I won’t even get into, but most anyone who has a child in public school anywhere in English Canada is likely dealing with a strange new system that is not only incomprehensible to parents but reflects some questionable assumptions about what it means to “learn mathematics” in the first place. Some in Ontario are taking on that beast, and for the moment we’re happy to leave it alone.

Some school districts in B.C., by reports we’re receiving, are mixing supplemental materials with WNCP Math, which is a hopeful development — depending, of course, on what sort of supplementation is being used. We are recommending districts and schools look at JUMP and Singapore math, but these are not designed as supplements, but full-fledged instruction instruments. A good project for some ambitious person with time on their hands might be to examine potential supplementary resources and suggest ways they might be used to ameliorate problems in places where abandoning WNCP is unlikely to happen. Just a thought.

Oh, one more thing: I think you’ll find that wncp.ca is once more open for visitors. I’m told they had partially closed down for site maintenance at the time you had trouble getting in. Though that’s an unusual way to do things, I’m taking the statement at face value. You’ll find the historical documents there and the questions from publishers to be quite informative.