How would you teach someone to drive a nail into a board?
You might start with how you'd know when to nail something, and maybe get into leverage and momentum, but at some point, you'd also give them a hammer, right?
Alberta's K to 9 math curriculum is missing that last step – it teaches students to understand how math works (when to nail), but doesn't ensure they have reliable tools and techniques with which to do math (a hammer).
And that's one big reason why today's students are getting worse at math, as measured by the internationally-recognized Program for International Student Assessment study. As of December, Alberta has slid from number one in Canada in 2003 to third in terms of math proficiency. Internationally, Canada has fallen from sixth to 13th over that same period.
Local parent Jason Cooke says he's seen the results first-hand as a chemistry lab instructor at the University of Alberta.
"When we have math-related problems, we see students getting tied up in the basics," he says, with students pulling out calculators for even simple arithmetic.
Gerda de Vries, who's taught university-level math at the U of A since the early 1990s, says she and other professors are seeing more and more students making repeated mistakes on commonplace math operations.
"There's something seriously wrong here," she said.
What's missing?
Explanations for this decline abound. Alberta Education Minister Jeff Johnson says the problem is undertrained teachers.
"We need to be giving those educators the supports they need and we need to make sure educators have some specialized training in math," he said.
Ontario decided to spend $4 million on math training earlier this week for similar reasons.
Paul Kane math department head Dawn Rothwell, as well as the superintendents of the St. Albert public and Catholic boards, blames bad testing.
"There's a disconnect between how we're teaching and how we're testing," she says.
Today's math classes emphasize understanding math processes, but today's tests only care about the end result. Bringing back long-form answers to achievement tests would better reflect student skills, Rothwell says.
The evidence in favour of these solutions is unclear.
The 2010 Pan-Canadian Assessment Program (PCAP) study (a huge tri-annual report commissioned by the Council of Ministers of Education, Canada) surveyed about 32,000 students and 2,000 teachers to find what factors lead to better math scores. The U.S. National Mathematics Advisory Panel (NMAP) also did an exhaustive review in 2008 of how to improve math scores.
PCAP found no significant link between the amount of specialized math training a teacher had and student math scores. NMAP found that while untrained teachers certainly hurt students, the research was unclear on what sort of math training for teachers would help. While teacher training is part of the solution, then, it's by no means a silver bullet.
PCAP found that teachers who used short-answer or multiple-choice math tests generally had lower math scores than those who used more extended-response tests. But while changing the way we test might raise math scores by giving points for process, it wouldn't change the fact that students still get the wrong answer in the end.
Bring back the tools
While the causes of Alberta's math problems are complex, a quick look at the Alberta curriculum reveals an important one: a lack of hammers.
The Alberta math curriculum sets the bar for what gets taught in schools. If it's not in the curriculum, it won't necessarily get taught.
In the late 1990s, western provinces chose (based on the research at the time) to shift the math curriculum away from teaching algorithms and memorization (shortcuts or tools) and towards theory, says Robert Craigen, a professor of mathematics at the University of Manitoba and a founder of the Western Initiative for Strengthening Education in Math.
Alberta's curriculum now emphasises "mental math," in which students learn to think through problems (e.g. 6 + 6 is 12, so 6 + 7 = 12 + 1 = 13), and encourages students to develop their own tools and shortcuts – the idea being that this will help students understand how to apply math. Standard tools like times tables are no longer required elements.
By relying on students to develop their own tools and not giving them at least one that works, we create the risk that some will leave school without any of these basic skills. That forces students to do the equivalent of jury-rigging a bludgeon every time they have to drive a nail – a frustrating process that makes it tougher to master math.
A 2013 study by University of Western Ontario neuroscientist Daniel Ansari (who studies number processing in students) supports this theory. Using an fMRI scanner, Ansari found that students who relied on instant recall of facts (a tool) more when doing math had higher grades than those who relied on thinking it out.
Thinking it out works at first, he concludes, but you have to move beyond it to get good at math.
Students need both conceptual knowledge (theory) and computational fluency (tools, like automatic recall of facts) to succeed at math and life, NMAP says.
"These capabilities are mutually supportive," it found, and should not be seen as competing for class time.
Thousands of Albertans have come to this same conclusion. Cooke was one of the roughly 1,920 people who have signed Dr. Nhung Tran-Davies' petition at Change.org. The petition urges the province to bring basic math skills back to the curriculum.
Some parents and teachers, like Cooke, have started teaching their kids these skills on their own.
They shouldn't have to. Alberta should change its curriculum to guarantee that all students learn at least one proven way to do each basic mathematical operation. Manitoba took steps in this direction last year by requiring students to be able to "recall" (know by rote) certain math facts by certain grade levels.
It's great if you can figure out five ways to drive a nail, but in the end, you should still have a hammer at hand.
