Course correction needed in math

December 18, 2013

Published in the Chronicle Herald (Halifax)

When it comes to math skills, Canadian students are getting worse, not better. That was the finding of the Programme for International Student Assessment (PISA) released Dec. 3. Among the 65 nations that participated in the OECD study, Canada’s overall standing in math fell to 13th from 10th in 2009 and 7th in 2006.

Nova Scotia is no exception to this trend. The province has steadily declined since 2003 and its students scored significantly below the Canadian average. Clearly, something is wrong with the way Nova Scotia schools teach mathematics.

Unfortunately, the Department of Education chose to downplay this problem with a news release entitled, “Nova Scotia students perform well in international assessments.” While the release acknowledged a decline in math scores, it suggested that a newly introduced math curriculum in Nova Scotia schools would fix this problem.

The new math curriculum stems from a commitment the previous government made. Last year, former Education Minister Ramona Jennex announced that Nova Scotia would import and adopt Alberta’s math curriculum. The reasoning behind this announcement was that since Alberta students have some of the best test results in Canada, adopting their curriculum would lead to similar results in this province.

At a superficial level, this announcement made sense. After all, if Alberta’s math curriculum improved student achievement in that province, why wouldn’t it do the same here? There’s just one problem with this approach — it did nothing of the sort.

The reality is that Alberta’s math scores, as measured by PISA, have been in a free-fall since 2003. In fact, next to Manitoba, Alberta experienced the biggest decline in math skills over the last decade. While Alberta students used to perform well above the Canadian average in math, they are now merely average.

Alberta’s decline coincides with the adoption of a new math curriculum known as the Western and Northern Curriculum Protocol (WNCP). The WNCP downplays the importance of practice and memorization and encourages students to invent their own ways of solving math questions. Instead of learning the standard algorithms for addition, subtraction, multiplication, and division, students invent their own.

This approach to teaching and learning, often called romantic progressivism or constructivism, is widely pushed within faculties of education. “A teacher should be a guide on the side rather than a sage on the stage” is its mantra. The WNCP math curriculum was heavily influenced by this philosophy. Considering the large number of provinces that follow the WNCP, it should come as little surprise that math scores across the country are declining.

Instead of adopting a math curriculum that led to worse student achievement, Nova Scotia should consider better options. One is to look at the only province to maintain its high standing in math — Quebec. Unlike many other provinces, Quebec still has a math curriculum that places a strong emphasis on the mastery of fundamental skills.

In addition, at least one province using the WNCP math curriculum has made steps to reverse course. Manitoba’s education minister recently announced a new back-to-basics approach in math. Students in K-8 will now be expected to memorize their math facts, solve math questions without a calculator, and use traditional algorithms for basic math operations. Given that Manitoba is one of the lowest achieving provinces in the country, this announcement came not a moment too soon.

However, if Nova Scotia wants to make significant improvements to its math scores, the education minister should take even bigger steps than Manitoba. John Mighton’s JUMP math program could be just what this province needs.

The JUMP approach to math instruction is almost exactly opposite from WNCP. Instead of leaving students to figure out their own ways of solving math questions, JUMP helps students break a math problem down to its component parts. Students are taught math concepts sequentially and must practise a skill until it becomes automatic.

Several years ago, a research team from the University of Toronto, Ontario Institute for Studies in Education, and Toronto’s Hospital for Sick Children, conducted a randomized controlled study of JUMP math’s effectiveness. It divided approximately 300 students into two groups, one taught WNCP-style math and the other JUMP math. Students in the JUMP math program significantly outperformed students in the other group.

The widespread adoption of JUMP math, or something like it, could revolutionize math instruction in this province. It’s time for Nova Scotia to take bold action and reverse its longstanding decline in math skills. The status quo is unacceptable.

New tablets for pupils less useful than old math method they come with

August 23, 2013

Published in The Chronicle Herald (Halifax)

Math instruction this fall is going to look quite different for approximately 300 Grade 7 students. Two major businesses and the province of Nova Scotia are providing the funds to purchase tablet computers for these students and their teachers.

If this $1-million pilot project is successful, the program may even expand to other grade levels and schools.

I predict this pilot project will be a big success, but not because of the tablet computers.

Simply introducing more technology in classrooms has only a limited impact on learning and is hardly worth the significant costs involved. Instead, this pilot project will succeed because it will revolutionize math instruction.

Why?

Because these tablets will enable students to receive instruction from the Khan Academy, a non-profit education website created in 2006 by Salman Khan. With more than 3,000 instructional videos available online at no charge, the Khan Academy is used by students around the world to learn about subjects as diverse as history, mathematics, and cosmology.

Anyone who takes the time to watch some of the instructional math videos on the Khan Academy’s website will quickly see some familiar concepts.

For example, the videos show how to add and subtract by placing one number on top of the other and working digit-by-digit from right to left. Multiplication is demonstrated using the standard vertical format while the traditional long division algorithm is consistently used as well.

In fact, all of the standard mathematical algorithms for addition, subtraction, multiplication, and division feature prominently in these videos. Interestingly, this is the exact opposite of the approach recommended by education faculties where teachers are trained.

Under the influence of math education professors, provincial curriculum guides and math textbooks have been systematically expunged of the standard algorithms.

The underlying philosophy behind this “new math” approach is often called constructivism. Advocates say students need to construct their own ways of doing math.

So, they argue, instead of showing students the most efficient way of solving a question, teachers should give them open-ended word problems and encourage them to invent their own problem-solving strategies.

One of the most prominent “new math” advocates was the late John Van de Walle, formerly a math education professor at Virginia Commonwealth University. In his widely circulated book series, Teaching Student-Centered Mathematics, Van de Walle disparaged the teaching of standard algorithms for addition, subtraction, multiplication, and division. He also argued that skill-based drill and practice makes it harder for students to gain a deep conceptual understanding of mathematics.

Some math education professors go so far as to claim that teaching the standard algorithms to students is developmentally harmful.

Constance Kamii, professor of early childhood education at the University of Alabama, co-authored a widely influential paper in 1998 entitled “The harmful effects of algorithms in grades 1-4.” Even though the arguments contained in this paper have been thoroughly debunked by real math professors, Kamii’s dubious research is regularly cited by “new math” advocates.

The Atlantic Canada Mathematics Curriculum, which is used in Nova Scotia, was strongly influenced by these education professors and their disciples. In addition, commonly used math textbooks such as Math Makes Sense and Math Focus are also heavily infused with the constructivist approach as it is almost impossible to find any standard algorithms in either of these textbook series. Instead, students are given convoluted word problems, poorly designed algorithms, and unclear directions.

So when Grade 7 students in this pilot project receive their tablet computers and watch the Khan Academy instructional videos featuring standard math algorithms, they will finally be exposed to math that makes sense. Once they learn the most efficient way of solving math questions, students won’t be particularly interested in going back to the fuzzy math that appears in their textbooks.

Of course, all of this could be done without bringing a single tablet into any classroom. Teachers could teach the standard algorithms using textbooks that actually contain proper step-by-step directions. While watching a solid instructional video about a math technique is good, getting the same lesson from a teacher in the classroom who can answer questions is even better.

There is a certain amount of irony that the Nova Scotia students who use cutting edge technology are going to end up learning math the old-fashioned way. Students in this pilot project are fortunate because they are going to do math properly, not because they get to play with fancy tablets.