New ways of teaching math don’t pass the test

April 15, 2014

Published in the Calgary Herald.

In Alberta, when it comes to math education, an unstoppable force has met an immovable object. On one side, we have the unstoppable Dr. Nhung Tran-Davies, backed up by thousands of equally frustrated parents.

On the other, we have the immovable education minister, Jeff Johnson, supported by dozens of curriculum consultants and faculty of education professors who have staked their careers on discovery/inquiry math.

Tran-Davies is unstoppable because she has two key things on her side — public opinion and research evidence. Her petition calling on the government to restore conventional algorithms and the memorization of math facts has garnered more than 13,000 signatures, with more people signing up every day. In contrast, a counter-petition supporting discovery/inquiry math received a paltry 400 signatures.

As well, more than 200 parents, students and real mathematicians (not Math Ed types) recently converged at a rally demanding the basics be restored in math. Parents across the province are fed up with fuzzy math textbooks and unproven techniques and will no longer tolerate the education minister’s fuzzy answers to their serious concerns.

Even more importantly, Tran-Davies is supported in her position by considerable research evidence. Her call for the direct teaching of standard algorithms and the memorization of basic math facts recognizes that students cannot progress to higher level thinking in math unless they first have a solid understanding of foundational skills and concepts.

In their 2014 book, Visible Learning and the Science of How We Learn, which gives the most recent summary of the empirical research evidence, education researcher John Hattie and cognitive psychologist Gregory Yates note that students who do not know their basic math facts invariably struggle when they progress to higher levels of math. In other words, using various strategies to solve 5 x 6 is a waste of mental energy since students should know automatically that the answer is 30. They should have memorized this in elementary school.

“There was a period in which teachers were encouraged to believe that rote learning stood in antagonism to deeper understanding. This notion is misleading since all indices of knowledge display positive associations . . . . Repetition and consolidation are vehicles enabling knowledge to be stored within retrievable units, thereby accelerating mental growth through conceptual mastery and deeper understanding,” conclude Hattie and Yates.

In contrast, the Alberta initiative, Inspiring Education, has little empirical support. While its underlying philosophy goes by various names (i.e., inquiry-based learning, discovery learning, constructivism, etc.), the key idea in math is that students should develop their own problem-solving strategies. The widely used textbook series, Math Makes Sense, exemplifies this approach by asking students to figure out multiple ways of solving even the simplest of questions.

Despite its popularity among department of Education officials, many researchers have thoroughly debunked this approach. For example, in 2006, the Educational Psychologist published a study by education researchers Paul Kirschner, John Sweller and Richard Clark entitled, “Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry based teaching.”

The title of their article says it all. Kirschner, Sweller and Clark showed that constructivist methodologies are considerably less effective than traditional methodologies. They conclude that “. . . minimally guided instruction is less effective and less efficient than instructional approaches that place a strong emphasis on guidance of the student learning process.” Since Inspiring Education is based on constructivist philosophy, there is good reason to question its effectiveness.

Unfortunately, Johnson has remained impervious to the concerns of parents and ignored the compelling research evidence. While he recently conceded that students should memorize the multiplication tables, he still won’t commit to putting standard algorithms back in the math curriculum. Furthermore, constructivist math textbook series, such as Math Makes Sense and Math Focus, still remain the recommended resources from Alberta Education.

Considering that Johnson was co-chair of the original steering committee for Inspiring Education, it isn’t surprising that he remains wedded to the constructivist methodology. However, there comes a time when one must set aside his own personal preferences and acknowledge that the evidence points in a different direction. Now is the time for him to do this.

The battle between the unstoppable force, Tran-Davies, and the immovable object, Jeff Johnson, cannot go on forever. Johnson needs to climb down from his pedestal and acknowledge that Inspiring Education is lacking in both public support and research evidence. In this clash, for the good of Alberta students and their parents, the immovable object needs to move.