Recently, I was invited to Red Deer to take part as a public voice in a panel discussion on math education in Alberta. The Symposium was hosted by David Martin, a math teacher who some may recognize as an opposing voice to mine. On this occasion, he was a very gracious moderator.
I knew soon enough what I was in for when ATA’s Jonathan Tegthmeyer declared how “fuming mad” he was after learning of Alberta Education’s introduction of a 15-minute timed, no calculator portion in the Grade Six provincial achievement test. Apparently, he was so upset he got on the phone that night with the Ministry’s Chief of Staff, then went on to spew his disdain in an ATA editorial that called the advocated math changes a “knee-jerk reaction to back-to-basics crusaders with a manufactured math crisis.”
I, being one of these “crusaders”, sat back and smiled. The bitterness in the panel’s voices was palpable as they spoke of how good they think the “new math” curriculum was, how the new math wouldn’t harm bright students, how algorithms would impede understanding, how Provincial Achievement Tests should be eliminated, etc, etc, etc. For the first time since the Alberta Math Petition began, I appreciated the impact our advocacy was having on the education of our children. To the dismay of the panelists, the government was re-establishing best practices in the Alberta Math Curriculum.
Best practices are evidence-based, gold standards of practice for a discipline, and it exists in every profession. In medicine, for example, best practice is prescribing medications that have the most evidence for success in reducing morbidity or mortality. When a first-line therapy is ineffective, we systematically move on to a second or third line agent. In education, best practices in language arts include teaching students to read phonetically and write grammatically correct sentences. Just because some students struggle with their nouns and verbs does not abdicate teachers of their responsibilities to ensure mastery of a grammatically correct sentence. Likewise in mathematics, ensuring that students acquire mastery of the times table and standard algorithms (long division, vertical addition/subtraction, etc) is best practice as evident over hundreds of years of progress and practical application.
Yet, according to Jonathan Teghtmeyer and Martin’s panel, “there is no best practice” in mathematics; their reason deriving from a belief, pushed by the likes of Kohn, Boaler and Robinson, that memory work and algorithms induce math anxiety and hinder understanding while ad hoc methods of operation nurture creativity and number sense. As passionate and eloquent as these educators are, for they are masters in the art of teaching, it became quite clear that the chasm between the two sides of this math debate is in fact an imbalance in the art and science of teaching
If more respect were given to the science of teaching, then the panelists would appreciate the fact that the largest study ever done in education, Project Follow-Through, that followed thousands of students from 1967- 1977 had determined that Direct Instruction, not discovery or inquiry-type approaches, yielded students with significantly higher academic achievement, along with higher self-esteem and self-confidence. This finding has been echoed over the years by eminent researchers such as Hattie, Carnes, Kirschner, Sweller and Clark. In other words, best practice is teachers providing direct instructions on the best methods of calculation, to allow mastery through ample time and practice rather than letting students discover “personal strategies” to multiplying and dividing.
If more emphasis were placed on science, then one would also appreciate the findings of cognitive science. MRI studies of the brain have affirmed that not only does memorization and mastering of basic facts increase hippocampal connections in the brain, but it also enhances math performance as a result. Cognitive science affirms that rote learning lays the foundation for understanding, hence contradicting the popular narrative that memorization and algorithms hinder understanding. When facts and algorithms are transferred to long term memory through repetition and practice, the cognitive load on our working memory is diminished significantly, thereby reducing much frustration and anxiety in novice learners. Not to mention that knowledge is what powers understanding, critical thinking and creativity.
And if one truly appreciates science, then one would never try to eliminate quantitative measures of performance outcome. The 2015 PISA exams, which measured the academic performances of 15yr old students around the world, affirmed the 2012 findings that math skills in Alberta students have declined since the ideological shift to a discovery/inquiry-based approach in mathematics. Even the once highly-praised Finland is falling steadily since its move towards more inquiry-based learning. The countries which ranked on top are countries with a strong focus on traditional best practices. What is interesting is that the PISA was testing understanding and practical application rather than rote knowledge. Therefore, one can deduce that strong, evidence-based best practices indeed produce students with better understandings of math concepts and number sense. The key element of the 2015 PISA exams was that it highlighted how countries with a leaning towards minimally-guided instructions fared much worse on these exams. If, however, PISA scores were disregarded as per ATA admin’s wish, there still remain other measures such as the TIMMS and PATs (Provincial Assessment Tests) that have demonstrated similar declining outcome with the rise in discovery/inquiry-based methods. It comes as no surprise that top ranking Alberta schools in the Fraser Institute Report are schools that adhere to traditional best practices.
If, for some reason, the scientific evidence is not satisfactory, then one hopes that these educators would at least listen to the experts, ie, the mathematicians, on the essential nature of best practices. To have an overwhelming number of university mathematicians sign a Position Statement in 2014 declaring the critical importance of standard algorithms is no small feat. Mathematicians know that “the essence of mathematics is to not to make simple things complicated, but to make complicated things simple.” Standard algorithms have endured a thousand years because they are recognized universally as being the most effective, efficient, time-proven and elegant method of calculation. It is therefore only logical that teaching mastery of the algorithms is best practice.
If the expert opinions still fall on deaf ears, then ignore not the power of observation from frontline teachers. Junior/High school teachers have seen firsthand the weakened math skills since the deemphasis on fundamental best practices in elementary. University math professors have reported that student exams that were the norm 20yrs ago are now too difficult for incoming students. This fact should make Teghtmeyer and his colleagues shudder and think twice before further denigrating teachers who continue to use best practices in teaching. It is hard for those who do not work under authentic stress to know how critical it is to have rigors in teaching and testing in order to enhance fluency and mastery of knowledge and skills. When one rarely makes life and death decisions, one should be the last person to tear down any teachers as “old school”, for our 21st century society is built on the backs of these great teachers who cared enough to deliver best practices, despite being reprimanded for doing so.
If, however, the opinions of the mathematicians and frontline teachers are of little value, then take heed of actual case reports. Never before have 20,000 parents raised their voices to report ill-effects from a math curriculum, until now. Considering that each signature on our petition could represent two or three affected children in a household, one cannot be so arrogant as to dismiss the scope of the “new math” problem. The discovery/inquiry math has in fact negatively impacted thousands of bright students because convoluted approaches contravene logic and intuition. Considering how critical logical thinking and reasoning is for the field of science and engineering, one can imagine how many doors to science and engineering are closed for these students. The “manufactured math crisis” that Teghtmeyer alluded to in his editorial is more accurately rooted in the for-profit organizations and education consultants who, by embellishing accounts of problems in math, was able to push the government into shifting the curriculum to unproven discovery/inquiry-based ideologies. Unfortunately, this shift, as evident in the petition, has resulted in a net increase in the very thing they strive to reduce, ie math anxiety and weakened math skills. We are still dealing with the ramifications of their experiment.
Finally, if case reports, expert opinions, and scientific evidence are not convincing enough, then these educators should at least consider maintaining best practices for the sake of social justice. As evident in Project Follow Through, students that learn through direct instructions come out having better self esteem and confidence. That is already half the battle for students. Cognitive science meanwhile affirms that rote learning reduces cognitive workload thereby reducing learning anxiety. And PISA scores demonstrate that inquiry-based learning in fact disadvantage lower economic status students. This is an injustice. Moreover, a sign of an ailing education system is the emergence of a two-tiered system wherein the rich or the parents willing to carry a steep financial burden can afford to send their children to schools that have a record of excellence, while the rest of us settle with a second-rate experimental system. This is an injustice. Since the introduction of inquiry-based math, there has also been a doubling of children in tutoring. The cost of this further exacerbates the financial burden on families. And for those families that cannot afford either private schooling or tutoring, well, we’re stuck. Considering the fact that education is one of the greatest predictor of poverty, not ensuring that standards of excellence are met for our children is a great social injustice.
In summary, Alberta Education is in the midst of rewriting the curriculum in all subjects. The update that Alberta Education had made to the “new math” curriculum in response to our petition were far from being a knee-jerk reaction. It took many long months, exasperating meetings, much resistance, and nearly twenty thousand signatures for the government to appreciate the evidence for re-establishing best practices (eg. times table, standard algorithms). Being that some of the panelists I met in Red Deer are possibly on the advisory board for the curriculum rewrite, it is my hope that they and other educators are guided by logic and science, to enable the government to further implement best practices, such as introducing fractions earlier on, in the curriculum to improve the standard of excellence for our children. If we can find the right balance between the art and science of teaching, then we bring justice to our children as we nurture success in the majority of students while capturing and lifting up the students that do struggle. My hope is that the Minister of Education and Alberta Education learn from the lessons of the past and rein in failed ideologies to allow our children to stand, not on the shoulders of the local ATA administrator, next Ted Talk star or an education consultant, but rather on the shoulders of giants.