There’s a quote (incorrectly) attributed to William Butler Yeats that I love even if no one knows who actually said it: “Education should not be the filling of a pail, but the lighting of a fire.” If the educational goings on in Ontario last week are any indication, a fire has definitely been lit and Discovery Math is about to be thrown into the flames.
I don’t intend to make a political statement with this blog, although the conversation surrounding in Ontario has politics and math barely a hair’s breadth apart. So to be clear, this is not a blog about which political party I think understands math better. This is a blog about facts – the things we ask our students to research on the way to developing their own statement of belief. It’s also a blog about why school improvement has confounded governments of all politic leanings for decades. But let’s start with the facts.
Contrary to current Ministry of Education talking points, student achievement in Ontario is not in a state of crisis. Criticism of Discovery Math, however, has led some to widely condemn all inquiry-based learning, arguing for a return to the basics. This, to me, feels like a “throw the baby out with the bath water” response.
For those not familiar with Discovery Math, it’s an approach to the teaching of mathematics that encourages students to engage with problem solving in a variety of ways. Proponents argue that deepening conceptual understanding and encouraging novel ways of approaching problems will result in students having stronger competency at higher levels. So rather than just telling a child to memorize the times tables, Discovery Math also encourages them to understand what it means when 6 is multiplied by 8 to get a product of 48. Rather than just memorizing the answer, the child learns that multiplication is, in fact, repeated addition. They draw pictures of 6 groups of 8 items, or 8 groups of 6 items to realize a total of 48. Some will discover on their own that they can draw the 8s as two groups of 4 and the 6s as two groups of 3, but it comes out to the same number. They play around with different ways of representing the numbers and find, through discovery, that it always adds up to 48 no matter how they group the numbers. So the child discovers that 6 x 8 = 48, but also that 8 x 6 = 48. And for some, they will extend their understanding to find that 8 x 6 is equivalent to 4 x 2 x 2 x 3. As the child’s understanding grows, they realize that multiplication is more efficient than drawing pictures or repeated addition but the foundation of the concept of multiplication has been solidified.
“Back to basics” math emphasizes rote learning and memorization of algorithms, placing procedural understanding ahead of conceptual understanding or application. Proponents of traditional approaches to mathematics instruction argue that direct instruction, memorization, rote and drills lay a stronger foundation than conceptual understanding, and that mastery of the facts must be consolidated before deeper learning takes place. I agree with those who argue that math fluency – the ability to recall math facts with ease and automaticity – is important. Higher levels of math fluency free up working memory and allow more room in the brain for problem solving, but I will also argue that memorization alone does not suffice.
I find myself frustrated by the way proponents of Discovery Math and defenders of back-to-basics argue vociferously against one another. Such argument places people in camps when we should, instead, be focusing on the merits of both approaches. Math educator and author Cathy Fosnot has an excellent five-minute video entitled Basic Facts or Conceptual Understandings: A False Dichotomy. It’s worth viewing. In the video, Fosnot talks about how, during times of great social change and economic uncertainty, humans become anxious and begin to feel pessimistic about the future. There’s a longing for a past that felt simple, comfortable and predictable, and in response to remembrance of days gone by, we seek out the familiar. If our generation was well served by just learning the basics, why aren’t kids today served just as well? Who needs new-fangled math that parents can’t even understand? Fair questions, for sure, and I’m sympathetic as to why people may think the “new-fangled” approach the province adopted hasn’t worked. But what we’re failing to consider is whether a return to halcyon days is the answer. The future we are preparing our children for will be vastly different than our own, and arguing a dichotomy between yesterday and today fails to take into account tomorrow.
Internationally, Canada continues to do well with our public school system ranked 6th in the world in math, science and reading, ranking behind Singapore, Hong Kong, Japan, Macau and Estonia. In our back-to-basics discussion, it’s interesting that in the current back-to-basics debate, no one’s talking about the U.K. ranked 23rd or the United States ranked 31st, two countries that focus on procedural understanding, memorization and acceleration.
As someone who spent many years studying school improvement, I know that debates over curriculum or different approaches to teaching are often red herrings. The problem with curriculum is that it’s only as good as its implementation. And the problem with implementation is that it’s subject to so many factors that are beyond the government’s or school board’s control. Let me explain what I mean.
Imagine the world’s best math curriculum, developed at the world’s best university, by the world’s best researchers in math education and tested out by the world’s best instructors. The program works. We know it works because we set up an experiment, and rigorous pre and post-testing found that students being taught this curriculum outperformed students being taught a different curriculum. So with much fanfare and excitement, we package up the program, include well-written curriculum guides and lesson plans and ship it out to schools all across the province of Ontario.
In June, with lots of time to prepare for the new school year, every math teacher in the province receives a box of new materials. Inside the box they will find everything they need to teach the new curriculum. (Note: Ontario teachers don’t actually receive anything but a curriculum document. They don’t get boxes of materials with ready-made lesson plans, math manipulatives and posters to put up in the classroom – but for the sake of argument, let’s pretend they do). So each teacher unpacks the box, takes out the research-tested lessons and begins teaching math. And every student improves because the findings of the experiment said they would. Right? Wrong.
Despite excellent curriculum, there are myriad factors that influence student learning. Did the child eat breakfast? Is the school well resourced? Is the teacher skilled at teaching math? Is the principal fulfilling his or her role as an instructional leader? How many students are in the classroom? How many students with identified (or unidentified) needs are in the classroom? How many students in the class don’t speak English? Do students feel safe in the hallways or outside at recess? Is the school in a good state of repair? The list is endless and many items on it are beyond the control of teachers and principals.
Our school, Trafalgar Castle, is a member of CAIS, the Canadian Accredited Independent Schools. We are part of a network of exceptional schools across Canada that meet a rigorous set of standards. Trafalgar offers small class sizes, high levels of enrichment and support, a wide variety of activities, arts and sports outside the classroom, and teachers who are given the resources they need. As a result, Trafalgar has a 100% post-secondary acceptance rate and our students’ results on standardized tests show achievement that exceeds provincial and national standards.
As an independent school, we are fortunate to be able to control many of the factors that lead to student success. We keep class sizes small, we provide classroom materials to support learning and we actually have bins and bins of materials that get used for math lessons. We have the resources to support our teachers with ongoing professional learning and are blessed with a staff that demonstrates commitment, care and concern for every student. All those things go a long way to ensuring good learning outcomes for our girls.
Although we are an independent school and not part of the public education system, our families, our teachers, our staff and I care deeply about what happens to students in other schools. In fact, every single resident of Ontario should care because the absence of strong public schools weakens our province’s future economic potential, negatively impacts the health and wellness of our citizens and undermines our democratic institutions. And given that technology-based jobs are the future for this next generation, how prepared students are in math matters.
The tough thing about school improvement is that there are rarely quick wins. Change comes slowly and requires alignment across the system. Merely swapping out one curriculum for another without paying attention to the other forces at play won’t optimize the opportunity for improvement. I hope the public conversation and government changes around education in the province are thoughtful and measured because every child in Ontario needs to be ready for a future where math matters.