Assistant Head: Learning, Dean Van Doleweerd
Early in December, Bill Gates published an article on his GatesNotes site that highlighted some troubling and inspiring news about the struggles students currently face, in particular, struggles with math. In the article, Gates addresses the fact that math (and in particular, Algebra 1) was the course that was failed by more students than any other in American high schools. The result of failing Algebra so early in high school led to a 20 percent chance of a student actually completing high school, and thus a diminished chance of attending college or university. The article then went on to consider the issues surrounding current math instruction and how teaching strategies can change to better suit the needs of students today.
At Lakefield, we are not plagued with these kinds of results. All of our students attend university after high school graduation. Despite our students’ overall success, it is true that math courses tend to challenge students the most. This is not to say that they are not challenged in other subjects, but math consistently presents problems for many students. In Ontario, the math curriculum does not follow the traditional American model of Algebra 1, Geometry, Algebra 2, pre-Calculus, and then Calculus.
Our organization of math learning is designed differently; however, the struggles Gates references remain true in our math courses. This was magnified upon our return to school this year. After a long period of remote learning (for some students it was more than a full year), some significant gaps in skill development became evident. Many studies (McKinsey) have looked at the broad and complex issue of learning loss during the pandemic. Within these studies, the prominence of literacy and numeracy loss is well documented. While younger students have fallen behind on their overall growth as readers and writers, older students have fallen behind on more complex math and problem-solving skills (Education Week). The traditional struggles with math have only been exacerbated by the pandemic. Fortunately, there are some common designs that have been shown to help deepen math learning in classrooms.
In a 2018 study conducted by the New Teacher Project, researchers reviewed the lessons of over a thousand teachers. In those lessons and in the assessment of the standards, over 70 percent of students met the standards at the time of assessment. However, only 17 percent of students were able to demonstrate that same mastery over time. The study found a prime cause of their diminishing knowledge was an absence of challenging assignments being given to students. This lack of challenge failed to push students to a place where they developed or stored the skills and, as a result, they forgot them almost immediately. The study found that students spend hundreds of hours each school year completing work that is not sufficiently challenging to help them stay engaged and remain committed to the discovery and the development of understanding. The work ensured students could show that they meet required standards, achieve high grades, and feel good about their teachers, but they did not complete much meaningful learning. A form of this example is explored in David Epstein’s book, Range: Why Generalists Triumph in a Specialized World (or in this podcast). In his book, Epstein reviewed a study performed at the U.S. Air Force Academy that investigated the relationship between teacher quality and student success. The research showed that students who were given narrower and less challenging work felt better, enjoyed math more, and rated their professors higher. The second group completed broader work, struggled harder, and did not rate their professors as well. When the researchers revisited these students, those who were exposed to the more challenging curriculum retained more knowledge from class and were able to make the appropriate next steps in their mathematical development.
The challenge, however, lies in not accepting an either/or binary. In Gates’s article, he speaks of the need to not just increase the challenge, but to facilitate more engaging instruction. In a different study, conducted in 2018, the Education Trust focussed on math teaching and found that math classes often focussed on the tedium of procedural work with little opportunity to discuss or justify the thinking that went into problem-solving. There has to be an opportunity to explore, discover, and struggle in a subject that is difficult.
At Lakefield, we are continuing our efforts to meet the needs of all of our learners. While many students come into math class with enthusiasm and confidence, we acknowledge that it is a course where students arrive with a pre-existing fear. As such, we strive to incorporate experiences in our rooms that help to build confidence and also create the moments of challenge and discovery that Gates and the researchers with the New Teacher Project have observed as missing in many math classes. One of the ways we have sought to keep our classrooms forward-thinking is by embracing the work of Peter Liljedahl and his ideas surrounding Building Thinking Classrooms. This environment helps create situations that the Education Trust found missing from so many math spaces – places to discuss and explore the thinking involved in solving complex problems. Beyond this, we are also looking to tap into the broad spectrum of mathematical learning that is the experience of a Lakefield classroom. Students bring their experiences from around the globe to our classrooms to bear on the topics and problems we are considering in this article. We are also aware that, as is always the case, we are on the precipice of change. The pandemic has brought with it a new age of digitized learning. While we lament online learning for its many failings, there have been many discoveries that are indications of what is to come. Not the least of which are the ways in which the new world of Artificial Intelligence (AI) will change learning, math learning in particular, in ways that the innovation of the calculator could only offer a hint.
So, we too have witnessed and are actively working to resolve the issues that have long plagued the learning of mathematics, especially today as we face the ongoing challenges of learning during a pandemic. Beyond our current health crisis, this is a period of incredible transition. Both machine learning and AI developments are creating changes to both what and how we know. There are hints of what is coming – for example, robots everywhere, Seoul’s metaverse, and AI essay grading. Perhaps change has never come so quickly with so many significant consequences. That being said, we are also still working hard to solve the problems of today, while keeping a careful eye on the future.