Last June, over four hundred thousand Ontario students in Grades 3, 6, and 9 participated in EQAO’s mathematics standardized assessments and the results are in.
- Grades 3 and 6 students’ basic knowledge of fundamental math skills is stronger than their ability to apply those skills to a problem or think critically to determine an answer.
- Just over half (57%) of Grade 3 students say they enjoy math but this number goes down over time to about one-third (35%) by Grade 9.
- The instructional approaches that most commonly make up teachers’ mathematics program are independent practice (91% in Grade 3 and 96% in Grade 6) and direct instruction (91% in Grade 3 and 95% in Grade 6).
This data is valuable in helping us understand where things are in Ontario, but how we interpret and then use the data to drive our actions is even more critical. To help with this, we reached out to one of the experts.
Kyle Pearce (@MathletePearce) is a renowned math consultant from Windsor, Ontario and an advocate for “making math moments that matter”. In fact, that’s the name of his teacher capacity-building website, podcast, and webinar series – Make Math Moments That Matter. He and his colleague, Jon Orr (@MrOrr_Geek), focus on “sparking curiosity, fueling sense-making, and igniting [one’s] teacher moves”. We asked Kyle about some of the EQAO’s findings.
First of all, standardized tests as an assessment strategy have been heavily debated and remains a divisive topic. In her book, The Test, Kamenetz (2015) outlines many of the common concerns with standardized testing including “testing the wrong things,” and “penalizing diversity”. The diversity she is referring to includes that of culture, ethnicity, socio-economic status, as well as learning style and demonstration of understanding.
Furthermore, researchers propose that standardized tests may not be true indicators of individual performance. Daniel Koretz (2008) from the Harvard Graduate School of Education writes, “These tests can measure only a subset of goals…tests are generally very small samples of behavior that we use to make estimates of students’ mastery of very large domains of knowledge and skills.”
Arguments such as these are what cause people to cast doubt on the validity of standardized tests like EQAO’s province-wide assessments.
…Kyle suggests that these assessments serve an entirely different purpose and that the EQAO Mathematics Assessments get a bad rap in the media. “It’s actually a very rich assessment. It’s a lot more helpful than we give it credit for. Not necessarily at an individual or even classroom level…but it’s a great long-term monitoring tool to see whether the work we’re doing is actually making a difference.”
“It’s actually a very rich assessment. It’s a lot more helpful than we give it credit for. ”
Kyle goes on to say that although the longitudinal utility of these summative assessments should not be downplayed, some of the immediate findings point to the need for better formative assessments. The downward trend in student performance over time, and the correlation between a student’s performance in Grade 6 and Grade 3, begs the question, “When students struggle in Grade 3, what were we doing ahead of time? Did we know they were going to struggle? If not, we need to improve our [formative] assessment practices and our approach to remediate these areas of need.” His comments point to the importance of being able to respond to student needs in the moment rather than making sweeping changes for the next group of students the following year. After all, “they are a whole new group of kids with needs that may or may not be the same as those who wrote this year.”
According to the EQAO findings, Ontario students know how to solve basic math problems better than they know how to think critically about complex problems. So, how do we encourage deeper conceptual understanding that allows students to become more adaptable and resilient problem-solvers?
Kyle recommends giving students greater opportunity to practice the act of problem-solving. “That isn’t to say that we tell kids, ‘here’s how we solve this type of problem that involves this math concept – now go and do five of them,’ but rather allowing them to productively struggle through the problem-solving process.” Although many of us survived or even thrived in this environment when we were math students, it is reasonable to suspect that this instructional approach may contribute to students’ lack of problem-solving and critical thinking abilities.
Before diving into strategies for encouraging more authentic problem-solving, let’s investigate the impact these instructional approaches may have on students’ affinity towards (and their self-perceived ability for) math.
The percentage of students who report enjoying math (57%) is approximately the same percentage of those who consider themselves good at it (54%). Kyle reports that although it’s a sort of ‘chicken and egg’ situation, in his experience, “these numbers tend to move in tandem.” Unfortunately, according to this year’s EQAO results, this movement is one of decline from over half in Grade 3 to about one-third by Grade 9. What happens along the way that students lose their confidence and love for learning math?
“Our Kindergarteners are born with a productive disposition. If we are teaching math the way we were taught, which is a lot of monotonous repetition, nothing interesting happening, no curiosity or spark for engagement, it shouldn’t be a surprise that their productive disposition decreases over time.” He likens this form of instruction to handing students a checklist of things they’ll need in the future which does them a disservice and breeds the love of learning out of them. Sir Ken Robinson famously broached this idea in his TED Talk (2007) where he cautions educators about killing creativity through this same style of instruction.
“ If we are teaching math the way we were taught…it shouldn’t be a surprise that their productive disposition decreases over time. ”
“Think about people who do crosswords,” starts Kyle. “People don’t do them because they are [useful]. There is something inherent about the challenge…and the satisfaction you feel after you solve a problem.” This analogy Kyle puts forth alludes to the idea that people naturally enjoy activities that push them to the edge of their ability. In educational psychology, Vygotsky calls this the “zone of proximal development” (1963). In behavioural psychology, Csíkszentmihályi calls it a “flow state” (1990). Above, Kyle called it a “productive struggle”. We encounter this state of mind when we engage in activities that are just challenging enough to be difficult yet achievable and all of the aforementioned agree – the human brain naturally revels in it.
Although a lot of teachers are making efforts to move towards student-centred and inquiry-based learning in their classroom, the EQAO results indicate that over 90% of teachers report using direct instruction and individual practice whereas only 63% report using collaborative inquiry in their mathematics programs. It’s not surprising since this reflects how most of us were taught and have limited exposure to alternative methods when we were math students. So, as the Ministry of Ontario poses in their Capacity Building Series on inquiry-based learning (2013), “How can we provide opportunities for students to move beyond being passive recipients of knowledge to become knowledge builders, capable of creative and innovative solutions to problems?”
“If we do a bunch of [direct instruction] and try to link them together later, that’s really difficult to achieve. By having students actively engage in the problem-solving process, that’s how we create resilient problem solvers.” Kyle goes on to explain that this process is very deliberate and does not mean letting students take as long as they want to solve a problem. Rather, the key is acting as a facilitator and knowing when to pose specific questions to guide them in a particular direction and when to step aside before bringing the class back together to consolidate the learning.
“ By having students actively engage in the problem-solving process, that’s how we create resilient problem solvers. “
Kyle suggests, “As a starting point, to prove to themselves that kids know more than we often give them credit for, is to actually give them a problem to try before we try to rescue them. If we hold back even for just 10 minutes, it will allow them to build confidence that they can actually solve math problems without the teacher pre-teaching all of the steps, procedures, and strategies that will help you solve the problem most efficiently.”
This is not to suggest that a shift towards student-centred approaches is easy and can happen overnight – it is not. It requires a concerted and collaborative effort that can be impacted by a variety of factors including the teaching environment (2018).
This year’s EQAO findings highlight the need for better formative assessment, a greater focus on problem-solving skills, and increased support as teachers shift towards more student-centred modes of instruction. We know from our conversations with teachers, schools, and districts, that these issues are already top-of-mind for many. The only way the educational community can effectively respond to these findings is to continue these conversations within our schools and between districts.
Share this analysis of the EQAO results with your colleagues and pick up the conversation where we left off with Kyle. Together, discuss how your school can respond to these findings and Kyle’s recommendations. Changing the way we teach and learn will not happen overnight, but conversations like these are a great first step.
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Written By: Matt Murphy
Matt Murphy is the Educational Designer for Zorbit’s Math Adventure, a K-3 game-based learning platform for the classroom. Matt has a Masters degree in Curriculum Design from the University of New Brunswick and has over five years of experience working in educational technology as an Instructional Designer, and Gamification/Game-Based Learning Consultant.