Short formative pre-assessments can give teachers a quick read on a student’s foundational knowledge before starting a new unit, but they are often “filled with questions on the lower end of the depth of knowledge scale” and focus on a student’s “ability to get answers right or wrong, not their strengths and levels of understanding,” writes Josh Deis, a former teacher and current district math coordinator for Petaluma City Schools in California.
When students don’t perform well on these assessments, Deis, writing for the blog Peers and Pedagogy, argues that teachers end up backtracking and pre-teaching below-grade-level skills before embarking on the unit-specific materials they intended to teach.
“Before you know it, you are a week into a four-week unit, and you and your students have not engaged in the grade-level content of that unit yet.” If this pattern continues from unit to unit, teachers quickly run out of time to cover grade-level content, leaving students behind and unprepared for the next school year, Deis writes.
Rather than quizzing students about previously learned knowledge, consider occasionally diving into more challenging, grade-level content on day one of a new unit with a low-stakes, pre-assessment task. “A grade-level task on day one,” writes Deis, “allows teachers to assess students while they are engaged in a meaningful task.”
According to Deis, these sorts of tasks are also a meaningful way to give students the opportunity to activate prior knowledge themselves—while providing teachers some time and space to assess the best ways to support them as they begin to move toward more complex concepts.
Begin With the End
A simple way to provide students with an effective reach activity, writes Deis, is to start them off with a problem that comes from the very end of a unit they’re about to learn—or to devise a relevant problem that introduces new material that’s clearly related to material students have already encountered. This approach, Deis argues, supports a “just in time” approach to teaching, instead of a “just in case” approach that hinges on the expectation that students won’t be able to grapple with grade-level content—and puts the onus on the teacher to fill in gaps that become apparent in the process.
A “just in time” approach, Deis writes, allows teachers to “better understand how students are thinking about grade-level content,” and gives students the opportunity to do some heavy lifting at the outset of a new unit.
When adopting this approach, however, it’s important to know that kids might experience some degree of frustration as they grapple with content they’re not quite familiar with yet. In fact, it is helpful to provide students with this understanding, and explicitly lay out why struggling with complex problems is a crucial part of learning and retention.
Manu Kapur, a learning scientist and the father of the concept of productive struggle, told Edutopia in 2022 that if you’re not struggling at least some of the time in the classroom, “you’re probably not learning.”
A 2012 study by Kapur shows that occasionally providing students with challenging tasks that are “just beyond students’ reach,” and allowing them to struggle for 30 to 45 minutes before stepping in to correct and guide students with direct instruction, can double students’ comprehension, compared to when kids receive only direct instruction.
The findings line up with further research showing that students who take practice tests on material they haven’t learned yet significantly outperform peers on follow-up tests, as well as the findings of a 2018 study that suggests giving students the opportunity to make educated guesses and generate errors prior to studying information can improve their retention of it.
Preserve Student Agency
As students work through a challenging task, Deis writes that it is important for teachers to adopt a “facilitator” stance—meaning they should refrain from jumping in and “saving” their students. This not only allows for the task to serve as a formative assessment, it also serves as a way to “activate student agency,” according to Deis.
To illustrate how teachers can make use of this strategy—and what their role should look like—Deis walked through an example task given to third-grade students working on multiplication.
At the outset, it is important, Deis writes, to choose a low floor/high ceiling task. This means the task is “readily accessible to students with varying degrees of prior knowledge,” but also connects to new learning milestones they will be expected to reach in the next unit.
The task for Deis’ students was as follows: “There are five teams in the volleyball league. Every team has six players. How many players are in the volleyball league?”
It’s a great fit for students who have not yet formally studied multiplication because the numbers are “accessible” and students can solve it using addition skills they’d previously learned. Nonetheless, it is slightly out of their reach because they’ll be forced to apply those skills in a new manner.
A good pre-assessment task in a math classroom should ensure students are “not relying on trying to remember how their teacher ‘taught’ them to solve the problem,” Deis writes. It should push them to “rely on prior knowledge and the tasks’ context to make sense of the problem.”
Deis allows his students to work on their own to solve the problem, and by analyzing their efforts, reaches important conclusions that feed future lessons. For example, it became clear that some students already understood the problem was asking them to use multiplication and engaged in repeated addition to solve it, while others used diagrams to solve the problem.
To fill in his students’ knowledge gaps, Deis created a follow-up lesson to “build a bridge between the sense students were making and the essential mathematics of third grade.” This included walking through the problem from the lens of second-grade math (repeated addition), and leaning on the diagrams some of them drew to transition into a discussion of using multiplication as a faster way to solve the problem.
In Deis’ third-grade classroom, these task-based pre-unit assessments helped students take “large strides” toward crucial math concepts in a matter of days, building their confidence as “doers of mathematics” who are capable of learning grade-level content right out of the gate.