IFL Mathematics fellow
Designing for academic rigor in a thinking classroom starts with the choice of task with which students will engage. Likewise when striving to improve student achievement, we ask our school partners to begin by analyzing the tasks students experience. If we want students to truly understand mathematics, as opposed to a series of tricks, sayings, and acronyms, then we have to ensure they have a regular diet of high-level tasks that require thinking and reasoning about mathematics. Low-level tasks do not yield student engagement in rigorous thinking. However, diving into the use of high-level tasks is intense and takes time. The two most common questions we receive are What is a high-level task? Is the endeavor of moving to a diet of high-level tasks worth it?
What is a high-level task?
The research from the QUASAR project resulted in a list of criteria for what constitutes a task requiring a high level of cognitive demand. These are some of the most salient points about high-level tasks:
- The mathematics in the task can be represented in multiple ways (e.g., visual diagrams, manipulatives, symbols, problem situations), and connections among multiple representations is expected, which helps to develop meaning.
- Students have to exert some degree of effort, which means that though general procedures can be followed, they cannot be followed mindlessly.
- There is not a predictable, well-rehearsed approach or pathway explicitly suggested by the task, task instructions, or a worked-out example, in other words, not “I do, we do, you do” tasks.
- Students need to engage with the conceptual ideas that underlie the procedures in order to successfully complete the task and develop understanding of the nature of mathematics, processes, and/or relationships.
- Considerable cognitive effort is required, and likely a bit of anxiety for the student will result because of the unpredictable nature of the solution process required.
See the full list of criteria for both high-levels tasks—those tasks that require a great deal of cognitive demand—and low-level tasks—those that do not require much cognitive effort.
In the end, the use of high-level tasks makes it more likely that students will grapple with the math. Requiring students to productively struggle with the math not only puts the learning on the students, but it also is one of the eight proven effective math teaching strategies (NCTM 2014, Principles to Actions).
Is the endeavor of moving to a diet of high-level tasks worth it?
Teachers from our partner districts share their experiences with using high-level tasks as they began implementing them as a regular part of their math instruction.
Aaron Fitzpartrick, a second grade teacher from Chartiers Valley Primary School, has recently begun using high-level tasks with his students. After his very first time using a high-level task during a learning lab, he said: “I really think it opened a new wave of confidence not only with the kids, but myself as well. Stepping out of my ‘comfort zone’ was a risk taken with positive results and a step in the right direction with the students.” Through the coaching process associated with learning labs, Aaron became familiar with the amount of preparation needed to engage students in such tasks.
Chris Schroth, a Syracuse City School District sixth grade teacher, said: “I’ve learned to believe in my students and that I need to give them the credit they deserve. The first couple high-level tasks were hard on my kids, and I let them struggle through them; however, by coming back to them over and over again, they are starting to get the hang of what is being asked of them. For instance, the task we did [in a learning lab with the IFL] was wildly successful, and I believe in our pre-conference meeting I doubted my kids and thought that most were going to fail at it, and I was dead wrong. They did a task that dealt with material they had never seen and got through it. I was extremely impressed by them.”
When teachers use high-level tasks as the basis for their teaching, students are presented with the opportunity to engage in rigorous thinking. Cat Haist, who teaches eighth grade math in East Haddam School District, explains: “I love using [high-level] tasks primarily because student engagement is so much higher. I’ve actually had students arguing about whose answer is ‘correct’ (and they both were!) merely because their work was represented differently. IFL tasks enable me to take THEIR ideas and summarize them, which is so much more meaningful to all of us than for me to simply tell them the process and the how-to’s.”
Getting students to the point of debating and justifying their thinking takes work. Teachers and students alike need to engage and be willing to persevere in the process. Schroth shares what was most difficult in his classroom: “I think the biggest challenge for me was sticking with the tasks when the students struggled. The first couple times I felt like a failure because the students just couldn’t get through the problem. They didn’t want to try to work through it because they didn’t know it, and I couldn’t help every single student out. I wanted to give up on the tasks and chalk it up to my kids weren’t ready for them and it was too difficult for them. I hated seeing that struggle and I hated seeing that disappointment in their faces when they couldn’t do it. However, after going over those first couple tasks with the classes afterwards and showing them what I was looking for, you could almost see the light bulb going off for more and more of them… I decided to keep exposing my kids to the tasks, and I believe they are getting more and more comfortable with the idea of a high-level task, and I believe that the majority of the students are starting to believe in themselves in that they are capable of getting through a task.”
Implementation is difficult on several fronts and takes time to develop. Early on in the process and when instructional focus slips, there is a chance that a high-level task is not implemented in a way that maintains its demand. Sometimes teachers inadvertently diminish the cognitive demand of a high-level task by shifting the focus of the work to “getting the answer” as opposed to pressing for meaning, concepts, or understanding of the mathematics. Sometimes teachers rush through the task, rather than providing adequate time for students to explore, grapple, and make sense of the mathematics, which also results in lowering the cognitive demand. The instructional choices that teachers make when implementing a high-level task can result in either maintaining the demand of the task or lowering the demand. See a full list of the factors that result in the maintenance or decline of the task’s cognitive demand.
Haist, who has been using high-level tasks for a few years and continues to work on how to ensure rigor in her classroom, says: “One of my biggest challenges is to stay focused on my desired lesson outcomes. This year I’ve been really focused in all my lessons to assess daily student learning… By reflecting on the essential components of a task (and every lesson, for that matter), I am better able to use the tasks to advance all student learning.”
In the end, yes, using high-level tasks in math classrooms is worth the effort and energy. Not only do high-level task offer students opportunities to think and reason about mathematics, but engaging in such tasks regularly also changes how students see themselves. As Schroth concludes, “What I have found when using high-level tasks is that my students are starting to believe in themselves with regards to figuring out problems.”
Special thanks to the contributing teachers in our partner districts:
- Cat Haist, eighth grade math teacher in East Haddam, CT
- Chris Schroth, sixth grade math teacher in Syracuse, NY
- Aaron Fitzpatrick, second grade math teacher in Pittsburgh, PA