What would a sixth grade math lesson look like that requires no computation at all?
While this may seem like a silly question, it's one I ask myself a lot. In the K-12 space, it's common to equate doing mathematics with performing computations. And indeed, as an adult, performing computations mentally is something I do all the time; I value my own fluency with the four operations and flexible understanding of fractions and rates. (I use a calculator a lot, but value the fact that I can quickly tell when I have mistyped something.) All students should have engaging opportunities to develop computational fluency.
But performing computations mentally or with pencil and paper is not all of math. It's certainly not what academic mathematicians do, nor is it what physicists, engineers, artists, architects, or doctors spend most of their professional lives doing. Experts in math-related fields rely on technology to support computations, and instead focus their time on problem-solving and reasoning.
I sometimes recognize that computational requirements can actually form a "barrier" to opportunities for doing math. A grade-level task might require reasoning and problem-solving, but also require computation in ways that prevent engagement for some students. How might students engage with problem-solving and reasoning, while minimizing these barriers? Especially at a time when students have had diminished school-based opportunities to develop computational skills due to the pandemic and resultant educator shortages, and especially at the secondary level, it is important to consider how students might engage with grade-level mathematics in ways that don't require as much computation.
Here's a thought experiment. Consider this 6th grade learning target: Students will be able to solve problems involving unit price. Typically, this means students answering questions like this:
"At the store, 6 avocados cost $7.74. What is the cost of 1 avocado?"
And students doing work like this:
What are the computational barriers from prior grades that might get in the way of students having opportunities to reason and problem solve about unit price? There are likely many, but let's consider multidigit division as a primary one. What would it look like for students to reason and problem-solve in ways that don't require performing any division? A simple answer is to allow students to use calculators. Tweaking the task, though, can minimize computational barriers while also maintaining a focus on grade-level problem-solving and reasoning. For example, the task could instead be:
"At the store, 6 avocados cost $7.74. Write an expression that gives the cost of 1 avocado and explain how you know."
And student work might look like this:
Comparing these tasks and responses leads to some interesting questions. Which student has met the learning target? Which responses gives more evidence of understanding of unit price?
I'll close by reiterating that I think computations are important. I value my own abilities to compute. All students should have opportunities to develop computational fluency. But, it is nonetheless important for us to consider when we are using computations as an artificial barrier to having opportunities to reason and problem-solve. Is there an appropriate classroom- or school-level balance between computationally heavy experiences and non-computational experiences with mathematics?
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