When Teachers Pay Attention to How Their Students Think, Kids Can Make More Sense of Math

Jun 9, 2022 5:48:42 PM

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Amid COVID school disruptions, research has shown that for most students across the U.S., recent learning gains have been lower-than-typical in math. Given this current reality, educators are strategizing about how to efficiently meet students where they are and provide student-centered mathematics instruction based on appropriate and high expectations. They are working to meet individual needs while providing a learning experience that gets students excited about math. 

It’s tough work and there is no easy answer.

Perhaps now is the right time to consider alternatives to grade-level standards when it comes to setting high expectations for individual students, particularly when these standards are grounded in some assumptions that may no longer hold.

Could a focus on student thinking serve a more central role?

In recent years, teaching mathematics has centered on a common set of standards that focus the content through grade-level slices. Standards provide a shared reference and set a baseline for expectations around mathematics for all students. They set expectations for the content all students should have the opportunity to learn at each grade level. Textbooks, assessments, and accountability are all designed around those slices. Additionally, standards also help to assure that adults do not set low expectations of students. They can work for good, for sure. 

Ideally, mathematics learning standards reflect a network of ideas coherently connected together, much like how a plotline develops in a novel. New ideas build on previous ideas in a logical fashion. It keeps the student engaged and interested. When standards are developed, these mathematical progressions are sliced into grade-level-sized chunks designed to be taught over nine months, the standard length of a school year. This is based on the assumption that the opportunity to learn—time spent in the mathematics classroom over a year—is adequate to learn the content for their grade. 

Kids’ Ages and Math Experiences Don’t Line up Like in the Before Times

An issue arises when we begin setting expectations driven by student age, not prior opportunity to learn, nor based on what was previously learned, nor how a student is currently thinking about mathematics. 

In a post-COVID-19 world, we can no longer assume that a student’s age and mathematical experiences line up in previously expected ways. They may not even be close.

Yet our curricular, assessment, and accountability systems, along with our expectation-setting mechanisms, still operate on this assumption. 

As such, there are many conversations about the need to accelerate students’ learning to help them catch up and get back on track with respect to grade-level expectations. For many students, acceleration in the form of folding in missed content with grade-level content works. The mathematical story can be reshaped in many ways and maintain coherence. In those cases, it is reasonable to use grade-level expectations for learning. 

Yet we must also ask about the students for whom those grade-level expectations might not be the best fit. At some point, trying to set mathematics expectations based on student age rather than student thinking must hit an impasse. 

This has been made all too clear given the uneven learning opportunities our students have experienced throughout COVID-19.  The problem is that there simply is no good answer to this question, even though one is needed: 

If not simply grade-level standards, what expectations should we have for our students?  

Student Thinking Transcends Grade Levels

The wonderful thing about mathematics is its emphasis on thinking. Thinking transcends grade levels.

Instead of focusing first on age-based, grade-level standards that assume a prior opportunity to learn, we might instead examine how we can set high expectations that include individual student thinking—where they are now, and where we want them to be. 

Too many students already have a tense relationship with mathematics and see it as a collection of disparate facts and procedures rather than a coherent system that makes sense. How is it that mathematics makes perfect sense, yet students often think the exact opposite? Left unquestioned, the current situation could too easily further separate students from experiencing that connectedness and the beauty in mathematics. 

In a rush to catch up, or accelerate students’ learning, we risk ignoring how students are thinking about mathematics and connecting ideas. We might consider building students’ ways of thinking as optional, rather than essential. It’s time to find better ways to set high expectations for learners that focus more on individual student thinking than on students’ ages. 

Ted Coe

With over 25 years of experience as a teacher, professor, department chair, administrator, and non-profit director, Ted Coe uses his experiences to weave together thought-provoking perspectives in mathematics education. He is energetic and passionate about mathematics teaching and learning and has worked full-time as a high school mathematics teacher, a community college faculty member, the mathematics chair at two community colleges, as an assistant dean at the university level, and as Director of Mathematics at Achieve. As NWEA’s Director of Content Advocacy and Design, Ted works to promote high-quality mathematical experiences for all. His work entails advocating for mathematics both within NWEA and around the nation. Ted earned his B.A.E., M.Ed., and Ph.D. degrees from Arizona State University, each with a focus on mathematics education.

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