In 2019, I spent summer vacation plowing through the Eureka math curriculum, grades 6-8, making videos of every problem, followed by returning to the start and creating text versions of the hints I had first recorded. As I wrote at the time, it was amazing professional development, as I had to get inside every single problem, whether I liked it or not, and figure out what exactly was going on, so that I could then create a student-friendly explanation. It was amazing.
I have continued to work for ASSISTments. Their current goal is to have “skill-tagged” every individual problem in their multiple data bases by December 2021. What does this mean for me? It means I get another round of “professional development” as I read through problem after problem, identifying the curriculum standard(s) in the problem. This weekend, I finished tagging 10,570 unique problems from the Grade 3 Eureka math curriculum. While I haven’t taught Eureka math for the past two years, I still believe it is a high-quality curriculum, so I’ve enjoyed learning about its expectations for Grade 3 while I work to skill tag.
What I found most interesting, both frightening and also intriguing, was how much the Grade 3 curriculum contained content that we find students struggling with once they get to 6th Grade, where I am currently teaching. How is it that 3rd graders are working on problems with distributive property, yet the same concept appears to confound them when it shows up again in 6th Grade and 7th Grade?
This 3rd Grade standard clearly sets the stage for using the distributive property in 6th and 7th Grade, when the standards shift to an algebraic approach.
Do students lose their understanding, or did they never have it in the first place?
The following problems demonstrate an expectation for students to understand and use inverse operations to solve numerical problems; this is a mathematical practice that leads directly into using inverse operations in algebra to find the unknown, which leads further to concepts in calculus where inverse functions are used to find unknown values.
I don’t have any answers, but I wonder why, if we are starting students in these concepts so early, they are struggling so much.
From my own experience, I memorized my way through math for the entirety of my school career. I had the capacity to memorize huge chunks of information at a time, so I learned to memorize and apply what I would need, such as memorizing the entire unit circle for sine and cosine, which I would then write down at the start of every test before I read the problems. It wasn’t until my second round working as a Teaching Assistant for Calculus I that I had the breakthrough that the values on the unit circle came from the sine and cosine graphs, in a sort of “unravelled” form. Making that connection meant I did not need to memorize the values, as I had a context for them, finally. But if it was that hard for me, a capable, motivated, dedicated student with years of really amazing teachers, to make that connection, perhaps that gives some insight into why kids are still struggling three, six, ten years after they first encounter the concepts of distributive property or inverse operations? I have no answers or solutions, but I was fascinated as I read problem after problem in 3rd Grade, thinking about how much my 6th Grade students are still struggling with many of the same concepts.
Attribution: all questions from from released items on the Massachusetts Comprehensive System (MCAS) test