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This summer I had the opportunity to observe a Eureka Math training on coherence across the 6–8 grade band in Anaheim. While I was encouraged by the mastery with which the trainers delivered their sessions, the part of the experience that impressed me most was an instance where the trainer used pointed questions and patience to enable participants to reason through a concept, which resulted in an ‘aha! moment’ for some of the participants. This experience also resulted in an ‘aha! moment’ for me, as I recognized that I struggle to allow students to experience frustration, which can be an important part of the discovery process as students apply their reasoning to find solutions to their questions


I observed a training session on coherence across the 6–8 grade band. We were analyzing the relationship between equivalent ratios and proportional relationships. Participants were comparing the graphs that represented two different situations and trying to determine the characteristics of a graph that represents a proportional relationship. As they worked through the problems, participants at one table could not agree about whether a graph representing a proportional relationship needed to pass through the origin. The participants sought the help of the trainer, wanting her to provide them with the answer. Instead, she encouraged them to continue to talk through what they understood about equivalent ratios and multiplicative comparisons to help them draw their own conclusions. This was a clear example of facilitating independent thinking through a productive struggle. The trainer was available to provide guidance, but she resisted the urge to “settle the argument,” allowing the participants to use their mathematical reasoning to find the answer.


Besides enjoying the opportunity to witness effective mathematical practice in action, the situation I observed taught me two things: first, that I am not always eager to engage in the hard work of mathematical discovery as a student and as a teacher. I sometimes just want to know the answer, and it can feel frustrating to me to have to evaluate my thinking, especially since I was often taught mathematics by watching a teacher carry out a procedure and then repeating that procedure several times until I could replicate the steps with automaticity. Initially, some of the participants at this event also just wanted the answer. Observing this reminded me of how students may feel as they engage in rigorous mathematical practices, and it should help me to be patient with them. When the teachers at the table experienced the aha! moment, understanding not only that a graph representing a proportional relationship would pass through the origin but why (recognizing that if y is the product of x and the scale factor k, then whenever x has a value of 0, y will also have a value of 0), I was reminded of how much deeper their understanding of the concept was than if the trainer had supplied the answer for them

This experience also reminded me of how apt I can be to provide answers too quickly because I’m pressured by time or because it feels uncomfortable to me to let go of control and allow students to explore a concept. I am fully convinced of the value of having students discover mathematical relationships through exploration and analysis of patterns, but sometimes I still have to fight the urge to take on the role of the “Sage on the Stage”, and not impede the students’ productive struggle. This is one of the reasons why I appreciate the Eureka Math curriculum — it is carefully designed to allow students to experience mathematics and participate in the valuable work of discovering patterns and relationships. Eureka helps teachers, like me, to facilitate students’ ownership of their learning and fight the urge to provide the answers at the first sign of a struggle

This post was written by Grade 12 Eureka Math writer, Sara Lack.

© Great Minds 2016