This post is sponsored by Curriculum Associates
The Common Core State Standards have introduced a new level of rigor to math curriculum. No longer focused on rote tasks and memorization, today’s math curriculum requires students and teachers to think of numbers and mathematical functions in new terms. In this Q&A, Forsyth County School’s Mathematics Specialist Brian Lack discusses the challenges of this transition and how his district is supporting teachers in this endeavor.
The new common core and College and Career Readiness Standards are much more rigorous. How have you adjusted your curriculum and instructional models to accommodate the new standards? What challenges have you encountered and what are a few strategies you’ve used to overcome them?
The biggest hurdle we have faced has been helping teachers understand the depth and meaning of the standards accurately. Each elementary teacher is extremely constrained when it comes to time and because of this, they often rely on publishers’ interpretations of the standards. However, I have seen so many products that water down the rigor. One of the best things about the common core is that it is helping to create a level of consistency we did not have before.
To address these issues, we are focusing on restructuring teachers’ notions about what teaching math means. Take computational fluency for instance, we are getting our teachers away from teaching the standard method of rote learning for how to add and subtract. Research shows that teaching the algorithms too early can lead to weaknesses in number sense. Yet teachers often feel pressured to move on in math, and because of their own experiences as students of math, they default to teaching algorithms even when they are not necessarily developmentally appropriate.
We are helping our teachers to overcome these challenges by pushing beyond the printed language of each standard. We do this through providing instructional leaders in schools who offer coaching, modeling, co-teaching, observation and feedback.
Along those same lines, how should professional development evolve to better support teachers through this transition?
Differentiation is one of the great contradictions in education. We expect our teachers to differentiate instruction to meet students’ needs, but we rarely practice this type of learning to adults. Educators in elementary school typically do not have strong backgrounds in math content, and all of our teachers come to the classroom with different experiences and degrees of confidence. We have to embrace this by formatively assessing teacher strengths and weaknesses and design PD relevant to those differences. We should do this, in part, by embracing our modern technological capacity to differentiate PD, in addition to engaging in personalized and interactive face-to-face learning.
What would be your No. 1 recommendation for teachers as they tackle implementation of the new, more rigorous math standards?
What I have learned through my experience in working with all types of adults is that the key for tackling the rigor of the new standards goes back to an individual’s fundamental beliefs about teaching and learning mathematics, which for most of us is shaped by experience. It is not just about “using more manipulatives” or “trying more open-ended questions.” Educators need to reflect on their own background as students of mathematics and make connections to teaching practices they were exposed to in the classroom. They have to question for themselves what it was about math that did not make sense and how teaching practices contributed to that. They have to want to learn about math in a different way than they were taught.
Teachers then have to get past the misconception of math as a set of rules and procedures and instead think of it as a set of patterns and relationships—this is where the rigor comes in. Teachers need to provide students with rich tasks and discussion. They have to take a common equation such as 7 x 6 = 42 and instead of teaching students how to memorize the fact, teach them how to group and decompose numbers and work with place value and properties to provide a more robust idea of the number relationships. Teachers are learning how to teach math differently because of the new, more rigorous curriculum, and that is good for students.
Can you share ways in which you are ensuring both your instruction and materials have the right level of rigor?
We use Karin Hess’ Cognitive Rigor Matrix, which, according to Hess’ website, is a combined model that superimposes two existing models for describing rigor that are widely used in the United States—Bloom’s Taxonomy and Webb’s Depth-of-Knowledge levels. We find this to be the most powerful tool for assessing rigor.
We also implemented the Ready Common Core Math series in part because it uses this matrix as a framework for applying levels of rigor. Tasks in Ready Common Core are leveled by Depth-of-Knowledge (DOK). There are outlines and examples for the different DOK levels within the program, so our teachers have a good understanding of what rigor looks like with respect to each standard. In addition, for each unit we provide our K–5 teachers with a set of rigorous questions. These questions have provided our teachers with a concrete model for the level of rigor to which the standards should be taught. I love it when our teachers share epiphanies such as “I never realized that this fraction standard could be so challenging!” and one teacher recently had this to say, “My students ask me almost every day, ‘When are we going to do the ‘hard problems’ because they are so much fun?’”
Brian Lack, Ph.D. is the K–8 Mathematics Specialist at Forsyth County Schools in Cumming, Ga.