When I was a classroom teacher, I had an underappreciation for how important understanding the Shifts in the mathematics standards, Focus, Coherence, and Rigor, were to implementing “The Iowa Academic Standards for mathematics.” I knew the three Shifts as a list, could parrot them back when asked and understood what the definitions meant.
However, since I did not have a deep understanding of the Shifts and the relationship to the implementation of the standards, I treated the standards as a checklist and called it a curriculum, but they are neither. This lack of understanding prevented me from making the impact on curriculum, instruction, pedagogy, or assessment practices that I wanted to make in my classroom. For example, if I understood the first Shift, Focus, then I would have spent more time on linear functions than my curriculum recommended because it is one of the major works. As a result, I feel my students were not as prepared to be College and Career Ready to successfully pursue career-training programs, the military, and attend college without taking a remedial math course.
In the article The Structure is the Standards, Phil Daro, William McCallum, and Jason Zimba, the authors of the Common Core State Standards Mathematics, explain what the standards are: “The standards are meant to be a blueprint for math instruction that is more focused and coherent. The focus and coherence in this blueprint is largely in the way the standards progress from each other, coordinate with each other and most importantly cluster together into coherent bodies of knowledge. Crosswalks and alignments and pacing plans and such cannot be allowed to throw away the focus and coherence and regress to the mile-wide curriculum.”
These authors are describing the Shifts in instruction and the relationships that cannot be ignored to fully implement the standards in the way that better prepares students to be College and Career Ready for the world today.
The Shifts are Focus, Coherence, and Rigor and the order is purposeful. Without Focus, then Coherence and Rigor are less likely to happen. Likewise, without having Coherence, Rigor is unlikely to happen. An educator will see evidence of these Shifts across the grade-levels, grades, and daily lessons.
- Focus – across the grade level, not during a single lesson
- Coherence – in lessons that build on prior learning meaningfully and in lessons that successfully connect supporting standards to major work of the grade
- Rigor – daily, within a daily lesson, as defined by the particular lesson standards
There are many resources to learn about the Shifts:
Before the adoption of the mathematics standards, mathematics education was a mile wide and an inch deep, with too many topics to cover at each grade level. If it still feels like that now, then focus may be missing. Focus is a greater focus on fewer topics that happens across the curriculum and not in a daily lesson. The major works and clusters of a grade level can take up to 85 percent of classroom time. The Focus on Number and Operations and Algebraic Thinking in K-8 is intentional to ensure students are ready for the expectations of high school and those of College and Career Readiness.
Resources for Focus
- Content Visibly Emphasized
- Major Work in K-8 (scroll down for progression arrow)
- Focus by Grade Level
- HS Focus
Coherence is linking topics within the grade and thinking across grades. Mathematics topics are connected understandings and cannot be taught through tricks and mnemonics. Within a grade, “supporting” standards are labeled as such because they have very strong connections to the major work of the grade level. As educators, what we do in the fall matters for the spring; likewise, what we do in kindergarten matters for high school. The Coherence Map linked below is dynamic, and is frequently updated with new resources such as tasks, progressions, and assessment items. Some of these resources can be used to identify learning gaps in the standards or used for extension activities.
Resources for Coherence
Rigor can be described as three-legged stool because it requires that educators balance conceptual understanding, procedural skills and fluency, and application with approximately equal intensity.
Resources for Rigor
Want to learn more about the Shifts in mathematics and how to impact curriculum, instruction, pedagogy, and assessment? Join the IA Core Advocates for Mathematics. This is a community of Iowa educators interested in learning more about the Shifts and their impact on ensuring all students in IA are College and Career Ready in mathematics.
Call to Action: Join the IA Core Advocates - Mathematics today and participate as much or as little as you like: G+ groups, Twitter Chats, webinars, or just receive the email updates.