Understanding Focus, Rigor, and Depth

Richard Kingham | Published  June 16, 2021

When it comes to math education, we all want the same thing: students who are confident critical thinkers and problem solvers. Unfortunately, the classroom is often dominated by teaching models that overemphasize hitting benchmarks and proceeding to the next topic, leaving us with students who misunderstand math and feel intimidated by it. These models treat students like machines, and grades serve as markers reflecting how well the machines are operating. 

Common Core seeks to humanize math education again with three key instructional shifts that influence how we design and teach math curriculum: focus, rigor, and coherence.



Building focus into the Common Core is more than just reducing the number of standards. It instead allows educators to spend more time delving deeper into specific concepts and skills. Key ideas at each appropriate grade level are strategically placed to foster deeper understanding of mathematical structures that will overlap as students progress in their education. Teachers can more easily make the connections between various concepts and thus provide more coherent instruction. 

In kindergarten, for example, the key ideas that have been identified as critical areas of focus are:

(1) representing, relating, and operating on whole numbers, initially with sets of objects; and

(2) describing shapes and space.

Students spend a majority of their instructional time building understanding and fluency in these two critical areas. By spending more time on these activities, they interact with math more personally. They develop their own connections and conceptual understanding by identifying numerical relationships, creating varied representations, and seeing how numbers work. 

Once kindergartners have explored these fundamental concepts up close, they will be able to build a variety of other skills, including those in the next grade level, like addition and subtraction. It is important to note that although greater emphasis is placed on the critical areas, the concepts and skills delineated in the Common Core are not meant to be taught in isolation, but rather integrated into the broader curriculum to encourage students to make meaningful connections. 



For many people, a “rigorous education” evokes learning that is difficult for students. In Common Core, however, rigor refers primarily to the way teachers instruct, and for students means mastery of mathematical concepts. There are three aspects of rigor in Common Core: conceptual understanding, procedural skills and fluency, and application. 

  1. Conceptual Understanding: Teacher instruction is geared toward helping students access concepts in a number of ways and moves well beyond “how to get the answer.” This in turn supports fluency and application. 
  2. Procedural Skills and Fluency: This isn’t simply about students rehearsing information. A student can achieve fluency by knowing various methods and identifying the most efficient strategy to solve a problem, even if they cannot immediately recall a fact. The teacher facilitates instruction in a way that allows students to practice a skill enough to develop their speed and accuracy. In Math STEMscopes, both the Elaborate and the Explore/Explain cycle of instruction afford many opportunities for students to practice skills and gain fluency.  
  3. Application: This is the ultimate goal of math education. Application means that students can recognize when certain concepts are at work in and outside the classroom, and use their understanding to approach and solve problems. In STEMscopes Math, real-world connection offers countless everyday scenarios in which students can exercise their mathematical understanding. Real-world connection also helps them transfer knowledge from one context to another. 


Math is not a collection of isolated skills. It is more like a complex machine made of interconnected parts. Coherence encourages students and teachers to embrace this fact by framing math education as an extension of previous learning instead of a series of distinct lessons. Consider, for example, the interplay between kindergarten lessons and first grade lessons from STEMscopes Math. 

In kindergarten, students learn three ways to represent the number “five.” They may have drawn pictures or used objects, number paths, ten-frames, or rekenreks. When they learn how to “make a ten” in first grade they are building on their understanding that began in kindergarten while preparing for adding larger numbers in second grade. By the time they get to the more advanced mathematical processes of second grade, they will have several tools and strategies at their disposal for representing numbers. 

STEMscopes Math has two curriculum elements dedicated to this purpose: Accessing Prior Knowledge (APK) and Foundation Builder Elements. They are written from “foundational standards” that enable teachers to assess students’ understanding of previous skills. In Engage, for example, teachers may find an APK with an addition activity under a multiplication scope, because addition is the skill students build on to learn multiplication. 



Benchmarks and standardized testing aren’t going anywhere, but these three aspects of Common Core help teachers prepare students for required exams without sacrificing quality. Moreover, they enrich and expand the learning process for this generation of math students. Whether your school district’s primary teaching model is Common Core or you want to incorporate different Common Core elements into your classroom, STEMscopes Math is the perfect resource for applying this promising approach. 


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