Redefining Rigor in the K–8 Math Classroom

Rigor in K-8 Math: What does it really look like?

When you hear the word rigor in a math classroom, what comes to mind?

For many, it might be speed. Fluency. Maybe even acceleration, or learning “above grade level.” But experts in math education agree: rigor isn’t about racing ahead or memorizing faster. It’s about digging deeper, and doing so in ways that meet each student where they are.

So what does rigor look like in K-8 math? And how can schools achieve it without overwhelming students or teachers? We sat down with math educators and curriculum experts to unpack this essential concept.

Misconceptions About Rigor

According to Susan Resnick, Consulting Author of Marshall Cavendish Education’s Primary Mathematics, we often confuse rigor with acceleration: “Sometimes the public thinks that rigor means acceleration, that we're going to push the kids into a higher grade... But what happens is that we create a lot of surface knowledge and not a lot of depth. Rigor is about going deeper, not necessarily faster.”

Instead, Resnick and others stress that true rigor lies in:

• Applying known concepts in unfamiliar contexts
• Combining ideas in new ways
• Grappling with non-routine problems
• Explaining solutions clearly and flexibly

This kind of thinking prepares students not just for the next test—but for challenges they’ll face in high school, college, and careers we can’t yet imagine.

Rigor Is Not About Doing More, Earlier

Jessica Kaminski, M.Ed., Math Content Specialist at Marshall Cavendish Education, has seen firsthand how misconceptions about rigor lead to misplaced pressure. She shares that “we tend to see that rigor means more for many people. It could mean students completing more problems.” She adds that acceleration can create a false sense of challenge. I've heard from some parents who have seven or six-year-olds that they say are doing long division. But when I talked to those students, they had no idea what processes they were doing. They were just following steps. When students can take something and break it down into its tiny pieces to explain the way those pieces interact- that's true rigor.” Essentially, rigor is about ensuring that every student, regardless of ability, can access the problem, understand the WHY behind what they’re doing, then go deeper. Regurgitating the lesson does not equate to true comprehension and mastery of the lesson, and rigor is what bridges that gap.

What True Rigor Looks Like

At its core, rigor is about:

• Conceptual understanding: Students don’t just do the math, they understand it. They know why something works, not just how.
• Multiple entry points: All students can engage with the content, whether they’re working with manipulatives or ready for abstract thinking.
• Diverse strategies: Students are encouraged to solve problems in more than one way and explain their reasoning.
• Perseverance and reasoning: Problem-solving is not a one-shot task. Students try, fail, revise, and keep going.

Chris Coyne, National Education Consultant for Marshall Cavendish Education, further emphasizes the importance of students building a foundation of understanding first and how fluency and speed are secondary. He shares how the foundation is key so when students progress through school, and math becomes more complex, students can “deal with any problem-solving situation… we want our students to become critical thinkers rather than just answer-getters.” Ultimately, rigor in K-8 math is about students being thorough in their problem-solving. Moving beyond rote memorization and recall, the focus is on strengthening students’ ability to analyze problems and discern which strategy is most appropriate. This approach fosters critical thinking and adaptable problem-solving skills, which are essential for successfully navigating future challenges.

The CPA Approach: A Foundation for Rigor

One of the most effective frameworks for achieving rigor is the Concrete-Pictorial-Abstract (CPA) approach, central to the Singapore Math methodology and Marshall Cavendish Education’s Primary Mathematics curriculum.

Education Consultant Karie Gladis explains why the CPA approach is so powerful and effective: “Thinking is invisible, right? It’s in the student’s head. And we, as teachers and educators, need to find ways to make that thinking visible.” The goal of CPA is to provide students with multiple ways to access and make sense of a problem, rather than relying on rote memorization of a single method. Coyne expands on this by highlighting the environment that CPA helps create: “By the end [of the lesson], the hope is that the students become efficient, and they may not need the manipulatives. They may not need the models. And if they do, they can draw their own models to organize the information.One thing Primary Mathematics encourages is a culture where students approach problems with an open mind. We may struggle a bit with a problem today but by having an entry point and viewing it as an opportunity for growth instead of failure, we may be able to solve it tomorrow. Some mistakes may be made. And while we're learning, mistakes are ok. While we're learning a particular learning objective or a concept, there's a lot of value in an incorrect answer.” It’s truly amazing to witness how this approach fosters a learning culture where students feel safe to explore, experiment, and share their thinking–even when it’s imperfect. By normalizing mistakes and encouraging flexible problem solving, the CPA approach builds confidence and resilience when facing new mathematical challenges.

Rigor Looks Different for Every Student

In any classroom, there is a wide range of learners, and a common misconception is that rigor should be reserved only for top-performing or “advanced” students. In reality, rigor should be accessible to all students and intentionally encouraged for every learner, regardless of their current level.

Resnick, who has a Master’s degree in Learning Disabilities, addresses this misconception directly: “Sometimes educators withhold rigor from kids who are perceived as struggling. What I've learned is that sometimes the kids who look like they're struggling are the ones who can come up with a more creative or non-traditional way.” Her insight reinforces the importance of introducing a variety of strategies through the CPA approach, allowing all students, not just a select few, to engage deeply with the material.

For some students, rigor might take the form of working with manipulatives or using bar models to explore a concept. For others, it might involve solving a non-routine problem or explaining their thinking to a peer. Regardless of the method, the CPA approach fosters persistence and resilience—critical traits for students who are building confidence and overcoming math anxiety. As Coyne notes, “That's how that growth mindset develops, how productive struggle works. And the researchers will tell us that's a great way to build mathematical confidence in students.”

The Role of Lesson Design

The structure of a math lesson matters (a lot). Primary Mathematics lessons follow a three-phase structure that naturally builds rigor and supports deeper learning:

1. Readiness Phase
   Low-floor, high-ceiling problems connect to real-life situations and activate prior knowledge. Students get curious and start thinking.
2. Engagement Phase
   Students explore concepts through guided inquiry, questions, and collaboration. Teachers scaffold thinking and push for reasoning, not just answers.
3. Mastery Phase
   Students practice fluency and reflect on what they’ve learned. Here, they gain confidence and tackle more complex problems independently.

This intentional progression ensures that students aren’t just memorizing steps, they’re truly understanding the why behind the math. Each phase builds on the last, helping students make connections, persevere through challenges, and grow their problem-solving skills. By the time they reach mastery, students are equipped to apply what they’ve learned in new and meaningful ways. It’s a structure that turns curiosity into comprehension and comprehension into confidence.

Rigor Is a Culture, Not a Checklist

Ultimately, rigor is not a one-off activity. It’s a daily culture in the classroom and one that’s attainable for all educators. Kaminski successfully built this culture in her own classroom and shared what that looks like: “my students know that we're always going to be diving deeper. We're never done. If you're done, that's just an opportunity to look for more connections and for us to go further. And to me, that is truly a rigorous math classroom.” She also shared that it’s noisy––filled with conversation, questioning, and collaboration. While “noisy” may not sound ideal, she says it allows her to listen, assess, and adjust in real-time, creating a dynamic environment where learning never stagnates.

The Bottom Line: Rigor Is About Trust

Rigor doesn’t have to be intimidating. With a well-designed curriculum, a supportive classroom culture, and the right tools, it becomes a natural part of how students learn and grow. Overall, it’s about students trusting the process and ultimately, building trust in themselves. 

Looking to bring deeper math learning to your school? Explore how Primary Mathematics by Marshall Cavendish Education supports rigorous, effective math instruction for every student.

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