Deep Mathematical Understanding through Problem-Based Core Math Programs

Before becoming a fourth grade teacher, I spent four years as a classroom assistant, which gave me a strong foundation in understanding how students learn. When I stepped into my own classroom and started using i-Ready Classroom Mathematics, a comprehensive, problem-based core math program, I cherry-picked certain lessons and strategies, heavily supplementing them with materials I thought better fit the standard. 

My lessons were structured around modeling and guided instruction—essentially an "I do, you do" format—where I demonstrated, and then students practiced. However, this framework left little room for student discussion, reasoning, or reflection. Students who didn’t initially understand concepts had little chance to learn from their mistakes. Instead, they simply corrected their answers and moved on.

The Limitations of Traditional Math Instruction Methods

Despite my efforts, my lessons lacked depth. I found myself constantly supplementing with additional materials to fill perceived gaps, feeling like the program itself wasn’t meeting my students’ needs. I spent more time searching for resources than analyzing the principles of effective math instruction. Instead of leveraging the program to its fullest potential, I was unknowingly working against it, creating extra work for myself and limiting my students’ opportunities for true mathematical thinking. They made progress despite this, but they didn’t reach the potential I knew they were capable of, and I had to ask myself why.

Building Deep Mathematical Understanding: What Was Missing?

It wasn’t until I stepped back and re-evaluated my approach that I realized the issue: I was trying to force my own methods instead of fully utilizing the program’s instructional design as it was intended. This shift in mindset—working with the program rather than against it—was the turning point in my teaching journey.

Core Math Program Analysis: The Foundation for Student Success

Through my study of Principles to Actions: Ensuring Mathematical Success for All, I gained a deeper understanding of what drives mathematical success. It isn’t just about having rigorous standards—it’s about enacting the right practices, policies, and instructional strategies to bring those standards to life in the classroom. I realized the importance of selecting and implementing a core program that instills deep mathematical understanding and real-world application rather than relying on students memorizing procedures. 

Essential Elements of Effective Mathematics Instruction

When evaluating a core math program, it’s crucial to ensure it supports these key areas:

• Conceptual Understanding. Does the program help students grasp the underlying principles of mathematics rather than just procedures?
• Procedural Fluency. Does it provide opportunities for students to develop efficient and accurate methods for solving problems?
• Strategic Competence. Are students encouraged to develop, represent, and solve mathematical problems in different ways?
• Adaptive Reasoning. Does it promote logical thought, reflection, explanation, and justification of mathematical ideas?
• Productive Disposition. Does it foster a positive attitude toward mathematics and a belief in the value and ability to engage with it?

By ensuring a program addresses these essential elements, educators can create an environment where students build lasting mathematical understanding, confidence, and success.

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How a Fully Implemented Problem-Based Math Program Transformed My Classroom

Once I realized i-Ready Classroom Mathematics already met all these guiding principles, I committed to implementing it as it was designed. I followed lesson structures, engaged students in discourse, emphasized problem solving and conceptual understanding, and soon saw a transformation!

Student Engagement through Mathematical Discourse

My students were not just learning math; they were thinking mathematically. Their ability to reason, justify their answers, and tackle complex problems improved significantly, and their assessment results reflected this growth. They became more engaged in problem solving and persevering through challenges rather than giving up at the first sign of difficulty. They learned to reason abstractly and quantitatively, making connections between numbers, symbols, and real-world applications. Classroom discussions flourished as students constructed viable arguments and critiqued one another’s reasoning, fostering a culture of collaboration and critical thinking. 

Through mathematical modeling, my students started to view math as a tool for understanding the world and applying their skills in meaningful ways. They became strategic in selecting appropriate tools, including manipulatives, diagrams, and digital resources, to enhance their understanding. 

Problem-Solving Skills Development in Elementary Math

Attending to precision became a natural part of their work, as they focused on accuracy, clear explanations, and mathematical language. As students looked for and used structure, they started recognizing patterns and relationships, using them to simplify complex problems. They also developed the ability to spot repeated reasoning, identifying general methods that could be applied across different problems.

This shift didn’t happen overnight, but by fully committing to the program’s structure and aligning it with the fundamental mathematical principles in Standards for Mathematical Practice, I witnessed my students grow into confident, capable mathematicians. They were no longer just memorizing procedures—they were thinking, reasoning, and understanding mathematics on a deeper level.

Developing Mathematical Problem-Solving Skills in Fourth Grade Students

As educators, our goal should be to move beyond covering standards and instead focus on building mathematical thinkers. By ensuring that our instructional approach promotes problem solving, reasoning, and meaningful discourse, we empower students to view mathematics as a powerful, interconnected discipline rather than a set of isolated skills.

Reflecting on my own journey, I now see how fully implementing a well-designed program transformed my classroom. My students became more confident, engaged, and capable mathematicians, and I became a more effective educator. When we commit to best practices in math instruction, we set our students on the path to long-term success.

Want more from Meghan? Check out her episode of the Extraordinary Educators™ Podcast.

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Ready to Transform Your Mathematics Instruction?

Explore these proven strategies for building deep mathematical understanding in your elementary classroom.

Learn more about the research behind effective mathematics instruction: Evidence for ESSA: i-Ready Classroom Mathematics

Build deeper mathematical understanding: A Deeper Approach to Math Practice Adds Up to Big Results

Core math program implementation guide: Four Must-Haves for Your Core Math Solution

Comprehensive approaches to elementary math instruction: Bringing Clarity to Math Instruction and Understanding

Evidence-based strategies for developing student problem-solving skills: Mathematical Problem-Solving Techniques

Practical guidance for meeting grade-level expectations: Common Core State Standards for Mathematics