My son is neurodiverse, and for years, comprehension, both in reading and mathematics, was his greatest challenge. I’ll never forget teaching him to write and saying, “Put your eyes on the paper.” Without hesitation, he literally placed his head on the desk, eyes down. That moment captured just how differently he processes the world and how much more intentional our teaching must be to reach every learner.
Even so, he could read words by the time he was three. Phonological awareness and decoding came quickly. But understanding grasping meaning, nuance, and intent was a different journey altogether. Mathematics has mirrored this path. He’s always been fluent with math facts and computations, but applying strategies, solving problems, and making sense of new contexts took far longer.
This year, as a seventh grader, he passed all of his state assessments in both reading and mathematics for the first time. For him, success was never a question of if, but of when. And that’s how we should frame learning for every student. The timeline may vary, but all students are capable of reaching deep comprehension when we provide the right structures, strategies, and support.
Over the years, I’ve noticed striking parallels between reading and math instruction strategies that support comprehension across both disciplines. Whether you’re a reading teacher, a math teacher, or teach both, these shared approaches can be powerful in meeting the needs of diverse learners like my son.
1. Visualization: Seeing Meaning Before Understanding It
In literacy, visuals play a foundational role in comprehension. The word “dog” is just an abstract set of letters until a child connects it to an image and eventually builds that image internally. According to the Science of Reading, dual coding theory (Paivio, 1986) highlights that information is better understood and remembered when presented both verbally and visually. Beck, McKeown, & Kucan (2013) emphasize the importance of connecting vocabulary to familiar contexts and imagery to foster deeper understanding. Visuals also reduce cognitive load by shifting some processing to the visual cortex (Mayer, 2005).
Mathematics is no different. NCTM’s Principles to Actions (2014) calls for instruction that “uses and connects multiple representations including words, symbols, diagrams, tables, graphs, and physical models to deepen students’ understanding” (p. 29). Tools like number lines, tape diagrams, and area models bridge the gap between concrete and abstract reasoning, particularly for multilingual learners and neurodiverse students.
For my son, visualization has always been key. It cuts through figurative language and abstract phrasing that can feel overwhelming. When math and reading are anchored to something he can see and manipulate, his understanding deepens and his confidence grows.
Why it matters:
Visuals support both comprehension and retention through dual coding.
They reduce barriers by offloading linguistic or working memory demands.
They shift instruction from rote recall to meaningful understanding.
Visuals aren’t extras, they’re the architecture for comprehension.
2. Prior Knowledge: The Soil for New Learning
Cognitive science tells us that comprehension isn't just about skill, it’s about schema. E.D. Hirsch (2003) famously showed that background knowledge plays a greater role in understanding text than decoding ability. Students who know baseball understand a baseball story more fully, regardless of reading level.
The same is true in mathematics. NCTM emphasizes that effective teaching "builds on students’ existing knowledge, skills, and experiences" (NCTM, 2014, p. 10). When students can connect a new idea to something they’ve seen before—like extending area models from multiplication to binomial expansion—their understanding sticks.
For my son, prior knowledge is the gateway. His memory is remarkable, he can recall dates, times, and details of lived experiences with astonishing precision. Tapping into that reservoir through familiar models and scenarios gives him a cognitive launching pad for new learning.
Examples:
Revisiting number lines when exploring slope in algebra.
Using tape diagrams to transition from whole number operations to ratios and rates.
Activating lived experiences (e.g., shopping or sports) to ground abstract problems.
Knowledge isn’t built in isolation, it’s layered. When we teach with continuity and coherence, we help students weave a web of understanding.
3. Grammar and Procedure: Necessary but Not Sufficient
Grammar is essential in reading. It provides the structure that helps students navigate meaning distinguishing between “Let’s eat grandma” and “Let’s eat, grandma.” But grammar alone doesn’t ensure comprehension. Students still need vocabulary, context, and an understanding of the author’s intent to make sense of what they read.
Mathematics mirrors this balance. Procedural fluency, accuracy with facts and algorithms, is one of the five strands of mathematical proficiency (NRC, Adding It Up, 2001). Yet when fluency dominates instruction, students often miss the bigger picture: why the math works and how to apply it in new contexts.
The goal isn’t to downplay fluency, but to situate it within a broader landscape that includes conceptual understanding, reasoning, problem-solving, and productive struggle.
For my son, fluency comes easily. He’s always had an uncanny memory, able to recall the score, MVP, and date of every Super Bowl ever played, or list the make and model of nearly every car on the road. Math facts were no different. His recall was remarkable, much like memorizing spelling words or vocabulary definitions. But just as grammar alone doesn’t guarantee reading comprehension, procedures without understanding can feel hollow.
4. Embracing Revision as a Path to Mathematical Comprehension
In English class, revision is expected. Students revisit drafts, refine ideas, and clarify meaning, not because the first attempt was a failure, but because iteration leads to insight (I revised this post many times). Graham & Perin (2007) found that revising writing improves coherence, organization, and overall comprehension.
So why don’t we treat math the same way?
Too often, an incorrect answer in math is seen as the end of the road. But what if we reframed it as the beginning of something deeper?
Math classrooms can foster comprehension by encouraging students to revise their thinking:
Compare strategies with peers to see new perspectives
Revisit errors to trace where reasoning diverged
Strengthen solutions by adding representations or justifications
Revision in math isn’t just about fixing mistakes, it’s about developing perseverance and treating missteps as opportunities to understand more deeply.
For my son, revision has always been a struggle. He tends to see the world in black and white, so analyzing why something is wrong doesn’t come naturally. But that’s exactly where his productive struggle intensifies, where he begins to flex new ways of thinking and build true comprehension. NCTM’s Principles to Actions (2014), which emphasizes that effective teaching "uses student errors as opportunities for learning" and encourages teachers to create an environment where students examine and revise their mathematical thinking. In this way, revision is not remediation, it’s reasoning.
5. Creating Space for Interpretation and Creativity
In language arts, students craft poems, stories, and personal essays—valuing the process as much as the final product. Mathematics should offer parallel opportunities:
Multiple solution paths to a rich task.
Chances to pose new questions, not just answer existing ones.
Time to represent ideas creatively through models, graphs, stories, or even code.
Creative mathematics, like creative writing, fuels engagement and helps students see themselves as sense-makers, not just answer-getters. For my son, this can be a challenge, he needs tools and structures to spark creativity, and that’s okay. Open-ended prompts can feel both freeing and overwhelming: Write a story about whatever you want. Solve this however you choose. That openness can be intimidating, yet it’s often in these moments, when the path isn’t prescribed, that the most powerful breakthroughs happen. In both reading and math, it’s where we encounter the unexpected.
Conclusion: Comprehension Is More Than Correct Answers
Comprehending mathematics isn’t about speed or memorization. It’s about building meaning through visualization, connection, fluency, revision, and creativity.
My son’s journey reminds me that learning is not linear, and it’s certainly not standardized. His growth didn’t come from a single breakthrough but from layered supports over time. He needed space to see math, hear it, feel it, and make sense of it in his own way.
We owe that same opportunity to every student.
So let’s redefine comprehension:
Not when students get the right answer, but when they understand the idea behind it.
Not if they’ll get there, but when, on their own timeline, with the right tools.
Not what they know, but how they make meaning.
Because ultimately, comprehension, like learning itself, is deeply human. And it can’t be rushed, packaged, or automated. It has to be built, one connection at a time.
Further Reading & Resources
Beck, I. L., McKeown, M. G., & Kucan, L. (2013). Bringing Words to Life: Robust Vocabulary Instruction. Practical strategies for making vocabulary meaningful through visuals and context.
Graham, S., & Perin, D. (2007). Writing Next. Research on how revision improves writing—and why iteration matters.
Hirsch, E. D., Jr. (2003). “Reading Comprehension Requires Knowledge—of Words and the World.” American Educator. Classic article on the role of background knowledge in understanding.
Mayer, R. E. (2005). The Cambridge Handbook of Multimedia Learning. How visuals and words work together to deepen comprehension.
National Council of Teachers of Mathematics (2014). Principles to Actions. Guidance on connecting multiple representations, using errors as learning opportunities, and fostering reasoning.
National Research Council (2001). Adding It Up. Describes the five strands of mathematical proficiency, including procedural fluency and conceptual understanding.
Paivio, A. (1986). Mental Representations: A Dual Coding Approach. Explains why combining verbal and visual information improves learning.