Naomi Church
National Mathematics Director
When we talk about helping students succeed in math, the conversation often centers on content: Can they solve equations? Explain their thinking? Choose the right strategy? These skills matter—but there’s one strand of mathematical proficiency that is just as essential, and too often overlooked: productive disposition.
Defined by the National Research Council (2001) as “the habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy,”productive disposition is about mindset. It’s not fixed or innate—it’s something we cultivate. The way we structure learning environments, provide feedback, and celebrate effort can profoundly impact how students see themselves as mathematical thinkers.
Why It Matters
Students who believe they cansucceed in math are more likely to persist through challenges, take intellectual risks, and engage more deeply with content. On the other hand, when a student internalizes the belief that they’re “just not a math person,” that mindset can become a self-fulfilling prophecy.
This strand of proficiency is deeply connected to the Engagement principle of Universal Design for Learning (UDL), which emphasizes the importance of motivation, persistence, and learner agency. Encouraging productive disposition means helping students see math as something they can do—and even enjoy.
Making It Real in the Classroom
Here are a few powerful strategies educators can use to nurture productive disposition in any math setting:
- Support risk-taking. As Dylan Wiliam notes in Educational Leadership (September 2012), “If students know the classroom is a safe place to make mistakes, they are more likely to use feedback for learning.” Many students experience math as black and white—all right or all wrong—with little space for exploration. Game-based learning environments like those in My Math Academy®help reframe math as a space for playful problem-solving, where errors are part of the learning process. These environments encourage persistence without penalty and support a culture of safe failure.
- Use just-in-time scaffolding. Coined by Dr. Juli Dixon of the University of Central Florida, this approach builds on Vygotsky’s Zone of Proximal Development and focuses on offering only the support a student needs, exactly when they need it. This method helps learners build confidence as they experience authentic success. You can see this in action by exploring the Shapey Parade game in My Math Academy. Try intentionally selecting incorrect answers to observe how just-in-time scaffolds gradually appear—gently guiding students back on track without removing the challenge or doing the thinking for them.
- Attend to precision. One of the biggest barriers to a productive disposition in math class is feeling like math doesn’t make sense; like the rules keep changing and students can’t get a handle on it. In their article 13 Rules That Expire, Karp, Bush, and Dougherty caution against teaching shortcuts or tricks that don’t hold up over time. These tricks or rules that expire are taught with the best of intentions and end up creating unintentional barriers to learning, mindset and disposition in the long run. Instead, build a classroom culture where language, notation, and representations are consistent and meaningful. In My Math Academy, precise language and conceptual understanding are carefully embedded, helping students connect ideas in ways that endure.
- Make math meaningful. Dan Meyer famously asked, “If math is the aspirin, then how do you create the headache?” In other words: How do we create authentic problems that math can help solve? When students see how math connects to their interests and everyday lives, it becomes relevant—and even exciting. In My Math Academy, students become helpful problem solvers in playful and purposeful contexts, developing not only understanding but also a sense that math matters.
When we invest in building productive disposition, we’re doing more than teaching math—we’re shaping how students see themselves as learners. We’re reinforcing that effort matters, that challenges can be overcome, and that success in math isn’t reserved for a select few. That belief? It’s transformative. And it starts with how we teach.
Productive disposition is just one of the five strands that make up mathematical proficiency. To see how all five strands work together to support meaningful math learning, check out this overview.
Read more from Naomi here.
This article was edited in collaboration with ChatGPT, an AI language model developed by OpenAI.
