# Can Tactical Decision Games Accelerate Mathematical Expertise? Exploring how mental representations and sensemaking transform the way we learn complex mathematics. - **Source:** [Commoncog](https://commoncog.com) - **Published:** 2026-11-09 - **Topic:** [careers](https://brifing.si/c/careers) - **Original article:** - **On Brifing:** https://brifing.si/s/de87cf93-71b4-4b7b-bb33-20ebd81b2c83 ## Workshop Deadline Extended The application deadline for the ShadowBox Tactical Decision Game Design Workshop has been extended to November 13, 2026. Only five seats remain for this exclusive training session led by John Schmitt. The extension provides a final opportunity for interested participants to join the cohort and learn advanced decision-making frameworks. ## Sensemaking as Expertise Sensemaking is defined as the core mechanism of expertise, where novices learn to perceive situations like experts. By applying the Data-Frame Theory, individuals can organize information through cognitive frames. This process involves using mental constructs like schemata and scripts to interpret external reality, which is essential for mastering complex subjects. ## The Role of Schemata Cognitive frames act as internal images of external reality, guiding attention and memory retrieval. According to researchers like Piaget and Neisser, these mental representations become more differentiated through experience. In mathematics, these structures allow experts to organize information efficiently, providing a common representational format for solving various types of problems. ## Visualizing Mathematical Problems Expert mathematicians do not primarily rely on symbols when solving equations. Instead, they construct internal mental objects that allow for intuitive solutions. For example, visualizing a line intersecting a circle makes the answer immediate. This ability to translate between abstract equations and mental images is a hallmark of high-level mathematical proficiency. ## The Power of Daydreaming David Bessis argues that professional mathematicians spend significant time daydreaming to create new mental objects. This practice enables them to solve entire classes of problems through intuition rather than brute computation. By building these representations early, mathematicians create a foundation that makes increasingly complex concepts easier to grasp and master. ## Limitations of Grinding Many students struggle because they rely solely on grinding through problem sets, which focuses on computation. While this strategy may yield temporary success, it eventually hits a wall when problems become too complex. True mastery requires constructing the right mental representations, a method often overlooked in traditional school curricula and teaching. ## The Compounding Effect Mental representations act as building blocks for higher-level mathematical concepts. As students create more objects in their minds, their ability to invent new ones improves, leading to a compounding effect in learning. This explains why children of mathematicians often excel; they are taught to focus on mental objects rather than just exercises. ## Nurturing Mathematical Intuition Bessis encourages parents to help children describe their dreams and internal visualizations from a young age. This practice builds the necessary groundwork for describing unique mental images. By fostering this skill, educators and parents can help students develop the internal representations required to navigate advanced mathematics with greater ease and clarity. ## The French Mathematical Success France produces nearly 20% of all Fields Medallists despite having less than 1% of the global population. This success is attributed to rigorous programs that emphasize these specific cognitive methods. Many top mathematicians confirm that this approach to building mental representations is the secret behind their professional success and expertise. ## Redefining Mastery Learning Traditional mastery learning often focuses on completing problem sets from easy to hard. However, this approach misses the critical step of constructing the mental frames that make computation trivial. If a student relies only on intelligence to grind through exercises, they fail to develop the deep intuition required for higher-level innovation. ## Bridging Theory and Practice The Data-Frame Theory provides a concrete mechanism for improving sensemaking in any domain, including mathematics. By understanding how experts organize their thoughts, educators can design better training interventions. Tactical Decision Games serve as a practical tool to accelerate this process by forcing participants to construct and test their mental frames. ## Accelerating Future Expertise Transitioning from computational grinding to representation-building is essential for long-term mathematical growth. By adopting these cognitive strategies, students can scale their abilities far beyond traditional expectations. This shift in perspective not only improves academic performance but also equips learners with the tools to tackle complex, novel problems throughout their lives. ## Sources covering this story - https://commoncog.com/can-tactical-decision-games-accelerate-maths/ — --- _Summary written by Brifing from the original reporting. Copyright in the original article belongs to its publisher; read the full piece at the link above._