Variant Limits

By Triseum

Business Category

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Description: Category: Calculus, which is critical to STEM degrees, has one of the highest failure rates of any college course. In fact, the Mathematical Association of America estimates the failure rate for Calculus I is reaching 38 percent. Additionally, calculus was recently ranked number one on the top ten list of courses most disliked by students, as reported by College Stats. Variant: Limits is aimed at significantly reducing calculus failure rates while making the learning experience more enjoyable. It connects mathematics and game play,empowering students to take a more active role in the learning process and engage with and understand the content on a deeper level.The high-stakes adventure leverages effective forms of instruction, leading to achievement and retention of knowledge in Calculus I through immersive learning.

Skills and Ideas Taught:

Variant: Limits promotes conceptual understanding of:

• Finite Limits: Introduction to limits, one-sided limits, and limits of combined functions.

• Continuity: Limit definition of continuity at a point, continuity of combined functions, and the intermediate value theorem.

• Infinite Limits: Horizontal and vertical asymptotes.

The student learning objectives within Variant: Limits are:


• Given the graph of a function, the learner will be able to approximate the limit of the function as x approaches a given value.

• Given a function graphically the learner will be able to determine whether or not the function is continuous at a particular point of its domain.

• The learner will be able to identify when a function is continuous from the left and from the right at a particular point.


• The learner will be able to relate the graphical representation of a function to the graphical concept of limit.

• The learner will apply the rules and principles of limits to determine the limit of a function.


• The learner will be able to relate the notion of continuity to both the notion of limit and the value of a function at a point.

• The learner will use the properties of continuity and relate them to corresponding properties of limits.

• The learner will be able to apply the Intermediate Value Theorem in various different contexts.


• The learner will be able to determine function behaviors as x infinitely increases or decreases.

• The learner will be able to identify vertical asymptotes and oscillating behaviors of functions.

Through game play, the player explores and applies conceptual understanding of limits, by selecting limits, changing operators,manipulating functions, and applying concepts like the Intermediate Value Theorem to interact with the 3D environment. Students playing Variant: Limits are drawn into an interactive world of game play. The experience allows them to develop a conceptual understanding of calculus without reliance on definitions, terminology, formulas, and calculations via a heuristic, experiential learning environment.

Goal or Challenge: Variant: Limits introduces essential gameplay narrative that explains immediate objectives, with the option to discover supplemental backstory and lore to unlock additional information about the planet and technology. In Variant: Limits, the player takes on the role of Equa, who is the main character for the Variant series. Equa interacts with two additional characters: 1) the Preceptor, an artificial intelligence whose role is to guide Equa, and 2) Celare, a floating wisp that explains the planet.  The goal of the game is to save the planet that is threatened by powerful and unnatural geomagnetic storms. Equa must attune the Energy Limiters to reconnect bridges, power transport pads, get passed the security system, and access emergency energy nodes. If Equa can energize the node, the storms will stop.

Primary Audience: All calculus students in high school or college, not just those struggling or failing, serve as the primary end user and can benefit from game play. Students are engaged with an interface that allows them to develop a conceptual understanding of calculus via an experiential learning environment without reliance on terminology, formulas and calculations. Additionally, instructors and students were tightly integrated into Triseum’s design, development and testing process, ensuring that Variant: Limits meets their needs from a teaching and learning perspective.

Assessment Approach: Combating static learning experiences, Variant: Limits allows students to explore, develop new knowledge, and practice college-level calculus concepts visually in a 3D environment. Students don’t just memorize and regurgitate information, but rather apply it. Variant:Limits motivates learners and elicits a state of flow in a learning experience. Where typical homework platforms rely on repetitive “drills”or address lower level mathematical concepts, Variant: Limits presents complex experiential explorations. As students achieve learning objectives and advance to higher levels, they are inspired to keep going.A series of hooks and analytics are programmed into the game and are reported via the instructor portal.  These analytics capture data in time, attempts, puzzle actions, and competitions of puzzles and math instances.  Each puzzle is then mapped to the student learning objective and core competency presented within the game.  Coupled with the information in the portal, instructors can determine the level of competency each student has achieved.  In addition, a stealth assessment system has been programed by using the in-game hooks and analytics.  Ultimately, the stealth assessment system will be represented within the instructor portal.

Game Engine: Unity

Operating System: Windows 7, Windows 8, Windows 10, MAC OS 10 Sierra and higher

Platform: PC

Special Hardware: None