Our Philosophy

Developing how students think, reason, and solve problems.

MathStudium is built around the idea of studying mathematics more deeply—to explore ideas, work through challenging problems, and develop a lasting appreciation for mathematical thinking.

The MathStudium problem-solving model

Understand, Explore, Solve, Reason.

The model is iterative. Problem solving does not always proceed in a straight line.

A student may discover through checking or explaining a solution that an assumption needs to be reconsidered, another representation tried, or a different approach pursued.

UnderstandIdentify what the problem asks, what information is available, and what must be determined.
ExploreLook for patterns, relationships, representations, and possible approaches. Make connections and test ideas.
SolveDevelop and carry out an approach. Monitor the work and adapt when necessary.
ReasonCheck whether the solution makes sense and explain why it works.

We use this framework for developing thoughtful, independent problem solvers.

What students practice

A solution is more than an answer.

Working through unfamiliar problems asks students to do more than recall a procedure.

Read carefullyDetermine what information is relevant.
Recognize relationshipsMake connections and identify useful structure.
Develop and test ideasExplore possible approaches and revise when necessary.
Check whether it makes senseEvaluate whether the reasoning and result hold up.
Consider multiple approachesCompare representations, strategies, and solution paths.
Show your thinkingCommunicate what you did, why you did it, and why it works.
Challenge & competition

Challenge gives learning somewhere to go.

Students need opportunities to work beyond what is immediately comfortable. A meaningful challenge asks students to make decisions rather than simply follow instructions. It gives them room to try an approach, discover that it does not work, reconsider the problem, and try again.

Competitions provide a particularly clear setting for this kind of mathematical thinking. Recognition and achievement are meaningful, but they are not the measure of everything a student gains from the experience.

We define success more broadly than a score or a medal. A student who learns to stay with an unfamiliar problem, find a new approach, explain an idea clearly, or recognize an error they would previously have missed is making meaningful progress.