Math = Mathematical thinking

At SF Math Circle, we view math as much more than numbers or arithmetic. Math is a way of thinking about the world.

Mathematical thinking is the kind of thinking you do when you're trying to figure things out — whether you’re trying to understand and predict the movements of the stars, evaluate medical treatments, assess the fairness of electoral procedures, or even just schedule your errands.

Mathematical thinking is embodied and social: We think better and understand more when we think with our whole bodies and when we connect our thinking with others’.

At SF Math Circle, our goal is to promote and develop mathematical thinking.

Awareness, Enjoyment, Empowerment

We focus on three areas in particular — awareness, enjoyment, and empowerment:

  • We help students to gain an awareness of what mathematical thinking is and to associate math with mathematical thinking.

  • We help students to see mathematical thinking as something that they enjoy doing.

  • We help to empower students to use mathematical thinking effectively in their lives.

What does mathematical thinking look like?

When we are seriously invested in trying to figure things out and sharing what we’ve found, we find that it’s very useful (and even natural!) to engage in certain mathematical habits of mind, including:

  • Making observations

  • Looking for patterns

  • Finding similarities and differences

  • Wondering

  • Making and testing predictions

  • Finding and using strategies

  • Understanding and explaining

Creating contexts for mathematical thinking

We view mathematical thinking as more fundamental than any content. As a result, our primary aim is to create contexts in which students will have the opportunity to engage in and develop their mathematical thinking, rather than to introduce students to specific concepts, procedures, or results.


We believe that everyone can engage in and enjoy mathematical thinking. Our commitment to accessibility has 4 major parts:

  • We design activities around engaging, hands-on puzzles and games with the goal of making them intrinsically compelling for students.

  • Our activities have low floors and high ceilings — they have easy-to-understand instructions and don’t require extensive background knowledge to get started, but they are rich enough to support and encourage deep exploration.

  • We have students explore in small groups where they have the opportunity to collaborate with their peers and to receive personalized attention and support from instructors.

  • We encourage students to adopt a growth mindset in Math Circle (and beyond!).