Authentic Math Experiences

In September and October we took a little peek into Shelly Schaefer's first grade Bridges classroom. Wanting perspective from an advanced educator and mathematician, we invited Eric Stade to reflect on what he read about Shelly's classroom. Eric received a PhD in Mathematics at Columbia in 1988. He currently directs the Math for Elementary School Teachers' program at the University of Colorado at Boulder. In 2011, he became a President's Teaching Scholar, a lifetime designation representing the highest University honor for excellence in teaching and research. Here's what he has to say...


According to, the second-best job of 2011 is "mathematician." Shelly Schaefer gets this (although she might give top honors not to "software engineer," as the folks at did, but instead to "first grade math teacher"). By cultivating the inner mathematician in each of her students, she is affording them the opportunity to "get" it too.

Doing mathematics (in contrast to working math problems) entails creativity, curiosity, experimentation, and discovery (and attendant pitfalls: false starts, blind alleys, red herrings, etc.) All of these things (even the pitfalls) are neat, interesting things. Sadly, many students never get to see this; the drudgery of working too many math problems dissuades them before they've really had the chance to do mathematics.

On the other hand, you can't have worked that many math problems by the first grade. Shelly has deftly taken advantage of this fact.

In reflecting on an inspiring math moment, she speaks of engaging her first-grade students in the processes of conjecture and proof; of moving "to more of an inquiry-based approach;" of letting "the students do most of the talking, having students pose some of the questions, and allow them to struggle with disequilibrium as they try to figure out solutions on their own." She is encouraging her students to approach mathematics more in the way that research mathematicians (typically) do, and less in the way that elementary school students (typically) do. She is giving them access to "authentic" math experiences.

Which are, as the study indicates, empowering, satisfying, and awesome. Now mathematicians might tend to shy away from such terms--we're a circumspect bunch, as a rule. But we do like what we do; you can look it up.