Author Archives: Paul Reimer

Traveling Practices

Our work as learners, educators, and researchers takes us into spaces where we encounter new ideas, people, and experiences. We may enter schools, classrooms, faculty lounges, community centers, or other places of learning where we hope to better understand the patterns of interaction among individuals we meet. While our attention may be on what we hope to learn, better understand, and influence, the way in which we go about this work is of equal importance.

I recently read several pieces from A Journey in Mathematics Education Research: Insights from the Work of Paul Cobb. In this collection, Anna Sfard writes an epilogue that describes the evolution of work and practice of mathematics education researcher Paul Cobb. Knowing that Cobb is an avid traveler, Sfard uses a traveling metaphor to share “journeying” practices that Cobb and his colleagues developed and adhered to over decades of work in mathematics education.

In this blog, I’ll share the first four dos and don’ts of Paul’s practice.

Don’t embark on a new expedition without consulting those who were there before you. Whatever new discovery you subsequently make, it has to be clearly related to what was known before you began.

Don’t travel alone. Traveling together is not only safer, but also richer in opportunities. A good team is much more than the sum of its parts.

While visiting foreign places remember that the otherness of its inhabitants is your problem, not theirs. If you cannot understand what they are saying, the odds are that it is not because they make no sense but because you insist on speaking your language, which is obviously not the one they use.

Reciprocate to those whom you meet on your way. Don’t just be a visitor. Try to make the location you explore a better place to live. Your commitment to the locals is not any lesser, perhaps even greater, than is your obligation toward your own community, which is waiting to hear your story.

There is much to consider in these practices, whether you’re a teacher, a mathematics coach, or a mathematics education researcher. As our early math team at the AIMS Center continues our work in early learning classrooms, I am more keenly aware of the impact our presence has and have begun to explore Paul’s traveling practices with my early learning colleagues. It is clear that our hopes and goals for our work both shape and are shaped by the ways in which we go about our work. Traveling together, seeking to understand, and committing to reciprocation are practices that can help to ensure rewarding journeys, whether we are the visitors or those who welcome visitors into our midst.


Oh, the Possibilities

Our early math team continues to explore what might be possible for young children in the context of number development and play. We recently designed a linear board game called “Frog Splash” to help preschoolers begin to count the hops of a frog as it nears a swimming hole. After trying this game with children,… Continue Reading

Play Can Be Hard Fun

In a previous blog post, I asked several questions related to the work of our early childhood mathematics team: What teacher knowledge is needed in order to enhance adult-child interactions and help children learn the most in play contexts? What experiences can support preschool teachers in deepening their knowledge of children’s mathematical thinking and the… Continue Reading

Making the Most of Mathematical Play

If you have been following our early math team’s work with three- and four-year-olds, you’ll know that we’re exploring the ways children develop knowledge and understanding in the context of mathematical play. We’re not interested in “social knowledge”, or the kind of knowledge that requires transmission from one person to another. Rather, we’re engaged in… Continue Reading

Playful Learning

The AIMS Center Research Division’s early math team is currently interviewing and videotaping 3 and 4 year olds in order to illustrate the developmental stages in learning to count that researchers have identified. We are specifically interested in collecting video clips that illustrate a child’s path in moving from one stage to the next. We… Continue Reading


My work with the AIMS team began last month after 20 years in public education, first as an elementary teacher and later as a mathematics coach. I have spent a lot of hours in TK-12 classrooms, walking alongside teachers as they explored ways to make their classrooms places where authentic mathematics learning could happen. In… Continue Reading