Author Archives: Paul Reimer

Telling Stories

Our early math team has just finished up our work at several preschool sites for this school year and we’ve been reflecting on our experiences thus far. In conversations with teachers about what we’ve learned and how this experience has deepened our understanding of children’s mathematics, we’ve told lots of stories about particular children that are shaped by our own ways of describing and interpreting what we’ve seen. And we’ve remarked on several occasions how grateful we are for the partnerships we’ve experienced during the 2016-17 school year.

In my last blog post I wrote about several “journeying” practices that Paul Cobb and his colleagues developed and adhered to over decades of work in mathematics education. In a collection she helped to edit, A Journey in Mathematics Education Research: Insights from the Work of Paul Cobb, Anna Sfard writes an epilogue in which she shares these journeying practices. Sfard suggests that those of us who work in contexts where we are seeking to understand will benefit from considering how these practices might shape our work and reflection.

In this blog, I’ll share a few more of the journeying practices that seem especially relevant to the telling of stories shaped by our experiences.

While traveling, keep your eye on your tools as much as on what you are supposed to use them for. Improving the tools for exploring is part and parcel of your mission as an explorer.

While reporting on the results of your expedition, be multivocal. Avoid the pitfalls of monological discourse. Never talk as if you were the spokesperson of the world itself. In the insights you offer to others, seek to be of help rather than to be right.

Watch your stories. Remember that the narratives inspired by your travels, far from being merely shaped by phenomena they describe, have the power of shaping these phenomena in return.

Always bear in mind that it is your responsibility to be understood. The value of your travelogue depends not only on its being a collection of original insights, but also on its potential for becoming a solid basis on which others will be able to build through their own explorations. For this to happen, you have to make your discourse as clear and immune to misunderstandings as humanly possible.

These practices provide a significant challenge to all of us who seek to understand and tell stories about what we’ve seen and experienced. Central to this understanding, I’m discovering, are the ways we think about telling our narratives. As Sfard points out, “Trying to be understood by others may be the best way to understand oneself.”


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… Continue Reading

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