Rigor and Play: A Recipe for Early Math Learning, Confidence, and Enjoyment

By Debbie Leslie, Director of Curriculum Development at UChicago STEM Education and Everyday Math Author

Published in

Inspired Ideas

8 min readNov 22, 2023

“Rigor” is a word we hear and use a lot in education, but do we have a shared understanding of what it looks like or means, especially in early childhood? What is a math activity or task that you would consider “rigorous” for young learners? What makes it rigorous? Do you think your task matches an activity that a parent would consider rigorous? How about an administrator?

We often use “rigor” to mean challenging or difficult — something that stretches students beyond their comfort zones and what they already know and can do — but things can be challenging in different ways. For example, if you are 5 years old…

A math worksheet may be difficult because your fine motor skills aren’t yet developed enough to comfortably circle the correct responses, even if you know what those responses are; or
A group discussion of solution strategies to a math problem may be challenging because it is hard for you to sit still, not because you aren’t interested in, can’t explain, or don’t understand the strategies.

Why rigor matters in early math

But why should we care about rigorous early math experiences at all? Can’t these wait until children are older? We believe that the answer is a resounding “no.” There is compelling research evidence establishing the importance of early math experiences for later success in math and literacy (e.g., Duncan et al., 2007; Claessens and Duncan, 2009). However, a recent high-profile study of PreK programs in Tennessee raised questions about what these learning experiences should look like (Durkin et al., 2022), and at least one of the authors of this study has raised concerns about the ways in which many preschools have enacted academic content.

Against this backdrop and concerning rhetoric that often seems to pit academics vs. play for young children, it is important to keep in mind that early math learning experiences can and should be cognitively rich and rigorous, but they should also be playful and appropriate for ALL aspects of young learners’ development (Bassok et al., 2014; Hirsh-Pasek et al., 2020; NAEYC/NCTM, 2010; Weissberg et al., 2016).

What rigorous early math looks like

As early childhood math curriculum developers, we love to develop math activities that are in this “sweet spot” of rigor and play and that support the development of the whole child and nurture young children’s enjoyment of math.

As we strive to provide rigorous mathematics experiences for young children, we focus on ways that an activity, question, or task challenges children’s mathematical THINKING, not their abilities to write, sit still, or some other skill that comes with a bit more development and maturation.

We aim to develop tasks that young children can (and want to!) engage with cognitively, even if some of those other important skills are still very much developing.

For example, compare the “Making 10” worksheet on the left with the Hiding Bears activity on the right, which comes from Kindergarten Everyday Mathematics.

Both activities address the concept of complements of 10, which is the focus of a kindergarten math standard in the Common Core (K.OA.4) and many other state standards. But the activities are different in important ways. To explore these differences, ask yourself:

Which activity offers more opportunities for mathematical thinking and problem-solving? Why?
Which activity is likely to elicit more mathematical language and discourse? In what ways?
Which activity would be easier to scaffold or stretch for different learners?
Which activity is likely to be more interesting and engaging for children, and why?
What aspect or aspects of each activity might make it challenging for children, and in what ways?

The Hiding Bears activity engages children in mathematical thinking and problem-solving as they develop and use strategies to figure out how many bears are hiding and discern their own patterns in the responses. In contrast, the Making 10 worksheet enables them to simply rely on the pattern established by the problem sequence. Due to the game format of Hiding Bears, children also are more likely to engage in mathematical conversation and to enjoy and sustain their attention to the task for longer periods of time. The optional recording features of the game that can be layered on as children are ready — starting with the 2-column table and progressing to recording turns with equations — also make the activity appropriately rigorous for a wide range of kindergarten children.

Ask yourself the same questions for the following pairs of tasks:

In each of these comparisons, the activities on the right provide richer opportunities for mathematical thinking, conversation, engagement, and differentiation than the activities on the left. And, although people rarely associate play with rigor, the playful, open-ended nature of the Kindergarten Everyday Mathematics activities on the right actually contributes to their mathematical rigor. Specifically:

The triangle collage activity and discussion allow children to find and talk about a wide variety of triangles, rather than just equilateral triangles sitting on their bases.
The backpack comparisons, which children do with their own backpacks in the Everyday Mathematics lesson, prompt children to consider various ways that objects can be “big” and explore ways of investigating these dimensions, whereas the worksheet focuses on vague, and possibly confusing, visual comparisons.

Across each of these comparisons, the worksheet format of the activity on the left, which may seem more rigorous at first glance because of the paper-and-pencil format, actually limits the opportunities for mathematical rigor in that activity.

This is because the opportunities for mathematical thinking are constrained by the number or arrangement of problems on the page, or because the challenge stems more from the direction-following or fine-motor skills than it does from the math skills required to complete the task.

Young children’s paper-and-pencil skills generally lag behind their thinking skills, so worksheets often are not the best way for them to explore new ideas deeply or to show what they know and understand.

How to create playful and productive mathematical rigor for young children

The comparisons above highlight examples of how active, interactive, and playful activities can provide rigorous and enjoyable math learning experiences for young children such as those advocated for in the joint NAEYC/NCTM position paper on early mathematics (NAEYC/NCTM, 2010) and by numerous early childhood experts (e.g., Bassok et al., 2014; Hirsh-Pasek et al., 2020; Weissberg et al., 2016). Based on this research and these recommendations, below are some questions we ask ourselves in our curriculum development work that may also be helpful for you as you think about engaging children in age-appropriate, fun, AND rigorous math learning experiences:

What important math ideas or skills do I want this activity to address?
How can the activity allow for playful, open-ended exploration?
How can it promote thinking and talking about math?
How can it help children see math as interesting and connected to their lives and other things they are learning about?
How can it build children’s enjoyment and confidence as doers and learners of math?

We hope the examples in this piece, as well as the questions above, will help you think about how to make early mathematics rigorous in ways that will build children’s love of math and their confidence as math learners, rather than erode their math inclinations at an early age because their math experiences were hard in all the wrong ways.

For more on Everyday Mathematics, click here.

Debbie Leslie taught Pre-Kindergarten, Kindergarten, and First Grade for 10 years in Connecticut and in the Chicago area. She is currently Director of Curriculum Development and Director of Education Outreach and Early Childhood Initiatives at UChicago STEM Education at the University of Chicago. Leslie has been the early childhood author team leader for Everyday Mathematics since 2004. She also works on several other projects that draw on her STEM background and her interest in high-quality curriculum development and professional learning, especially in the areas of math, science, and early childhood education. She holds a Bachelor’s Degree in Molecular Biochemistry and Biophysics from Yale University and a Master’s Degree in Teaching from the University of Chicago and is a doctoral candidate in Educational Policy Studies at the University of Illinois at Chicago.

References

Bassok, D., Claessens, A., & Engel, M. (2014, June 14). The Case for the New Kindergarten: Both Playful and Academic. Education Week, 3.

Claessens, A., Duncan, G., & Engel, M. (2009a). Kindergarten skills and fifth-grade achievement: Evidence from the ECLS-K. Economics of Education Review, 28(4), 415–427. https://doi.org/10.1016/j.econedurev.2008.09.003

Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., Pagani, L. S., Feinstein, L., Engel, M., Brooks-Gunn, J., Sexton, H., Duckworth, K., & Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428–1446. https://doi.org/10.1037/0012-1649.43.6.1428

Durkin, K., Lipsey, M. W., Farran, D. C., & Wiesen, S. E. (2022). Effects of a statewide pre-kindergarten program on children’s achievement and behavior through sixth grade. Developmental Psychology, 58, 470–484. https://doi.org/10.1037/dev0001301

Hirsh-Pasek, K., Blinkoff, E., Golinkoff, R., & Hadani, H. (2020). A new path to education reform: Playful learning promotes 21st-century skills in schools and beyond. Brookings. https://www.brookings.edu/wp-content/uploads/2020/10/Big-Ideas_Hirsh-Pasek_PlayfulLearning.pdf

National Association for the Education of Young Children, & National Council of Teachers of Mathematics. (2010). Early Childhood Mathematics: Promoting Good Beginnings. National Association for the Education of Young Children.

Weisberg, D. S., Hirsh-Pasek, K., Golinkoff, R. M., Kittredge, A. K., & Klahr, D. (2016). Guided Play: Principles and Practices. Current Directions in Psychological Science, 25(3), 177–182. https://doi.org/10.1177/0963721416645512