Exploring The Roles Of Pattern And Spatial Skills In Early Mathematics Development

Training Studies.

Study 2 (2018-2019)

Zippert, E., Douglas, A., Tian, F., & Rittle-Johnson, B. (2021). Helping preschoolers learn math: The impact of emphasizing the patterns in objects and numbers. Journal of Educational Psychology. https://doi.org/10.1037/edu0000656


Preschoolers’ repeating patterning knowledge is predictive of their concurrent and later math and numeracy knowledge, but strong experimental evidence is needed to determine if these relations are causal. The purpose of the current study was toexamine the causal effects of repeating patterning and numeracy tutoring on repeating patterning, numeracy, and general mathematics knowledge in the year prior to kindergarten(i.e.,preK). Children in preK (N = 211) were randomly assigned to receive 5 sessions of researcher-delivered tutoring (a) on repeating patterns and numeracy or (b) on numeracy (and literacy as an active control), or received no tutoring and business as usual classroom instruction (control). Children who received tutoring in repeating patterning and numeracy improved in their repeating patterning knowledge the most. However, children’s general math and numeracy knowledge improved similarly across conditions, and a specific aspect of numeracy emphasized during the tutoring did not improve. Children’s repeating patterning knowledge is malleable, but this initial attempt to demonstrate causal links between repeating patterning and math knowledge was not successful. Results parallel mixed success in research training other skills, such as working memory or spatial skills, for improving mathematics knowledge. Findings are discussed in terms of the relations between patterning, numeracy, and general math knowledge in preschooler


At the completion of the study, a letter was sent home with parents and teachers to provide a summary of our findings. Letter found here.

Assessment Studies

Frame Study: Visual support as a tool to understanding repeating patterns (2021)

Click here to view a poster presented at the Cognitive Developmental Society 2021 conference on the results of our study.


Perceptual information cues learners to attend to specific relevant features in problems, but past research has focused on school-age children. The current study examined whether adding visual support helped preschoolers understand repeating patterns, an important aspect of  math development. Participants were randomly assigned to receive patterns with or without a box frame around the part that repeats to draw attention to the pattern unit (see attached figure).  Children (n = 64; mean age = 4.3) were assessed via one synchronous Zoom session. Participants received baseline (n = 3), training (n = 10), and posttest (n = 6)  trials. Performance did not differ by condition at baseline. The added frame did not improve performance for training trials (M = .56 vs .55 for frame vs. control, respectively) or posttest trials (M = .44 vs .47 for frame vs. control, respectively) or impact the types of errors children made. These null results suggest that young learners might need alternative visual support. For example, past research on visual support for mathematics problems has supported existing visual aspects of a problem (e.g. changing the color), instead of adding extra visual information, which in this case may have been too visually complex or confusing.

Data files, protocol, and the assessment can also be found on the project's Open Science Framework page.

Study 1d: Developing a new Early Patterning Assessment, with repeating and growing patterns (2019-2020)

Rittle-Johnson, B., Douglas, A., Zippert, E., Özel, S. & Tang, J. (2020) Early Patterning Assessment. Available from B. Rittle-Johnson, Vanderbilt University, Nashville, TN 37203. Study1dAssessment_Fall2020.pdf

Click here for a short demo of the assessment.

Conference Presentations:

Click here to view a poster presented at the Society for Research in Child Development's 2021 conference on kindergarteners' understanding of different types of patterns.

Click here to view a poster presented at the Society for Research on Educational Effectiveness' 2021 conference on how our Early Patterning Assessment was developed and used to measure preschoolers' and kindergarteners' understanding of different types of patterns.


The Early Patterning Assessment (EPA) is a research instrument including a repeating pattern knowledge subscale (EPA-Repeating) and a growing pattern knowledge subscale (EPA-Growing). The EPA-repeating is a reliable measure used in-person (Fall 2019, Spring and Summer 2022) or online (Fall 2020) with 4-6 year olds.  However, the EPA-growing has only been shown to be reliable when given in-person (Fall 2019) with 5-6 year olds enrolled in Kindergarten. Please note, it has not been tested or normed to be a standardized measure. The majority of children who have been involved in our studies have been White, middle- to upper-middle-class. However, our latest round of data collection (Summer 2022) included a more divserse sample of children, as well as economically-disadvantaged children, and our findings were comparable to our samples of White, middle- to upper-middle-class children. We ask anyone who uses our measure to share their de-identified item-level data with us so we can integrate data sets across labs to validate the measure better.

A summary of the results of the study can be found here. Additionally, at the completion of the Fall 2019 and Fall 2020 data collections a letter was sent home to parents to provide a summary of our findings. Letters found here and here.

Data files and versions of the assessment can also be found on the projects Open Science Framework page.

Part 1: Textbook Analysis

We examined content coverage in popular math textbooks to get a sense of the impact that implementation of the Common Core may have had on the inclusion of patterning and to inform the design of our new Early Patterning Assessment, including growing patterns. See description of textbook analyses and results here.

Part 2: Pilot 1 with Kindergarten students, in-person, Fall 2019

See PDF of original assessment here.

Part 3: Pilot 2 with Pre-K and Kindergarten students, online, Fall 2020

See PDF of revised assessment here. Online version of assessment available upon request.

Click here for an overview of how to create a version of the online assessment for yourself.  This will allow you to collect data using the online assessment.

Part 4: Pilot 3 with Kindergarten students, in-person, Spring and Summer 2022

See PDF of repeating patterning assessment used here.  

Click here to see a short report of our findings from this round of data collection. Includes information about the patterning assessment and relations between children's repeating patterning, numeracy, and spontaneous focusing on patterns knowledge.

Study 1c (Kindergarten Follow Up) (2018)

Zippert, E., Douglas, A.-A., & Rittle-Johnson, B. (2020). Finding patterns in objects and numbers: Repeating patterning in pre-K predicts kindergarten mathematics knowledge. Journal of Experimental Child Psychology. doi: 10.1016/j.jecp.2020.103965

*Funded by Heising-Simons Grant


The goal of this study was to evaluate how well children’s pattern and spatial skills in preschool predict their mathematics knowledge after entering formal schooling (near the end of Kindergarten).  It builds on the data and findings from Study 1a.


At the completion of the study, a letter was sent home with parents and teachers to provide a summary of our findings. Letter found here.

Study 1b (2017)

Zippert, E., Clayback, K. & Rittle-Johnson, B.  (2019). Not Just IQ: Patterning Predicts Preschoolers’ Math Knowledge Beyond Fluid Reasoning.  Journal of Cognition & Development. doi: 10.1080/15248372.2019.1658587


Early math skills are critical for later academic achievement; thus, we must identify skills that support young children’s math development. This study explored how repeating patterning skills contribute to mathematics development in preschool. Correlations showed that patterning skills were significantly related to math skills (i.e. magnitude comparison, verbal arithmetic) after controlling for general cognitive skills including general and spatial intelligence. These findings suggest that patterning should be included in early math standards.


At the completion of the study, a letter was sent home with parents and teachers to provide a summary of our findings. Letter found here

Study 1a (2016-2017)

Rittle-Johnson, B, Zippert, E. L., Boice, Katherine L.  (2018). The Roles of Patterning and Spatial Skills in Early Mathematics Development.  Early Childhood Research Quarterly.  DOI: 10.1016/j.ecresq.2018.03.006.


Because math knowledge begins to develop at a young age to varying degrees, it is important to identify foundational cognitive and academic skills that might contribute to its development.  The current study focused on two important, but often overlooked skills that recent evidence suggests are important contributors to early math development: patterning and spatial skills.  We assessed 73 preschool children’s repeating patterning skills, spatial skills, general cognitive skills and math knowledge at the beginning of the pre-kindergarten year. We re-assessed their math knowledge near the end of the school year.  Children’s patterning and spatial skills were related and were each unique predictors of children’s math knowledge at the same time point and seven months later. Further, patterning skills predicted later math knowledge even after controlling for prior math knowledge. Thus, although patterning and spatial skills are related, patterning skills are a unique predictor of math knowledge and growth. Both theories of early math development and early math standards should be expanded to incorporate a role for patterning and spatial skills.


At the completion of the study, a letter was sent home with parents and teachers to provide a summary of our findings. Letter found here.

Pilot Study (2015-2016)


At the completion of the study, a letter was sent home with parents and teachers to provide a summary of our findings. Letter found here.