Kindergarteners’ Understanding of Different Types of Patterns

• In Event: Poster Session 07
  In Poster Session: PS 07 Topic - Cognitive Processes

Abstract

Children’s early repeating and growing patterning skills play an important role in their math development (Wijns et al., 2019; Zippert et al., 2020). However, little is understood about the developmental trajectory of patterning skills in relation to varying pattern rules and patterning tasks (e.g. Rittle-Johnson et al., 2013). The current study aimed to expand our understanding of how the difficulty of repeating and growing patterns vary by task types and pattern rules.

We assessed 47 kindergarteners individually during the Fall of their kindergarten year using a patterning assessment that we developed. The assessment consisted of a repeating patterning and a growing patterning subscale that measured children’s ability to complete various patterning tasks (e.g. extend patterns). Both subscales used model patterns with several pattern rules (classified as easiest to hardest a priori). The order in which the subscales were administered was counterbalanced.

Children had high patterning knowledge on average, though there was wide variability (see Table 1). Children’s repeating and growing patterning knowledge were positively correlated, r(45) = .39, p < .01, and they were significantly better at completing repeating than growing patterning tasks, t(46) = 7.79, p < .001. Notably, accuracy was higher among children who completed repeating patterns first than among children who completed growing patterns first (15% higher on growing items and 7% higher on repeating items).

A Rasch model with a Laplace approximation and empirical Bayesian prediction method (Cho & Rabe-Hesketh, 2011) was conducted to examine item difficulty and children’s patterning knowledge on the same scale (see Figure 1). It suggested that the easiest task was identifying repeating patterns while the most difficult was identifying the pattern rule of growing patterns. The analysis only partially supported our hypotheses about the difficulty of repeating and growing patterns based on their pattern rules. For example, we hypothesized that the difficulty of repeating pattern units would increase with the number of unique elements. However, pattern units with three and four unique elements (i.e. ABCD and ABC) had similar IRT difficulty estimates. We also predicted that growing patterns with a change-by-2 pattern rule would be harder than ones with a change-by-1 rule. However, this was only true for two of three patterning tasks. Additionally, we predicted that growing patterns created with objects would be easier to complete than those created with numerals. Contrary to this prediction, accuracy was similar for these two item types though children’s errors differed based on whether the patterns used objects or numerals.

The findings have several implications for future research. First, the wide range in accuracy suggests that the assessment will be suitable for kindergarteners of varying patterning knowledge. Second, the results suggest that repeating pattern understanding may serve as a foundation for the development of more complex patterning skills (e.g. growing patterns).
Finally, our results provide insight into the developmental trajectory of pattern understanding in relation to varying pattern rules. Further research is required to better understand the sequence in which children develop proficiency with repeating and growing patterns of different pattern rules and tasks.

Authors

• Ashli-Ann Douglas, Vanderbilt University
  Presenting Author

• Jake Kaufman, Vanderbilt University
  Non-Presenting Author

• Bethany Rittle-Johnson, Vanderbilt University
  Non-Presenting Author