Abstract Title Page

Title: A New Teacher-Based Assessment of Preschoolers’ Patterning Skills Author(s): Erica L. Zippert, Abbey M. Loehr, Bethany Rittle-Johnson

Abstract Body Word count: 979.

Background

Children’s math knowledge develops rapidly in the preschool years, varies substantially (Starkey, Klein, & Wakeley, 2004), and is strongly predictive of later math achievement (Duncan et al., 2007). While theory and research on math development have concentrated primarily on the contributions of number skills (Sarama & Clements, 2004), children’s patterning skills have also been found to predict concurrent and later math knowledge (e.g., Rittle-Johnson, Fyfe, Hofer, & Farran, 2015). This research focuses on young children’s skills with repeating patterns (i.e., linear patterns that have a repeating unit, such as ABABAB).

Young children’s repeating patterning skills become systematically more sophisticated in preschool and kindergarten (Clements & Sarama, 2009; Rittle-Johnson, Fyfe, McLean, & McEldoon, 2013; Starkey et al., 2004). Children first learn to work with simple alternating AB patterns such as a red-blue pattern, and then learn to identify patterns with three and four item units (e.g., ABB/AABB patterns). One of the earliest emerging patterning skills is completing patterns—identifying the missing item in a pattern. A more difficult skill, extending patterns, requires continuing an existing pattern by at least one unit of repeat. An even more difficult patterning skill is abstracting patterns—recreating a model pattern using a different set of materials. By the end of preschool, many children can complete and extend repeating patterns, and some can even abstract them (Clements & Sarama, 2009; Papic et al., 2011; Rittle-Johnson et al., 2015). Purpose

Only one valid and reliable instrument currently exists to assess patterning skills in preschoolers (Rittle-Johnson et al., 2015). Our goal was to create a new measure that would be easier for teachers to use, and include easier tasks than on the existing measure. This is imperative if teachers are to use assessments to appropriately plan lessons and measure student learning (Purpura & Lonigan, 2015). Methods

Participants (see Table 1) were 73 children (54% female) from six preschools in Tennessee who were on average 4 years 6 months (SD=4 months) when first assessed.

Our study employed a single-group longitudinal design with assessments at 2 time points. Children were assessed during the first and final quarter of the school year.

Teacher-Based Patterning. This new patterning assessment was developed using pre-existing patterning worksheets found on websites with resources for early-childhood educators. Children were presented with 10-items, worth 1-point each, of pictures of model patterns and given a set of small, laminated pictures to complete the patterning task. See Figure 1 for sample items for the 4 types of tasks. The first two pattern completion tasks were easier and most prevalent on websites: (a) what comes next and (b) missing item. The third was extending patterns. The fourth task type was only found on one website, but was included because it potentially involved abstracting patterns. See Table 2a/b for a list of items, including the complexity of the pattern unit. It took approximately six minutes to administer. We generated item difficulty and ability estimates using a Rasch model with a Laplace approximation and empirical Bayesian prediction method that has been shown to be stable for sample sizes around 50 (Cho & Rabe-Hesketh, 2011).

Research-based patterning. This assessment measures preschoolers’ ability to extend, and abstract repeating visual patterns, and consisted of nine items varying in difficulty, described and validated in previous studies (e.g., Miller, Rittle-Johnson, Loehr, & Fyfe, 2016; Rittle-Johnson et al., 2013; Rittle-Johnson et al., 2015). IRT ability estimates were also obtained using the same procedure as above.

Math knowledge. The REMA Short-Form contains a subset of items from the Research-Based Early Mathematics Assessment (Weiland et al., 2012). IRT ability estimates were generated using a partial credit model.

Spatial ability. Block Design, a subtest of the WPPSI-IV (Wechsler, 2012) was used to measure spatial ability.

Verbal ability. The Picture Vocabulary Test from version 1.6 of the NIH Toolbox app assessed children’s receptive vocabulary. Age-corrected standardized scores were used to control for verbal ability, and represent general intelligence (Sattler, 2008).

At Time 1(T1), all measures were administered. At time 2(T2), the teacher-based patterning and math assessments were administered. Results Evidence for Reliability of Teacher-Based Patterning Assessment

Internal consistency was good for both T1(Cronbach’s a = .83) and T2(Cronbach’s a = .87). Further, relative performance was stable over time, with a high test-retest correlation r(73) = .61, p < .01. Evidence for Validity of Teacher-Based Patterning Assessment First, we tested convergent validity by correlating students’ T1 Teacher-Based patterning with Research-Based patterning scores r(73) = .575, p < .01.

Concurrent and predictive validity was established by correlating Teacher-Based patterning scores at T1 with math knowledge at T1 and T2, rmathT1(73)=.654, p<.01, rmathT2(73)=.657, p<.01. Low but significant correlations between Teacher-Based patterning and verbal and spatial ability demonstrated discriminant validity rverbal(73)=.320, p < .01, rspatial(73)=.361, p<.01.

To examine construct validity, we considered the item difficulty of each item at each time point (see Tables 2a/b). As with past research, AB patterns were generally easier for children than patterns with more complex pattern units. At T1, pattern completion tasks—what’s next and missing item—were often easier than extend tasks. Performance on the final task type – potentially abstracting patterns – was more variable and dependent on the pattern unit. Finally, at T2, but not at T1, task difficulty seemed to depend on which type of complex pattern unit it was, with AABB patterns being systematically easier than ABC patterns. Conclusions The new teacher-based patterning measure has been demonstrated to be both reliable and valid. For example, it relates strongly valid measures of patterning and mathematics, but not to measures of more distant constructs. More research is needed to understand why item type seemed to drive T1 teacher-pattern performance, while unit size appeared to drive T2 performance. Regardless, its ease of administration and strong psychometric properties, teachers should be encouraged to use it to assess patterning knowledge in their preschool classrooms, with the option of dropping abstract items given their variability in difficulty, and extended administration time.

References Cho, S.-J., & Rabe-Hesketh, S. (2011). Alternating imputation posterior estimation of models

with crossed random effects. Computational Statistics and Data Analysis, 55, 12-25. doi:10.1016/j.csda.2010.04.015

Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., . . . Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43, 1428-1446. doi:10.1037/0012-1649.43.6.1428

Miller, M. R., Rittle-Johnson, B., Loehr, A. M., & Fyfe, E. R. (2016). The influence of relational knowledge and executive function on preschoolers’ repeating pattern knowledge. Journal of Cognition and Development, 17, 85-104. doi:10.1080/15248372.2015.1023307

Papic, M. M., Mulligan, J. T., & Mitchelmore, M. C. (2011). Assessing the development of preschoolers' mathematical patterning. Journal for Research in Mathematics Education, 42, 237-268.

Purpura, D. J., & Lonigan, C. J. (2015). Early numeracy assessment: The development of the preschool numeracy scales. Early Education and Development, 26. doi: 10.1080/10409289.2015.991084

Rittle-Johnson, B., Fyfe, E. R., Loehr, A. M., & Miller, M. R. (2015). Beyond numeracy in preschool: Adding patterns to the equation. Early Childhood Research Quarterly. doi:10.1016/j.ecresq.2015.01.005

Rittle-Johnson, B., Fyfe, E. R., McLean, L. E., & McEldoon, K. L. (2013). Emerging understanding of patterning in 4-year-olds. Journal of Cognition and Development, 14, 376-396. doi:10.1080/15248372.2012.689897

Sarama, J., & Clements, D. H. (2004). Building blocks for early childhood mathematics. Early Childhood Research Quarterly, 19, 181-189. doi:10.1016/j.ecresq.2004.01.014

Sattler, J. M. (2008). Assessment of children: Cognitive applications (5th ed.). San Diego, CA: Author.

Starkey, P., Klein, A., & Wakeley, A. (2004). Enhancing young children's mathematical knowledge through a pre-kindergarten mathematics intervention. Early Childhood Research Quarterly, 19, 99-120. doi:10.1016/j.ecresq.2004.01.002

Wechsler, D. (2012). Wechsler preschool and primary scale of intelligence-fourth edition. San Antonio, TX: The Psychological Corporation.

Weiland, C., Wolfe, C. B., Hurwitz, M. D., Clements, D. H., Sarama, J. H., & Yoshikawa, H. (2012). Early mathematics assessment: Validation of the short form of a prekindergarten and kindergarten mathematics measure. Educational Psychology, 32, 311-333.

Table 1 Sample Characteristics Frequency Percent (%) Ethnicity

African-American 34 46.6 Caucasian or White 31 42.5 Biracial/Mixed Race 3 4.1 Hispanic or Latino 3 4.1 Asian or Pacific Islander 2 2.7

Financial Assistance* None 32 43.8 Some 13 17.8 Full 26 35.6

Language(s)* Multiple languages 9 12.3 English only 64 87.7

Special Education Services Yes 6 8.1 No 67 91.9

*Notes. Financial data were missing for two participants. Languages spoken at home included Kurdish, Nepali, Spanish, and Amharic.

Table 2a

Descriptive Statistics for Items on Teacher-Based Patterning Assessment Time 1

Item number, type, and pattern unit Proportion

correct (SD) Item-total correlation Item difficulty (SE)

9. Abstract AB

.57 (.50) .46 -.60 (.26) 5. Missing ABB

.55 (.50) .40 -.54 (.26)

3. Missing AB

.51 (.50) .60 -.38 (.26) 1. What's next AB

.47 (.50) .49 -.09 (.26)

2. What's next ABC

.42 (.50) .34 -.04 (.26) 4. Missing ABC

.42 (.50) .40 .08 (.26)

7. Extend AABB

.42 (.50) .78 .14 (.26) 6. Extend AB

.40 (.49) .77 .19 (.26)

10. Abstract ABBB

.40 (.49) .42 .19 (.26) 8. Extend ABC

.25 (.44) .60 .87 (.27)

Notes. Items are listed in order of observed difficulty, and item number indicates order in which item was given. Negative item difficulty values indicate less challenging items

Table 2b Descriptive Statistics for Items on Teacher-Based Patterning Assessment Time 2

Item number, type, and pattern unit Proportion

correct (SD) Item-total correlation Item difficulty (SE)

9. Abstract AB

.74 (.44) .52 -.65 (.29) 1. What's next AB

.71 (.45) .65 -.51 (.29)

6. Extend AB

.70 (.46) .78 -.44 (.28) 3. Missing AB

.68 (.46) .73 -.37 (.28)

5. Missing ABB

.59 (.49) .43 .09 (.28) 7. Extend AABB

.58 (.49) .83 .15 (.28)

10. Abstract ABBB

.56 (.50) .62 .22 (.28) 2. What's next ABC

.49 (.50) .66 .53 (.27)

4. Missing ABC

.48 (.50) .51 .59 (.27) 8. Extend ABC

.47 (.49) .64 .65 (.27)

Notes. Items are listed in order of observed difficulty, and item number indicates order in which item was given. Negative item difficulty values indicate less challenging items

Figure 1. Sample Items on the Teacher-Based Patterning Assessment

What comes Next Pattern AB

“What comes next in the pattern? Use one of these.” [Experimenter gestures to

response options.]

Missing Item Pattern ABC

“Find the missing bead [experimenter gestures to response options] to complete the pattern [experimenter gestures across

pattern].”

Extend Pattern AABB

“Can you complete the pattern?” [Experimenter gestures to circles on the

right of the pattern.]

Abstract Pattern ABBB

“Can you make the same kind of pattern using your pictures?” [Experimenter gestures to boxes below the model

pattern.]