Robin L. Hojnoski

Home Numeracy Environments of Preschoolers: Examining Relations Among Mathematical Activities, Parent Mathematical Beliefs, and Early Mathematical Skills

Research Findings: Early mathematical skills and knowledge are strongly related to long-term achievement, and yet the knowledge base regarding the mechanisms through which young children develop these skills and knowledge is limited. Although research has examined the relation of the home numeracy environment and childrens early mathematics performance, results have been equivocal. The purpose of this study was 2-fold: (a) to describe parent-reported home mathematical activities and beliefs about mathematics and (b) to examine the relation between these constructs and preschool-age childrens general school readiness skills as well as specific numeracy-related skills. Practice or Policy: Descriptive results suggest that parents engage in a range of mathematical activities in the home with varying frequency. Furthermore, results indicate relations between parent-reported mathematical activities and beliefs, but no statistically significant relations with preschool childrens early mathematics performance were demonstrated.

Preliminary Evidence of the Technical Adequacy of Additional Curriculum-Based Measures for Preschool Mathematics

There has been increased attention to the development of assessment measures for evaluating mathematical skills in young children in order to inform instruction and intervention. However, existing tools have focused primarily on number sense with little attention to other areas of mathematical thinking such as geometry and algebra. The purpose of this study is to describe preliminary reliability and validity evidence for several curriculum-based measures designed to assess mathematical skills in preschool children. Interscorer, test–retest, alternate-form reliability, and concurrent validity of five tasks—Cardinality, Pattern Completion, Shape Naming Fluency, Shape Selection Fluency, and Shape Composition—were examined in a small sample of preschool-age children at risk for academic difficulties because of demographic characteristics. Results indicated strong interscorer reliability, moderate to strong test–retest reliability, and adequate alternate-form reliability. Concurrent validity coefficients ranged from weak and nonsignificant to strong, positive significant correlations. However, non-domain specific correlations were demonstrated, and there was no clear pattern of convergent and divergent validity. Findings are discussed in the context of necessary research in early math measurement for preschoolers.

Embedding Mathematical Dialogue in Parent–Child Shared Book Reading: A Preliminary Investigation

Research Findings: Shared book reading provides a meaningful context for rich conversations to occur between a child and an adult and offers opportunities for children to be exposed to a range of vocabulary and concepts that often extend beyond their everyday experiences. Few studies have examined parent–child shared book reading as a context for embedding mathematical discussion. The purpose of this study was to examine systematically the effect of training parents to focus on mathematical concepts and vocabulary during shared book reading. Specific research questions were as follows: (a) Did parents increase their use of math talk during shared storybook reading following training? (b) Did parents generalize intervention strategies? And (c) did children increase their use of math talk during shared storybook reading? Results from a yoked multiple-baseline design with 6 dyads indicated variability across the dyads with 2 general patterns. Math talk increased following training for 3 of the dyads, whereas verbal mathematical behavior did not show consistent change for the other 3 dyads. Practice or Policy: Results are discussed in the context of home support for early mathematical development.

Innovations and Future Directions for Early Numeracy Curriculum-Based Measurement: Commentary on the Special Series.

The purpose of this extended commentary article is to frame the set of studies in the first of two issues and recommend areas of inquiry for future research. This special series issue features studies examining the technical qualities of formative assessment procedures that were developed to inform intervention. This article intends to emphasize issues in the current set of studies that do not appear central to early numeracy curriculum-based measurement (EN-CBM) research. To the extent possible, we expect that this two-volume series will result in scientific and practical advances. Despite this lofty intention, this series can neither represent all issues important to stakeholders nor characterize the full body of applied and basic research in early numeracy assessment. As such, we focus on a set of theoretical frameworks to guide the current and future development of EN-CBM.

Comparison of Observational Methods and Their Relation to Ratings of Engagement in Young Children

Although, collectively, results of earlier direct observation studies suggest momentary time sampling (MTS) may offer certain technical advantages over whole-interval (WIR) and partial-interval (PIR) recording, no study has compared these methods for measuring engagement in young children in naturalistic environments. This study compared direct observations of child engagement using WIR, PIR, and MTS methods to continuous duration recording (CDR), using measurement error, correlations, and inter-observer agreement. Results indicated that MTS consistently demonstrated measurements closer to CDR compared with PIR and WIR, although in this study, the differences between MTS and PIR across indicators were not as great as has been demonstrated in the literature. WIR, PIR, and MTS were all strongly correlated with CDR, although there were issues with under and overestimations. Finally, the four observational methods were all moderately to strongly correlated with expert ratings of engagement, although none was significantly correlated with teacher rankings of classroom engagement.

Cross-Age Peer Coaching: Enhancing the Peer Interactions of Children Exhibiting Symptoms of ADHD

Previous research demonstrates that children with attention-deficit/hyperactivity disorder (ADHD) can experience social difficulties. Therefore, the current study examined the effects of cross-age peer coaching on social behaviors of first graders with significant symptoms of ADHD using a multiple baseline design. Four students who met criteria for ADHD participated, along with four third- or fourth-grade coaches without ADHD. Coaching pairs met each morning to establish a goal for the younger child to meet during free time. Although results were variable, findings suggested that the cross-age coaching program led to decreases in negative social behavior, and was highly acceptable to participants.

Parent–child mathematical interactions: examining self-report and direct observation

ABSTRACT Variability in children’s early-learning home environments points to the need to better understand specific mechanisms of early mathematical development. We used a sample of 66 parent–preschool child dyads to describe parent-reported mathematical activities in the home and observed parent–child mathematical activities in a semi-structured play session. Data were examined to better understand the two methods of assessing the context of parent–child interactions related to mathematics. Parents reported engaging in a range of mathematical activities about 3–5 times per week, on average. Results from observed interactions indicated that parents engaged in math content/concept interactions in 32.5% of all observed intervals and children engaged in math content/concept interactions in 24.2% of all observed intervals. Although observed parent and child math content interactions were highly correlated, observed parent and child mathematical interactions were not correlated with parent-reported math activities.

Increasing Teacher Mathematical Talk During Shared Book Reading in the Preschool Classroom: A Pilot Study

ABSTRACT Research Findings: Shared book reading provides opportunities for adults to engage in literacy-related interactions with children in meaningful ways. Research has examined various dimensions of adult and child behavior during shared book-reading interactions with some focus on how book type affects the reading experience. Little research, however, has examined systematically the use of shared book reading in a mathematical context. Thus, the purpose of the study was twofold: (a) to examine the effect of book type on teacher use of mathematical talk during shared book reading in preschool classrooms and (b) to examine the effect of training teachers specifically to use mathematical talk during shared book reading. A multielement design with 2 female preschool teachers who taught in inclusion classrooms in an urban school district was used. Results generally indicated that the use of mathematical storybooks resulted in increased teacher mathematical talk compared to the use of nonmathematical storybooks. Training and instructional supports resulted in an increase in mathematical talk over that achieved by mathematical storybooks alone. Practice or Policy: Because shared book reading is a common practice in preschool classrooms, strategically choosing books to address mathematical skills can increase attention to mathematics throughout daily routines and provide a means of increasing teacher mathematical talk.

Considerations for Time Sampling Interval Durations in the Measurement of Young Children's Classroom Engagement.

Classroom engagement is important to young children’s academic and social development. Accurate methods of capturing this behavior are needed to inform and evaluate intervention efforts. This study compared the accuracy of interval durations (i.e., 5 s, 10 s, 15 s, 20 s, 30 s, and 60 s) of momentary time sampling (MTS) in approximating the duration of classroom engagement as measured by continuous duration recording (CDR). Twenty-four sessions of children in large-group instruction were observed using the Behavioral Observation of Students in School for Early Education (BOSS-EE). In general, shorter intervals produced engagement estimates that more highly correlated with CDR data and had less measurement error relative to estimates from longer intervals. Findings suggest that selection of MTS interval duration may affect the accuracy of estimates for children with low levels of engagement to a greater extent relative to children with high levels of engagement. Implications and future directions are discussed.

Assessing the Classification Accuracy of Early Numeracy Curriculum-Based Measures Using Receiver Operating Characteristic Curve Analysis.

Receiver operating characteristic curve (ROC) analysis was used to investigate the ability of early numeracy curriculum-based measures (EN-CBM) administered in preschool to predict performance below the 25th and 40th percentiles on a quantity discrimination measure in kindergarten. Areas under the curve derived from a sample of 279 students ranged from .65 to .82. Optimal cut scores were associated with sensitivity ranging from .44 to .79, specificity ranging from .49 to .91, and classification accuracy ranging from .60 to .79. Among a validation sample of 140 students, sensitivity ranged from .36 to .83, specificity ranged from .46 to .89, and classification accuracy ranged from .57 to .79. Results indicate that EN-CBM administered in preschool predicts math performance in kindergarten and can be a valuable component of an evidence-based decision-making process.