Symbolic number knowledge is strongly related to mathematical performance for both children and adults. We present a model of symbolic number relations in which increasing skill is a function of hierarchical integration of symbolic associations. We tested the model by contrasting the performance of two groups of adults. One group was educated in China (n = 71) and had substantially higher levels of mathematical skill compared to the other group who was educated in Canada (n = 68). Both groups completed a variety of symbolic number tasks, including measures of cardinal number knowledge (number comparisons), ordinal number knowledge (ordinal judgments) and arithmetic fluency, as well as other mathematical measures, including number line estimation, fraction/algebra arithmetic and word problem solving. We hypothesized that Chinese-educated individuals, whose mathematical experiences include a strong emphasis on acquiring fluent access to symbolic associations among numbers, would show more integrated number symbol knowledge compared to Canadian-educated individuals. Multi-group path analysis supported the hierarchical symbol integration hypothesis. We discuss the implications of these results for understanding why performance on simple number processing tasks is persistently related to measures of mathematical performance that also involve more complex and varied numerical skills.

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Adults ( N = 72) estimated the location of target numbers on number lines that varied in numerical range (i.e., typical range 0–10,000 or atypical range 0–7,000) and spatial orientation (i.e., the 0 endpoint on the left [traditional] or on the right [reversed]). Eye-tracking data were used to assess strategy use. Participants made meaningful first fixations on the line, with fixations occurring around the origin for low target numbers and around the midpoint and endpoint for high target numbers. On traditional direction number lines, participants used left-to-right scanning and showed a leftward bias; these effects were reduced for the reverse direction number lines. Participants made fixations around the midpoint for both ranges but were less accurate when estimating target numbers around the midpoint on the 7,000-range number line. Thus, participants are using the internal benchmark (i.e., midpoint) to guide estimates on atypical range number lines, but they have difficulty calculating the midpoint, leading to less accurate estimates. In summary, both range and direction influenced strategy use and accuracy, suggesting that both numerical and spatial processes influence number line estimation.

Supporting young students’ oral language development is vital in ensuring their future success as readers. One important way that early childhood teachers can foster language development is by having extended conversations with students. The authors share research about the importance of rich teacher–student conversations and explain how less verbal students may miss out on conversational opportunities. The authors also explain how to create conditions in the classroom that are supportive of students’ engagement and talk, then give specific strategies for encouraging extended conversations.

Using play to meet specific learning goals in pre‐k can be challenging. In this article, we discuss why play is an essential activity for pre‐k learning. We share some research on the importance of supporting unconstrained, trifecta skills like oral language in the context of child‐centered, playful activities. We explain the importance of teacher scaffolding during play to meet specific language learning goals. Finally, we give practical strategies for planning and implementing play activities that will make a difference for children's language growth.

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The goal of the present study focused on the use of eye tracking technology to investigate the relationship between reference point use and performance on an atypical number line estimation task. University students (N=53; M=20.8 years) completed 33 number line trials, a post-task questionnaire, and a brief math assessment. Patterns of error and fixation data were analyzed. The results presented show that adult participants adjust their strategies in response to the scale used and that the use of implicit reference points benefits performance for targets located above the midpoint value. In sum, the varying performance demonstrated within an adult population using an atypical scale suggests that adults use proportional reasoning strategies to estimate the location of a number.iii

Previous research has identified specific classroom practices that are associated with greater academic and self-regulation gains for students in prekindergarten (PreK) and kindergarten (K) classrooms. These practices include reducing time in transition, more time in sequential activities, more opportunities for associative and cooperative interactions, more math, teachers’ using higher levels of instruction, positive classroom climate, and more teacher listening to children. This cross-sectional study aims to determine whether these specific classroom practices are associated with higher student engagement. A secondary goal was to examine whether economically disadvantaged (ED) students in more engaged classrooms scored higher on measures of math, language, and literacy. Researchers collected individual student assessment data in math, language, and literacy for a sample of 407 PreK and K students and conducted day-long observations in their classrooms. In addition to collecting behavioral count data on the focal classroom practices, observers rated students’ engagement across the day. Results revealed that students who experienced more of the beneficial classroom practices also showed higher engagement. Covariate-adjusted standardized mean difference effect sizes showed the greatest differences for transition time, sequential activities, associative and cooperative interactions, teachers’ listening, the amount of instruction, behavior approvals, and teacher tone, indicating that students experiencing more of these practices were more engaged than students experiencing fewer of these practices. To address our secondary goal of exploring between-group differences on assessments, we created groups based on ED status and engagement (operationalized using a median split for student engagement). While assessment scores were higher for non-ED students than ED students, regardless of their level of engagement, based on the literature researchers expected that ED students who were more engaged would have higher scores on assessments than their less engaged counterparts. Contrary to this hypothesis, there were few differences across groups. The largest positive effect sizes were for math and vocabulary. ED students with higher engagement had lower, not higher, scores on measures of literacy and passage comprehension. However, the magnitude of these effect sizes was small. Results provide preliminary evidence that these specific classroom practices are associated with greater student engagement.