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Conceptual and procedural instruction order may affect students' learning and generalization of math skills. This study compared two instruction sequences, concepts-first and iterative, and their effect on fraction performance through a class-wide intervention. Fourth-grade students (N = 114) were randomly assigned to the concepts-first, iterative, or control group. The primary conceptual assessment showed that the iterative and concepts-first groups performed similarly, demonstrating medium effect sizes compared with control. The primary procedural assessment again demonstrated that both intervention groups outperformed the control, this time with large to very large effects. In addition, the iterative group outscored the concepts-first group with a medium effect size, though it was not statistically significant. Generalization assessments measuring skill transfer found no differential effects. Overall, iterative instruction was at least as effective as a concepts-first sequence during a fraction intervention.

Approaches to discourse analysis in educational research tend to operate within the boundaries of particular video-based research traditions. We examine four of these traditions that are especially relevant to the learning sciences--conversation analysis, discursive psychology, interaction analysis, and video-cued ethnography--and instead of assuming that they are incommensurate, we examine their interconnections and areas of synthesis to make space for methodological innovations. In looking for unforeseen or de-emphasized points of synergy, we consider four approaches to each tradition: (1) making claims about internal processes; (2) inviting research participants to reflect on the video records; (3) formulating conjectures about the video data; and (4) noticing and documenting patterns. We examine the above approaches in the context of a research-practice partnership between educational researchers and a non-profit organization focused on outdoor family play, focusing in particular on autonomy-supportive parenting. Through this methodological reflection, we raise a number of novel considerations regarding how video-based educational researchers can understand what is relevant to the participants, engage with data selection, and formulate claims about recognizable phenomena in the data. We conclude by discussing problems of practice in video-based educational research that this mixed-tradition approach can address.

The traveling salesperson problem (TSP) is an NP-Hard problem that computers find difficult to solve. Humans are surprisingly good at solving the TSP, with solutions within 10% of optimal for problems with up to 100 points, constructed in time linear with the number of points. We propose that humans solve the TSP by initially clustering the points and then connecting them first within and then between clusters. In this study, 67 participants first clustered 40 stimuli and then solved them as TSPs. Strikingly, participants' TSP solutions perfectly followed their clusters for 52% of the stimuli. Further, participants' TSP solutions' were more congruent with their clusters for stimuli with statistically higher levels of clustered structure. This provides strong evidence for the clustering proposal. Random TSP solutions, however, showed no such congruence to cluster structure. These findings suggest that clustering might be a fundamental ability for reasoning about graph-theoretic algorithmic problems.

Human solutions to the Traveling Salesperson Problem (TSP) are surprisingly close to optimal and unexpectedly efficient. We posit that humans solve instances of the TSP by first clustering the points into smaller regions and then solving each cluster as a simpler TSP. Prior research has shown that participants cluster visual stimuli reliably. That is, their clustering and re-clustering of the same stimulus are similar, especially when the stimulus is relatively more clustered. In this study, participants solved the same TSP instances twice. On the second presentation, half of the instances were flipped about the horizontal and vertical axes. Participants solved the TSP reliably, with their two tours of the same instance sharing 77 percent of the same edges on average. In addition, within-participant reliability was higher for more clustered versus more dispersed instances. Our findings are consistent with the proposal that people use clustering strategies to solve the TSP.

Traditional statistics instruction emphasizes a .05 significance level for hypothesis tests. Here, we investigate the consequences of this training for researchers’ mental representations of probabilities –– whether .05 becomes a boundary, i.e., a discontinuity of the mental number line, and alters their perception of differences between p-values. Graduate students (n = 25) with statistical training viewed pairs of p-values and judged whether they were ‘similar’ or ‘different’. After controlling for covariates, participants were more likely and faster to judge p-values as ‘different’ when they crossed the .05 boundary (e.g., .047 vs. .052) compared to when they did not (e.g., .027 vs. .032). This categorical perception effect suggests that traditional statistical instruction creates a psychologically real divide between so-called statistically significant and non-significant p-values. Such a distortion is undesirable given modern approaches to statistical reasoning that de-emphasize dichotomizing p-values.

Purpose: The /r/ productions of young children acquiring American English are highly variable and often inaccurate, with [w] as the most common substitution error. One acoustic indicator of the goodness of children's /r/ productions is the difference between the frequency of the second formant (F2) and the third formant (F3), with a smaller F3-F2 difference being associated with a perceptually more adultlike /r/. This study analyzed the effectiveness of automatically extracted F3-F2 differences in characterizing young children's productions of /r/--/w/ in comparison with manually coded measurements. Method: Automated F3-F2 differences were extracted from productions of a variety of different /r/- and /w/-initial words spoken by 3- to 4-year-old monolingual preschoolers (N = 117; 2,278 tokens in total). These automated measures were compared to ratings of the phoneme goodness of children's productions as rated by untrained adult listeners (n = 132) on a visual analog scale, as well as to narrow transcriptions of the production into four categories: [r], [w], and two intermediate categories. Results: Data visualizations show a weak relationship between automated F3-F2 differences with listener ratings and narrow transcriptions. Mixed-effects models suggest the automated F3-F2 difference only modestly predicts listener ratings (R² = .37) and narrow transcriptions (R² = .32). Conclusion: The weak relationship between automated F3-F2 difference and both listener ratings and narrow transcriptions suggests that these automated acoustic measures are of questionable reliability and utility in assessing preschool children's mastery of the /r/--/w/ contrast. [ABSTRACT FROM AUTHOR]

Traditional statistics instruction emphasizes a.05 significance level for hypothesis tests. Here, we investigate the consequences of this training for researchers' mental representations of probabilities — whether.05 becomes a boundary, that is, a discontinuity of the mental number line, and alters their reasoning about p‐values. Graduate students with statistical training (n = 25) viewed pairs of p‐values and judged whether they were "similar" or "different." After controlling for several covariates, participants were more likely and faster to judge p‐values as "different" when they crossed the.05 boundary (e.g.,.046 vs..052) compared to when they did not (e.g.,.026 vs..032). This result suggests a categorical perception‐like effect for the processing of p‐values. It may be a consequence of traditional statistical instruction creating a psychologically real divide between so‐called statistical "significance" and "nonsignificance." Such a distortion is undesirable given modern approaches to statistical reasoning that de‐emphasize dichotomizing the p‐value continuum. Traditional statistics instruction and practice emphasize a p <.05 categorical boundary. Our results suggest a categorical perception‐like effect for graduate students' processing of p‐values, creating a psychologically real divide between so‐called statistical 'significance' and 'non‐significance'. [ABSTRACT FROM AUTHOR]