Constructing explanatory models, in which students learn to visualize the mechanisms of unobservable entities (e.g., molecules) to explain the working of observable phenomena (e.g., air pressure), is a key practice of science. Yet, students struggle to develop and utilize such models to articulate causal-mechanistic explanations. In this paper, we argue that representational gesturing with the hands (i.e., gesturing that models semantic content) can support the development of explanatory models. Through case studies examining middle school students gesturing during sensemaking, we show that representational gestures can support students in at least four ways: (a) they make underlying mechanisms visible, (b) they facilitate translation of a spatial model to a verbal explanation, (c) they enable model articulation while relying less on scientific terminology, and (d) they present opportunities for students to embody causal agents. In these ways, representational gesturing can be considered an epistemic tool supporting students during sensemaking and communication. We argue that instruction should attend to students' gestures and, as appropriate, encourage students to gesture as a means of aiding the construction and articulation of causal-mechanistic explanations. While our study explores one form of embodied representation, we encourage the field to explore embodied expressions as epistemic tools for learning.

The purpose of this study is to investigate the extent that there is a typology of high schools based on their orientation toward science, technology, engineering, and mathematics (STEM), as well as the extent to which school-level demographic variables and student high school outcomes are associated with subgroup membership in the typology, by analyzing data from a large nationally representative sample of high schools (n = 940) from the High School Longitudinal Study of 2009 (HSLS:09) using latent class analysis (LCA). We used a three-step LCA approach to identify significantly different subgroups of STEM-oriented high schools, what covariates predict subgroup membership, and how subgroup membership predicts observed distal outcomes. We find that there are four significantly different subgroups of STEM-oriented high schools based on their principal's perceptions: Abundant (12.3%), Support (23.3%), Bounded (10.1%), and Comprehensive (54.3%). In addition, we find that these subgroups are associated with school demographics, such as the percent of students eligible for free and reduced-price lunch, school locale, and control (public or private). Subgroup membership is also associated with student outcomes, such as postsecondary program enrollment and intent to pursue a STEM degree.

A growing body of evidence reveals the need for research on, and consideration for, children's and students' own--self-guided--spontaneous use of mathematical reasoning and knowledge in action. Spontaneous focusing on numerosity (SFON) and quantitative relations (SFOR) have been implicated as key components of mathematical development. In this chapter, we review existing research on SFON and SFOR tendencies in the broader context of the development of mathematical skills and knowledge and examine how the state-of-the-art evidence on SFON and SFOR is relevant for the field of mathematics education. We discuss individual differences in SFON and SFOR, associations between spontaneous focus on mathematical features and mathematics achievement, the contributions of situational contexts that implicitly prompt attention to number, and ways to increase children's focus on number regardless of their baseline level tendencies. We conclude that children's and students' tendencies to focus on number and quantitative relations--spontaneous or otherwise--are key components of mathematical development and education. [For the complete volume, "Constructing Number: Merging Perspectives from Psychology and Mathematics Education. Research in Mathematics Education," see ED616587.]

Identifying the mathematical skills or knowledge components needed to solve a math problem is a laborious task. In our preliminary work, we had two expert teachers identified knowledge components of a state-wide math test and they only agreed only on 35% of the items. Previous research showed that machine learning could be used to correctly tag math problems with knowledge components at about 90% accuracy over more than 100 different skills with five-fold cross-validation. In this work, we first attempted to replicate that result with a similar dataset and were able to achieve a similar cross-validation classification accuracy. We applied the learned model to our test set, which contains problems in the same set of knowledge component definitions, but are from different sources. To our surprise, the classification accuracy dropped drastically from near-perfect to near-chance. We identified two major issues that cause of the original model to overfit to the training set. After addressing the issues, we were able to significantly improve the test accuracy. However, the classification accuracy is still far from being usable in a real-world application.

65 undergraduate students from a North American university interacted with MetaTutorIVH, an agent-based multimedia learning environment that fosters self-regulated learning (SRL) strategy use (e.g., metacognition) while presenting information on several human body systems. Participants completed a self-paced task to study the influence of relevant content and an agents' expressed emotions on metacognitive judgments, gaze behaviors, and science learning. The goal of this study was to examine eye gaze behavior and metacognitive process use relative to their perceived relevancy of content based on discrepancies between multimedia materials and artificial agent's facial expressions. Results indicate an increase in overall fixation duration on multimedia content (e.g., text, diagram) when the text was perceived as less relevant, specifically revealing longer time spent fixating on text when the text was perceived as less relevant compared text and diagrams that were perceived as relevant. Further analyses reveal an increase in diagram fixation duration when the text was judged as being less relevant, but when compared to instances where the text and diagrams were both seen as only somewhat relevant. Across trials, there was no indication of the actual relevancy of content influencing the gaze behaviors of participants.

In this chapter, we focus on the ways two community college instructors worked with students to demonstrate the solution of contextualized algebra problems in their college algebra lessons. We use two classroom episodes to illustrate how they sought to elicit students' mathematical ideas of algebraic topics, attending primarily to teachers' questioning approaches. We found that the instructors mostly asked questions of lower cognitive demand and used a variety of approaches to elicit the mathematical ideas of the problems, such as using examples relevant to the students and dividing the problems into smaller tasks, that together help identify a solution. We conclude by offering considerations for instruction at community colleges and potential areas for professional development.

Narrative and collaboration are two core features of rich interactive learning. Narrative-centered learning environments offer significant potential for supporting student learning. By contextualizing learning within interactive narratives, these environments leverage students' innate facilities for developing understandings through stories. Computer-supported collaborative learning environments offer students rich, collaborative learning experiences in which small groups of students engage in constructing artifacts, addressing disciplinary challenges, and solving problems. Narrative and collaboration have distinct affordances for learning, but combining them poses significant challenges. In this paper, we present initial work on solving this problem by introducing collaborative narrative-centered learning environments. These environments will enable small groups of students to collaboratively solve problems in rich multi-participant storyworlds. We propose a novel framework for designing and developing these environments, which we are using to create a collaborative narrative-centered learning environment for middle school ecosystems education. In the learning environment, students work on problem-solving scenarios centered on how to support optimal fish health in aquatic environments. Results from pilot testing the learning environment with 45 students suggest it supports the creation of engaging and effective collaborative narrative-centered learning experiences.

Touchscreen-based smart devices, such as smartphones and tablets, offer great promise for providing blind and visually-impaired (BVI) users with a means for accessing graphics non-visually. However, they also offer novel challenges as they were primarily developed for use as a visual interface. This paper studies key usability parameters governing accurate rendering of haptically-perceivable graphical materials. Three psychophysically-motivated usability studies, incorporating 46 BVI participants, were conducted that identified three key parameters for accurate rendering of vibrotactile lines. Results suggested that the best performance and greatest perceptual salience is obtained with vibrotactile feedback based on: (1) a minimum width of 1 mm for detecting lines, (2) a minimum gap of 4 mm for discriminating lines rendered parallel to each other, and (3) a minimum angular separation (i.e., cord length) of 4 mm for discriminating oriented lines. Findings provide foundational guidelines for converting/rendering visual graphical materials on touchscreen-based interfaces for supporting haptic/vibrotactile information access.

We identify two polar life cycles of scholarly creativity among Nobel laureate economists with Tinbergen falling broadly in the middle. Experimental innovators work inductively, accumulating knowledge from experience. Conceptual innovators work deductively, applying abstract principles. Innovators whose work is more conceptual do their most important work earlier in their careers than those whose work is more experimental. Our estimates imply that the probability that the most conceptual laureate publishes his single best work peaks at age 25 compared to the mid-50 s for the most experimental laureate. Thus, while experience benefits experimental innovators, newness to a field benefits conceptual innovators.