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Reasoning about visual representations in science requires the ability to control one's attention, inhibit attention to irrelevant or incorrect information, and hold information in mind while manipulating it actively--all aspects of the limited-capacity cognitive system described as humans' executive functions. This article describes pedagogical intuitions on best practices for how to sequence visual representations among pre-service teachers, adult undergraduates, and middle school children, with learning also tested in the middle school sample. Interestingly, at all ages, most people reported beliefs about teaching others that were different from beliefs about how they would learn. Teaching beliefs were most often that others would learn better from presenting representations one at a time, serially; while learning beliefs were that they themselves would learn best from simultaneous presentations. Students did learn best from simultaneously presented representations of mitosis and meiosis, but only when paired with self-explanation prompts to discuss the relationships between the graphics. These results provide new recommendations for helping students draw connections across visual representations, particularly mitosis and meiosis, and suggest that science educators would benefit from shifting their teaching beliefs to align with beliefs about their own learning from multiple visual representations.

The COVID-19 pandemic necessitated a systematic change in course modalities due to the nationwide suspension of in-person instruction, resulting in the transition to emergency remote distance learning via Zoom. This transition certainly facilitated affordances of flexibility and continuity, but with it brought issues of unfamiliarity, lack of confidence, anxiety, distractions, and validity from both the instructors and the student perspectives. This in situ study aimed to better understand the students' learning experiences with Zoom by assessing the social, cognitive, and behavioral factors influencing learner's mind-wandering and its effect on online engagement. Undergraduate students from 14 classes across two research institutions in California (N = 633) were recruited to participate in an online survey while distance learning through a pandemic. Structural equation modeling was used to conduct a path analysis to explain the factors impacting students' online engagement mediated by students' frequency to mind-wander. Study findings revealed that (1) self-efficacy and trait anxiety had significant direct effects on students' mind-wandering; (2) self-efficacy, trait anxiety, task-value beliefs, and mind-wandering had significant direct effects on students' online engagement; and finally (3) the frequency of students' mind-wandering partially mediated the relationship between self-efficacy and engagement and between trait anxiety and engagement. Identifying these structural relationships further confirmed our hypotheses on sources contributing to students' mind-wandering while learning remotely, provided insights into potential mechanisms underpinning students' online engagement, and suggests practical pedagogical learning experience design recommendations for instructors to immediately implement while teaching and learning with Zoom.

Negative relationships between mathematics anxiety and achievement appear in many countries globally (Lee, 2009; OECD, 2013), suggesting that mathematics anxiety could be an underconsidered factor in regions with persistently low mathematics achievement. We draw on a national sample of students and their teachers in Belize to examine relations between mathematics anxiety and achievement. The data replicated the negative relationships between students' math anxiety and achievement observed in many higher achieving, higher resourced regions, and importantly also revealed that teachers' mathematics anxiety predicted their students' mathematics attitudes and sometimes achievement. The effects were small overall so the robustness of this relationship is not clear, but they provide novel data toward building a comprehensive theory of mathematics anxiety's relationship to achievement across cultural, gender and age contexts, and offer insight into how addressing mathematics anxiety might improve mathematics teaching and achievement in low resourced countries. [This article was published in "Mind, Brain, and Education" (EJ1277351).]

This study tested a novel approach to capitalizing on the benefits of play for informal math learning. Two experiments evaluated a platform called "Fraction Ball," that provides an embodied, playful, and physically active learning experience by modifying the lines on a basketball court to support rational number learning. In the Pilot Experiment, 69 fifth-sixth graders were randomly assigned to play a set of four different Fraction Ball games or attend normal physical education (PE) class and completed rational number pretests and posttests. After strategic improvements to expand the intervention, the same protocol was implemented in the Efficacy Experiment with 160 fourth-sixth graders. Playing Fraction Ball for four PE class periods (Pilot Experiment) improved students' ability to convert fractions to decimals. Playing a revised version of six different Fraction Ball games for six PE class periods (Efficacy Experiment) significantly improved children's rational number understanding as reflected by higher scores in overall accuracy, with positive impacts on several subtests. Fraction Ball represents a low-cost, highly scalable intervention that promotes math learning in a fun and engaging approach.

Two studies explore gender gaps that favor girls in low-stakeslearning contexts yet are not evident in high-stakesachievement measures. Study 1 (n = 386) combined controldata across multiple experiments testing student’s learningfrom a challenging proportional reasoning lesson to exploreconsistent gender gaps in favor of girls. This learning gap couldnot be explained by the baseline mathematics, affective,motivational, or Executive Function individual differences wemeasured. In Study 2 (n =178), we experimentally manipulatedpressure, raising the stakes by telling some students that theirperformance would determine whether or not their entire classreceived an incentive. Gender gaps in favor of girls remainedin the absence of pressure, but when external pressure wasimposed before or after learning, the female advantagedisappeared. These data suggest managing feelings of pressurein learning or testing contexts may be an important step inultimately increasing female representation in math-intensivefields.

Linking ideas, concepts, and disciplinary content is an underused yet effective educational strategy for fostering students' higher order thinking. A body of psychological research on analogical reasoning can inform the challenge of encouraging higher order thinking in schools. We focus in particular on the teaching of mathematics and highlight alignments between a psychologically based definition of higher order thinking and educational goals as described within U.S. mathematical practice standards. Finally, this analysis implicates policies for supporting students' higher order thinking including requiring assessments that capture these skills; disseminating assessment data meaningfully to help improve teachers, schools, or curricula; and designing professional development that draws explicit attention to these skills.

Individual differences in Executive Function (EF) are well established to be related to overall mathematics achievement, yet the mechanisms by which this occurs are not well understood. Comparing representations (problems, solutions, concepts) is central to mathematical thinking, and relational reasoning is known to rely upon EF resources. The current manuscript explored whether individual differences in EF predicted learning from a conceptually demanding mathematics lesson that required relational reasoning. Analyses revealed that variations in EF predicted learning when measured at a delay, controlling for pretest scores. Thus, EF capacity may impact students' overall mathematics achievement by constraining their resources available to learn from cognitively demanding reasoning opportunities in everyday lessons. To assess the ecological validity of this interpretation, we report follow-up interviews with mathematics teachers who raised similar concerns that cognitively demanding activities such as comparing multiple representations in mathematics may differentially benefit their high versus struggling learners. Broader implications for ensuring that all students have access to, and benefit from, conceptually rich mathematics lessons are discussed. We also highlight the utility of integrating methods in Science of Learning (SL) research.

We describe a new approach to the use of video-based technology for conducting controlled experiments in classroom contexts. Specifically, we describe a process for editing video recordings of live classroom lessons to create multiple versions, such that only one aspect of the lesson is systematically varied. Other aspects of the instruction are all held constant, including audio, curricular content, student participation, and other notoriously hard-to-control details of the interactional context that impact learning (e.g., gestures, affect). These edited lesson versions can be randomly assigned to students by condition within classrooms to meet a high standard for random assignment. This technology provides opportunities for deriving causal data on the efficacy of teaching practices through stimuli approximating a typical everyday classroom context.

Comparing multiple solutions to a single problem is an important mode for developing flexible mathematical thinking, yet instructionally leading this activity is challenging (Stein, Engle, Smith, & Hughes, 2008). We test 1 decision teachers must make after having students solve a problem: whether to only verbally discuss students' solutions or make them visible to others. Fifth grade students were presented with a videotaped mathematics lesson on ratio in which students described a misconception and 2 correct strategies. The original lesson was manipulated via video editing to create 3 versions with constant audio but in which the compared solutions were a) presented only orally, b) visible sequentially in the order they were described, or 3) all solutions were visible after being described throughout the discussion. Posttest and delayed posttest measures revealed the greatest gains when all solutions were visible throughout the discussion, particularly better than only oral presentation for conceptual knowledge. Sequentially showing students visual representations of solutions led to the lowest gains overall, and the highest rates of misconceptions. These results suggest that visual representations of analogs can support learning and schema formation, but they can also be hurtful--in our case if presented as visible in sequence.

Deictic linking gestures, hand and arm motions that physically embody links being communicated between two or more objects in the shared communicative environment, are explored in a cross-cultural sample of mathematics instruction. Linking gestures are specifically examined here when they occur in the context of communicative analogies designed to link two distinct yet mutually informative representations. Video coding of eighth-grade mathematics lessons in the United States, Japan, and Hong Kong revealed that teachers in the higher achieving regions (Hong Kong and Japan) used reliably more linking gestures concurrent with verbal linkages than did U.S. teachers. Further, they were significantly more likely to tailor their gesture use to the recency of students' experiences with source than U.S. teachers. The overall data align with growing evidence that U.S. teachers may not systematically capitalize on pedagogical opportunities to draw linkages between representations and that gestures may play a key role in doing so.

A cross-cultural comparison between U.S. and Hong Kong preschoolers examined factors responsible for young children's analogical reasoning errors. On a scene analogy task, both groups had adequate prerequisite knowledge of the key relations, were the same age, and showed similar baseline performance, yet Chinese children outperformed U.S. children on more relationally complex problems. Children from both groups were highly susceptible to choosing a perceptual or semantic distractor during reasoning when one was present. Taken together, these similarities and differences suggest that (a) cultural differences can facilitate better knowledge representations by allowing more efficient processing of relationally complex problems and (b) inhibitory control is an important factor in explaining the development of children's analogical reasoning. (Contains 1 figure and 1 table.)

We investigated whether worked examples could be used to reduce cognitive load on mathematics learners who may have reduced available cognitive resources due to experiencing anxiety or excess stress. Across 2 days, 280 fifth-grade students learned from a difficult lesson on ratio, half of whom reviewed worked examples at key problem-solving opportunities during instruction. We also measured two sources of students' worry during learning: math anxiety and worries about learning during the pandemic. We explored the attentional and affective effects of worked examples and worries in addition to their effects on learning. Results suggest that math anxiety, but not pandemic learning worries, negatively predicted procedural and conceptual learning from the lesson. In line with previous research and cognitive load theory, math anxiety also predicted greater mind wandering during testing and lower situational interest during learning. Critically, reviewing worked examples during learning mitigated these effects on learning and engagement. Pandemic-related learning worries were unrelated to learning outcomes but did predict affective and motivational outcomes. Educational implications are discussed. Educational Impact and Implications Statement: Math lessons that compare different solution strategies are effective but demanding, especially for anxious students who have thoughts and worries that compete for their attention. Reviewing worked examples—which are fully-worked out examples of problem solutions—can promote learning by drawing students' attention directly to the key parts of the compared strategies. In our study, we show that having students review worked examples during a ratio lesson that compared two strategies greatly reduced the negative impacts of math anxiety on their learning and attention. [ABSTRACT FROM AUTHOR]

Laboratory studies have demonstrated beneficial effects of making comparisons on children's analogical reasoning skills. We extend this finding to an observational dataset comprising 42 children. The prevalence of specific comparisons, which identify a feature of similarity or difference, in children's spontaneous speech from 14-58 months is associated with higher scores in tests of verbal and non-verbal analogy in 6th grade. We test two pre-registered hypotheses about how parents influence children's production of specific comparisons: 1) via modelling, where parents produce specific comparisons during the sessions prior to child onset of this behaviour; 2) via responsiveness, where parents respond to their children's earliest specific comparisons in variably engaged ways. We do not find that parent modelling or responsiveness predicts children's production of specific comparisons. However, one of our pre-registered control analyses suggests that parents' global comparisons-comparisons that do not identify a specific feature of similarity or difference-may bootstrap children's later production of specific comparisons, controlling for parent IQ. We present exploratory analyses following up on this finding and suggest avenues for future confirmatory research. The results illuminate a potential route by which parents' behaviour may influence children's early spontaneous comparisons and potentially their later analogical reasoning skills., (© 2023 Massachusetts Institute of Technology.)