We review several new and emerging methods of non-invasive neuromodulation and consider their potential to enhance creative cognition. This review covers the following techniques: transcranial electric stimulation (tES) (which includes transcranial direct current stimulation (tDCS), transcranial alternating current stimulation (tACS), and transcranial random noise stimulation (tRNS)), transcranial magnetic stimulation (TMS), transcranial focused ultrasound stimulation (tFUS), and neurofeedback training (NFT). For each technique, we explain the basic mechanism of action, review relevant research demonstrating its ability to enhance creative cognition, consider limitations and advantages, and suggest future research directions. Lastly, we offer broader conclusions and recommendations for the field of creativity neuromodulation.

The present study tested the learning avoidance model by examining the degree to which learning avoidance in various afterschool settings mediated the negative association between math anxiety and math achievement. Participants consisted of 207 third to sixth graders. Using a path model, findings showed that students’ math anxiety was negatively associated with both standardized math achievement test scores and parent-reported math school grades. Additionally, higher math anxiety was associated with more negative homework behaviors and less frequent participation in math-related extracurricular activities. Finally, the association between math anxiety and math achievement was partially mediated by negative math homework behaviors and participation in math extracurricular activities. Effort in math exam preparation did not contribute to explaining the association between math anxiety and math achievement. Overall, these findings support the learning avoidance model and suggest that avoidance behaviors in everyday learning in the afterschool setting may contribute to explaining the undesired math achievement among highly math anxious students.

Introduction: Reasoning is a complex form of human cognition whose nature has long been debated. While a number of neurocognitive mechanisms for deductive reasoning have been offered, one of the most prominent accounts is Mental Model Theory (MMT). According to MMT, humans are able to manipulate and represent information for reasoning and problem solving by leveraging the brain's evolved visuospatial resources. Thus, when solving deductive reasoning problems, reasoners build mental models of the essential pieces of information conveyed in the premises, with their relations to each other represented spatially-even when the information contained within a reasoning problem is not intrinsically spatial. Crucially, taking a spatially-based approach, such as building mental models, supports higher accuracy on deductive reasoning problems. However, no study has empirically tested whether explicitly training this mental modeling ability leads to improved deductive reasoning performance.Method: Therefore, we designed the Mental Models Training App, a cognitive training mobile application which requires participants to complete increasingly difficult reasoning problems while using an external mental modeling tool. In this preregistered study (https://osf.io/4b7kn), we conducted a between-subjects experiment (N = 301) which compared the Mental Models Training App to 3 distinct control conditions in order to examine which specific components (if any) of the training were causally responsible for improved reasoning performance.Results: Results demonstrate that, when compared to a passive control condition, the Mental Models Training App led to improvements in adults' verbal deductive reasoning performance both during and after the training intervention. However, contrary to our preregistered hypotheses, the training-induced improvements were not significantly larger than the effects of the active control conditions- one which included adaptive practice of the reasoning problems, and one which included adaptive practice as well as a spatial alphabetization control task.Discussion: Therefore, while the present results demonstrate the ability of the Mental Models Training App to enhance verbal deductive reasoning, they do not support the hypothesis that directly training participants mental modeling ability yields improved performance beyond the effects of adaptive practice of reasoning. Future research should examine the long-term effects of repeated usage of the Mental Models Training App, as well as transfer effects to other forms of reasoning. Finally, we present the Mental Models Training App as a free mobile application available on the Apple App store (https://apps.apple.com/us/ app/mental-models-training/id1664939931), in the hope that this translational research may be utilized by the general public to improve their reasoning ability.

Teachers' mathematical knowledge has important consequences for the quality of the learning environment they create for their students to learn mathematics. Yet relatively little is known about how teachers reason proportionally, despite the fact that proportional reasoning is foundational for several mathematics concepts and that ratios and proportional relationships constitute a major component of the middle school mathematics curriculum. In this study, we investigated how teachers reasoned proportionally on a nonroutine ratio task and the extent to which their proportional reasoning was able to predict their overall understanding of the relevant concepts: ratios and proportional relationships. Using data collected from 238 US mathematics teachers, we found that teachers' proportional reasoning could be grouped into four categories: incorrect, additive, relative, and proportional reasoning. Our results also indicated that teachers' overall knowledge of ratios and proportional relationships aligned with the way they reasoned proportionally, meaning that teachers who used incorrect reasoning on a separate task received the lowest scores on average on the ratios and proportional relationships measure, whereas those who reasoned proportionally had the highest mean scores on average. Implications of the study include the need to shift attention to the way teachers reason in relation to the two elements of proportional reasoning (covariance and invariance) to capture the nuances in their understanding of ratios and proportional relationships.

Advanced mathematics is seen as an integral component of secondary teacher preparation, and thus most secondary teacher preparation programs require their students to complete an array of advanced mathematics courses. In recent years, though, researchers have questioned the utility of proposed connections between advanced and secondary mathematics. It is simply not clear in many cases-to researchers, teacher educators, and teachers themselves-exactly how advanced mathematics content is related to secondary content. In this paper, we propose using a conceptual analysis-a form of theory in which one explicitly describes ways of reasoning about a particular mathematical idea-to address this issue. Specifically, we use conceptual analyses for the foundational notions of equivalence and inverse to illustrate how the ways of reasoning needed to support productive engagement with tasks in advanced mathematics can mirror and reinforce those that are similarly productive in school mathematics. To do so, we propose conceptual analyses for the key concepts of equivalence and inverse and show how researchers can use these conceptual analyses to identify connections to school mathematics in advanced mathematical tasks that might otherwise be obscured and overlooked. We conclude by suggesting ways in which conceptual analyses might be productively used by both teacher educators and future teachers.

In this article, the authors describe the two interpretations of mathematical expressions, as a process and as a product. They begin with an initial discussion of Tall's (2013) interpretations of expressions and connect this to state standards. Next, they describe the different interpretations of algebraic expressions based on their work with middle and high school students. They conclude with an example of how they provided instruction that promotes a deep understanding of the interpretations of expressions.

This article focuses on using simulations of practice in teacher education. We studied preservice teachers' engagement with a popular simulations platform, which creates "mixed-reality simulations" of five digital avatars controlled by a single live interactor. Because simulations are only an approximation of real practice, our overarching goal was to understand how mathematical stereotypes might arise in simulated spaces. We used Discourse analysis to classify the stereotypes present and the EQUIP observation tool to understand how PTs made participation opportunities available. We found that the simulations might have perpetuated overtly racist and sexist stereotypes and that negatively stereotyped students were afforded lower-quality opportunities to participate. We discuss how to mitigate potential harm caused and offer guidance for redesigning more equitable and antiracist simulations. Our goal is to raise critical questions for our field around the use of simulations of practice.

Because implementing and orchestrating collaborative problem-based learning (PBL) in K-12 classrooms requires teachers to manage multiple activities and access various teaching resources at the same time, this is an exceptionally complex task for designers to develop tools for orchestration support as well as for teachers to coordinate. The aim of the present study was to explore what classroom teachers perceived to be essential to support orchestration in PBL, but also to surface potential areas of tension between teacher and designer goals through a co-design approach. Thirteen K-12 classroom teachers were interviewed to find out what teachers consider integral to support orchestration in game-based PBL environments. We present the primary features that were identified as essential from the teacher interviews, which include the ability to (1) conduct assessment, (2) intervene and scaffold in different ways, and (3) visualize information. In addition, we discuss the design tensions between the goals of the teachers and designers as we work together on a shared view of what it means to design an intelligent assistant for classroom orchestration and present the design documents with implications.

Eye gaze patterns can reveal user attention, reading fluency, corrective responding, and other reading processes, suggesting they can be used to develop automated, real-time assessments of comprehension. However, past work has focused on modeling factual comprehension, whereas we ask whether gaze patterns reflect deeper levels of comprehension where inferencing and elaboration are key. We trained linear regression and random forest models to predict the quality of users' open-ended self-explanations (SEs) collected both during and after reading and scored on a continuous scale by human raters. Our models use theoretically grounded eye tracking features (number and duration of fixations, saccade distance, proportion of regressive and horizontal saccades, spatial dispersion of fixations, and reading time) captured from a remote, head-free eye tracker (Tobii TX300) as adult users read a long expository text (6500 words) in two studies (N = 106 and 131; 247 total). Our models: (1) demonstrated convergence with human-scored SEs (r = .322 and .354), by capturing both within-user and between-user differences in comprehension; (2) were distinct from alternate models of mind-wandering and shallow comprehension; (3) predicted multiple-choice posttests of inference-level comprehension (r = .288, .354) measured immediately after reading and after a week-long delay beyond the comparison models; and (4) generalized across new users and datasets. Such models could be embedded in digital reading interfaces to improve comprehension outcomes by delivering interventions based on users' level of comprehension.

Recent work reveals a left digit effect in number line estimation such that adults' and children's estimates for three-digit numbers with different hundreds-place digits but nearly identical magnitudes are systematically different (e.g., 398 is placed too far to the left of 401 on a 0-1000 line, despite their almost indistinguishable magnitudes; Lai et al., 2018, https://doi.org/10.1111/desc.12657). In two preregistered studies (N = 218), we investigate the scope and malleability of the left digit effect. Experiment 1 used a typical forward-oriented 0-1000 number line estimation task and an atypical reverse-oriented 1000-0 number line estimation task. Experiment 2 used the same forward-oriented typical 0-1000 number line estimation task from Experiment 1, but with trial-by-trial corrective feedback. We observed a large left digit effect, regardless of the orientation of the line in Experiment 1 or the presence of corrective feedback in Experiment 2. Further, analyses using combined data showed that the pattern was present across most stimuli and participants. These findings demonstrate a left digit effect that is robust and widely observed, and that cannot be easily corrected with simple feedback. We discuss the implications of the findings for understanding sources of the effect and efforts to reduce it.