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.

The Individual Development Plan (IDP) is a common mentoring tool in higher education. Students and postdoctoral researchers can use an IDP to facilitate conversations with their mentors and create action plans to support future goals. The entire process helps mentees achieve both short- and long-term objectives. Little is known about how historically underrepresented minority groups are supported during this process. This study investigated IDP implementation at 504 minority serving institutions (MSIs) that primarily serve African American, Hispanic/Latinx, and Native-American populations. Using content analysis, we systematically reviewed the publicly available IDP tools and policies at each MSI. Although several crucial mentoring components and implementation strategies were identified, there was a noticeable absence of emphasis on multicultural mentoring guidance and psychosocial support throughout the process. Our findings offer decision-makers and faculty mentors insights into supporting minority trainees and lay the foundation for future research in the field of IDPs.

This paper reports on the results of a four-day teaching experiment that supported two algebra teachers to develop a combinatorial meaning for algebraic structure. The purpose of the teaching episodes was to support the teachers (a) to establish a combinatorial understanding for algebraic structure (Tillema & Burch, 2022) by generalizing the cubic identity, (a + b)3 = a3 + 3a2b + 3ab2 + b3, as a symbolization of quantitative and combinatorial relationships out of a contex-tualized problem (Tillema & Gatza, 2016) and (b) to develop a combinatorial meaning as a mobilization of their understanding through a series of algebraic tasks (cf. Thompson et al., 2014). The findings from this study contribute to research literature on teachers' mathematical meanings within secondary algebra by investigating how teachers' combinatorial meanings developed and how differences in their combinatorial meanings impacted their algebraic reasoning. The findings demonstrate a combinatorial pathway for supporting the development of expanding and factoring as reversible polynomial operations (cf. Sangwin & Jones, 2017).

Children's beliefs about the contribution of effort and ability to success and failure shape their decisions to persist or give up on challenging tasks, with consequences for their academic success. But how do children learn about the concept of challenge? Prior work has shown that parents' verbal responses to success and failure shape children's motivational beliefs. In this study, we explore another type of talk-parent and child talk about difficulty-which could contribute to children's motivational beliefs. We performed secondary analyses of two observational studies of parent-child interactions in the United States (Boston and Philadelphia) from age 3 to fourth grade (Study 1, 51% girls, 65.5% White, at least 43.2% below Federal poverty line) and at first grade (Study 2, 54% girls, 72% White, family income-to-needs ratio M [SD] = 4.41 [2.95]) to identify talk about difficulty, characterize the content of those statements, and assess whether task context, child and parent gender, child age, and other parent motivational talk were associated with the quantity of child and parent difficulty talk. We found that many families did discuss difficulty, with variation among families. Parents and children tended to use general statements to talk about difficulty (e.g., That was hard!), and task context affected child and parent difficulty talk. In the NICHD-SECCYD dataset, mothers' highlighting how task features contributed to task difficulty was positively correlated with their process praise, suggesting that this talk could be motivationally relevant.

Adolescents' (n = 342, 169 boys) general algebra and algebra word problems performance were assessed in 9th grade as were intelligence, academic achievement, working memory, and spatial abilities in prior grades. The adolescents reported on their academic attitudes and anxiety and their teachers reported on their in-class attentive behavior in 7th to 9th grade. There were no sex differences on the general algebra measure or for mathematics achievement, but boys had an advantage on the algebra word problems measure (d = .51) and for spatial abilities (ds = .29 to .58). Boys had higher mathematics self-efficacy (d = .24 to .33), lower mathematics anxiety (ds = -.31 to -.53) and were less attentive in classrooms (ds = -.28 to -.37). A series of structural equation models revealed the sex difference for algebra word problems was mediated by spatial abilities and mathematics anxiety, controlling myriad confounds. Public Significance Statement Sex differences in mathematics are typically small but larger for word problems. The latter assess the ability to use mathematics in problem-solving situations and are often included on high-stakes tests. Boys' higher spatial abilities appeared to provide them with an advantage and girls' mathematics anxiety a disadvantage in solving algebra word problems.

Who has mathematical authority in your classroom, and what does authority look like? Find out different ways you can help students gain authority.

Self-regulated learning (SRL), learners' monitoring and control of cognitive, affective, metacognitive, and motivational processes, is essential for learning. However, cognitive and metacognitive SRL strategies are not typically used accurately leading to poor learning outcomes. Intelligent tutoring systems (ITSs) attempt to address this issue by prompting and scaffolding learners to engage in SRL via using pedagogical agents. However, current literature does not examine the extent to which learners' deployed strategies are functional or dysfunctional in relation to pedagogical agent scaffolding. The current study collected 117 undergraduate students' data as they learned with MetaTutor, an ITS about the human circulatory system. Participants were randomly assigned to either the (1) Prompt and Feedback Condition where pedagogical agents scaffolded cognitive and metacognitive SRL strategies or (2) Control Condition where no prompts or feedback were provided. Results demonstrated that learners who received prompts by the pedagogical agents to engage in SRL had higher learning gains as well as greater frequencies across most strategies compared to those in the Control Condition who relied on self-initiated strategy use. While sequential transitions across all strategies were not significant between conditions, further analysis grounded in Complex Systems Theory found that learners who were prompted to engage in strategies demonstrated a significantly lower degree of repetition and balance between repetitive and novel patterns of strategy use. The findings suggest that pedagogical agents within MetaTutor successfully scaffolded the functional deployment of cognitive and metacognitive SRL strategies and are indicative of higher learning after interacting with ITSs.

This report documents how one undergraduate student used set-based reasoning to reinvent logical principles related to conditional statements and their proofs. This learning occurred in a teaching experiment intended to foster abstraction of these logical relationships by comparing the relationships between predicates within the conditional statements and inference structures among various proofs (in number theory and geometry). We document the progression of Theo's set-based emergent model (Gravemeijer, 1999) from a model-of the truth of statements to a model-for logical relationships. This constitutes some of the first evidence for how students can abstract such logical concepts in this way and provides evidence for the viability of the learning progression that guided the instructional design.

We examined the relationships between different aspects of mathematics engagement for 285 students in their first year of high school in the United States. Path Analyses were used to trace the relationships between students’ self-reported prior motivation and appraisals of control and value of mathematics, perceptions of teacher support and peer support. These variables and observed teacher and peer support as coded from video by researchers, were examined as potentially impacting students’ self-reported in-the moment affect and task-level control and value appraisals Our results showed three key contributions. First, significant paths corresponded to relationships predicted by Control Value Theory (CVT) across a particularly robust set of variables and over the course of their first semester in high school. Second, results added further nuance by considering the objects that students’ in-the-moment emotions were directed toward, showing distinctions between positive and negative emotions directed at the mathematics task, students’ teachers and peers, and selves. Third, results more closely considered the impact of both observed and perceived aspect of support from peers and teachers in the classroom, in both its academic and social forms. Implications are discussed for theory and practice. © 2022, The Author(s).

This study explored how different formats of instructional visuals affect the accuracy of students' metacognitive judgments. Undergraduates (n = 133) studied a series of five biology texts and made judgments of learning. Students were assigned randomly to study the texts only (text only), study the texts with provided visuals (provided visuals group), study the texts and generate their own visuals (learner-generated visuals group), or study the texts and observe animations of instructor-generated visuals (instructor-generated visuals group). After studying the texts and making judgments of learning, all students completed multiple-choice comprehension tests on each text. The learner-generated and instructor-generated visuals groups exhibited significantly higher relative judgment accuracy than the text only and provided visuals groups, though this effect was relatively small. The learner-generated visuals group also required more study time and was more likely to report the use of visual cues when making their judgments of learning.