Is There a Mathematician on Board?

As convergence science is emerging as a theme in cancer research, scientists from diverse backgrounds, including mathematics, are increasingly entering our research community. The captain of a Southwest Airlines flight recently paged in jest for a mathematician to help support fuel calculations that would enable a flight to arrive safely at the American Association for Cancer Research (AACR) Annual Meeting, epitomizing the need for well-trained mathematicians to address pressing problems. Here, we summarize the roles mathematicians can play in cancer research and the support needed to facilitate their entry into the cancer research field. The inclusion of scientific diversity across quantitative and engineering disciplines is critical for advancing the understanding and treatment of cancer.

Extent of magnitude representation deficit and relationship with arithmetic skills in children with 22q11.2DS.

BACKGROUND: Previous studies have produced conflicting results concerning the extent of magnitude representation deficit and its relationship with arithmetic achievement in children with 22q11.2 deletion syndrome. More specifically, it remains unclear whether deficits are restricted to visuospatial content or are more general and whether they could explain arithmetical impairment. METHODS: Fifteen 5- to 12-year-old children with 22q11.2 deletion syndrome and 23 age-matched healthy controls performed a non-symbolic magnitude comparison task. Depending on the trial, participants had to compare stimuli with high or low visuospatial load (visuospatial stimuli or temporal sequence of visual stimuli). The participants also completed a battery of arithmetic skills (ZAREKI-R) and a battery of global cognitive functioning (WISC-V or WPPSI-IV), from which working memory and visuospatial indices were derived. RESULTS: Children with 22q11.2DS responded as fast as healthy controls did but received fewer correct responses, irrespective of visuospatial load. In addition, their performance in the non-symbolic magnitude comparison task did not correlate with the ZAREKI total score, while the working memory index did. CONCLUSION: Children with 22q11.2DS might suffer from a global magnitude representation deficit rather than a specific deficit due to visuospatial load. However, this deficit alone does not seem to be related to arithmetic achievement. Working memory might be a better concern of interest in favoring arithmetic skills in patients with 22q11.2 deletion syndrome. TRIAL REGISTRATION: Clinicaltrials, NCT04373226 . Registered 16 September 2020.

Emotion regulation skills as a mediator of STEM teachers' stress, well-being, and burnout.

The teaching profession highly stressful, and teachers are often faced with challenging situations. This is particularly the case in STEM (science, technology, engineering, and math) education, which is a uniquely demanding and challenging field. This study examined the role of emotional regulation (ER) skills in STEM teachers' stress, well-being, and burnout. The sample included 165 STEM teachers in middle and high schools who completed standard online questionnaires on ER, stress, well-being, and burnout. They were also asked to comment on three videos depicting authentic mathematical and pedagogical situations. The results indicated that contrary to popular belief, seniority was not linked with levels of stress, difficulties in ER, lower levels of well-being, or higher levels of burnout. A structural equation model and bootstrapping analysis showed teachers' levels of stress predicted their well-being, and this link between stress and well-being was mediated by teachers' level of difficulty in ER. The study highlights the importance of STEM teachers' well-being and suggests the need to reduce stress and burnout by providing tools for teachers to regulate their emotions in the classroom.

Learners' Spontaneous Gesture Before a Math Lesson Predicts the Efficacy of Seeing Versus Doing Gesture During the Lesson.

Gestures-hand movements that accompany speech and express ideas-can help children learn how to solve problems, flexibly generalize learning to novel problem-solving contexts, and retain what they have learned. But does it matter who is doing the gesturing? We know that producing gesture leads to better comprehension of a message than watching someone else produce gesture. But we do not know how producing versus observing gesture impacts deeper learning outcomes such as generalization and retention across time. Moreover, not all children benefit equally from gesture instruction, suggesting that there are individual differences that may play a role in who learns from gesture. Here, we consider two factors that might impact whether gesture leads to learning, generalization, and retention after mathematical instruction: (1) whether children see gesture or do gesture and (2) whether a child spontaneously gestures before instruction when explaining their problem-solving reasoning. For children who spontaneously gestured before instruction, both doing and seeing gesture led to better generalization and retention of the knowledge gained than a comparison manipulative action. For children who did not spontaneously gesture before instruction, doing gesture was less effective than the comparison action for learning, generalization, and retention. Importantly, this learning deficit was specific to gesture, as these children did benefit from doing the comparison manipulative action. Our findings are the first evidence that a child's use of a particular representational format for communication (gesture) directly predicts that child's propensity to learn from using the same representational format.

The Ungrading Learning Theory We Have Is Not the Ungrading Learning Theory We Need.

Ungrading is an emancipatory pedagogy that focuses on evaluative assessment of learning. Self-regulated learning (SRL) has consistently been referred to as the learning theory that undergirds ungrading, but SRL-with its deficit frame in the literature and in practice-fails to uphold ungrading's emancipatory aims. An asset-framed learning theory-one that combines the cultural orientation of funds of knowledge with the power dynamics of community cultural wealth-is proposed as an alternative to SRL. The proposed learning theory aligns ungrading to its emancipatory aims and may provide an opportunity to better understand the learning that occurs in ungraded classrooms. Scholarly and practical impacts for Science, Technology, Engineering, and Mathematics (STEM), and specifically biology, educational research and practice include investigating the plausibility of mixing learning theories, aligning learning theory to emancipatory aims and researching how faculty activate funds of knowledge and community cultural wealth, both individually and collectively, in ungraded STEM classrooms.

New measures of number line estimation performance reveal children's ordinal understanding of numbers.

Children's performance on the number line estimation task, often measured by the percentage of absolute error, predicts their later mathematics achievement. This task may also reveal (a) children's ordinal understanding of the target numbers in relation to each other and the benchmarks (e.g., endpoints, midpoint) and (b) the ordinal skills that are a necessary precursor to children's ability to understand the interval nature of a number line as measured by percentage of absolute error. Using data from 104 U.S. kindergartners, we measured whether children's estimates were correctly sequenced across trials and correctly positioned relative to given benchmarks within trials at two time points. For both time points, we found that each ordinal error measure revealed a distinct pattern of data distribution, providing opportunities to tap into different aspects of children's ordinal understanding. Furthermore, children who made fewer ordinal errors scored higher on the Test of Early Mathematics Ability and showed greater improvement on their interval understanding of numbers as reflected by a larger reduction of percentage of absolute error from Time 1 to Time 2. The findings suggest that our number line measures reveal individual differences in children's ordinal understanding of numbers, and that such understanding may be a precursor to their interval understanding and later mathematics performance.

Mentorship Interventions in Postgraduate Medical and STEM Settings: A Scoping Review.

BACKGROUND: Mentorship is critical to success in postgraduate science, technology, engineering, math, and medicine (STEMM) settings. As such, the purpose of this study is to comprehensively explore the state of mentorship interventions in postgraduate STEMM settings to identify novel practices and future research directions. The selection criteria for reviewed articles included: 1) published between 2002 and 2022, 2) peer-reviewed, 3) in English, 4) postgraduate mentees, 5) a program where mentorship is a significant, explicit focus, and 6) a description of mentee outcomes related to the mentorship intervention. Overall, 2583 articles were screened, and 109 articles were reviewed. RESULTS: Most postgraduate STEMM mentorship intervention studies lack strong evidence to evaluate the effectiveness of the intervention, with only 5.5% of articles designed as randomized controlled trials. Most mentorship interventions (45.6%) were created for faculty, and few (4%) were for postdoctoral researchers. Also, only 18.8% of interventions focused on underrepresented groups in STEMM. Most interventions (53.7%) prescribed a dyadic structure, and there was more mentorship training for mentors than mentees. CONCLUSION: Overall, these findings identify gaps in mentorship interventions and provide step-by-step guidance for future interventions, including a consideration for underrepresented groups and postdoctoral scholars, robust mentorship training, and more randomized controlled trials.

Identifying conceptual neural responses to symbolic numerals.

The goal of measuring conceptual processing in numerical cognition is distanced by the possibility that neural responses to symbolic numerals are influenced by physical stimulus confounds. Here, we targeted conceptual responses to parity (even versus odd), using electroencephalogram (EEG) frequency-tagging with a symmetry/asymmetry design. Arabic numerals (2-9) were presented at 7.5 Hz in 50 s sequences; odd and even numbers were alternated to target differential, 'asymmetry' responses to parity at 3.75 Hz (7.5 Hz/2). Parity responses were probed with four different stimulus sets, increasing in intra-numeral stimulus variability, and with two control conditions composed of non-conceptual numeral alternations. Significant asymmetry responses were found over the occipitotemporal cortex to all conditions, even for the arbitrary controls. The large physical-differences control condition elicited the largest response in the stimulus set with the lowest variability (one font). Only in the stimulus set with the highest variability (20 drawn, coloured exemplars/numeral) did the response to parity surpass both control conditions. These findings show that physical differences across small sets of Arabic numerals can strongly influence, and even account for, automatic brain responses. However, carefully designed control conditions and highly variable stimulus sets may be used towards identifying truly conceptual neural responses.

Maths performance of adults with and without developmental coordination disorder (DCD): The role of working memory and maths anxiety.

Previous studies have shown that children with Developmental Coordination Disorder (DCD)/Dyspraxia have poorer maths performance compared to their neurotypical (NT) counterparts. However, no studies have explored the cognitive and emotional factors affecting the maths performance of adults with DCD. This study, therefore, investigated the role of working memory (WM), maths anxiety (MAS), and maths self-efficacy on the maths performance of adults with DCD. We found that adults with DCD had lower WM and maths performance and were more maths anxious than their NT peers. However, there were no significant differences in maths self-efficacy. When looking at the predictors of maths performance, we found a positive relationship between WM resources and the DCD maths performance, possibly indicating that they relied more on WM resources to perform simple mental arithmetic tasks than NTs. On the other hand, MAS had an inverse relationship with the NT maths performance but not with the DCD performance. The reasons and implications of these findings will be discussed.

Intervention effects on low performing preschoolers' early mathematical skills: Adding fundamental motor skill practice as a supporting method.

BACKGROUND: This study examined the effects of (1) combined early numeracy and fundamental motor skills (MovEN), (2) early numeracy, and (3) fundamental motor skills intervention programs on children's early mathematical and fundamental motor skills, and how individual background variables affect the effectiveness of these interventions. PROCEDURE: Together 50 preschoolers participated in the interventions (16 × 45 min sessions). Children's early numeracy, mathematical problem-solving, and fundamental motor skills were measured once before and twice after the interventions. MAIN FINDINGS: The results showed that the MovEN and early numeracy -interventions were effective in improving children's early numeracy, and mathematical problem-solving. Whereas the MovEN and fundamental motor skills interventions improved children's fundamental motor skills. From individual factors, only updating ability predicted the intervention's effectiveness over and above prior performance. CONCLUSION: The results suggest that children's early mathematical and fundamental motor skills can be supported effectively at the same time with the MovEN -intervention.

Bridging cognitive neuroscience and education: Insights from EEG recording during mathematical proof evaluation.

BACKGROUND: Much of modern mathematics education prioritizes symbolic formalism even at the expense of non-symbolic intuition, we contextualize our study in the ongoing debates on the balance between symbolic and non-symbolic reasoning. We explore the dissociation of oscillatory dynamics between algebraic (symbolic) and geometric (non-symbolic) processing in advanced mathematical reasoning during a naturalistic design. METHOD: Employing mobile EEG technology, we investigated students' beta and gamma wave patterns over frontal and parietal regions while they engaged with mathematical demonstrations in symbolic and non-symbolic formats within a tutor-student framework. We used extended, naturalistic stimuli to approximate an authentic educational setting. CONCLUSION: Our findings reveal nuanced distinctions in neural processing, particularly in terms of gamma waves and activity in parietal regions. Furthermore, no clear overall format preference emerged from the neuroscientific perspective despite students rating symbolic demonstrations higher for understanding and familiarity.

Fostering excellence: Nurturing motivation and performance among high- and average-ability students through need-supportive teaching.

When students with high cognitive abilities disengage from school, this implies a severe loss of talent to students themselves and to society. Hence, it is important to understand how teachers can prevent disengagement and underachievement in high-ability students. Whereas a large body of research has demonstrated that need-supportive teaching (i.e., the provision of autonomy support, involvement, and structure) and differentiated instruction relate positively to students' academic development, it remains unclear whether such practices would be equally, more, or less beneficial for high-ability students. Drawing on data from a longitudinal four-wave study among early adolescents from Flanders (N = 3586), this study showed that need-supportive teaching in math classes was positively associated with intrinsic motivation, behavioral engagement, and math performance in high-ability students, both at the level of between-student differences and at the level of changes in students over time. Standardized estimates were typically between 0.05 and 0.20 at the between-person level, indicating small effect sizes, with more modest effect sizes at the within-person level. Importantly, these associations were found to be generally equivalent across high- and average-ability students. Comparing the provision of need-supportive teaching to either high- or average-ability students, high-ability students particularly reported more autonomy support from their math teachers than average-ability students, with small effect sizes (i.e., Cohen's d between 0.16 and 0.27). These findings underline the importance of need-supportive teaching to support the motivational and academic development of both high- and average-ability students.

Accuracy of progress monitoring decision rules to evaluate response to instruction with two computer adaptive tests.

Computer adaptive tests have become popular assessments to screen students for academic risk. Research is emerging regarding their use as progress monitoring tools to measure response to instruction. We evaluated the accuracy of the trend-line decision rule when applied to outcomes from a frequently used reading computer adaptive test (i.e., Star Reading [SR]) and frequently used math computer adaptive test (i.e., Star Math [SM]). Analyses of extant SR and SM data were conducted to inform conditions for simulations to determine the number of assessments required to yield sufficient sensitivity (i.e., probability of recommending an instructional change when a change was warranted) and specificity (i.e., probability of recommending maintaining an intervention when a change was not warranted) when comparing performance to goal lines based upon a future target score (i.e., benchmark) as well as normative comparisons (50th and 75th percentiles). The extant dataset of SR outcomes consisted of monthly progress monitoring data from 993 Grade 3, 804 Grade 4, and 709 Grade 5 students from multiple states in the United States northwest. Data for SM were also drawn from the northwest and contained outcomes from 518 Grade 3, 474 Grade 4, and 391 Grade 5 students. Grade level samples were predominately White (range = 59.89%-67.72%) followed by Latinx (range = 9.65%-15.94%). Results of simulations suggest that when data were collected once a month, seven, eight, and nine observations were required to support low-stakes decisions with SR for Grades 3, 4, and 5, respectively. For SM, nine, ten, and eight observations were required for Grades, 3, 4, and 5, respectively. Given the length of time required to support reasonably accurate decisions, recommendations to consider other types of assessments and decision-making frameworks for academic progress monitoring are provided.

Evaluating language models for mathematics through interactions.

There is much excitement about the opportunity to harness the power of large language models (LLMs) when building problem-solving assistants. However, the standard methodology of evaluating LLMs relies on static pairs of inputs and outputs; this is insufficient for making an informed decision about which LLMs are best to use in an interactive setting, and how that varies by setting. Static assessment therefore limits how we understand language model capabilities. We introduce CheckMate, an adaptable prototype platform for humans to interact with and evaluate LLMs. We conduct a study with CheckMate to evaluate three language models (InstructGPT, ChatGPT, and GPT-4) as assistants in proving undergraduate-level mathematics, with a mixed cohort of participants from undergraduate students to professors of mathematics. We release the resulting interaction and rating dataset, MathConverse. By analyzing MathConverse, we derive a taxonomy of human query behaviors and uncover that despite a generally positive correlation, there are notable instances of divergence between correctness and perceived helpfulness in LLM generations, among other findings. Further, we garner a more granular understanding of GPT-4 mathematical problem-solving through a series of case studies, contributed by experienced mathematicians. We conclude with actionable takeaways for ML practitioners and mathematicians: models that communicate uncertainty, respond well to user corrections, and can provide a concise rationale for their recommendations, may constitute better assistants. Humans should inspect LLM output carefully given their current shortcomings and potential for surprising fallibility.

Ten recommendations for hosting a Diversity, Equity, Inclusion, and Justice (DEIJ) journal club.

Despite advances and social progress, the exclusion of diverse groups in academia, especially science, technology, engineering, and mathematics (STEM) fields, across the US and Europe persists, resulting in the underrepresentation of diverse people in higher education. There is extensive literature about theory, observation, and evidence-based practices that can help create a more equitable, inclusive, and diverse learning environment. In this article, we propose the implementation of a Diversity, Equity, Inclusion, and Justice (DEIJ) journal club as a strategic initiative to foster education and promote action towards making academia a more equitable institution. By creating a space for people to engage with DEIJ theories* and strategize ways to improve their learning environment, we hope to normalize the practice and importance of analyzing academia through an equity lens. Guided by restorative justice principles, we offer 10 recommendations for fostering community cohesion through education and mutual understanding. This approach underscores the importance of appropriate action and self-education in the journey toward a more diverse, equitable, inclusive, and just academic environment. *Authors' note: We understand that "DEIJ" is a multidisciplinary organizational framework that relies on numerous fields of study, including history, sociology, philosophy, and more. We use this term to refer to these different fields of study for brevity purposes.

Mentorship for Transfer Student Success in STEM Research: Mentor Approaches and Reflections.

Mentorship has been widely recognized as an effective means to promote student learning and engagement in undergraduate research experiences. However, little work exists for understanding different mentors' perceived approaches to mentorship, including mentorship of students from backgrounds and educational trajectories not well represented in science, technology, engineering, and mathematics (STEM). Transfer students, in particular, face unique trajectories in their pursuit of research opportunities, yet few studies investigate how mentors describe their approaches to supporting these students. Using semistructured interviews, this study examines how mentors approach mentoring students from diverse backgrounds as research trainees, with an emphasis on transfer students. First, using phenomenography as an analytical approach, we identified four categories describing variations in how mentors reflected upon or accounted for the transfer student identity in their approaches. We find that research mentors vary in their understanding and exposure to the transfer student identity and may have preconceived notions of the transfer student experience. Second, we present vignettes to illustrate how mentors' approaches to the transfer student identity may relate or diverge from their general approaches to mentoring students from different backgrounds and identities. The emerging findings have implications for developing effective mentorship strategies and training mentors to support transfer students.

The Value of Support: STEM Intervention Programs Impact Student Persistence and Belonging.

In response to unwaveringly high attrition from STEM pathways, STEM Intervention Programs (SIPs) support STEM students in effort to increase retention. Using mixed methods (survey and focus groups), we studied students at one university who were either supported or unsupported by SIPs to understand how students may differ in experiences believed to contribute to STEM persistence. We evaluated: sense of belonging, scientific self-efficacy, scientific community values, scientific identity, and STEM involvement. The enrollment status of students two and a half years postsurvey was also tracked. SIP students reported significantly higher science identity and sense of belonging and were more involved in STEM-related activities than counterparts unsupported by SIPs. Differences in these measures were correlated with race/ethnicity, college generation status, and age. Notably, SIP students had higher odds of persisting in STEM than students not supported by SIPs. Focus group data provide additional meaning to the measured survey constructs and revealed nuanced qualitative differences between SIP and non-SIP student experiences. Overall, being involved in a SIP at our institution trends positively with theoretical models that explain STEM student persistence. SIPs have the potential to provide and/or facilitate meaningful and critical support, and students without those intentional supports may be left behind.

A review of undergraduate research programs aimed at underrepresented students.

It is well-understood that the science, technology, engineering, and mathematics (STEM) fields have unique challenges that discourage recruiting and retaining underrepresented minorities. Research programs aimed at undergraduates have arisen as a critical mechanism for fostering innovation and addressing the challenges faced by underrepresented minorities. Here, we review various undergraduate research programs designed to provide exposure to undergraduates, with a focus on underrepresented minorities in STEM disciplines. We provide insight into selected programs' objectives, key features, potential limitations, and outcomes. We also offer recommendations for future improvements of each research program, particularly in the context of mentorship. These programs range from broad-reaching initiatives (e.g., Leadership Alliance) to more specific programs targeting underrepresented students. By offering a nuanced understanding of each program's structure, we seek to provide a brief overview of the landscape of diversity-focused STEM initiatives and a guide on how to run a research program effectively.

Fostering diversity in mathematics cognition.

Integrating diverse perspectives in psychological science can enhance innovation in research and allow research teams to better study diverse populations of individuals through an authentic lens. Despite recent efforts to better address issues of race and ethnicity in research samples, the field of psychology broadly-and the area of mathematics cognition specifically-has largely failed to support scientists from diverse racial and ethnic backgrounds. In this essay, we consider the unique contributions that scholars of color can make to psychological research in mathematics cognition. Next, we reveal common challenges faced by scholars of color and challenges to recruiting and maintaining scholars of color in our community with a focus on Black scholars. Finally, we propose actions for diversifying the "pipeline" of promising scholars.

The roles of mathematical language and emergent literacy skills in the longitudinal prediction of specific early numeracy skills.

Mathematical language (i.e., content-specific language used in mathematics) and emergent literacy skills predict children's broad numeracy development. However, little work has examined whether these domains predict development of individual numeracy skills (e.g., cardinality, number order). Thus, the aim of the current study was to examine longitudinal relations among mathematical language, emergent literacy skills, and specific early numeracy skills. Participants included 114 preschool children aged 3.12 to 5.26 years (M = 4.17 years, SD = 0.59). Specifically, this study examined whether mathematical language and three emergent literacy skills (print knowledge, phonological awareness, and general vocabulary) in the fall of preschool predicted 12 individual early numeracy skills in the spring, controlling for age, sex, rapid automatized naming, parent education, and autoregressors. Results indicated that mathematical language predicted development of most of the early numeracy skills (e.g., set comparison, numeral comparison, numeral identification), but findings for emergent literacy skills were not robust. Among the three emergent literacy skills, only print knowledge was a significant predictor of development in some specific numeracy skills, including verbal counting, number order, and story problems. Results highlight the important role of mathematical language in children's numeracy development and provide the foundation for future work in designing interventions to improve early numeracy skills.