Scaffolding learning: From specific to generic with large language models.

Large language models such as ChatGPT have been shown to excel in solving complex math problems. However, they cannot solve basic arithmetic problems such as 758*639 = 484,362. This makes us ponder if LLMs have been trained to solve math and science problems in the right way. When a student learns math at school, she or he starts with arithmetic, then moves to word problems, polynomials, and calculus. Each skill she or he acquires will be used in the next stage to solve more advanced problems. In this paper we propose Scaffolding Learning for LLMs, which imitates how a student learns a subject in a step-by-step manner. For example, we first train an LLM to perform highly specific operations such as multiplication and division, and then apply such "skills" in a more generic task such as solving word problems. This is related to Curriculum Training, which trains a model on tasks following a specific order, such as training on easy tasks first and then gradually increases the difficulty. Our proposed approach goes from specific tasks to generic ones, which can be considered as a special case of Curriculum Training. Our empirical studies show that when an LLM has "mastered" a specific skill, only a small amount of training is required to teach it to apply the skill to a more generic application.

A bird's-eye view of research practices in mathematical cognition, learning, and instruction: Reimagining the status quo.

Research on mathematical cognition, learning, and instruction (MCLI) often takes cognition as its point of departure and considers instruction at a later point in the research cycle. In this article, we call for psychologists who study MCLI to reflect on the "status quo" of their research practices and to consider making instruction an earlier and more central aspect of their work. We encourage scholars of MCLI (a) to consider the needs of educators and schools when selecting research questions and developing interventions; (b) to compose research teams that are diverse in the personal, disciplinary, and occupational backgrounds of team members; (c) to make efforts to broaden participation in research and to conduct research in authentic settings; and (d) to communicate research in ways that are accessible to practitioners and to the general public. We argue that a more central consideration of instruction will lead to shifts that make research on MCLI more theoretically valuable, more actionable for educators, and more relevant to pressing societal challenges.

An Exploratory Mixed-Methods Analysis of Factors Contributing to Students' Perceptions of Inclusion in Introductory STEM Courses.

In this exploratory mixed-methods analysis of students' perceptions of inclusion in introductory STEM courses for STEM majors, we asked students to rate inclusion in their class and to provide an open-text explanation of their rating. Analyzing 1930 qualitative responses resulted in a codebook containing academic, identity, and nonspecific categories. The majority of responses (>80%) cited academic factors such as interactions between students and instructors or course elements and policies. Most academic responses aligned with evidence-based teaching practices fostering inclusion, describing a range of strategies and policies instructors can implement to increase students' perceptions of inclusion. A small number of student responses indicated that their perception of the required knowledge background for the course impacted course inclusivity. Few differences in frequency distributions were found between subgroups examined (gender, race and ethnicity, self-reported inclusion score, and discipline). Additionally, tracking a subset of students (135) across three courses revealed that most (80%) cited different factors influencing their perception of inclusion in each course. This suggests students' perceptions of inclusive practices are complex, and most students recognize multiple factors that influence their inclusion. Overall, our findings suggest instructors can significantly influence students' perceptions of inclusion by using multiple inclusive teaching strategies and course policies.

Gestures can help children learn mathematics: how researchers can work with teachers to make gesture studies applicable to classrooms.

The gestures we produce serve a variety of functions-they affect our communication, guide our attention and help us think and change the way we think. Gestures can consequently also help us learn, generalize what we learn and retain that knowledge over time. The effects of gesture-based instruction in mathematics have been well studied. However, few of these studies are directly applicable to classroom environments. Here, we review literature that highlights the benefits of producing and observing gestures when teaching and learning mathematics, and we provide suggestions for designing research studies with an eye towards how gestures can feasibly be applied to classroom learning. This article is part of the theme issue 'Minds in movement: embodied cognition in the age of artificial intelligence'.

The relationship between technological pedagogical content knowledge and belief among preservice mathematics teachers.

The increasing interest in exploring beliefs about teaching mathematics with technology has led educators to employ belief systems as a framework for understanding the impact of technology on math instruction. However, the complex nature of pre-service teachers' beliefs in teaching mathematics with technology involves various dimensions. This study aims to investigate the predictive relationship between Technological Pedagogical Content Knowledge (TPACK) sub-components and beliefs in teaching mathematics with technology, revealing a statistically significant direct impact. Utilizing a correlational research approach, we collected data from a cohort of 159 Malaysian pre-service teachers with a focus on mathematics education. Structural Equation Modelling (SEM) was employed to analyze the proposed model. The measurement model exhibited a satisfactory fit with the collected data. Notably, technological knowledge (25 %), technological pedagogical content knowledge (69 %), and technological content knowledge (39 %) significantly influence discovery learning, while technological knowledge (24 %), technological pedagogical content knowledge (74 %), and technological content knowledge (30 %) significantly influence multiple representations. This underscores the critical role of TPACK in shaping educators' perspectives and practices, providing a crucial avenue for enhancing technology integration in teaching mathematics.

Associations between parents' autonomy supportive management language and children's science, technology, engineering, and mathematics talk during and after tinkering at home.

We conducted a time series analysis of parents' autonomy supportive and directive language and parents' and children's STEM (science, technology, engineering, and mathematics) talk during and after a problem-solving activity (i.e., tinkering). Parent and child dyads (N = 61 children; Mage = 8.10 years; 31 boys; 54% White) were observed at home via Zoom. After tinkering, a researcher elicited children's reflections, and approximately 2 weeks later dyads reminisced together about the experience. During tinkering, the more autonomy supportive STEM talk parents used in 1 min, the more children talked about STEM in the next minute. During reminiscing, parents' autonomy support was also associated with children's STEM talk. Results suggest the importance of considering how both the content and style of parents' talk can support children's STEM engagement.

Counting on Change: Conquering Challenges in Teaching Pharmaceutical Calculations.

All pharmacists are expected to accurately perform pharmaceutical calculations to ensure patient safety. In recent years, there have been trends in declining performance on the North American Pharmacist Licensure Examination related to calculations. Understanding the cause of this decline and determining methods to correct underlying issues could benefit pharmacy administration, faculty, students, and patients. The aims of this commentary are to present the factors impacting the students' pharmaceutical calculations abilities, discuss the consequences of declining math skills, and provide a call to action for scholarship of teaching and learning pertaining to calculations, as well as increased administrative support to rectify this challenge.

Instructional Influencers: Teaching Professors as Potential Departmental Change Agents in Diversity, Equity, and Inclusion.

At many research-intensive universities in North America, there is a disproportionate loss of minoritized undergraduate students from Science, Technology, Engineering, and Mathematics (STEM) majors. Efforts to confront this diversity, equity, and inclusion (DEI) challenge, such as faculty adoption of evidenced-based instructional approaches that promote student success, have been slow. Instructional and pedagogical change efforts at the academic department level have been demonstrated to be effective at enacting reform. One potential strategy is to embed change agent individuals within STEM departments that can drive change efforts. This study seeks to assess whether tenure-track, teaching-focused faculty housed in STEM departments are perceived as influential on the instructional and pedagogical domains of their colleagues. To answer this, individuals across five STEM departments at large, research-intensive campuses identified faculty who were influential upon six domains of their instruction and pedagogy. Social network analysis of individuals in these departments revealed heterogeneity across the instructional domains. Some, like the teaching strategies network, are highly connected and involve the majority of the department; while others, like the DEI influence network, comprise a significantly smaller population of faculty. Importantly, we demonstrate that tenure-track, teaching-focused faculty are influential across all domains of instruction, but are disproportionately so in the sparsely populated DEI influence networks.

Adapting STEMM in Hawai'i: Necessary actions for one of the most diverse places in the United States.

Hawai'i's diverse population prime it to be an exemplary environment to study representation in science, technology, engineering, mathematics, and medicine (STEMM). In actuality, Hawai'i has low STEMM enrollment and therefore, low representation in STEMM. What primarily inhibits Hawai'i from having a strong STEMM workforce is the lack of education in STEMM, resources allocated to STEMM, and mentorship to succeed in STEMM. Other factors such as cultural values, high costs of living, and geographical barriers also contribute to Hawai'i's low STEMM enrollment. To combat these issues, I offer suggestions to encourage STEMM enrollment, such as directing funds toward after-school education. I also suggest combatting the lack of resources by providing more online opportunities for students and workers. As for Hawai'i's low mentorship, I suggest that more programs be created within communities and universities to create a platform for mentors and mentees to network. This manuscript seeks to highlight these areas of improvement and recognize lessons to be learned from Hawai'i, thus serving as a resource for individuals internationally.

Building integrated number sense in adults and children: Comparing fractions-only training with cross-notation number line training.

Mounting evidence points to the predictive power of cross-notation rational number understanding (e.g., 2/5 vs. 0.25) relative to within-notation understanding (e.g., 2/5 vs. 1/4) in predicting math outcomes. Although correlational in nature, these studies suggest that number sense training emphasizing integrating across notations may have more positive outcomes than a within-notation focus. However, this idea has not been empirically tested. Thus, across two studies with undergraduate students (N = 183 and N = 181), we investigated the effects of a number line training program using a cross-notation approach (one that focused on connections among fractions, decimals, and percentages) and a within-notation approach (one that focused on fraction magnitude representation only). Both number line approaches produced positive effects, but those of the cross-notation approach were larger for fraction magnitude estimation and cross-notation comparison accuracy. In a third study (N = 63), we adapted the cross-notation number line training for use in place of typical classroom warm-up activities for middle school students. Similar to the results with undergraduate students, the cross-notation training program yielded positive benefits for middle school students over a typical warm-up activity (fraction arithmetic practice). Together, these results suggest the importance of an integrated approach to teaching rational number notations, an approach that appears to be uncommon in current curricula.

The intersection of parent questions, child skills, and activity context in informal science, technology, engineering, and math learning.

Adult verbal input occurs frequently during parent-child interactions. However, few studies have considered how parent language varies across informal STEM (science, technology, engineering, and math) activities. In this study, we examined how open and closed parent questions (a) differed across three STEM activities and (b) related to math, science, and vocabulary knowledge in their preschool-aged children. A total of 173 parents and their preschool children (Mage = 4 years) from lower socioeconomic households were video-recorded participating in three STEM-related activities: (a) a pretend grocery store activity, (b) a bridge-building challenge, and (c) a book read about a science topic. Parent questions were categorized as open or closed according to the presence of key question terms. Results indicate that the three activities elicited different frequencies of parent open and closed questions, with the grocery store activity containing the most open and closed questions. Children's science knowledge was predicted by the frequency and proportion of parent open questions during the book read. These results enhance our understanding of the role of parent questions in young children's language environments in different informal learning contexts.

Knowing what they know: Preschool teachers' knowledge of math skills and its relation to instruction.

Math experiences during the preschool years play an important role in children's later math learning. Preschool teachers exhibit considerable variability in the amount and types of mathematics activities they engage in with their students; one potentially important source of these individual differences is adults' knowledge of early math development. The current study aimed to describe preschool teachers' knowledge of numeracy, patterning, and spatial/geometric skills developed in preschool and its relation to their reported mathematics instruction. Participants (N = 83) completed a survey in which they judged whether particular early math skills could be observed in typically developing 4-year-olds in the United States and reported their frequency of engaging in different math instructional activities. Pre- and in-service preschool teachers' knowledge varied across the different domains (i.e., numeracy, patterning, and spatial/geometric) of mathematical thinking, but their reported frequency of instruction did not. Teachers who were found to be more accurate in their knowledge of early math development were more likely to report higher frequency of math instruction; looking specifically at the domains, the strength of association between knowledge and instruction was the strongest for numeracy. Such findings highlight the possibility that supporting preschool teachers' knowledge of the range of math skills their students can be developing may be one component of improving early math teaching and learning.

Reflections: enhancing critical thinking in science education by implementing philosophy elements into training.

In this work, I describe the trajectory of philosophy and science as separate disciplines from their early days as quite overlapping fields to their clear divergence in the latest centuries. From personal experience, I discuss the benefits of exposure to philosophy and closely related courses in undergraduate studies and bring to the forefront the positive aspects of integrating philosophy of science courses in graduate science, technology, engineering, and mathematics (STEM) curriculum. I also briefly offer some additional steps institutions can take to foster unity between areas of science and philosophy by incorporating interdisciplinary activities.

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.

Nurse academics' self-reported insights into the teaching of undergraduate nursing numeracy: A national cross-sectional study.

AIMS: The aim of this research was to explore the teaching of undergraduate nursing numeracy in tertiary education settings in Australia. Specifically, it explored and identified: (1) the most common basic numeracy concepts taught, (2) additional training and resources to support numeracy teaching, (3) who is best placed to teach numeracy and (4) the preferred methods of teaching medication calculations. BACKGROUND: Nurse academics are required to teach nursing numeracy to undergraduate nursing students who enter university unprepared to accurately calculate medication dosages. It is important that students understand numeracy concepts as this is then applied to contextualised clinical applications. Nurse academics teach basic numeracy; however, the literature reveals that nurse academics do not consider themselves mathematics teachers and that experts in this area are better suited to teaching this skill. There are a dearth of studies about the nurse academics who conduct the teaching and this study seeks to fill that gap by exploring firsthand the nurse academics' self-reported insights into the teaching of undergraduate nursing numeracy. DESIGN: Cross-sectional survey. The setting was Australian universities that deliver an accredited undergraduate nursing degree. METHODS: Purposive sampling was used to recruit Australian nurse academics (n = 170), sessional or permanent who currently teach all aspects of nursing numeracy and medication calculations to undergraduate nursing students. Data were collected between Nov 2023 - Feb 2024 using an online survey platform and analysed using a descriptive content analysis. RESULTS: Nurse academics taught basic arithmetic most commonly (92 %), yet most (90 %) had not received professional development or additional training in how to teach these concepts. To assist with numeracy teaching, resources were requested (47 %) as were the need for mathematics learning support staff (82 %). The formula method was most commonly taught (91 %), however, most participants (94 %) were willing to learn and to teach other methods of calculating medications. CONCLUSIONS: This research suggests an evidenced-based education framework be created to support and guide nurse academics when teaching all aspects of nursing numeracy and medication calculations. Building the teaching capacity of nurse academics in this vital area will enhance student competence and contribute to patient safety.

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.

How teachers make connections among ideas in mathematics instruction.

Conceptual understanding involves understanding connections among ideas within a domain. In this chapter, we consider how teachers support students in learning about connections among ideas in mathematics. We review research focusing on teachers' connection making in mathematics classrooms, and we consider several dimensions of variability in that connection making. Across three corpora of lessons that varied in students' grade levels (first grade to college), cultural settings (United States and China), and mathematics content, we found that all teachers produced linking episodes, but the frequency with which they did so varied substantially, raising new questions about the sources and consequences of that variability. Teachers of first-grade students in China routinely engaged their students in co-constructing links; teachers of middle schoolers and college students in the United States typically explained links to students. Linking episodes targeted many different types of connections, including connections between representations, connections between principles and exemplars, connections between procedures and concepts, and connections between concepts and real-world instantiations. Across all three corpora, teachers expressed linked ideas multimodally in a majority of linking episodes. Based on the findings, we present several hypotheses about how teacher behaviors may support students' understanding of connections among ideas, and we suggest directions for future work.

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.

Arithmetic fluency and number processing skills in identifying students with mathematical learning disabilities.

BACKGROUND: Students with mathematical learning disabilities (MLD) struggle with number processing skills (e.g., enumeration and number comparison) and arithmetic fluency. Traditionally, MLD is identified based on arithmetic fluency. However, number processing skills are suggested to differentiate low achievement (LA) from MLD. AIMS: This study investigated the accuracy of number processing skills in identifying students with MLD and LA, based on arithmetic fluency, and whether the classification ability of number processing skills varied as a function of grade level. METHODS AND PROCEDURES: The participants were 18,405 students (girls = 9080) from Grades 3-9 (ages 9-15). Students' basic numerical skills were assessed with an online dyscalculia screener (Functional Numeracy Assessment -Dyscalculia Battery, FUNA-DB), which included number processing and arithmetic fluency as two factors. OUTCOMES AND RESULTS: Confirmatory factor analyses supported a two-factor structure of FUNA-DB. The two-factor structure was invariant across language groups, gender, and grade levels. Receiver operating characteristics curve analyses indicated that number processing skills are a fair classifier of MLD and LA status across grade levels. The classification accuracy of number processing skills was better when predicting MLD (cut-off < 5 %) compared to LA (cut-off < 25 %). CONCLUSIONS AND IMPLICATIONS: Results highlight the need to measure both number processing and arithmetic fluency when identifying students with MLD.

Empowering STEM students: A university-wide mentorship program fostering retention and belonging.

In the face of a challenging climate STEM (Science, Technology, Engineering and Mathematics) higher education that is resistant to Diversity, Equity, and Inclusion efforts aimed to increase and retain students from historically excluded groups (HEGs), there is a critical need for a support structure to ensure students from HEGs continue to be recruited retained. The Biology Undergraduate and Master's Mentorship Program (BUMMP) embodies this commitment to fostering scientific identity, efficacy, and a sense of belonging for first-generation and historically underserved undergraduate and master's students at UC San Diego. The mission of BUMMP is to cultivate a sense of belonging, instill confidence, and nurture a strong scientific identity amongst all its participants. At its core, the three pillars of BUMMP are (1) mentorship, (2) professional development, and (3) research. Quality mentorship is provided where students receive personal guidance from faculty, graduate students, postdocs, and industry leaders in navigating their career pathways. Complementing mentorship, BUMMP provides paid research opportunities and prioritizes professional development by offering workshops designed to enhance students' professional skills. These three pillars form the backbone of BUMMP, empowering students from all backgrounds and ensuring their retention and persistence in STEM. So far, we've served over 1350 mentees, collaborated with 809 mentors, and had over 180 mentees actively engaged in BUMMP-sponsored research activities. The primary focus of this paper is to provide a programmatic guideline for the three pillars of BUMMP: mentorship, professional development, and research. This will offer a blueprint for other institutions to establish similar mentorship programs. Additionally, the paper highlights the impact of the BUMMP program and surveyed mentees who have participated in the mentorship and research component of BUMMP. We showed that mentorship and research experience enhance students' sense of belonging, science identity, and science efficacy, which are key predictors of retention and persistence in pursuing a STEM career. Overall, BUMMP's expansive efforts have made a tremendous impact at UC San Diego and will continue to foster a community of future leaders who will be prepared to make meaningful contributions to the scientific community and beyond.