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This project explored what constitutes "ethical practice of mathematics". Thematic analysis of ethical practice standards from mathematics-adjacent disciplines (statistics and computing), were combined with two organizational codes of conduct and community input resulting in over 100 items. These analyses identified 29 of the 52 items in the 2018 American Statistical Association Ethical Guidelines for Statistical Practice, and 15 of the 24 additional (unique) items from the 2018 Association of Computing Machinery Code of Ethics for inclusion. Three of the 29 items synthesized from the 2019 American Mathematical Society Code of Ethics, and zero of the Mathematical Association of America Code of Ethics, were identified as reflective of "ethical mathematical practice" beyond items already identified from the other two codes. The community contributed six unique items. Item stems were standardized to, "The ethical mathematics practitioner…". Invitations to complete the 30-min online survey were shared nationally (US) via Mathematics organization listservs and other widespread emails and announcements. We received 142 individual responses to the national survey, 75% of whom endorsed 41/52 items, with 90-100% endorsing 20/52 items on the survey. Items from different sources were endorsed at both high and low rates. A final thematic analysis yielded 44 items, grouped into "General" (12 items), "Profession" (10 items) and "Scholarship" (11 items). Moreover, for the practitioner in a leader/mentor/supervisor/instructor role, there are an additional 11 items (4 General/7 Professional). These results suggest that the community perceives a much wider range of behaviors by mathematicians to be subject to ethical practice standards than had been previously included in professional organization codes. The results provide evidence against the argument that mathematics practitioners engaged in "pure" or "theoretical" work have minimal, small, or no ethical obligations., (© 2024. The Author(s).)

Background: Mindfulness practices enhance executive function skills and academic achievement, spurring interest in integrating mindfulness interventions into education. Embedding mindfulness practice into a digital math game may provide a low‐cost, scalable way to induce mindfulness and boost game‐based learning, yet this approach remains unexplored. Objectives: We investigated the learning benefits of integrating mindfulness exercises in a digital math learning game and examined how students' trait mindfulness might moderate the outcomes. Methods: Two classroom studies were conducted with 404 5th and 6th grade students from six public schools in the U.S. (nStudy 1 = 227, nStudy 2 = 177). The two randomized controlled experiments assigned students to one of the three conditions: passive control (playing the digital learning game Decimal Point), story‐enriched active control, or mindfulness‐enriched condition. Trait mindfulness, learning gains, and in‐game problem‐solving (including problem‐solving duration, error count and correctness after reminder) were assessed. Study 2 included a manipulation check to better understand the effects of the mindfulness intervention. Results: Findings showed no significant differences in learning gains, problem‐solving duration or error count among the conditions. Students' trait mindfulness did not moderate these outcomes. Mindfulness reminders in the mindfulness‐enriched game led to more correct answers after errors than jokes in the story‐enriched game. Study 2 revealed that we failed to induce higher state mindfulness through the mindfulness inductions. Conclusions: Mindfulness prompts could be especially beneficial for students experiencing frustration during gameplay, warranting more exploration for digital game‐based instruction. We highlight barriers and future directions for fostering mindfulness through computer‐based instruction in classrooms. Lay Description: What is currently known about this topic?: Researchers focus on digital games as productive learning environments for math, with potential for higher learning gains compared with traditional methods. However, results are mixed, and not all games lead to improved math outcomes.Executive function (EF) skills are crucial for math learning, and mindfulness‐based interventions show promise in enhancing EF skills in school‐aged students.Embedding mindfulness practice into a digital math game may provide a low‐cost, scalable way to induce mindfulness and, in turn, boost EF skills and game‐based learning, yet this approach remains unexplored What does this paper add?: This paper presents the results of two randomized control trials investigating the feasibility and benefits of incorporating mindfulness exercises into a digital math game designed for middle school students. Benefits are compared to those of a story‐enriched and regular version of the same digital math learning game.The paper also explores variations in the effects of the mindfulness‐enriched game based on students' initial trait mindfulness levels.We observe that listening to mindfulness inductions at the beginning of game sessions do not induce mindfulness, and therefore does not benefit math learning.We find that mindfulness prompts received after recurrent errors can be beneficial for students' problem solving. Implications of study findings for practitioners: Our study provides important information on how digital learning game designers should attempt to induce mindfulness in a digital game to promote learning.Digital learning game designers should consider incorporating mindfulness exercises into their games strategically. Presenting mindfulness inductions in audio format at the beginning of game sessions may not induce mindfulness or benefit math learning. Instead, designers should focus on integrating mindfulness prompts at moments when students encounter frustration within the learning game.Beyond embedding audio mindfulness exercises in the game, learning designers should also consider alternative technological and game features to induce mindfulness within a learning game. [ABSTRACT FROM AUTHOR]

Spatial reasoning is critical to early mathematics learning, but it is unclear how early elementary educators learn to teach and are supported in teaching its comprising skills. One view of the available supports can be found by examining the alignment of spatial reasoning skills and mathematics education standards, as standards provide the content of the intended curriculum children are expected to learn at each grade level. This study used content analysis methods to investigate how spatial reasoning might be taught through broadly adopted early elementary education standards in the United States, the Kindergarten through Grade 2 Common Core State Standards for Mathematics. The paper describes the frequency and degree of explicitness with which 38 spatial reasoning skills are therein represented. Findings indicate that most standards implicitly relate to some form of spatial reasoning through a pedagogical reach of teaching expertise, but few standards contain explicit spatial linkages. The implications and limitations of this analysis are discussed in relation to teaching spatial reasoning in early elementary grades and students' opportunities to learn these critical skills. [ABSTRACT FROM AUTHOR]

Background: Providing students with worked out problem solutions is a beneficial instructional technique in STEM disciplines, and studying examples that have been worked out incorrectly may be especially helpful for reducing misconceptions in students with low prior content knowledge. However, past results are inconclusive and the effects of incorrect worked examples alone or in combination with correct examples remains unclear. Objectives: We aim to address whether studying incorrect examples alone or in combination with correct examples can support the reduction of students' fraction misconceptions, operationalized as errors made with high confidence. Methods: After incorrectly solving a sampling problem, 130 students in 4th through 11th grade in the U.S. were randomly assigned to a condition in an online problem set focused on fraction equivalence. Students studied either single‐type worked examples (i.e., correct or incorrect; n = 49) or combination‐type worked examples (correct and incorrect; n = 41) or engaged in a problem‐solving control (n = 50). Results: Studying a combination of correct and incorrect worked examples was as effective as the problem‐solving control with feedback at improving fraction equivalence knowledge and reducing the rate of high‐confidence errors. Students in both the combination condition and the problem‐solving with feedback condition outperformed those who studied either correct or incorrect worked examples alone. Conclusions: Results support the inclusion of a combination of correct and incorrect worked examples when teaching students with low prior content knowledge. Studying a combination of example types within an online tutor helps to reduce misconceptions about fractions, a topic students commonly struggle with. A problem‐solving task with corrective feedback worked equally well. Lay Description: What is already known about this topic: Studying worked examples of mathematical solutions improves student learning.Incorrect examples, either alone or in combination with correct examples, are particularly effective for improving learning for students with low prior knowledge in the target content.Comparing correct and incorrect examples is also effective at improving problem‐solving but this effect may be specific to those with high prior knowledge.Still unknown are the impacts of these different combinations of examples on misconceptions in particular. What this paper adds: We show that studying a combination of correct and incorrect examples reduces math misconceptions.Problem‐solving with corrective feedback within an online tutor also has this effect. Implications for practice and/or policy: Using a combination of example types will help reduce students' misconceptions about fractions. [ABSTRACT FROM AUTHOR]

This case study examined the current assessment practices in the math school of a large research university in the United States. After reviewing a sample of course syllabi offered in the spring 2021 semester, we descriptively summarized the use of 19 assessment methods in the school and examined the assessment patterns by subjects, class standings, and class size. Our study found that traditional homework and written tests were the most frequently used assessments in the school, while the use of learner-centered assessments was rare. Among the 19 assessment methods, we found significantly different usage of quizzes, participation scores, and projects by various course characteristics. Our case study demonstrates the gap between the recommended and actual assessment practice in U.S. higher education. We call for more future research that explores strategies to effect changes and increase the use of learner-centered assessment in higher education institutions. [ABSTRACT FROM AUTHOR]

Across multiple countries the term "big ideas" of mathematics has become a construct advocated as important for teachers' mathematical knowledge. Indeed, several policy or position statement documents about math learning in the United States (U.S.) have stated that "big ideas" of math is a crucial construct for teacher knowledge. With this study we sought to determine if there was consistency about this "big idea" construct that teachers of mathematics in the U.S. are advised to know. To this end, we conducted a content analysis of resources for U.S. teachers of preschool through grade 12. We determined that few resources defined a big idea and those that did lacked agreement with each other. Although most resources delineating big ideas cited Charles (2005) as the basis of their use of the construct, our analysis of the actual big ideas in each resource revealed inconsistent implementation of Charles' theoretical perspective. Thus, to move research and practice forward by more precisely defining and prioritizing this abstract construct we (a) clarified a definition, (b) specified five criteria, and (c) constructed a scholar- and teacher-friendly framework: The Big Ideas Framework. This framework consists of three ordinal levels to distinguish and prioritize the importance of big ideas based on relative size and power: Mighty Mega Math Ideas, Power Math Ideas, and Strong Math Ideas. Moreover, the big ideas construct has focused on Mathematical Knowledge for Teaching (MKT), whereas we urge the field to shift its theoretical perspective to value the entire construct or at least the two most powerful levels of the framework as aspects of Common Content Knowledge. In other words, we urge teachers and mathematics teacher educators to foreground Mighty Mega Math Ideas and Power Math Ideas with P-12 students and families to empower those we serve. Furthermore, given the dearth of peer-reviewed research about big ideas, we encourage a new branch of scholarship to analyze the impact of the practical recommendations we offered here. [ABSTRACT FROM AUTHOR]

Teachers set the tone for their classrooms, but what teacher beliefs shape students' sense of belonging? We investigate how teachers' mindsets—or their beliefs about learning and school—relate to adolescents' individual and collective reports of classroom belonging. Our pre-registered analyses include a multilevel design of how 1,200 US middle school students (ages 11–13; 50% female; 49% low income; 40% White, 30% Latinx, 13% Black, 9% Asian) and their teachers responded to surveys on educational mindsets. We find teachers' growth mindset and confidence in teaching positively relate to students' math class belonging—explaining between 30 and 40% of belonging among classes. Our data suggest a teacher's own sense of school belonging is unrelated to the belonging students feel in class, suggesting teachers' broad feelings of belonging may not influence students' specific classroom feelings of belonging as anticipated. These findings reinforce the notion that what teachers think and believe influence how students feel when in class. [ABSTRACT FROM AUTHOR]

When asked to estimate how much their state or nation has contributed to history, people typically provide unreasonably large estimates, claiming that their group has contributed much more to history than nongroup members would estimate, demonstrating collective overclaiming. Why does such overclaiming occur? In the current study we examined factors that might predict collective overclaiming. Participants from 12 U.S. states estimated how much their home state contributed to U.S. history, completed measures of collective narcissism and numeracy, and rated the importance of 60 specific historical events. There was a positive relationship between collective overclaiming and collective narcissism, a negative relationship between collective overclaiming and numeracy, and a positive relationship between collective overclaiming and the importance ratings of the specific events. Together, these results indicate that overclaiming is partially and positively related to collective narcissism and negatively related to people's ability to work with numbers. We conclude that collective overclaiming is likely determined by several factors, including the availability heuristic and ego protection mechanisms, in addition to collective narcissism and relative innumeracy. [ABSTRACT FROM AUTHOR]

Using Future of Families and Child Wellbeing data (N = 4488, waves collected between 2001 and 2010), the current study examined mothers' and fathers' trajectories of engagement in learning activities (e.g., reading, storytelling, playing with toys) from infancy to age 5, predictors of the trajectories (family poverty, coresidence, child temperament), whether those trajectories predicted children's academic skills (vocabulary knowledge, reading, and math ability) at age 9, and moderators of the trajectories. Mothers' and fathers' learning activities decreased significantly over time as children got older, and rates of decline were greater when families experienced poverty and were nonresident. Children's academic skills were significantly lower when mothers and fathers reported higher rates of decline in learning activities during early childhood; effect sizes were small. Highlights: Examined both mothers' and fathers' learning activity trajectories from infancy to age 5. Found that mothers' and fathers' engagement in learning activities decreased significantly from infancy to age 5. Children's academic skills were significantly lower when mothers and fathers reported higher rates of decline in learning activities during early childhood; effect sizes were small. [ABSTRACT FROM AUTHOR]