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In school, at least in the US, we were taught to multiply by hand according to a standard algorithm. Most people find that algorithm difficult to use, and many children fail to learn it. We propose a new way to make sense of this difficulty: to treat explicit computation as perceptually supported physical and mental action. Based on recent work in neuroscience, we trace the flow of arithmetic information to emphasize demands on visual working memory and attention. We predict that algorithms that make moderate demands on memory and attention will work better than others that make stronger demands. We suggest that the judicious use of spatial schemas can reduce such cognitive demands. Experimental evidence from children in an inner-city school supports this claim. Our work suggests new ways to think about instruction. The goal should be to minimize demands that present obstacles and maximize instead what human eyes, bodies, and brains do well. (Contains 7 figures and 2 tables.)

The article presents three activities that promote probabilistic thinking with middle school students in the U.S. Activity 1 uses experimental probability as students play the game of rock, paper, and scissors. In activity 2, a table and a tree diagram help students understand the theoretical probability behind the game. Activity 3 allows three people to play the game. The results of these activities can give teachers valuable insight into adapting these activities to fit their classroom needs.

A "crisis account" of shortages of well-qualified scientists, engineers, mathematicians and technologists has shaped education policy in the UK and the USA for decades. The apparent poor quality of school science education along with insufficient numbers of well-qualified teachers have been linked to skills shortages by government and other agencies since at least the time of the Second World War. There is, however, an alternative account that challenges the received view of a skills deficit and questions the evidence for sustained and long-term shortages across the sector. This paper provides an historical account of some of the main events that have characterised debates over the supply and demand of science and engineering professionals in the UK and the USA and the implications that this has had for science education policy. Starting from the end of the Second World War, the paper looks at the key challenges to the evidence that underpins the shortage debate and considers the consequences that more than seven decades of crisis accounts have had on the recruitment and retention of highly skilled scientists and engineers. The paper shows that while the shortage debate has a long history, it is one that is characterised by poor quality data as well as methodological and conceptual challenges. It argues that there is no consensus view about the existence of a skills deficit and that while there may have been short-lived shortfalls in specialist areas, there is little evidence in support of widespread and far reaching shortages as the rhetoric often claims.

Calls to advance students' ability to engage in mathematical reasoning practices including conjecturing, generalising and justifying (CGJ) place significant new demands on teachers. This case study examines how Mathematics Studio provided opportunities for a team of U.S. middle school teachers to learn about these practices and ways to promote them in the classroom. Findings demonstrate how CGJ readings and focused discussions, coupled with repeated cycles of collaborative lesson planning, observation and debrief, supported the development of teacher knowledge, professional community, and teaching resources. In addition, this paper explores the role school leadership played in facilitating Math Studio to ensure these learning opportunities were realised. Documenting how Math Studio features and participants contributed to teachers' ability to implement CGJ focused lessons not only provides insights into the difficulties teachers have shifting instruction, but also adds to our understanding of school-embedded professional development more generally.

This synthesis paper explores current leadership training in science, technology, engineering and mathematics (STEM) education in Bulgaria. The analysis begins with discussion of global factors influencing the implementation of leadership training in STEM education in general and then presents information about the current status of leadership training in Bulgaria with emphases on the country's economics, politics and geographical location as specific factors influencing leadership education. A short background of Bulgaria is presented with regard to population, gross domestic product, educational system, engineering force and possible need for leaders in industry in Bulgaria and the European Union. The paper provides an overall view about the current status of leadership training in all Bulgarian universities offering STEM education and concentrates specifically on two major universities by examining their currently offered programmes. As part of the discussion, similar training elements in other European countries and the USA are presented. (Contains 1 table.)

Math education in the United States remains resistant to systemic change, and our country pays the price. Stemhagen's article "Democracy and School Math" further confirms this trend. Despite repeated calls for reform, decades of research on how people learn, millions of dollars invested in teacher professional development, and years of politicized debate, the math wars rage on--between those who believe students have the capacity to construct their own mathematical ideas and others who insist mastery of the traditional canon must come first. Meanwhile, algebra failure among secondary students remains rampant and elementary education majors report the greatest rates of math anxiety of any college major. Adults and children alike joke about being terrible at math, seemingly unaware of the extent to which this innumeracy serves as a barrier to full participation in democracy as well as to the realization of their individual goals, hopes, and dreams. In the math education community itself, there is little discussion of the unique role mathematics can play in preparing students for democracy. In this short paper, I offer a more detailed conceptualization of democratic mathematics education and discuss the role of constructivism in bringing these ideas to fruition. I suggest that a shift in the power dynamic that characterizes most mathematics classrooms will be a key component in moving beyond the gridlock.

Definitions play an essential role in mathematics. As such, mathematics teachers and students need to flexibly and productively interact with mathematical definitions in the classroom. However, there has been little research about mathematics teachers' understanding of definitions. At an even more basic level, there is little clarity about what teachers must know about mathematical definitions in order to support the development of mathematically proficient students. This paper reports on a qualitative study of pre-service secondary mathematics teachers choosing, using, evaluating, and interpreting definitions. In an undergraduate capstone course for mathematics majors, these future teachers were assigned three tasks which required them to (1) choose and apply definitions of functions, (2) evaluate the equivalence of definitions of functions, and (3) interpret and critique a secondary school textbook's definition of a specific type of function. Their performances indicated that many of these pre-service mathematics teachers had deficiencies reasoning with and about mathematical definitions. The implications of these deficiencies are discussed and suggestions for teacher educators are proposed. (Contains 3 tables and 1 figure.)

This paper reports upon particular aspects of a study carried out by Delice in 2003, the main aim of which was to compare the performance of students in the 16-19 age group from Turkey and England on trigonometry of "A-level standard" and then to compare the curriculum and assessment provision in each country to seek possible explanations for differences in performance. Overall, the Turkish students did much better with the algebraic, manipulative aspects of trigonometry, the English students did better with the application of trigonometry to practical situations. The comparison of curriculum and assessment provision in the light of these results raises several issues about the current A-level mathematics syllabus. It may be that there is a tendency to think that mathematics is very much the same in any country, however this research supports previous work [Kawanaka, T., Stigler, J.W. and Hiebart, J. (1999) Studying Mathematics Classrooms in Germany, Japan and the United States: Lessons from the TIMSS Video Study] where mathematics was indeed found to be taught and learnt differently and the roles of teachers and students were different across three countries (Germany, Japan and the USA). The paper begins by briefly describing the research and presenting some of the results. There then follows a discussion of these results within the context of curriculum and assessment provision within each country. Finally, issues for the current A-level syllabus arising out the results are presented.

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]

The ten scholarly papers in Sex, Drugs and Body Counts explore the generation and propagation of numbers that drive policy decisions in the U.S. government regarding human trafficking, drug trade, and armed conflict (including the war on terror). Each of these papers, written by different authors, provides an illuminating insight into how some of the numbers we hear or read in the news are derived. While the general message of the papers tends to be depressing, namely that the numbers driving U.S. policy vary from being slightly suspect to clearly fabricated, the book does provide positive examples of how accurate numbers can be obtained and how the numbers that are being used can be interpreted. As a teaching resource, the book provides instructors an opportunity to deepen their understanding of how quantitative data are used in U.S. policy, allowing them to explore these issues in class. Individual papers from the book could be used in a general education course (either in mathematics or in a field related to the topics) as a way to introduce students to reading quantitatively dense material. In a course more focused on the topics of the book and with a more quantitatively literate audience, the entire book could probably be assigned as reading. [ABSTRACT FROM AUTHOR]

This paper draws from a broad study that explored mathematics teachers’ engagement with textbooks within the Lesson Study context. In the current paper, we report on teachers’ use of mathematics textbook activities to inform their instructional decisions during collaborative lesson planning of numeric and geometric patterns. The study took place within the Lesson Study (LS) context – a teacher development practice that emphasises, inter alia, collaborative lesson planning. Data was collected by observing teachers during collaborative lesson planning and through interviews. Data analysis was informed by the Mathematics Knowledge for Teaching (MKT) framework and Modes of teacher engagement with the textbook. Findings suggest that teachers’ instructional decisions are mainly stimulated by the textbooks, teachers use textbook activities with fidelity, and they seldom adapt the activities drawn from the textbooks. However, where adaptation occurs teachers do it superficially. We contend that the capacity to conduct in-depth interrogation of the text is a derivative of mathematics subject matter knowledge (SMK) as well as pedagogical content knowledge (PCK). Therefore, the widespread adoption of text without interrogation could be indicative of the lack of requisite content knowledge and pedagogical skills. [ABSTRACT FROM AUTHOR]

Introduction: The authors examined a tablet computer application (iPad app) for its effectiveness in helping students studying pre-algebra to solve mathematical word problems. Methods: Forty-three visually impaired students (that is, those who are blind or have low vision) completed eight alternating mathematics units presented using their traditional literacy medium or an iPad app. Twenty percent of the mathematics problems included graphics such as maps, line graphs, and bar graphs. During each session, teachers of visually impaired students rated the amount of support they provided for students and the student motivation. Results: Students answered more mathematics problems correctly when using the iPad app and, overall, teachers reported that their students were more motivated with the app than with their traditional literacy medium. Students often used the hints provided in the app when they did not solve a problem correctly the first time. Discussion: Visually impaired students and their teachers found the app and graphics to be easy to use and motivating. The built-in Scratch pad was used by almost all students who were print users. Implications for practitioners: The study results contribute to the growing body of knowledge about the potential value of tablet-type devices for use by visually impaired students. [ABSTRACT FROM AUTHOR]

Background: Teachers often rely on the use of open‐ended questions to assess students' conceptual understanding of assigned content. Particularly in the context of mathematics; teachers use these types of questions to gain insight into the processes and strategies adopted by students in solving mathematical problems beyond what is possible through more close‐ended problem types. While these types of problems are valuable to teachers, the variation in student responses to these questions makes it difficult, and time‐consuming, to evaluate and provide directed feedback. It is a well‐studied concept that feedback, both in terms of a numeric score but more importantly in the form of teacher‐authored comments, can help guide students as to how to improve, leading to increased learning. It is for this reason that teachers need better support not only for assessing students' work but also in providing meaningful and directed feedback to students. Objectives: In this paper, we seek to develop, evaluate, and examine machine learning models that support automated open response assessment and feedback. Methods: We build upon the prior research in the automatic assessment of student responses to open‐ended problems and introduce a novel approach that leverages student log data combined with machine learning and natural language processing methods. Utilizing sentence‐level semantic representations of student responses to open‐ended questions, we propose a collaborative filtering‐based approach to both predict student scores as well as recommend appropriate feedback messages for teachers to send to their students. Results and Conclusion: We find that our method outperforms previously published benchmarks across three different metrics for the task of predicting student performance. Through an error analysis, we identify several areas where future works may be able to improve upon our approach. Lay Description: What is already known about this topic: Open‐ended questions are used by teachers in the domain of mathematics to assess their students understanding but automated support for these types of questions are limited in online learning platforms. Recent advancements in areas of machine learning and natural language processing have led to promising results in a range of domains and applications. What this paper adds: Emulating how teachers identify similar student answers can be used to build tools that support teachers in assessing and providing feedback to student open‐ended work. Implications for practice: Developing better automated supports can increase the amount of direct feedback students receive to guide their learning. [ABSTRACT FROM AUTHOR]

The importance of students' problem-posing abilities in mathematics has been emphasized in the K-12 curricula in the USA and China. There are claims that problem-posing activities are helpful in developing creative approaches to mathematics. At the same time, there are also claims that students' mathematical content knowledge could be highly related to creativity in mathematics, too. This paper reports on a study that investigated USA and Chinese high school students' mathematical content knowledge, their abilities in mathematical problem posing, and the relationships between students' mathematical content knowledge and their problem-posing abilities in mathematics.

The authors comment on the article by Morris and Hiebert in three ways. First, they add thoughts about why improvement efforts often focus on teachers, rather than teaching. Second, they offer evidence from U.S. lesson study research that focus on teaching can improve both students' learning and teachers' learning. Finally, they suggest that the instructional products and common assessments advocated by Hiebert and Morris are not sufficient, and that they need to be accompanied by practice-based, collegial learning in which teachers build shared knowledge and commitments for the hard work of improvement. Their research indicates that lesson study focuses on teaching, but improves teachers as well, increasing mathematical knowledge and beliefs that support instructional improvement, as well as improving student learning. (Contains 2 figures.)

The claim that faculty conduct research is one of the main justifications for the modern university. Supposedly, academe carries out important, cutting-edge inquiries in which society has an interest. In fact, states this author, research at American universities is becoming narrow and artificial, out of touch with social realities, and of interest mainly to other academics. This development the author calls scholasticism, after the medieval philosophers whom one remembers as being similarly ingrown. In recent decades, conservative critics of academe have focused on political correctness--the tendency of academics to privilege liberal perspectives to the exclusion of conservative ones. But scholasticism may pose a greater threat to the heart of university life, which is the intelligent construction of arguments. Rather than address important issues thoughtfully, today's academics are becoming pedants, mostly writing only for other specialists. Scholasticism is squeezing the intellectual life out of academe, and driving it toward other venues, including government and the blogosphere. In this article, the author describes the rise of scholasticism and asks about causes and cures: Why has obscurantism mushroomed in recent decades, and what can be done about it? He relies mostly on the trends he has seen in his own department and at New York University over more than thirty years. (Contains 35 footnotes.)

The purpose of this paper is to show the similarities as well as the differences of fundamental fraction knowledge owned by preservice elementary teachers from the United States (N = 89) and Taiwan (N = 85). To this end, we examined and compared their performance on an instrument including 15 multiple-choice test items. The items were categorized into four different types of fundamental fraction constructs, including part-whole relationship, quotient, equivalence, and meanings of operations. Each item was embedded in the area, linear, or set model except for the items constructed out of the meaning of operations. Several items were featured with a pictorial illustration. Quantitative analysis showed that U.S. preservice teachers were significantly outperformed by their Taiwanese counterparts overall. The difference between the two groups was statistically significant on 12 of 15 items. Findings suggest that preservice elementary teachers from both countries need to be better prepared in their understanding of the meaning of fraction multiplication or division operations. Findings also suggest that U.S. preservice elementary teachers need to be more knowledgeable in dealing with fraction problems embedded in a linear model. Further research is suggested to study the issues raised from the findings. (Contains 9 tables.)

This paper seeks to identify significant trends in mathematics curricula and teaching approaches in two education systems: the United States (a highly decentralised education system) and England (a highly centralised education system), with focus on 16-to-19-year-olds. The paper adopts a two-fold perspective: an historical overview, and comparison of the areas of convergence and divergence across both education systems. The trajectory of mathematical development is expressed through timelines of core concepts and ideas which chronicle the sequence of events and philosophies that have shaped the development of mathematics teaching and learning. By tracing the trajectory of mathematics through history, the paper provides a greater awareness of how different factors influence how mathematics is taught across two disparate educational jurisdictions. The paper affords opportunities to reflect on and draw conclusions about what constitutes meaningful mathematics teaching and curriculum approaches for 21st century learner. [ABSTRACT FROM AUTHOR]

Peer review is the gold standard for scientific communication, but its ability to guarantee the quality of published research remains difficult to verify. Recent modeling studies suggest that peer review is sensitive to reviewer misbehavior, and it has been claimed that referees who sabotage work they perceive as competition may severely undermine the quality of publications. Here we examine which aspects of suboptimal reviewing practices most strongly impact quality, and test different mitigating strategies that editors may employ to counter them. We find that the biggest hazard to the quality of published literature is not selfish rejection of high-quality manuscripts but indifferent acceptance of low-quality ones. Bypassing or blacklisting bad reviewers and consulting additional reviewers to settle disagreements can reduce but not eliminate the impact. The other editorial strategies we tested do not significantly improve quality, but pairing manuscripts to reviewers unlikely to selfishly reject them and allowing revision of rejected manuscripts minimize rejection of above-average manuscripts. In its current form, peer review offers few incentives for impartial reviewing efforts. Editors can help, but structural changes are more likely to have a stronger impact. [ABSTRACT FROM AUTHOR]

This paper introduces a bibliometric, citation network-based method for assessing the social validation of novel research, and applies this method to the development of high-throughput toxicology research at the US Environmental Protection Agency. Social validation refers to the acceptance of novel research methods by a relevant scientific community; it is formally independent of the technical validation of methods, and is frequently studied in history, philosophy, and social studies of science using qualitative methods. The quantitative methods introduced here find that high-throughput toxicology methods are spread throughout a large and well-connected research community, which suggests high social validation. Further assessment of social validation involving mixed qualitative and quantitative methods are discussed in the conclusion. [ABSTRACT FROM AUTHOR]

Mathematics Learning Support (MLS) has been widely available in Higher Education Institutions in the United States (US) for decades. However, until recently, there has been little research that considered the extent of provision. In this paper, we present the results of a survey of MLS with responses from 268 institutions across the US, which indicate that such support is well established across responding institutions. To place these results in context, we compare them to other recent international surveys of provision. We discuss what these findings mean and the collaborative opportunities that are available for US and international practitioners and researchers in this area. [ABSTRACT FROM AUTHOR]

Background: Computer‐based assessment allows for the monitoring of reader behaviour. The identification of patterns in this behaviour can provide insights that may be useful in informing educational interventions. Objectives: Our study aims to explore what different patterns of reading activity exist, and investigates their interpretation and consistency across different task sets (units), countries, and languages. Three patterns were expected: on‐task, exploring and disengaged. Methods: Using log data from the PISA 2012 digital reading assessment (9226 students from seven countries), we conducted hierarchical cluster analyses with typical process indicators of digital reading assessments. We identified different patterns and explored whether they remained consistent across different units. To validate the interpretation of the identified patterns, we examined their relationship to performance and student characteristics (gender, socio‐economic status, print reading skills). Results and Conclusions: The results indicate a small number of transnational clusters, with unit‐specific differences. Cluster interpretation is supported by associations with student characteristics—for example, students with low print reading skills were more likely to show a disengaged pattern than proficient readers. Exploring behaviour tended to be exhibited only once across the three units: It occurred in the first unit for proficient readers and in later units for less skilled readers. Major Takeaways: Behavioural patterns can be identified in digital reading tasks that may prove useful for educational monitoring and intervention. Although task situations are designed to evoke certain behaviours, the interpretation of observed behavioural patterns requires validation based on task requirements, assessment context and relationships to other available information. Lay Description: What is already known about the subject matter?: Students differ in how they read, comprehend and use digital information.Indicators from process data provide insight about how students engage with digital reading tasks. What does this paper add to the subject matter?: Based on multiple process indicators, a small number of clusters indicating different behavioural activity can be distinguished.These clusters can be described as on‐task, passive, hasty, exploring, disengaged, persistent and lost interest.A meaningful interpretation of the clusters must consider the requirements of the underlying tasks. Implications for practice and/or policy: Knowledge of how students engage with digital resources may provide useful feedback for teachers to guide students' learning or intervene when they struggle.Educational monitoring: The high comparability of country‐specific results suggests an invariant set of solution strategies in the digital reading assessment. [ABSTRACT FROM AUTHOR]

Background: Valuable safeguards against fast‐spreading conjectures about learning in times of fear and uncertainty are evidence‐based approaches to the assessment of the impact of sudden and unforeseen disruptions on learning practices. The present research focused on physics learning in such times because conceptual and computational literacy in physics is critical to the development of a scientifically and technologically literate society. Objectives: The present research aimed (a) to offer an objective assessment of whether performance differences in a physics course of the general education curriculum existed between the face‐to‐face medium (familiar mode of instruction) and the online medium (unfamiliar mode of instruction) for both male and female students, and then (b) to develop a response to the evidence collected to ensure a quality education for all parties involved. The research intended to fill two critical gaps in the extant literature: mixed findings concerning students' performance in the face‐to‐face and online mediums as well as scarce coverage of specific domains of knowledge that are critical to STEM learners. Methods: Students' performance was examined as a function of the type of assessment (formative and summative), instructional mode (online and face‐to‐face), and gender. An understudied student population of STEM students of Middle Eastern descent without prior formal exposure to online instruction was targeted. Results and Conclusions: In both formative and summative assessments, male students performed better online than face‐to‐face, whereas the performance of female students was either higher online or equivalent between instructional mediums. The evidence collected suggested that consideration be given to remedies that foster academic success in the face‐to‐face instructional medium, particularly for male students. Takeaways: An evidence‐based approach to learning dismantled emotion‐driven expectations regarding the impact of the online medium on physics learning, and encouraged new perspectives about instruction. Lay Description: What is already known?: Ongoing debates on the impact of the pandemic on students' learning shape decisions regarding future reliance on the online medium for instruction. What this paper adds: The extant literature is mixed concerning performance in the face‐to‐face and online mediums, including particular domains of knowledge critical to STEM learning.This study focused on physics learning in an understudied population of STEM students who were unaccustomed to online instruction.Performance was higher online than face‐to‐face, but gender differences emerged. Implications for practice: Lessons learned focused on the flexibility of online learning and on the need to develop materials to enhance learning in males enrolled in face‐to‐face or hybrid/blended classes. [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]

Background: The sudden growth in online instruction due to COVID‐19 restrictions has given renewed urgency to questions about remote learning that have remained unresolved. Web‐based assessment software provides instructors an array of options for varying testing parameters, but the pedagogical impacts of some of these variations has yet to be examined. Objectives: The current study examines whether question order affects student performance on online college math assessments. Drawing on the literature of testing and math anxiety, we hypothesized that difficult questions near the beginning of an assessment would have a destructive effect on student confidence, which would in turn have a deleterious effect on their performance. Methods: We employed an observational 'big data' methodology, analysing 23,468 final exams completed by students in 10 different courses over eight semesters at a Math Emporium in a large technical university in the eastern United States. Students were freshmen and sophomores enrolled in non‐engineering math courses. We regressed the final score on the difficulty level of the first and second questions, controlling for several other factors. Results and Conclusions: We found that several factors—day of the week, amount of time before the deadline, number of minutes spent on the exam—have more of an impact on score than question order. This pattern was consistent across sexes. Takeaways: Our findings contradict some previous studies, which have found that difficult early questions degrade student performance, and that this affect is more pronounced in females. This work enriches our understanding of how students respond to online assessment. Lay Description: What is already known about this topic: Previous studies have had mixed results about the effect of question difficulty ordering on student performance.Furthermore, few studies have examined this issue for computer assessments. What this paper adds: We employ a novel methodology with a uniquely large data set.Our findings indicate that difficulty ordering has no effect on student performance. Implications for practice: Math instructors can use the random ordering feature of computer assessment generating tools because question order does not affect performance. [ABSTRACT FROM AUTHOR]

The article presents the report of the president of the Operations Research Society of America (ORSA) in the U.S. to the membership. He outlines the problems and activities of the society including the amendment to eliminate associate membership, affiliation with the division of mathematics of the national research council, commemorative plaque for the Lanchester prize, consideration of employment of full-time staff member, quality of presentations at ORSA meetings, plans for an international conference on operations research and management sciences and participation in management of the society by members from industry.

For the past forty years, United States school districts have increasingly hired mathematics specialists to support the teaching and learning of mathematics. Despite the prevalence of this professional development structure, this is a relatively new research topic for the mathematics education field. In this paper, we report findings from an exploration of literature between 1981 and 2018 to examine the role of mathematics specialists (MSs). In particular, we examine: (a) MS positioning across research; (b) historical trends of school‐based MS research; and (c) orientations of school‐based MSs within research. Using the McGatha and Rigelman framework as an analytic lens, we found that beyond the positions identified in their framework (coach, intervention specialist, teacher), there were four additional MS positionings within the research (learner, other p‐12 stakeholder, university stakeholder, unknown). Ultimately, we forward an expansion to the McGatha and Rigelman framework to include these new categories, as well as contextual descriptions and working definitions to support future research in more accurately and robustly capturing the ways in which MSs are investigated and reported on in research. [ABSTRACT FROM AUTHOR]

This paper discusses issues centered around three topics related to studying textbooks in an information age. First considered are the multiple roles of textbooks, from a source of content and questions to a vehicle for changing the curriculum. Second are some of the lessons we have learned from studies comparing student performance with different textbooks within the United States, including the recognition that a common test given to students using two different curricula cannot cover the differences between the curricula and still be fair to all the students. Third is the consideration of textbooks as a delivery system and their comparison with electronic delivery of curriculum, including a discussion of the overt nature of textbooks as compared to the covert nature of electronic systems. We distinguish this use of electronic devices from the use of computers and calculators to do mathematics. Finally, predictions are given regarding the future of textbooks in an age of electronic delivery systems. The perspective of this paper is from the United States and based on the author's four decades of experience directing studies of instruction and student performance with different mathematics textbooks. [ABSTRACT FROM AUTHOR]

In a recent paper Engle et al. (Commun Math Phys 354:231–246, 2017) showed that there is a unique state on the reduced holonomy–flux ∗ -algebra of homogeneous isotropic loop quantum cosmology, that is invariant under residual diffeomorphims. This result has been claimed to be true both for the Ashtekar–Bojowald–Lewandowski framework and for that introduced by the present author. Unfortunately, the uniqueness proof relies on an incorrect argument which spoils the second case. In our short note, we are going to patch this issue, this way keeping the nice uniqueness result in both cases. Moreover, we will even extend the underlying operator algebraic statements as this might help later for studying higher-dimensional models. [ABSTRACT FROM AUTHOR]

The ability to produce timely and accurate flu forecasts in the United States can significantly impact public health. Augmenting forecasts with internet data has shown promise for improving forecast accuracy and timeliness in controlled settings, but results in practice are less convincing, as models augmented with internet data have not consistently outperformed models without internet data. In this paper, we perform a controlled experiment, taking into account data backfill, to improve clarity on the benefits and limitations of augmenting an already good flu forecasting model with internet-based nowcasts. Our results show that a good flu forecasting model can benefit from the augmentation of internet-based nowcasts in practice for all considered public health-relevant forecasting targets. The degree of forecast improvement due to nowcasting, however, is uneven across forecasting targets, with short-term forecasting targets seeing the largest improvements and seasonal targets such as the peak timing and intensity seeing relatively marginal improvements. The uneven forecasting improvements across targets hold even when “perfect” nowcasts are used. These findings suggest that further improvements to flu forecasting, particularly seasonal targets, will need to derive from other, non-nowcasting approaches. [ABSTRACT FROM AUTHOR]

Sexual scientists typically default to appraising the reliability of their self-report measures by calculating one or more α coefficients. Despite the prolific use of α, few researchers understand how to situate and make sense of α within the psychometric theories used to develop the measures used in their research (e.g., latent variable theory) and many unknowingly violate the assumptions of α. In this paper, we describe the disconnect between α and latent variable theory and the subsequent restrictive assumptions α makes. Simultaneously, we introduce an alternative metric of reliability—omega (ɷ)—that is compatible with latent variable theory. Subsequently, we provide a tutorial to walk readers through didactic examples on how to calculate ɷ metrics of reliability using the getOmega() function—a simple open-source function we created to automate the estimation of ɷ. We then introduce the Measurement of Sexuality and Intimacy Constructs (MoSaIC) project to provide insight into the state of reliability in sexuality science. We do this through contrasting α and ɷ estimates of reliability across seven sexuality measures, selected based on their emerging and pre-existing relevance and influence in the field of sexuality, in both a queer (LGBTQ+) sample (n = 545) and a United States' representative sample (n = 548). We finish our paper with pragmatic suggestions for editors, reviewers, and authors. By more deeply understanding one's options of reliability metrics, sexual scientists may carefully consider how they present and assess their measures' reliability, and ultimately help improve our science's replicability. [ABSTRACT FROM AUTHOR]

This paper focuses on commonalities and differences of three approaches to large-scale professional development (PD) in mathematics education, based on two studies from Germany and one from the United States of America. All three initiatives break new ground in improving PD targeted at educating 'multipliers,' and in all three cases specific design principles for successful PD are defined, implemented, and discussed. All three teams systematically investigate the success of their PD activity and thereby discuss their theoretical assumptions, research questions, methods, and results. Given the goal of scaling up, the initiatives are pilot projects due to the relatively small number of participants. The paper highlights the diversity of approaches, each including various specific strengths but also some limitations. This is done by analyzing the three studies regarding the features 'large-scale PD and scientific knowledge on it', 'goals and design of PD', 'research design and methods', and 'research results and implications'. Overall, the studies help to understand the enormous challenges of the field when aiming at large-scale PD and systematically investigating and reflecting its impact. One prominent challenge is teacher educators' double role of intervening and investigating. All three studies recommend a continued or even stronger focus on participants' practice and its challenges. It makes sense to assume that the focus on participants' practice and strengths is even more important when starting further cascades. [ABSTRACT FROM AUTHOR]

This paper examines the relationships among the quality and quantity of parent-child shared book reading (SBR) engagements and children's reading and mathematics outcomes in preschool. Additionally, we explore how child and family characteristics predict the quality and quantity of SBR. Quantity was measured using parental reports of the frequency of SBR. Quality was measured by observational protocols evaluating for questioning, vocabulary, and discussion depth. A structural equation model was estimated using data from a nationally representative sample of 700 children living in the United States from the Early Childhood Longitudinal Study-Birth cohort. Results indicated that the quality of book reading was associated with children's mathematics outcomes, and the quantity was associated with reading outcomes controlling for contextual variables. Socioeconomic status, race or ethnicity, and children's age predicted the quality and quantity of book reading experiences. These findings indicate that frequent exposure to high-quality book reading may positively impact children's mathematics and reading development, but that variation in SBR exists. SBR is a common practice among many parents; helping parents understand the multiple benefits of the practice may further increase the frequency and quality of the engagement. Implications for research and practice are addressed. Highlights This paper describes the relationship between parental book reading practices, mathematics, and reading outcomes., Structural equation models reveal relationships between the quantity of book reading and children's reading outcomes, as well as the quality of book reading and children's mathematics outcomes., High-quality book reading may positively impact academic achievement in multiple domains, but results may vary based on contextual factors. [ABSTRACT FROM AUTHOR]

Constraints arise naturally in many scientific experiments/studies such as in, epidemiology, biology, toxicology, etc. and often researchers ignore such information when analyzing their data and use standard methods such as the analysis of variance (ANOVA). Such methods may not only result in a loss of power and efficiency in costs of experimentation but also may result poor interpretation of the data. In this paper we discuss constrained statistical inference in the context of linear mixed effects models that arise naturally in many applications, such as in repeated measurements designs, familial studies and others. We introduce a novel methodology that is broadly applicable for a variety of constraints on the parameters. Since in many applications sample sizes are small and/or the data are not necessarily normally distributed and furthermore error variances need not be homoscedastic (i.e. heterogeneity in the data) we use an empirical best linear unbiased predictor (EBLUP) type residual based bootstrap methodology for deriving critical values of the proposed test. Our simulation studies suggest that the proposed procedure maintains the desired nominal Type I error while competing well with other tests in terms of power. We illustrate the proposed methodology by re-analyzing a clinical trial data on blood mercury level. The methodology introduced in this paper can be easily extended to other settings such as nonlinear and generalized regression models. [ABSTRACT FROM AUTHOR]

About the year 2000, the Department of Mathematics and Computer Science, Albany State University (ASU), Albany, Georgia, USA envisioned the need to have a comprehensive curriculum revision based on recommendations of the Conference Boards of The Mathematical Sciences, the American Mathematical Society, the Mathematical Association of American, and based on the need to create attractive career pathways for our students in emerging fields and professions. Many Mathematics graduates were progressing to graduate schools in the fields of Applied Mathematics and Statistics. In subsequent years, our graduates started seeking jobs in the financial sector to become portfolio managers, Wall Street traders, bankers, insurers, and wealth fund managers. MATH 4330 Mathematics of Compound Interest course was created to give our students the opportunity to garner strong background to become confident future wealth managers. This course is inherently an attractive course to internationalize as economic growth is in the national interest of every nation, and the deep understanding of national and international financial institutions' functions is most essential. In this paper, I present the internationalization of Math 4330 Mathematics of Compound Interest, the associated outcomes, and the broader impact on students. [ABSTRACT FROM AUTHOR]

We analyse the output-unemployment relationship using an approach based on cross-recurrence plots and quantitative recurrence analysis. We use post-war period quarterly U.S. data. The results obtained show the emergence of a complex and interesting relationship. [ABSTRACT FROM AUTHOR]

Research universities in the United States have larger mathematics faculties outside their mathematics departments than inside. Members of this 'extensive' faculty conduct most mathematics research, their interests are the most heavily published areas of mathematics, and they teach this mathematics in upper division courses independent of mathematics departments. The existence of this de facto faculty challenges the pertinence of institutional and national policies for higher education in mathematics, and of philosophical and sociological studies of mathematics that are limited to mathematics departments alone. [ABSTRACT FROM AUTHOR]

Objectives: A large body of research exists on families and their impact on children's developmental outcomes. Fewer studies examine family processes within different family structures and their impact on adolescents. This study extends prior work by evaluating associations between family structure (two biological parents, single-parent—mother only, and blended families with a step parent), family functioning (communication, cohesion and flexibility) and adolescents' logic and reasoning skills and math performance. Methods: A convenience sample of 269 African American adolescents was recruited from a university-based summer enrichment program. The sample was mostly female (63%), with a mean age of 16.34 years. Data were derived from the baseline assessment during which participants completed the Family Adaptability and Cohesion Evaluation Scales (FACES IV), a computer-administered test of cognitive skills, and a paper-based math performance test. Results: Families with different structures varied in their family functioning (Wilks' ʌ = 0.942, F(6, 496) = 2.486, p = 0.022, η2 = 0.835). Families differed on the dimensions of cohesion (F(2, 250) = 5.80, p = 0.003, η2 = 0.044), flexibility (F(2, 250) = 5.48, p = 0.005, η2 = 0.042) and communication (F(2, 250) = 5.80, p = 0.003, η2 = 0.047). Different dimensions of family functioning significantly predicted both logic and reasoning skills (F(7, 244) = 2.14, p = 0.040, R2 = 0.06) and math outcomes (F(7, 142) = 3.16, p = 0.004, R2 = 0.14). Conclusions: Families with different household structures differ in their functioning, including in their levels of cohesion, flexibility and communication. Family functioning is more important than family structure in predicting African American adolescents' reasoning skills and math performance. [ABSTRACT FROM AUTHOR]

Prophylactic interventions such as vaccine allocation are some of the most effective public health policy planning tools. The supply of vaccines, however, is limited and an important challenge is to optimally allocate the vaccines to minimize epidemic impact. This resource allocation question (which we refer to as VID) has multiple dimensions: when, where, to whom, etc. Most of the existing literature in this topic deals with the latter (to whom), proposing policies that prioritize individuals by age and disease risk. However, since seasonal influenza spread has a typical spatial trend, and due to the temporal constraints enforced by the availability schedule, the when and where problems become equally, if not more, relevant. In this paper, we study the VID problem in the context of seasonal influenza spread in the United States. We develop a national scale metapopulation model for influenza that integrates both short and long distance human mobility, along with realistic data on vaccine uptake. We also design GA, a greedy algorithm for allocating the vaccine supply at the state level under temporal constraints and show that such a strategy improves over the current baseline of pro-rata allocation, and the improvement is more pronounced for higher vaccine efficacy and moderate flu season intensity. Further, the resulting strategy resembles a ring vaccination applied spatiallyacross the US. [ABSTRACT FROM AUTHOR]

This paper describes the theory of professional competence in teaching of mathematics developed through a cross-cultural examination of teaching practices of mathematics teachers recommended as competent by their principals in two selected high-achieving high schools of India and the United States. A detailed study of teacher cases from both of the research settings yielded a rich conceptualization of the relationship between teachers' professional knowledge base and professional competence in the teaching of mathematics. The substantive theory explains the processes of both the development and the display of professional competence and enables predictions of the ways teachers would most likely utilize to meet the performance expectations of their work environments. The study makes a unique contribution to the field of teacher education and views professional competence as a dynamic interplay of various components of teachers' professional knowledge base activated in actual teaching situations in the context of the classroom, school, and wider social culture. [ABSTRACT FROM AUTHOR]

Objectives: As gentrification continues in New York City as well as other urban areas, residents of lower socioeconomic status maybe at higher risk for residential displacement. Yet, there have been few quantitative assessments of the health impacts of displacement. The objective of this paper is to assess the association between displacement and healthcare access and mental health among the original residents of gentrifying neighborhoods in New York City. Methods: We used 2 data sources: 1) 2005–2014 American Community Surveys to identify gentrifying neighborhoods in New York City, and 2) 2006–2014 Statewide Planning and Research Cooperative System. Our cohort included 12,882 residents of gentrifying neighborhoods in 2006 who had records of emergency department visits or hospitalization at least once every 2 years in 2006–2014. Rates of emergency department visits and hospitalizations post-baseline were compared between residents who were displaced and those who remained. Results: During 2006–2014, 23% were displaced. Compared with those who remained, displaced residents were more likely to make emergency department visits and experience hospitalizations, mainly due to mental health (Rate Ratio = 1.8, 95% confidence interval = 1.5, 2.2), after controlling for baseline demographics, health status, healthcare utilization, residential movement, and the neighborhood of residence in 2006. Conclusions: These findings suggest negative impacts of displacement on healthcare access and mental health, particularly among adults living in urban areas and with a history of frequent emergency department visits or hospitalizations. [ABSTRACT FROM AUTHOR]

The social functions of urbanized areas are highly dependent on and supported by the convenient access to public transportation systems, particularly for the less privileged populations who have restrained auto ownership. To accurately evaluate the public transit accessibility, it is critical to capture the spatiotemporal variation of transit services. This can be achieved by measuring the shortest paths or minimum travel time between origin-destination (OD) pairs at each time-of-day (e.g. every minute). In recent years, General Transit Feed Specification (GTFS) data has been gaining popularity for between-station travel time estimation due to its interoperability in spatiotemporal analytics. Many software packages, such as ArcGIS, have developed toolbox to enable the travel time estimation with GTFS. They perform reasonably well in calculating travel time between OD pairs for a specific time-of-day (e.g. 8:00 AM), yet can become computational inefficient and unpractical with the increase of data dimensions (e.g. all times-of-day and large network). In this paper, we introduce a new algorithm that is computationally elegant and mathematically efficient to address this issue. An open-source toolbox written in C++ is developed to implement the algorithm. We implemented the algorithm on City of St. George’s transit network to showcase the accessibility analysis enabled by the toolbox. The experimental evidence shows significant reduction on computational time. The proposed algorithm and toolbox presented is easily transferable to other transit networks to allow transit agencies and researchers perform high resolution transit performance analysis. [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]

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]

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]

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