BackgroundThe COVID-19 pandemic has created ethical challenges for intensive care unit (ICU) professionals, potentially causing moral distress. This study explored the levels and causes of moral distress and the ethical climate in Dutch ICUs during COVID-19.MethodsAn extended version of the Measurement of Moral Distress for Healthcare Professionals (MMD-HP) and Ethical Decision Making Climate Questionnaire (EDMCQ) were online distributed among all 84 ICUs. Moral distress scores in nurses and intensivists were compared with the historical control group one year before COVID-19. ResultsThree (...) hundred forty-five nurses (70.7%), 40 intensivists (8.2%), and 103 supporting staff (21.1%) completed the survey. Moral distress levels were higher for nurses than supporting staff. Moral distress levels in intensivists did not differ significantly from those of nurses and supporting staff. “Inadequate emotional support for patients and their families” was the highest-ranked cause of moral distress for all groups of professionals. Of all factors, all professions rated the ethical climate most positively regarding the culture of mutual respect, ethical awareness and support. “Culture of not avoiding end-of-life-decisions” and “Self-reflective and empowering leadership” received the lowest mean scores. Moral distress scores during COVID-19 were significantly lower for ICU nurses (p < 0.001) and intensivists (p < 0.05) compared to one year prior.ConclusionLevels and causes of moral distress vary between ICU professionals and differ from the historical control group. Targeted interventions that address moral distress during a crisis are desirable to improve the mental health and retention of ICU professionals and the quality of patient care. (shrink)

Individuals who experience stereotype threat – the pressure resulting from social comparisons that are perceived as unfavourable – show performance decrements across a wide range of tasks. One account of this effect is that the cognitive pressure triggered by such threat drains the same cognitive resources that are implicated in the respective task. The present study investigates whether mindfulness can be used to moderate stereotype threat, as mindfulness has previously been shown to alleviate working-memory load. Our results show that performance (...) decrements that typically occur under stereotype threat can indeed be reversed when the individual engages in a brief mindfulness task. The theoretical implications of our findings are discussed. (shrink)

Within the literature that circulates in the discourses organizing nursing education, there are embedded assumptions that link student performance on maths examinations to safe medication practices. These assumptions are rooted historically. They fundamentally shape educational approaches assumed to support safe practice and protect patients from nursing error. Here, we apply an institutional ethnographic lens to the body of literature that both supports and critiques the emphasis on numeracy skills and medication safety. We use this form of inquiry to open an (...) alternate interrogation of these practices. Our main argument posits that numeracy skills serve as powerful distraction for both students and teachers. We suggest that they operate under specious claims of safety and objectivity. As nurse educators, we are captured by taken‐for‐granted understandings of practices intended to produce safety. We contend that some of these practices are not congruent with how competency actually unfolds in the everyday world of nursing practice. Ontologically grounded in the materiality of work processes, we suggest there is a serious disjuncture between educators' assessment and evaluation work where it links into broad nursing assumptions about medication work. These underlying assumptions and work processes produce contradictory tensions for students, teachers and nurses in direct practice. (shrink)

The hypothesis of extended cognition holds that mental states and processes need not be wholly contained within biological confines. Yet the theory is plausible, and informative, only when it can set principled outer limits upon cognitive extension: it should not permit unrestricted expansion of the mental into the material environment. I argue that true cognitive extension occurs only when the subject takes responsibility for the contribution made by a non-neural resource, in a manner that can be illuminated by appeal to (...) theoretical resources from contemporary virtue epistemology. (shrink)

Global policy transfer has become increasingly popular in recent years, and one recent example of such policy transfer is the England–China Teacher Exchange, which was initiated in 2014 with the explicit aim of raising attainment in maths in English primary schools by trialling concepts used in Shanghai schools, Shanghai rising to the top of the PISA rankings in 2009. However, as this paper will argue this is an overly simplistic attempt to transfer a policy between two wholly different contexts, the (...) lack of success of the policy seen in the very limited impact on student attainment in the participating schools. Whilst such policy transfer has increasingly taken place in the context of isomorphism and global pressures to adopt policy from high performing education systems, it is argued that policy needs to be explicitly reconsidered in terms of the local context it is being imported into if it is to be embedded in an effective manner, as well as rooted firmly in research. It is also argued that the England–China Teacher Exchange reflects a broader ideological focus in coalition government policy on the marketisation of education alongside the PISA rankings, rather any wider consideration of how this particular policy would drive up standards. (shrink)

In J.M. Coetzee’s novel The Schooldays of Jesus (2016), the question of finding the ‘right education’ for a young child is a central and recurring theme. In particular, the novel presents us with t...

This book offers a unique analysis of how ideas about science and technology in the public and scientific imaginations (in particular about maths, logic, the gene, the brain, god, and robots) perpetuate the false reality that values and politics are separate from scientific knowledge and its applications. These ideas are reinforced by cultural myths about free will and individualism. Restivo makes a compelling case for a synchronistic approach in the study of these notoriously 'hard' cases, arguing that their significance reaches (...) far beyond the realms of science and technology, and that their sociological and political ramifications are of paramount importance in our global society. This innovative work deals with perennial problems in the social sciences, philosophy, and the history of science and religion, and will be of special interest to professionals in these fields, as well as scholars of science and technology studies. (shrink)

Long ago, when Alexander the Great asked the mathematician Menaechmus for a crash course in geometry, he got the famous reply ``There is no royal road to mathematics.'' Where there was no shortcut for Alexander, there is no shortcut for us. Still, the fact that we have access to computers and mature programming languages means that there are avenues for us that were denied to the kings and emperors of yore. The purpose of this book is to teach logic and (...) mathematical reasoning in practice, and to connect logical reasoning with computer programming in Haskell. Haskell emerged in the 1990s as a standard for lazy functional programming, a programming style where arguments are evaluated only when the value is actually needed. Haskell is a marvelous demonstration tool for logic and maths because its functional character allows implementations to remain very close to the concepts that get implemented, while the laziness permits smooth handling of infinite data structures. This book does not assume the reader to have previous experience with either programming or construction of formal proofs, but acquaintance with mathematical notation, at the level of secondary school mathematics is presumed. Everything one needs to know about mathematical reasoning or programming is explained as we go along. After proper digestion of the material in this book, the reader will be able to write interesting programs, reason about their correctness, and document them in a clear fashion. The reader will also have learned how to set up mathematical proofs in a structured way, and how to read and digest mathematical proofs written by others. This is the updated, expanded, and corrected second edition of a much-acclaimed textbook. Praise for the first edition: 'Doets and van Eijck's ``The Haskell Road to Logic, Maths and Programming'' is an astonishingly extensive and accessible textbook on logic, maths, and Haskell.' Ralf Laemmel, Professor of Computer Science, University of Koblenz-Landau. (shrink)

This study examined whether stimulation of immigrant and national pupils’ use of high‐quality helping behaviour during cooperative learning in classrooms boosts their maths‐related talk more than in an educational situation in which such stimulation is largely absent . A total of 59 elementary‐age pupils enrolled in a CL maths curriculum of 11 lessons. They were video taped during two lessons while working together on maths assignments to assess their maths‐related talk. We found that the quality of maths‐related talk was higher (...) in the experimental condition. Furthermore, immigrant pupils’ used less maths‐related talk than the national pupils. Implications are discussed. (shrink)

The present research investigates gender gaps in the results of secondary school exit exams in mathematics in Poland in 2015. The analysis shows that, in the basic level exam, males are highly overrepresented at the upper end of the score distribution. The same pattern did not exist in the extended-level Matura. Two explanations are offered here. The differences are driven by gender self-selection in high school programs. Students who decide on maths-related tracks have more maths lessons than other students. Secondly, (...) a student who takes the extended Matura also has to take the basic Matura exam. As a result, the population of students taking the basic Matura is highly differentiated in terms of maths competence and motivation. Additionally, the analysis of differential item functioning shows that only a few items were flagged as having DIF. (shrink)

This study investigated how gender shapes the relationships between classroom environment, achievement goals and maths performance. Seventh-grade students (N?=?498) from five urban secondary schools filled in achievement goal orientations and classroom environment scales at the beginning of the second semester. Maths performance was assessed as an average grade four months later. The results indicated gender differences in the perception of teacher and peers support, achievement goals and maths performance. The effects of goal orientations, teacher and peers support on achievement were (...) moderated by gender. Furthermore, the interaction between classroom environment and performance goals on maths grades varied with gender. In the boys? sample, performance-avoidance goals interacted with teacher support, while in the girls? sample, performance-approach goals interacted with peers support in predicting maths grades. The educational implications of these gender differences are discussed. (shrink)

In a previous study we examined reading, spelling, and maths skills in an unselected group of 129 Italian children attending fifth grade by testing various cognitive predictors; results showed a high degree of predictors’ selectivity for each of these three behaviors. In the present study, we focused on the specificity of the predictors by performing cross-analyses on the same dataset; i.e., we predicted spelling and maths skills based on reading predictors, reading based on maths predictors and so on. Results indicated (...) that some predictors, such as the Orthographic Decision and the Arithmetic Facts tests, predicted reading, spelling and maths skills in similar ways, while others predicted different behaviors but only for a specific parameter, such as fluency but not accuracy, and still others were specific for a single behavior. To interpret these results, we propose a novel model of learning skills separately considering factors in terms of competence, performance and acquisition. Reading, spelling and calculation skills would depend on the development of discrete and different abstract competences. By contrast, overlap among behaviors would be accounted for by defective acquisition in automatized responses to individual “instances”; this latter skill is item specific but domain independent. Finally, performance factors implied in task’s characteristics may contribute to the partial association among learning skills. It is proposed that this new model may provide a useful base for interpreting the diffuse presence of comorbidities among learning disorders. (shrink)

Children’s math self-concepts—their beliefs about themselves and math—are important for teachers, parents, and students, because they are linked to academic motivation, choices, and outcomes. There have been several attempts at improving math achievement based on the training of math skills. Here we took a complementary approach and conducted an intervention study to boost children’s math self-concepts. Our primary objective was to assess the feasibility of whether a novel multicomponent intervention—one that combines explicit and implicit approaches (...) to help children form more positive beliefs linking themselves and math—can be administered in an authentic school setting. The intervention was conducted in Spain, a country in which math achievement is below the average of other OECD countries. We tested third grade students (N= 180;Mage= 8.79 years; 96 girls), using treatment and comparison groups and pre- and posttest assessments. A novelty of this study is that we used both implicit and explicit measures of children’s math self-concepts. For a subsample of students, we also obtained an assessment of year-end math achievement. Math self-concepts in the treatment and comparison groups did not significantly differ at pretest. Students in the treatment group demonstrated a significant increase in math self-concepts from pretest to posttest; students in the comparison group did not. In the treatment group, implicit math self-concepts at posttest were associated with higher year-end math achievement, assessed approximately 3 months after the completion of the intervention. Taken together, the results suggest that math self-concepts are malleable and that social–cognitive interventions can boost children’s beliefs about themselves and math. Based on the favorable results of this feasibility study, it is appropriate to formally test this novel multicomponent approach for improving math self-concepts using randomized controlled trial (RCT) design. (shrink)

Differences between the sexes in education is something of particular interest in much research. This study sought to investigate the possible differences between the sexes in math performance, and to deeply examine the causal factors for those differences. Beginning from the administration of the BECOMA-On (Online Evaluation Battery of Mathematics Skills) to 3,795 5th year primary students aged 10-11, in 16 Spanish autonomous communities and the 2 autonomous cities of Ceuta and Melilla. The results for each sex were compared (...) to their perceptions of self-efficacy about completing the test items, and with their interest in and motivation for mathematics. Statistically significant differences were seen in the variables examined. The boys were generally more engaged with science and technical subjects. Generalizing from studies such as this aims to more thoroughly explore, and improve this situation. (shrink)

Math anxiety (MA) has been suggested to decrease the math performance of students. However, it remains unclear what factors moderate this relationship. The purpose of this study was to analyze the link between MA and math performance. Studies that explored the relationship between MA and math performance, conducted from 2000 to 2019 (84 samples, N = 8680), were identified and statistically integrated with a meta-analysis method. The results indicated a robust negative correlation between MA and (...) class='Hi'>math performance. Furthermore, regarding the analysis of moderator variables, this negative link was stronger in the studies that involved Asian students, whereas it was the weakest in the studies that involved European students. Moreover, this negative link was stronger in the studies within a senior high school group, whereas it was the weakest in the studies within an elementary group. Finally, this negative link was strongest among studies that used a custom test and studies that assessed problem-solving skills. Potential explanations and implications for research and practice are discussed. (shrink)

In life reason and emotion are best when complementary. In fact active inquiry in philosophy and in science and mathematics do meet best in the learning process. Since significant meaning making activities can occur in mathematics, philosophy should be studied in the science class. "The notion that mathematics is cold-blooded and stories are warm-blooded must be rethought.".

ABSTRACTPrevious research has outlined high anxiety in connection with gamma modulation, identifying that gamma-band activity correlates with processing of threat perception, attention...

The purpose of this paper is to show that the mathematics of quantum mechanics is the mathematics of set partitions linearized to vector spaces, particularly in Hilbert spaces. That is, the math of QM is the Hilbert space version of the math to describe objective indefiniteness that at the set level is the math of partitions. The key analytical concepts are definiteness versus indefiniteness, distinctions versus indistinctions, and distinguishability versus indistinguishability. The key machinery to go from indefinite (...) to more definite states is the partition join operation at the set level that prefigures at the quantum level projective measurement as well as the formation of maximally-definite state descriptions by Dirac’s Complete Sets of Commuting Operators. This development is measured quantitatively by logical entropy at the set level and by quantum logical entropy at the quantum level. This follow-the-math approach supports the Literal Interpretation of QM—as advocated by Abner Shimony among others which sees a reality of objective indefiniteness that is quite different from the common sense and classical view of reality as being “definite all the way down”. (shrink)

In the paper “Math Anxiety,” Aden Evens explores the manner by means of which concepts are implicated in the problematic Idea according to the philosophy of Gilles Deleuze. The example that Evens draws from Difference and Repetition in order to demonstrate this relation is a mathematics problem, the elements of which are the differentials of the differential calculus. What I would like to offer in the present paper is an historical account of the mathematical problematic that Deleuze deploys in (...) his philosophy, and an introduction to the role that this problematic plays in the develop- ment of his philosophy of difference. One of the points of departure that I will take from the Evens paper is the theme of “power series.”2 This will involve a detailed elaboration of the mechanism by means of which power series operate in the differential calculus deployed by Deleuze in Difference and Repetition. Deleuze actually constructs an alternative history of mathematics that establishes an historical conti- nuity between the differential point of view of the infinitesimal calculus and modern theories of the differential calculus. It is in relation to the differential point of view of the infinitesimal calculus that Deleuze determines a differential logic which he deploys, in the form of a logic of different/ciation, in the development of his proj- ect of constructing a philosophy of difference. (shrink)

Much has been written about the free energy principle (FEP), and much misunderstood. The principle has traditionally been put forth as a theory of brain function or biological self-organisation. Critiques of the framework have focused on its lack of empirical support and a failure to generate concrete, falsifiable predictions. I take both positive and negative evaluations of the FEP thus far to have been largely in error, and appeal to a robust literature on scientific modelling to rectify the situation. A (...) prominent account of scientific modelling distinguishes between model structure and model construal. I propose that the FEP be reserved to designate a model structure, to which philosophers and scientists add various construals, leading to a plethora of models based on the formal structure of the FEP. An entailment of this position is that demands placed on the FEP that it be falsifiable or that it conform to some degree of biological realism rest on a category error. To this end, I deliver first an account of the phenomenon of model transfer and the breakdown between model structure and model construal. In the second section, I offer an overview of the formal elements of the framework, tracing their history of model transfer and illustrating how the formalism comes apart from any interpretation thereof. Next, I evaluate existing comprehensive critical assessments of the FEP, and hypothesise as to potential sources of existing confusions in the literature. In the final section, I distinguish between what I hold to be the FEP—taken to be a modelling language or modelling framework—and what I term “FEP models.”. (shrink)

An international group of distinguished scholars brings a variety of resources to bear on the major issues in the study and teaching of mathematics, and on the problem of understanding mathematics as a cultural and social phenomenon. All are guided by the notion that our understanding of mathematical knowledge must be grounded in and reflect the realities of mathematical practice. Chapters on the philosophy of mathematics illustrate the growing influence of a pragmatic view in a field traditionally dominated by platonic (...) perspectives. In a section on mathematics, politics, and pedagogy, the emphasis is on politics and values in mathematics education. Issues addressed include gender and mathematics, applied mathematics and social concerns, and the reflective and dialogical nature of mathematical knowledge. The concluding section deals with the history and sociology of mathematics, and with mathematics and social change. Contributors include Philip J. Davis, Helga Jungwirth, Nel Noddings, Yehuda Rav, Michael D. Resnik, Ole Skovsmose, and Thomas Tymoczko. (shrink)

We discuss the nature of reality in the ontological context of Penrose’s math-matter-mind triangle. The triangle suggests the circularity of the widespread view that math arises from the mind, the mind arises out of matter, and that matter can be explained in terms of math. Non-physicists should be wary of any claim that modern physics leads us to any particular resolution of this circularity, since even the sample of three theoretical physicists writing this paper hold three divergent (...) views. Some physicists believe that current physics has already found the basic framework for a complete description of reality, and only has to fill in the details. Others suspect that no single framework, from physics or other sources, will ever capture reality. Yet others guess that reality might be approached arbitrarily closely by some form of future physics, but probably based on completely different frameworks. We will designate these three approaches as the fundamentalist, secular and mystic views of the world, as seen by practicing physicists. We present and contrast each of these views, which arguably form broad categories capturing most if not all interpretations of physics. We argue that this diversity in the physics community is more useful than an ontological monoculture, since it motivates physicists to tackle unsolved problems with a wide variety of approaches. (shrink)

This is the first in a series of math books intended for those who have completed at least secondary school mathematics and have acquired 1) certain calculating skills, and 2) dissatisfaction with their understanding of what they are calculating. We will start our journey with numbers. Numbers are the oldest mathematical idea, but still also the most important one. We will go through the basics of numbers in a way that will give you the confidence to really understand numbers (...) and really know how to apply them. You will also learn all the essential elements of mathematics through the example of the world of numbers. The example of numbers will be used to illustrate what mathematical objects are and how they are applied, and what mathematical tools we use in their description and application. (shrink)

Explore how mathematics has shaped how we look at and understand the world. From figuring out Earth's circumference using geometry to developing load-bearing arches, young readers will be engaged as they learn about real world math applications.

Mathematics, even more than the other sciences, is often presented as essentially unique, as if it could not be any other way. And yet, prima facie alternative mathematics are all over the place, from non-Western mathematics to mathematics based on nonclassical logics. Taking inspiration from Robin Dembroff’s analysis of critical gender kinds, and from Andrew Aberdein and Stephen Read’s analysis of alternative logics, in this paper I will introduce a practice-centered framework for the study of alternative mathematics based on the (...) notion of critical math kind. After sketching a model of mainstream mathematics, I will provide examples of how deviation along several distinct dimensions can occur, and how deviations can vary in their gravity. I will then discuss how the framework can be used to think of questions concerning the alternativeness status and philosophical implications of alleged alternative mathematics, and help us in identifying alternatives that suit our purposes. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Math Anxiety:Making Room to BreatheValerie Allen (bio) and Todd Stambaugh (bio)"Don't do that to me, Professor," the student said, and everybody laughed, for by this late in the semester, the atmosphere was relaxed. The instructor in question had just reached the point in a worked problem when they could move from reasoning about specific numbers to stating a general principle: x≤y≤z, meaning that y—the value we sought—was always (...) going to be greater than or equal to one value (x) and less than or equal to the other (z). The student who had spoken had earned everyone's affection over the weeks, open about their difficulties with math, ready to risk being wrong, and to ask obvious questions that others may have been reluctant to owning. They had hung in there, despite presenting a classic case of math anxiety, a syndrome long recognized in the scholarship of teaching and learning.Among math anxiety's many symptoms, breathing disruption ranks high: hyperventilation (rapid breathing) and hypoventilation (barely or not breathing). When the energy-conserving parasympathetic nervous system is overtaken by the energy-expending sympathetic nervous system, the long exhalations that decelerate the heart rate are replaced by short, panting puffs from the upper lungs. The timed test provides the perfect environment for math anxiety to flourish. Stress diverts cognitive resources needed for procedural execution, so working memory consequently shrinks.Self-rated metrics for math anxiety have been in place for decades (Richardson and Suinn). Relatively trivial interventions can yield nontrivial results: deep breathing exercises and positive affirmations have a beneficial impact, as does writing about one's nerves immediately prior to an exam (Brunyé et al.). More systemic changes require a reorientation in teaching whereby conceptual mistakes are positively rewarded as opportunities for learning; students compose questions instead of answers; students solve problems together rather than perform solo (Boaler).Return now to that opening scenario to watch it become stereotype incarnate: the student was mature, Black, and female; the teacher, younger, white, and male; her comment was triggered by his shift from a specific [End Page 217] set of numbers into symbolic notation. There is robust evidence to demonstrate that certain demographics are consistently underrepresented in the U.S. math community: women and "African-Americans, Hispanics, American Indians, Alaska Natives, and Pacific Islanders," according to the Mathematical Association of America (MAA) ("Resources for Minority"). Routinely feeling that they do not belong, such groups are particularly vulnerable to math anxiety.Several remedies for such disparity suggest themselves: appointing more women and people of color in the profession; one-on-one tutorial assistance; research projects about the students' personal environment; privileging pre-test, low-stakes work over timed tests; assigning group rather than individual work. When all is said and done, however, such strategies "have little to do with mathematics content" (Martin 304). Mathematicians still need to be able to conceptualize, describe, and manipulate abstract objects, and there seems to be a suspicion that, at heart, abstraction is gendered masculine and colored white.It is possible that the rhetorical immediacy and context-dependence of Black English has misguidedly reinforced such a perception. For poet June Jordan, Black English "devolves from a culture that abhors all abstraction" (Jordan 367). Psychiatrist Alvin Poussaint asks, "Is there a way to say metamorphosis in Ebonics?" (O'Malley). Yet, despite Black English's avoidance of nominalization and similar verbosities that afflict academic prose, abstract logical reasoning flourishes in vernacular idiom, as linguist William Labov demonstrated half a century ago. Our aim is not to explain the asymptote in Black English but rather to consider a feature characteristic of those very minority cultures historically underrepresented in math—storytelling—and to ask how it may be foregrounded in mathematics, where it is decisively sidelined. Storytelling has been claimed by every culture and ethnic group at some point as the repository of wisdom, practical skills, religious beliefs, and shared identity and values; but when it gets corralled into the category of "fiction," and when it gets opposed to "fact," a narrowed concept of truth dispatches storytelling to kindergarten and recreational math. Word problems may supply scenarios but offer none of a plot's satisfactions... (shrink)

There is ample evidence from literature and clinical practice indicating mathematical difficulties in individuals with ADHD, even when there is no concomitant diagnosis of developmental dyscalculia. What factors underlie these difficulties is still an open question. Research on dyscalculia and neurotypical development suggests visual perception of numerosity (the number sense) as a building block for math learning. Participants with lower numerosity estimation thresholds (higher precision) are often those with higher math capabilities. Strangely, the role of numerosity perception in (...) math skills in ADHD has been neglected, leaving open the question whether math difficulties in ADHD also originate from a deficitary visual number sense. In the current study we psychophysically measured numerosity thresholds and accuracy in a sample of children/adolescents with ADHD, but not concomitant dyscalculia (N = 20, 8–16 years). Math abilities were also measured by tasks indexing different mathematical competences. Numerosity performance and math scores were then compared to those obtained from an age-matched control group (N = 20). Bayesian statistics indicated no difference between ADHD and controls on numerosity perception, despite many of the symbolic math tasks being impaired in participants with ADHD. Moreover, the math deficits showed by the group with ADHD remained substantial even when numerosity thresholds were statistically regressed out. Overall, these results indicate that math difficulties in ADHD are unlikely to originate from an impaired visual number sense. (shrink)

Explains how our innate pattern-making abilities allow us to perform mathematical reasoning.

Causal platonism asserts that mathematical objects cause neural states in human brains. I raise the following four objections to it. (i) Quantum entanglement does not show that one object can causally affect another, although one is nontemporal, nonspatial, and unchanging. (ii) Causal platonism can neither be justified a posteriori nor a priori. (iii) To postulate mathematical media to flesh out mathematical causation is to multiply mysteries beyond necessity. (iv) To say that mathematical causation is unintelligible and inexplicable is not to (...) complain about causation in general. (shrink)

Where does math come from? From a textbook? From rules? From deduction? From logic? Not really, Eugenia Cheng writes in Is Math Real?: it comes from curiosity, from instinctive human curiosity, "from people not being satisfied with answers and always wanting to understand more." And most importantly, she says, "it comes from questions": not from answering them, but from posing them. Nothing could seem more at odds from the way most of us were taught math: a rigid (...) and autocratic model which taught us to follow specific steps to reach specific answers. Instead of encouraging a child who asks why 1+1 is 2, our methods of education force them to accept it. Instead of exploring why we multiply before we add, a textbook says, just to get on with the order of operations. Indeed, the point is usually just about getting the right answer, and those that are good at that, become "good at math" while those who question, are not. And that's terrible: These very same questions, as Cheng shows, aren't simply annoying questions coming from people who just don't "get it" and so can't do math. Rather, they are what drives mathematical research and push the boundaries in our understanding of all things. Legitimizing those questions, she invites everyone in, whether they think they are good at math or not. And by highlighting the development of mathematics outside Europe, Cheng shows that-western chauvinism notwithstanding--that math can be for anyone who wishes to do it, and how much we gain when anyone can. (shrink)

In this paper, I discuss the social philosopher Pierre Bourdieu’s concept of habitus, and use it to locate and examine dispositions in a larger constellation of related concepts, exploring their dynamic relationship within the social context, and their construction, manifestation, and function in relation to classroom mathematics practices. I describe the main characteristics of habitus that account for its invisible effects: its embodiment, its deep and pre-reflective internalization as schemata, orientation, and taste that are learned and yet unthought, and are (...) subsumed by our practices, which we understand as something that “goes without saying.” I also propose that, similarly to Bourdieu’s concept of linguistic habitus, a math habitus is made up of a complex intertwining of collective and individual histories that turn into “nature,” which structure all individual and collective action and inform mathematical classroom practice. I suggest that individual math dispositions may be liable to reconstruction through the reconstruction of the collective math habitus, which follows from opening spaces for dialogue, problematization and reconstruction of the unthought categories of the doxa. This requires that students acquire new concrete and symbolic means with which to challenge their current sense of mathematics as a discipline, and mathematical practice tout court. Finally, I argue that community of inquiry, employed as a pedagogical model, provides an avenue for both: for opening those spaces for reflective dialogical inquiry into concepts and questions whose meanings and references have so far been taken for granted, and for acquiring critical thinking and dialogical skills and dispositions that are a necessary means for participating in such reflective inquiry that offers significant promise for reconstructing individual and collective habitus in school settings. (shrink)

Interest in science and math plays an important role in encouraging STEM motivation and career aspirations. This interest decreases for girls between late childhood and adolescence. Relatedly, positive mentoring experiences with female teachers can protect girls against losing interest. The present study examines whether visitors to informal science learning sites differ in their expressed science and math interest, as well as their science and math stereotypes following an interaction with either a male or female educator. Participants were (...) visitors to one of four ISLS in the United States and United Kingdom. Following an interaction with a male or female educator, they reported their math and science interest and responded to math and science gender stereotype measures. Female participants reported greater interest in math following an interaction with a female educator, compared to when they interacted with a male educator. In turn, female participants who interacted with a female educator were less likely to report male-biased math gender stereotypes. Self-reported science interest did not differ as a function of educator gender. Together these findings suggest that, when aiming to encourage STEM interest and challenge gender stereotypes in informal settings, we must consider the importance of the gender of educators and learners. (shrink)