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 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.".

This study explores whether gender stereotypes about math ability shape high school teachers’ assessments of the students with whom they interact daily, resulting in the presence of conditional bias. It builds on theories of intersectionality by exploring teachers’ perceptions of students in different gender and racial/ethnic subgroups and advances the literature on the salience of gender across contexts by considering variation across levels of math course-taking in the academic hierarchy. Analyses of nationally representative data from the Education Longitudinal (...) Study of 2002 reveal that disparities in teachers’ perceptions of ability that favored white males over minority students of both genders are explained away by student achievement in the form of test scores and grades. However, we find evidence of a consistent bias against white females, which although relatively small in magnitude, suggests that teachers hold the belief that math is just easier for white males than it is for white females. In addition, we find some evidence of variation across course level contexts with regard to bias. We conclude by discussing the implications of our findings for research on the construction of gender inequality. (shrink)

Enhancement of the teacher well-being level has grown into a general, pressing problem to be solved in the domain of education worldwide. Based on the theoretical perspective of the multi-level dynamically formed mechanical model of occupational well-being, this study initially constructed a mechanism model with the occupational well-being role of organizational support, job crafting, and the occupational well-being of new math teachers at primary and junior high schools, and conducted empirical research using structural equation modeling. The study found (...) out that organizational support, job crafting and basic psychological needs have prominent and positive effects on the occupational well-being of the new math teachers in primary up to junior high schools. It also argues that basic psychological needs may mediate the correlation between organizational support, job crafting, and the occupational well-being of the new math teachers. To sum up, the study findings reveal the mechanisms of the role in organizational support and job crafting on the occupational well-being of new primary up to junior high school math teachers. Also, the findings may be conducive to extending the research on the factors that influence the teacher well-being, notably fostering the study on that in the math teachers in the primary up to junior high schools of China. (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)

Stereotypes of girls having weaker mathematical abilities than boys are one factor reducing women’s representation in mathematics. Teachers, as powerful socializers, often hold math-gender stereotypes. Reducing math-gender stereotypes in teachers thus may foster women’s representation in mathematics. Yet knowing the stereotypes’ underlying assumptions is crucial to reducing it. Do math-gender stereotypes reflect elaborate, disproven theories about gender differences in math, meaning math-gender misconceptions? And if so, which math-gender misconceptions are behind math-gender stereotypes? This (...) is the focus of the present research. The relevant literature implies the existence of three distinct misconceptions: empathizing-systemizing, girls’ compensation, and girls’ non-compensability. We assessed these misconceptions in a student teacher sample using our newly developed Math-Gender Misconceptions Questionnaire. Our results offer support for the expected three-factor structure of math-gender misconceptions. All three math-gender misconceptions showed good to acceptable scale reliabilities. On average, preservice teachers did not hold math-gender misconceptions. But a subgroup of 48.2% of preservice teachers held at least one of the three misconceptions. The empathizing-systemizing misconception was the most prevalent among the three misconceptions. Descriptively, endorsing the math-gender stereotype correlated most strongly with the empathizing-systemizing and the girls’ compensation misconception. This may indicate that especially these two misconceptions partly underlie math-gender stereotypes. As a consequence, refutation instructions designed to reduce these misconceptions may be a promising method to weaken math-gender stereotypes. Further research is needed to investigate to what degree reducing the present misconceptions is related to reducing math-gender stereotypes. Hence, this study is the first one of a planned series of studies on the relation between math-gender misconceptions and math-gender stereotypes. (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)

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)

Seventy-five fun puzzles to help improve mathematical and thinking skills. Decipher various clues by adding, subtracting, multiplying, dividing, reading carefully, and using powers of reason. Transfer the information onto grids that are provided, and find the solution to a given set of circumstances. "...the book is a delightful collection of problem situations that teachers and students will enjoy using..."--Mathematics.

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)

Toddlerhood is characterized by rapid development in several domains, such as language, socio-emotional behavior and emerging math skills all of which are important precursors of school readiness. However, little is known about how these skills develop over time and how they may be interrelated. The current study investigates young children’s development at two time points, with about 7 months in between, assessing their language, socio-emotional and math language and numeracy skills with teacher ratings. The sample includes 577 (...) children from 18 until 36 months of age of 86 childcare classrooms. The results of the autoregressive path analyses showed moderate to strong stability of language, socio-emotional and math language and numeracy skills, although the magnitude of associations was smaller for the latter. The cross-lagged path analyses highlighted the importance of language and socio-emotional skills for development in the other domains. Differential relations were found for the autoregressive and cross-lagged paths depending on gender and age. Language skills appeared a stronger predictor of boys’ socio-emotional and math language and numeracy skill development compared to girls. Girls’ socio-emotional skills predicted growth in math. For boys, socio-emotional and math language and numeracy skills appeared to be unrelated. Language skills showed stronger relations with the development of math language and numeracy skills for younger children as compared to older children. Also, for older children math language and numeracy skills negatively predicted growth in their socio-emotional skills. The findings provide more insights in how language, math language and numeracy skills and socio-emotional skills co-develop in the early years and as such have important implications for interventions aimed to support children’s development. (shrink)

Six African countries participated in an intercontinental professional development workshop developed by the science and math staff at the University of Iowa and supported by the Africa-America Institute. The 11-day workshop was designed to produce changes in goal setting, assessment practices, instruction, and curriculum structures for high school teachers. The article provides a detailed description of the workshop and discusses evidence of workshop successes. Preworkshop and postworkshop vision statements and curriculum units were used to track the progression of five (...) Kenyan educators as they moved toward constructivist-based practices. Teachers enhanced their views of science and math learning outcomes and learning environment as the workshop progressed. Specifically, teachers moved from emphasizing better grades and exam scores to greater student use of science and math skills. They also shifted from a heavily teacher-centered classroom view to a more student-centered classroom view. (shrink)

In a context of high-stakes accountability in teacher education, concerns are emerging about challenges to the already tenuous position of elementary social studies teacher education. In this case study, the author administered a survey to elementary social studies teacher educators in Georgia and conducted follow-up interviews focusing on the impact of edTPA on elementary social studies teacher education and the ways in which they are navigating the new context of teaching elementary social studies methods. The findings (...) reveal the possibility of further decline of social studies in elementary teacher education programs due to elementary edTPA's singular focus on literacy and math content pedagogy along with the high-stakes nature of edTPA process. Implications for future research on edTPA and elementary social studies education are discussed. (shrink)

Motivation: Paralleling my own transformation from a Platonist to a radical constructivist, mathematics education has been experiencing for more than a decade a movement that started in theoretical foundations mostly originating in von Glasersfeld's work, and then reached professional organizations, which have been leading extensive efforts to reform school mathematics according to constructivist principles. However, the theories espoused by the researchers are, as yet, too abstract to lend themselves readily to implementation in the classroom. N2 - Purpose: I define a (...) shared experiential language (SEL) for the constructivist teacher to embody in order to transform her practice congruently according to constructivist principles. While SEL is comprised of Neuro-Linguistic Programming (NLP) subjective experience distinctions, what "makes it tick" is the constructivist epistemology with its insight that for consistent understanding to happen, new knowledge has to attach to prior experiences in a process of co-construction. Throughout the paper, I elaborate and validate this insight by numerous examples. Practical implications: Utilizing SEL allows understanding of mathematics to be rooted in each student's individual sensory experiences, thus shifting the responsibility for success in mathematics from the students back to those who guide them in co-constructing knowledge. This, in turn, should allow everybody access to understanding and so it should no longer be socially acceptable to fail in mathematics. (shrink)

This study examined individual differences in mathematics learning by combining antecedent (A), opportunity (O), and propensity (P) indicators within the Opportunity-Propensity model. Although there is already some evidence for this model based on secondary datasets, there currently is no primary data available that simultaneously takes into account A,O and P factors in children with and without Mathematical Learning Disabilities (MLD). Therefore the mathematical abilities of 114 school-aged children (grade 3 till 6) with and without MLD were analyzed and combined with (...) information retrieved from standardized tests and questionnaires. Results indicated significant differences in personality, motivation, temperament, subjective well-being, self-esteem, self-perceived competence and parental aspirations when comparing children with and without MLD. In addition, A, O and P factors were found to underlie mathematical abilities and disabilities. For the A factors, parental aspirations explained about half of the variance in fact retrieval speed in children without MLD, and SES was especially involved in the prediction of procedural accuracy in general. Teachers’ experience contributed as O factor and explained about 6% of the variance in mathematical abilities. P indicators explained between 52 and 69% of the variance, with especially intelligence as overall significant predictor. Indirect effects pointed towards the interrelatedness of the predictors and the value of including A, O and P indicators in a comprehensive model. The role parental aspirations played in fact retrieval speed was partially mediated through the self-perceived competence of the children, whereas the effect of SES on procedural accuracy was partially mediated through intelligence in children of both groups and through working memory capacity in children with MLD. Moreover, in line with the componential structure of mathematics, our findings were dependent on the math task used. Different A, O and P indicators seemed to be important for fact retrieval speed compared to procedural accuracy. Also, mathematical development type (MLD or typical development) mattered since some A, O and P factors were predictive for MLD only and the other way around. Practical implications of these findings and recommendations for future research on MLD and on individual differences in mathematical abilities are provided. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:John Davis, Teacher: A Recollection I first met John Davis in the late fifties when I was doing a two-year M.A. in philosophy at Western. John taught a graduate course in symboliclogic. It was both a philosophy course and across-listed course in the foundation ofmathematics. There was, as a result, a mixture of philosophy and mathematics students in the course. My most vivid memory ofJohn was ofan amazingly (...) energetic and enthusiastic teacher who was anything but indifferent to his subject matter and to his students. I, if I may introduce a personal note, suffered from an extreme form of math anxiety—I couldn't even understand a truth-table. John was always extremely patient with me and it is thanks to him that I managed to scrape through. Another vivid memory was of a man with a kind of Moorean passion for getting it right. When he didn't understand something, he let us know it. He was constitutionally incapable of intellectual pretence. I took away from my time with him the idea that philosophy was extremely difficult; but ifone worked very hard, it was possible to get the right answer. And no relativist he, John was profoundly convinced that there was a right answer to get. Robert A. lmlay... (shrink)

Davydov’s mathematics curriculum was designed according to the principles of the Cultural Historical Activity Theory. In this study, we analyzed some developmental effects of its realization in Grade 1, in relation to the children’s school readiness level, and their teacher’s experience. We assessed two groups of developmental effects: some general math abilities ; and some abilities, which are very specific to Davydov’s mathematics curriculum. At the beginning of the Grade 1, we divided all participants into three groups according (...) to their level of motivation, voluntary regulation, and logical preservation in terms of J. Piaget. After 1 year we measured general effects again and also measured specific effects. The results showed that all the children became significantly better in all general math abilities. It was also found that progress in math abilities does not depend on the initial level of school readiness of children. Children with different levels of voluntary regulation, motivational readiness, and the level of logical preservation show improvements in general math abilities. As for the mathematical skills specific to the Davydov’ program, the achieved level of their development is also not related to the initial parameters of readiness for school. Also, there were no differences in improvements in general effects and in specific effects between the classes with experienced and not-so-experienced teacher. So, there are some reasons to believe that the level of the child’s actual development does not play a fundamental role for education, which built in accordance with the principles of CHAT. (shrink)

On the basis of Bandura’s social cognitive theory, researchers often assume that a teachers’ self-efficacy will have a positive effect on teaching quality. However, the available empirical evidence is mixed. Building on previous research into TSE, we examined whether assessing class-/task-specific TSE gives a more accurate indication of the associations between TSE assessments and student-rated teaching quality. The analyses were based on the English sample of the Teaching and Learning International Survey Video Study. Mathematics teachers rated their self-efficacy beliefs using (...) generalized task-specific TSE items and class-/task-specific TSE items. Their students rated the quality of teaching in their math class. Multilevel regression analyses revealed stronger associations between student-rated teaching quality and class-/task-specific TSE than generalized task-specific TSE. We discuss possible reasons for these results and outline the potential benefits of using class-specific assessments for future TSE research. (shrink)

The aim of this study is to use a commognitive responsibility framework to visualize responsibility shift in collaborative problem solving during computer-supported one-to-one tutoring. Commognitive responsibility shift means that individuals’ cognitive responsibility shift can be reflected by the discourse in communication. For our sample, we chose a 15-year-old Chinese boy and his mathematics teacher with 6 years of teaching experience, both of whom have experienced computer-supported learning and teaching mathematics, respectively. We collected four tutoring videos online, and a 45-min (...) interview video from the teacher. We found that the third type of commognitive responsibility shift in both the teacher’s and student’s CPS behavior online is not only teacher–student comparison but also alternating-led, which includes teacher–student-led and student–teacher-led. (shrink)

A growing body of literature focuses on practice as a central aspect of teacher education. Whereas this approach emerged mainly from teacher preparation programs in specific content areas such as math, science, and literacy studies, socially related educational fields have served as a peripheral player alone. Recently, however, scholars have suggested incorporating a practice-based approach to teacher education into the social studies. In this article, we draw on complexity theory to reexamine this proposal, evaluating the connections (...) between teaching practices and democratic citizenship. First, we introduce complexity theory. Second, we offer a critical examination of key publications discussing practice-based teacher education, using the components of complexity theory as an organizing scheme. We then highlight practice-based teacher education’s reductive aspects, leading to an argument that promoting democratic citizenship through civics teacher education should be seen as a complex endeavor where borders are blurred, interactions are nonlinear, and reality changes frequently. Finally, we offer to supplement the practice approach with aspects of teacher education that stem from complexity theory. (shrink)

In physics education, equations are commonly seen as calculation tools to solve problems or as concise descriptions of experimental regularities. In physical science, however, equations often play a much more important role associated with the formulation of theories to provide explanations for physical phenomena. In order to overcome this inconsistency, one crucial step is to improve physics teacher education. In this work, we describe the structure of a course that was given to physics teacher students at the end (...) of their master’s degree in two European universities. The course had two main goals: To investigate the complex interplay between physics and mathematics from a historical and philosophical perspective and To expand students’ repertoire of explanations regarding possible ways to derive certain school-relevant equations. A qualitative analysis on a case study basis was conducted to investigate the learning outcomes of the course. Here, we focus on the comparative analysis of two students who had considerably different views of the math-physics interplay in the beginning of the course. Our general results point to important changes on some of the students’ views on the role of mathematics in physics, an increase in the participants’ awareness of the difficulties faced by learners to understand physics equations and a broadening in the students’ repertoire to answer “Why?” questions formulated to equations. Based on this analysis, further implications for physics teacher education are derived. (shrink)

Mathematical thinking skills are very important in mathematics, both to learn math or as learning goals. Thinking skills can be seen from the description given answers in solving mathematical problems faced. Mathematical thinking skills can be seen from the types, levels, and process. Proportionally questions given to students at universities in Indonesia (semester I, III, V, and VII). These questions are a matter of description that belong to the higher-level thinking. Students choose 5 of 8 given problem. Qualitatively, the (...) answers were analyzed by descriptive to see the tendency to think mathematically used in completing the test. The results show that students tend to choose the issues relating to the calculation. They are more use cases, examples and not an example, to evaluate the conjecture and prove to belong to the numeric argumentation. Used mathematical thinking students are very personal (intelligence, interest, and experience), and the situation (problems encountered). Thus, the level of half of the students are not guaranteed and shows the level of mathematical thinking. (shrink)

1. Transmission Jim’s teacher has just given him his marked maths exam. Jim knows that his mark is 7.25 out of 22. He also knows that the pass mark is 35%. Does Jim know he has failed? No, he doesn’t. Not yet. As you would expect from his mark, Jim is not very good with numbers. He’ll need a few minutes with pencil and paper to work out that 7.25 is less than 35% of 22. Only then will he (...) know that he has failed. This case exemplifies a common and important phenomenon: someone recognises the validity of an inference from a set of premises that he knows, and in so doing he acquires knowledge of the conclusion. Jim knows that his mark is 7.25 out of 22 and that the passmark is 35%. Then, by virtue of his calculation, he comes to recognise the validity of the inference from these premises to the conclusion that he has failed, thereby coming to know the sad truth. It is undeniable that there are many cases, like Jim’s, in which recognising the validity of an inference from known premises brings about knowledge of the conclusion, as this is the most natural characterisation of what goes on when we acquire knowledge by deductive inference. But can knowledge always be acquired in this way? Does recognition of the validity of an inference from known premises always bring about knowledge of the conclusion? (shrink)

1. A Road to Philosophy of Mathematics l became interested in philosophy and mathematics at more or less the same time, rather late in high school; and my interest in the former certainly influenced my attitude towards the latter, leading me to ask what mathematics is really about at a fairly early stage. I don ’t really remember how it was that I got interested in either subject. A very good math teacher came to my school when I (...) was in 9th grade and I got caught up in his course on solid geometry; but he soon left and math then lost its luster again in the hands of teachers who neither liked nor understood it. Calculus wasn’t taught in high school in those days, or at least not in mine: besides geometry we learned some algebra and trigonometry. I doubt that even the word “ philosophy ” passed the lips of any of my teachers. My mother, who worked for a publishing house, brought home for me copies of, among other works, the Jowett translations of Plato’s Dialogues, Will Durant’s Story of Philosophy and Courant and Robbins’ What Is Mathematics?; but I can’t remember why she did that: She wasn’t at all intellectual and, as far as I recall, my interests at the time were mostly confined to sports and girls—in some order. Maybe she just thought it was time for me to develop new interests. After high school, I went in 1948 to Lehigh University, then at least primarily an engineering school, on an athletic scholarship. There I had the good fortune in my first year to have an introduction to philosophy course with Lewis White Beck. He had just moved there from the University of Delaware and shortly thereafter moved on to the University of Rochester, where he became one of the leading lights of American Kant studies. My good luck was compounded when, in my second year, Adolph Gr¨ unbaum arrived at Lehigh, fresh from graduate school at Yale, and stayed at least long enough for me to graduate, before moving to the University of Pittsburgh as Andrew Mellon Professor of Philosophy of Science.. (shrink)

This paper discusses the phenomenon of Kāpil Maṭh (Madhupur, India), a Sāṃkhyayoga āśrama founded in the early twentieth century by the charismatic Bengali scholar-monk Swāmi Hariharānanda Ᾱraṇya (1869–1947). While referring to Hariharānanda’s writings I will consider the idea of the re-establishment of an extinct spiritual lineage. I shall specify the criteria for identity of this revived Sāṃkhyayoga tradition by explaining why and on what assumptions the modern reinterpretation of this school can be perceived as continuation of the thought of Patañjali (...) and Īśvarakṛṣṇa. The starting point is, however, the question whether it is possible at all to re-establish a philosophical tradition which had once broken down and disappeared for centuries. In this context, one ought to ponder if it is likely to revitalise the same line of thinking, viewing, philosophy-making and practice in accordance with the theoretical exposition of the right insight achieved by an accomplished teacher, a master, the founder of a “new”revived tradition declared to maintain a particular school identity. Moreover, I refer to a monograph of Knut A. Jacobsen (2018) devoted to the tradition of Kāpil Maṭh interpreted as a typical product of the nineteenth-century Bengali renaissance. (shrink)

Se presenta un estudio sobre las razones de profesores de matemáticas en servicio para estudiar una Maestría en Ciencias en Matemática Educativa. La investigación fue realizada analizando expedientes de cuatro procesos de admisión. Se consideraron 316 casos de los años 2018-2021. Los participantes respondieron en entrevista “¿Por qué decidiste estudiar la Maestría en Ciencias en Matemática Educativa?” Los resultados indican que buscar su desarrollo profesional fue la razón más declarada; esta predominancia se mantuvo (excepto en 2019); otras razones populares fueron (...) la modalidad del posgrado, el prestigio de la institución y su gusto por la enseñanza de la matemática. (shrink)

Anecdotal evidence has long lamented the status of social studies in elementary classrooms as observed by preservice teachers. As standardized testing has risen for mathematics and language arts, social studies has been pushed aside. In the aftermath of accountability legislation such as No Child Left Behind, research indicates that social studies is less visible in elementary classrooms due to an instructional focus on tested content areas (e.g. math, language arts, reading). In this study, approximately 90 elementary preservice teachers enrolled (...) in a social studies methods course responded to a survey and indicated the frequency and quality of lessons they observed over the course of a single semester. Findings report that preservice elementary teachers witnessed few, if any, lessons in social studies in the elementary classroom. Implications for teacher education are discussed. (shrink)

The stability of low student math scores has been a concern of education systems around the world for many years. While teaching practices are pointed out as a determining factor in student engagement and the quality of student learning, they are only the tip of the iceberg. Much work has shown that these practices are strongly colored by epistemological beliefs as well as by beliefs related to the teaching and learning of the school discipline under investigation. On this subject, (...) if some research reports a peremptory influence of beliefs on teaching practices, others present more moderate results by underlining, for example, the permeability of beliefs in pre-service training. Based on the results of a quantitative study that identified three belief profiles (pro-traditional, anti-traditionnal, flexible) among 190 future secondary school mathematics teachers in their final year of training, this contribution aims to shed qualitative light on the articulation between beliefs and teaching practices of eleven of them. The analysis of the semi-directive interviews highlights the reconcilable nature of transmissive and constructivist conceptions of teaching-learning. Moreover, the presence of similar pedagogical practices, supported in training, within profiles with contrasting beliefs argues in favor of a belief-practice non-linearity. (shrink)

A new AI system, called AlphaGeometry, trained under synthetic data has demonstrated the ability to solve geometric problems at the International Olympiad level. This essay considers the fact that human abilities to learn and do math as well as many other tasks are increasingly augmented with AI. Clearly, smart technologies like AlphaGeometry are redefining a number of concepts and institutions such as learning, schools, education, teacher-student relationships, creativity, etc, which are so fundamental for what we’ve thought of as (...) modern society, economy, and culture. What are we preparing for in mathematics education in the face of the possibility of the continued emergence of disruptive technologies, signaling the beginning of the end, if a new reality of mathematics is not taken into account? (shrink)

What does quilting have to do with electric circuit theory? The answer is just one of the fascinating ways that best-selling popular math writer Paul Nahin illustrates the deep interplay of math and physics in the world around us in his latest book of challenging mathematical puzzles, Mrs. Perkins's Electric Quilt. With his trademark combination of intriguing mathematical problems and the historical anecdotes surrounding them, Nahin invites readers on an exciting and informative exploration of some of the many (...) ways math and physics combine to create something vastly more powerful, useful, and interesting than either is by itself. In a series of brief and largely self-contained chapters, Nahin discusses a wide range of topics in which math and physics are mutually dependent and mutually illuminating, from Newtonian gravity and Newton's laws of mechanics to ballistics, air drag, and electricity. The mathematical subjects range from algebra, trigonometry, geometry, and calculus to differential equations, Fourier series, and theoretical and Monte Carlo probability. Each chapter includes problems--some three dozen in all--that challenge readers to try their hand at applying what they have learned. Just as in his other books of mathematical puzzles, Nahin discusses the historical background of each problem, gives many examples, includes MATLAB codes, and provides complete and detailed solutions at the end. Mrs. Perkins's Electric Quilt will appeal to students interested in new math and physics applications, teachers looking for unusual examples to use in class--and anyone who enjoys popular math books. (shrink)

ObjectiveWe aimed to explore profiles of subgroups of United States students based on their motivational and affective characteristics and investigate the differences in math-related behaviors, persistence, and math achievement across profiles.MethodWe used 1,464 United States students from PISA 2012 United States data in our study. First, we employed latent profile analysis and secondary clustering to identify subgroups of students based on motivational and affective factors. Next, we used regression to compare differences in math behavior, persistence, and achievement (...) among all identified subgroups.ResultsWe found five distinct groups of students with different patterns of motivation and affection. The subgroup of students with the lowest math anxiety and the highest motivation levels showed the highest math achievement and levels of persistence. The groups with high math interest, math self-concept, and instrumental motivation showed the most frequent math-related behaviors.ConclusionsOur findings reveal the complexity of the students’ motivational and affective profiles. Our findings are significant for teachers and educators to understand the diversity of students and provide theoretical and practical support for individualized and differentiated instruction. (shrink)

Paul Grobstein, Eleanor A. Bliss Professor of Biology at Bryn Mawr College, Pennsylvania, USA passed away Tuesday, June 28, 2011. Since Paul came to Bryn Mawr in 1986, he taught courses ranging from "Introductory Biology" and "Philosophy of Science" to "Evolution of Stories" and "The Brain and Education." Paul founded the Summer Institutes for K-12 Teachers, which brought hundreds of local educators to campus to consider new ways of teaching science and math. He served as chair of the Biology (...) Department and was instrumental in the establishment and success of the Center for Science in Society at Bryn Mawr College. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hard Times:Philosophy and the Fundamentalist ImaginationRandall Everett Allsup"Now, what I want is, Facts. Teach these boys and girls nothing but Facts. Facts alone are wanted in life. Plant nothing else, and root out everything else. You can only form the minds of reasoning animals upon Facts: nothing else will ever be of service to them. This is the principle on which I bring up my own children, and this (...) is the principle on which I bring up these children. Stick to the Facts!" So admonishes headmaster Gradgrind in the very beginning of Hard Times, Charles Dickens' prescient tale of education in the industrial world.1 Facts—"addition, subtraction, multiplication and division, settle everything somehow and never wonder"—Facts form the essence of Gradgrind's philosophy.2A close reading of Gradgrind's opening monologue will provide the starting off point for an examination of the role and place of philosophy in the music curriculum. I am particularly intrigued by the question Reimer posed in his opening. He asked us to consider, Who is philosophy of music education for? We will return to this question at the close of this brief reflection.For the moment, however, I would like to continue on to the second paragraph of Hard Times, where Dickens does something very interesting. Following Gradgrind's inglorious monologue, he casts the scene of a small schoolroom, a "plain, bare, monotonous vault."3 Headmaster Gradgrind stands in front; he is described with a "square wall of a forehead," his mouth is "wide, thin, and hard set," his voice "inflexible and dry."4 His hair "bristled on the skirts of his bald head, a plantation of firs to keep the wind from its shining surface, all covered with knobs, like the crust of a plum pie, as if the head had scarcely warehouse-room for the hard facts stored inside."5 A square wall of a forehead, a lumpy head like the crust of a plum pie: these words give us more than "hard Facts"—they are more than mere descriptors. It seems that Dickens, through metaphor, mood, dynamic contrast—through the aesthetic imagination—has imbedded a quiet rebuke to the bold commonsense of Facts.The Gradgrind philosophy finds easy parallel to current thinking in American education. In the fundamentalist imagination, sources of ambiguity must be rooted out—basic skills make adults out of reasoning animals. "Children should be tested on basic reading and math skills every year, between grades three and eight. Measuring is the only way to know whether all our children are learning—and I want to know, because I refuse to leave any child behind."6 The speaker, of course, is George W. Bush whose call to basic skills and episodic testing appeals [End Page 139] to our sense of reason. Like Gradgrind suggests, it is the principle on which we brought up our own children, and this is the principle on which we will bring up today's children. Such a philosophy of education proudly combines folk beliefs about teaching and learning with the hard science of thorough assessment.The President further recommends that our children "must also be educated in the values of our civil society. Some people think it's inappropriate to make moral judgments anymore. Not me. We must be willing to draw a clear line between right and wrong. Those clear lines must be supported by political leaders, public schools, and our public institutions. Educating our children about their moral and civil responsibilities will serve them—and the nation—every bit as well as the academic learning they require."7 In addition to discipline-based standards of knowledge, Facts (in this view) govern the rules of citizenship, provide moral clarity, and as we will see shortly, inform the aesthetic. It is worth noting that such a linear equation—those clear straight lines—currently places skeptics in the category of unpatriotic, miseducative, and morally corrupt.8The fundamentalist philosophy of education is a governing philosophy—it is a philosophy for, not with, its initiates. Judgments are passed, not reached; answers are given, not argued. Teachers in this setting—whether willing accomplices or not—define what needs to be known and... (shrink)

Examine how community college faculty in science, technology, engineering, and mathematics partnered with K–12 teachers to mentor community college science and math students and open their minds to pursuing a career in K–12 teaching. This report outlines the lessons learned by the community colleges that participated in AACC’s Teaching Scholar Partnerships, an initiative supported by the National Science Foundation.

In lieu of an abstract, here is a brief excerpt of the content:Hard Times:Philosophy and the Fundamentalist ImaginationRandall Everett Allsup"Now, what I want is, Facts. Teach these boys and girls nothing but Facts. Facts alone are wanted in life. Plant nothing else, and root out everything else. You can only form the minds of reasoning animals upon Facts: nothing else will ever be of service to them. This is the principle on which I bring up my own children, and this (...) is the principle on which I bring up these children. Stick to the Facts!" So admonishes headmaster Gradgrind in the very beginning of Hard Times, Charles Dickens' prescient tale of education in the industrial world.1 Facts—"addition, subtraction, multiplication and division, settle everything somehow and never wonder"—Facts form the essence of Gradgrind's philosophy.2A close reading of Gradgrind's opening monologue will provide the starting off point for an examination of the role and place of philosophy in the music curriculum. I am particularly intrigued by the question Reimer posed in his opening. He asked us to consider, Who is philosophy of music education for? We will return to this question at the close of this brief reflection.For the moment, however, I would like to continue on to the second paragraph of Hard Times, where Dickens does something very interesting. Following Gradgrind's inglorious monologue, he casts the scene of a small schoolroom, a "plain, bare, monotonous vault."3 Headmaster Gradgrind stands in front; he is described with a "square wall of a forehead," his mouth is "wide, thin, and hard set," his voice "inflexible and dry."4 His hair "bristled on the skirts of his bald head, a plantation of firs to keep the wind from its shining surface, all covered with knobs, like the crust of a plum pie, as if the head had scarcely warehouse-room for the hard facts stored inside."5 A square wall of a forehead, a lumpy head like the crust of a plum pie: these words give us more than "hard Facts"—they are more than mere descriptors. It seems that Dickens, through metaphor, mood, dynamic contrast—through the aesthetic imagination—has imbedded a quiet rebuke to the bold commonsense of Facts.The Gradgrind philosophy finds easy parallel to current thinking in American education. In the fundamentalist imagination, sources of ambiguity must be rooted out—basic skills make adults out of reasoning animals. "Children should be tested on basic reading and math skills every year, between grades three and eight. Measuring is the only way to know whether all our children are learning—and I want to know, because I refuse to leave any child behind."6 The speaker, of course, is George W. Bush whose call to basic skills and episodic testing appeals [End Page 139] to our sense of reason. Like Gradgrind suggests, it is the principle on which we brought up our own children, and this is the principle on which we will bring up today's children. Such a philosophy of education proudly combines folk beliefs about teaching and learning with the hard science of thorough assessment.The President further recommends that our children "must also be educated in the values of our civil society. Some people think it's inappropriate to make moral judgments anymore. Not me. We must be willing to draw a clear line between right and wrong. Those clear lines must be supported by political leaders, public schools, and our public institutions. Educating our children about their moral and civil responsibilities will serve them—and the nation—every bit as well as the academic learning they require."7 In addition to discipline-based standards of knowledge, Facts (in this view) govern the rules of citizenship, provide moral clarity, and as we will see shortly, inform the aesthetic. It is worth noting that such a linear equation—those clear straight lines—currently places skeptics in the category of unpatriotic, miseducative, and morally corrupt.8The fundamentalist philosophy of education is a governing philosophy—it is a philosophy for, not with, its initiates. Judgments are passed, not reached; answers are given, not argued. Teachers in this setting—whether willing accomplices or not—define what needs to be known and... (shrink)

Teaching mathematics and improving mathematics competence are pending subjects within our educational system. The PEIM (Programa Evolutivo Instruccional para Matemáticas), a constructivist intervention program for the improvement of mathematical performance, affects the different agents involved in math learning, guaranteeing a significant improvement in students’ performance. The program is based on the following pillars: (a) students become the main agents of their learning by constructing their own knowledge; (b) the teacher must be the guide to facilitate and guarantee such (...) a construction by being a great connoisseur of the fundamental aspects of the development of the child’s mathematical thinking; (c) the mathematical contents must be sequenced in terms of the complexity and significance for the student as well as contextualized at all times; and (d) the classroom must have a constructivist climate highlighting cooperative work among students. The implementation of PEIM along with the empirical evaluation conducted in several centers in Madrid and Zaragoza (Spain) confirm how students improve their mathematical competence. Both first- and second-grade students in elementary education were far more effective in solving problems, highlighting the use of more advanced strategies in their resolution and a lower incidence of conceptual errors. Moreover, it was possible to verify how the students proving greater difficulty, experienced an evolution in learning similarly to those who did not present it. The program provides customized education to allow the teacher to know at all times how he should be more influential on the students’ learning through mathematical profiles. Both teaching practice and teachers were observed, being that of the experimental group more prone to analyzing processes and allowing the construction of knowledge by students, due to their psycho-developmental training. As a result, we found several improvements through the implementation of the program that may serve, for upcoming years, as a basis for the necessary changes in the teaching of mathematics. (shrink)

International large-scale assessments, such as PISA, provide structured and static data. However, due to its extensive databases, several researchers place it as a reference in Big Data in Education. With the goal of exploring which factors at country, school and student level have a higher relevance in predicting student performance, this paper proposes an Educational Data Mining approach to detect and analyze factors linked to academic performance. To this end, we conducted a secondary data analysis and built decision trees (C4.5 (...) algorithm) to obtain a predictive model of school performance. Specifically, we selected as predictor variables a set of socioeconomic, process and outcome variables from PISA 2018 and other sources (World Bank, 2020). Since the unit of analysis were schools from all the countries included in PISA 2018 (n= 21,903), student and teacher predictor variables were imputed to the school database. Based on the available student performance scores in Reading, Math, and Science, we applied k-means clustering to obtain a categorized (three categories) target variable of global school performance. Results show the existence of two main branches in the decision tree, split according to the schools’ mean socioeconomic status (SES). While performance in high-SES schools is influenced by educational factors such as metacognitive strategies or achievement motivation, performance in low-SES schools is affected in greater measure by country-level socioeconomic indicators such as GDP, and individual educational indicators are relegated to a secondary level. Since these evidences are in line and delve into previous research, this work concludes by analyzing its potential contribution to support the decision making processes regarding educational policies. (shrink)

This article reclaims mathematics from the measures of profit and control by first presenting an anarchist analysis of mathematics? status quo societal uses and pedagogic activities. From this analysis, a vision for an anarchist math education is developed, as well as suggestions for how government school practitioners sympathetic to anarchism can insert this vision into their current work. Aspects to this vision include teacher autonomy, freedom from hierarchical curriculum structure and math class as a non-coercive, happy place. (...) Finally, mathematics is argued to be essential knowledge for anarchistic society for three potentialities: in solving social and technological problems through application, as an analytic technology and for increasing individual happiness via the aesthetic dimension. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 38.4 (2004) 71-80 [Access article in PDF] The Arts and the Creation of Mind: Eisner's Contributions to the Arts in Education Arthur Efland Professor Emeritus, Department of Art Education The Ohio State University In the last four years at least three books in arts education have dealt with the subject of cognition in relation to the arts. I refer to Charles Dorn's Mind in (...) Art, my book Art and Cognition, and Elliot Eisner's The Arts and the Creation of Mind, with the publication of the latter providing the occasion for this article.1 Each of these texts makes its case for the arts in education on somewhat similar grounds. All three share the view that the creation and understanding of works of art, though endowed with feeling and emotion, are nevertheless cognitive endeavors. But why have so many books appeared on the topic of cognition at this time? To answer this question it becomes necessary to describe the changes in our understanding of cognition and the problems these have created for the arts in education.Once cognition was the term used to designate propositional thinking with verbal and numerical symbols, whereas the current sense of the term embraces all forms of thought including mental images obtained through perception. In short it includes all forms of sentience by which the human organism comes to know itself and its environment. This change was to have a major impact upon curriculum reform initiatives in all studies but it was to have a revolutionary impact upon education in the arts for reasons explained later in this essay. However, an adequate story of cognition in the arts cannot be told without a discussion of Eisner's contributions to this discourse. The Waning of Behaviorism For the first half of the twentieth century the psychology that dominated educational practice was behaviorism. Its proponents included psychologists like Edward L. Thorndike, James B. Watson, and B.F. Skinner.2 Each strove to create a science of psychology that would match the rigor of physics or chemistry, where causes in relation to effects would be carefully observed and measured, making the explanation, prediction, and control of phenomena possible, especially those behaviors that fall under the control of the classroom teacher. The formation of connections called stimulus-response (S-R) bonds had become the molar unit to explain learning, much [End Page 71] like the way that differences in the structure of the atom was used to explain the behavior of the chemical elements of the Periodic Table. This bond between environmental stimuli and the organism's response was seen as the elementary unit of behavior while the IQ had become its measure. Invisible notions like mind and imagination were banished to metaphysical philosophy, outside the legitimate bounds of science.Though behaviorists never denied the existence of higher order thinking that is, abstract, sense-free thinking as found in pure mathematics, they were unable to explain how these human capacities emerge through the accumulation of such rudimentary stimulus-response events. Nevertheless, they recognized that humans do have a capacity for thinking that relies heavily upon symbols like words, numbers and the like. Moreover, certain subjects that require reason and logic, like math and theoretical physics, would be inconceivable without such symbols and the rules by which these are manipulated. By contrast it was assumed that the arts, which relied on sensory images, either did not employ this type of propositional thought, or did so to a far lesser degree. Thus the arts could be dispatched to the noncognitive or affective domains with little or no reduction in the learner's cognitive capacities. Indeed, these noncognitive realms, which gave play to feelings and emotions, were often seen as inimical to the acquisition of rational powers of thought. Intellectual power as it was then understood, required that feelings and emotions be brought under the control of reason.As long as behaviorism served as the dominant paradigm, the school curriculum could be divided into two or three broad divisions... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 39.1 (2005) 31-47 [Access article in PDF] Holistic Integrated Design Education: Art Education in a Complex and Uncertain World Christopher Nokes Egosystem All art is the solution to an initiating design problem that must be articulated, even if the problem is this: to create something without meaning. As such, all art is a literary process, whereby the idea is articulated before that idea is (...) re-presented as an art form. And this is precisely what I attempt to do in the classroom when I assign highly challenging, universal, socio-cultural based and interpretive design problems. Both intent and solutions are implicit in the design assignments given to students. In each case the design process is emphasised, and students define the problem, research (often collaboratively), brainstorm (diving deeply into the problem for potential solutions), develop alternative solutions, use free-hand sketches and storyboarding to track the design and decision-making process, and (finally) select the best design for development and evaluation. Definition of key terms, research and storyboarding are the initial steps in the process to solving each of the design problems. Some examples of problem solving performance tasks are provided below (Table 1).Regarding the last example, in my first year of teaching I accepted a position on agreement that I teach Grade 10 (sophomore) mathematics. Even though my teaching background favored art and history, this was not a hardship because my original degree was in architecture (University of Toronto, 1978). I realized quickly that my personal romance with D.N. Perkins's Knowledge as Design demanded that I attempt to teach mathematics as a design process (much to the dismay of the department head).1 Nevertheless, imaginative mathematical works of mind were explored, based on original "design problems." As well, collaborative math tests were developed (and structured as design problems), where students divided into groups or design teams, each team having a "competent mathematician" on [End Page 31] Click for larger viewTable 1 Works of Mind; Visual Arts as a Problem-Solving Design Process [End Page 32]board. Each team worked together to solve one challenging mathematical problem, or a series of challenging mathematical design problems, under a time limit. This ensured that each student had a role to play. A key group dynamic here is that students speak to each other as peers, in a way teachers cannot: "No! You don't do it that way, silly. It's like this!" says A. "Ok! Ok! Don't yell at me," says B tenderly. "It's like this?" "Yes!" says A. "See! You really are good at math!" It was a beautiful thing to watch. The so-called "stupid-at-math" students saw how the "brainy" math students interpreted and approached mathematics, while the "brainy" students pulled those students who always believed they were "stupid at math" up to their level. In the end (to say the least), it greatly increased the weaker students' comfort level entering the classroom, and (at best) it gave weaker math students confidence by dispelling some of the mystical mystery which mathematics seems to possess — mathematics is not a mystery, it is a problem waiting to be solved as any other design problem once you know the process. Click for larger viewTable 2 Components of the Egosystem This is holistic integrated design education (or HIDE). Transforming students from the traditional, isolated receiver of information to the holistic child requires a fundamental transformation of the associative-cognitive paradigm of learning behavior and psychology, based on the child's ego development in a kind of object-filled, symbolical, self-contained world.2 In actuality, the world is complex, multi-faceted, hyper-sensitive, with many people of different socio-cultural and intellectual frames of mind interacting; and it is (thus) hardly self-contained. The world has indeed evolved that far. Somehow, like all paradigms, the ego must undergo a similar evolution, a similar transformation.3 A new version of ego must be invented, one that takes into account all the stuff of objective reality — the... (shrink)

O artigo tem por objetivo problematizar o enunciado que diz da importância de ensinar matemática usando jogos. O material de pesquisa abrange todos os exemplares da Educação em Revista (ER), periódico do Sindicato do Ensino Privado do RS. Servindo-se de ferramentas teóricas oriundas do pensamento de Foucault, o artigo examina entrelaçamentos do enunciado estudado com outros do campo educacional, que geram efeitos de verdade no discurso da educação matemática contemporânea. O trabalho investigativo permitiu identificar: a) os vetores de sustentação do (...) referido enunciado encontram-se nas produções acadêmicas da área da Educação Matemática e em documentos oficiais; b) uma reatualização do enunciado evidenciando fortes aproximações entre os jogos escolares para ensinar matemática e as tecnologias digitais. As considerações finais apontam para a constituição de uma narrativa vitoriosa sobre o uso de jogos nas aulas de matemática, capturando professores e alunos. Palavras-chave: Educação Matemática. Escolas privadas. Jogos. Enunciado. Michel Foucault. The use of games in Mathematics classes: problematizing the truths of contemporary pedagogical discourse Abstract: The article aims to problematize the statement about the importance of teaching mathematics using games. The research material covers all the copies of Educação em Revista (ER), a periodical of the Private Teaching Union of RS. Using theoretical tools derived from Foucault's thought, the article examines the intertwining of the studied utterance with others in the educational field, which generate real effects in the discourse of contemporary mathematics education. The investigative work allowed us to identify: a) the support vectors of that statement are found in academic productions in the area of ​​Mathematics Education and in official documents; b) a re-updating of the statement showing strong similarities between school games to teach mathematics and digital technologies. The final considerations point to the constitution of a victorious narrative about the use of games in math classes, capturing teachers and students. Key-words: Mathematics Education. Private schools. Games. Statement. Michel Foucault. El uso de juegos en las clases de Matemáticas: problematizando las verdades del discurso pedagógico contemporáneo Resumen: El artículo tiene como objetivo problematizar la afirmación que dice sobre la importancia de enseñar matemáticas mediante juegos. El material de investigación cubre todos los ejemplares de Educação em Revista (ER), publicación periódica de la Unión de Docentes Privados de RS. Utilizando herramientas teóricas derivadas del pensamiento de Foucault, el artículo examina el entrelazamiento del enunciado estudiado con otros en el ámbito educativo, que generan efectos reales en el discurso de la educación matemática contemporánea. El trabajo investigativo permitió identificar: a) los vectores de apoyo de ese enunciado se encuentran en producciones académicas en el área de Educación Matemática y en documentos oficiales; b) una actualización de la declaración que muestra fuertes similitudes entre los juegos escolares para enseñar matemáticas y tecnologías digitales. Las consideraciones finales apuntan a la constitución de una narrativa victoriosa sobre el uso de juegos en las clases de matemáticas, capturando a profesores y alumnos. Palabras-clave: Educación Matemática. Escuelas privadas. Juegos. Enunciado. Michel Foucault. Data de registro: 05/09/2021 Data de aceite: 16/02/2022. (shrink)

Despite the general agreement that the interdisciplinary model of physical education (PE), based on the incorporation of core academic subjects into the PE curriculum, stimulates the holistic development of students, there is still a lack of methods for its implementation. Therefore, Eduball was created, i.e., a method that uses educational balls with printed letters, numbers, and other signs. Numerous studies have shown that children participating in activities with Eduballs can develop their physical fitness while simultaneously improving their academic performance, particularly (...) in math and language, including some writing skills. However, little is known about the effects of Eduball on children’s graphomotor skills, which are key for the academic performance of students throughout the entire schooling process. Here, we investigate whether 6-month participation in PE with Eduball stimulates graphomotor skills in primary school students, such as drawing prehandwriting letter patterns on unlined or lined paper and rewriting text on unlined or lined paper. Our results show that the Eduball class (N= 28) significantly improved these skills compared to the control class (N= 26) participating in traditional PE. For example, students from the experimental group wrote with a lower pen pressure and better stability of the line, in contrast to those from the control group. Therefore, this study demonstrates that the Eduball method successfully supports teachers in developing graphomotor skills in children. More broadly, our findings make clear once again that there is the need to integrate physical and cognitive development in education, which can be achieved by using an interdisciplinary model of PE. (shrink)

This article reports the macro-organizational structure of research articles in mathematics, based on an analysis of 30 published pure and applied mathematics articles. Math RAs eschew the Introduction-Methods-Results-Discussion structure for an Introduction-Results model that enables researchers to present new knowledge as clearly and succinctly as possible. Notable omissions from the mathematics RA structure are Method and Discussion sections, which mathematicians do not need because of the well-established methodology used in the field and the relative absence of extended discussion required (...) to interpret research findings. We contextualize the macrostructure of RAs in mathematics within the discourse conventions and disciplinary assumptions about knowledge in the field to suggest the value of such a strategy to teachers and students of academic writing. (shrink)

continent. 1.3 (2011): 201-207. “Poetry is experience, linked to a vital approach, to a movement which is accomplished in the serious, purposeful course of life. In order to write a single line, one must have exhausted life.” —Maurice Blanchot (1982, 89) Nikos Karouzos had a communist teacher for a father and an orthodox priest for a grandfather. From his four years up to his high school graduation he was incessantly educated, reading the entire private library of his granddad, comprising (...) mainly the Orthodox Church Fathers and the ancient classics. Later on in his life he sold the library for money, only to buy a little more time before he went broke again: “I carry sorrow like a cage/ I got no birds/ as I come back from her hair/ I see the profit emptied/ cool from terror.” (1993, Ι, 101) Nowadays—and ridiculously recently—we are more than apt to speak of a certain insouciance pertaining to the Greek form of expenditure: expenditure without any type of investment, sometimes not (even) symbolic. In the vaults of the European unconscious, this imprudent stance still conjures a “capital punishment” in the form of de-capitation, reflecting back the fear of excess and the terror of its consequences.1 Thus the Greek way of living is very close to what a stranger could have termed as “the Greek way of dying.” Yet, what is not often understood is that the Greek esprit , the same one that invented the maxim μηδ?ν ?γαν (“nothing in excess”), does not experience death solely as an imminent fear of bankruptcy. For it miraculously combines its unconditional acceptance with the promise of a resurrection that is always there in the scents of Spring, from Dionysus to the orthodox Christ: “Everyone resurrects himself through dying [….] Resurrection is the switching of mortalities.” (2002, 94) Hence, if an entire library was imprudently traded for a plate with seven olives, a sliced tomato and some fresh goat cheese, let us not be fooled: this is not the meal of the pauper, but that of “an aristocrat from God” (1993, II, 491) feeding his eloquent loudmouth, ridiculously cut open in an otherwise rock-solid caput . *** To speak of the Greek experience is to speak about a half-dead language that still utters in life what is seemingly excluded from it and thus forbidden to be talked about: death. Death as anything that is out of this world, as something that will never return . Still, along with an experience of death that recently waned as a worn-out academic fashion, the Greek experience is dead too. Nearly 2300 years of written words separating Homer from the fall of Byzantium equal 500 books on a library traded for money: “I am with the killed. Hence my deepest solitude. I do not feel this tremendous macho society, beyond from the fact that it is a ruthlessly consuming one. It is me who pays all the time .” (2002, 57) Let us do the math and see how much this dealing with the Greek experience is costing the poet and how much dealing with the Greek experience might cost us today. *** “I do not guarantee a single word.” (Karouzos, 1993, II, 454) Through its various dialects and forms, the Greek language speaks through an incessant historical dissemination. Anyone who is aware of this terrifying polymorphy and still calls himself a poet, must stand against a white sheet of paper, pen-in-hand, with a very particular duty: to be as fully inconsistent as possible. In the formally ironic uniqueness of the poem, the poet functions as “a band-aid for lesser and greater antinomies.” (1993, I, 251) Of course these antinomies are not exhausted in language—they are historical, political and, alas, existential. Yet, beyond appearances , it is language that ruthlessly encodes them through history, submitting the poet to the temptation of placing them one next to the other on a single white sheet. The closer their neighboring, the greater the scattering of the writer in the ironic uniqueness of the paper. In a work where poetic license is described as a “freedom-impasse” (2002, 51), this task is undertaken in full conscience of its personal consequences: “what I am interested in is to escape my individuality (envisioning the non-ego) […] Nevertheless, my dissociations never achieve duration.” (2002, 74-75) Hence, though poetry is the “deserted direction of will,” (1998, 62) the stance of the poet is not that of a Nietzschean “great man.”2 Whereas drunkenness provides a thread between the poem and the excess it both presupposes and infuses (“Poetry always enlarges. ‘Drunkenness’ is nothing more than that,” (2002, 85)), whereas language flashes in loudmouth spurts of déraison (“When I am alone I do something else. I utter words. For example, while having my ouzo and listening to music I am most likely capable of randomly shouting ‘Electricity!’” (2002, 138)), the poet never gives in to the double affirmation that would eventually risk the “element of pleasure in discourse.” (2002, 80)” It is exactly because the gap of the antinomies is so vast that poetry is not meant to be written with a hammer. Neither does writing consist in a reevaluation of those elements. In short, poetry is not an affirmation of difference, but the surprising beauty of chiming antinomies. We might never transcend them, but it is up to us to put them together. Yet again, this voisinage is not to be identified with the necessity of chance as an eternal return.4 On the contrary it is a return from that very return : Let us treat Yes as a No to No and No as a Yes […] And let us not forget that this pissed affirmation crumbled down Nietzsche’s intellect in the dark paths of this world. (2002, 88) This return from the “vicious circle” should in no way be taken as a form of artistic prudence. Rather it can be seen as a dribble of demonic inconsistency as Dionysus transforms himself into a Christ that is in turn de-theologized: “Who can forbid that? Every man is capable of his own theology, nothing can stop him.” (2002, 73-74) This is a turn towards an existential vision of the world, historically coinciding with a particular political defeat of the Left, to which the poet devoted all his life: after the defeat of the popular front I raised the question “why do we exist?” while others were asking “why we failed.” (2002, 57)5 But most of all it is a return to poetry that exceeds the existential question itself, going beyond the issue of faith. Poetry comes in as a question of return after a defeat that is confessed in full profanity. Though it accepts the necessity of the defeat, it does not affirm it. Though it negates it, the negation is not in the name of a promise to be delivered in the kingdom of heavens. Following a historical and existential defeat, poetry is born post mortem . It signals a return to Christ as “groundless religiousness in the surprise of the real as such” (2002, 72) which is at once a return to the refuge of childhood. It is not a question of endurance towards an eternal return. Rather it is a question on the possibility of an existential return. Returning in a world as someone who cannot enjoy any returns exactly because he is averse to guarantees. A return without returns. *** PHOTOCOPY OF HAPPINESS When I was young I used to pin down cicadas and step on ant nests. I used to stand there silent for hours. With threads I decapitated bees. Now I am a dead man breathing. (Karouzos, 1993, II, 336.) The return to the “paradise of childhood” (2002, 68) constitutes the devouring refuge of its own memory when defeat becomes the synonym of adulthood. The political struggles of a young communist in a country torn up by a civil war right after World War II fraught with incarcerations and exiles. Historically they resulted in the defeat of the communist movement in Greece and opened up a long turbulent road that would peak in the dictatorship of 1967. Existentially they led to a series of disillusionments: mental breakdown, divorce, abandonment of studies in law school. To the question “why do we exist” the answer was poetry. Still this exposé should not be read as a sweeping chronography of a man. For it actually happens to coincide with the historical fate of a nation that after its modern constitution never stopped dreaming of the glories of its past youth, in a present that was (and is) sweepingly disappointing. But isn’t this return to youth finally a way of compensating for a loss of youth that necessarily results in a losing adulthood? Will Greeks, the eternal children of Plato and Nietzsche, ever learn? How to return without dying, how to remember without wasting time? WE ARE IN THE OPEN MEANING Living the coldest mauve night right across Parthenon I went to take a piss on some foliage and I was enjoying the foliage as it was steaming. (Karouzos, 1993, II, 340) Beyond the historical tragedies of modern Greece and away from any personal disappointments, the relation that this land holds with language and history is mediated through the Greek light—whose omnipresence is the very condition of its transcendence. All historical contradictions from Dionysus to Christ took place under this light; all those disseminated dialects were spoken beneath its warmth. To paraphrase Lévinas,6 light is both the condition of the world and of our withdrawal from it—a withdrawal towards the invisibility of God, of the dead, of meta-physics, resulting from the temptation that all is still here, behind this light the visibility of which they once evaded: “birds, the allurement of God.” (1993, I, 17) Under that luminous sky, if Greeks can do anything at all, it is to envision a return that will never come. All they can do is write poetry—which is doing nothing; other than lending an ear to a disseminated language whispering a unity that cannot be promised, as an adulthood in defeat is ready to recognize. Trying “to trap the invisible in visibility” (1993, II, 483) they forget that they have grown up and one day they die—with the promise of return. Hence an additional meaning must be given to this return to childhood. It does not signal salvation but rather its promise. To the ears of an aged continent it means that the return to/of poetry is a losing game, a return without returns. “Europe, Europe… you are nothing more than the continuation of Barabbas.” (1993, I, 295) *** “Life is not there to verify theories.”7 The records show that Karouzos was finally given a second-class pension from the Greek government, at the time when he was being recognized by the literary press as one of Greece’s major contemporary poets. Being neither a bourgeois nor a nobelist, he proclaimed himself to be an anarcho-communist, unconditionally faithful to the utopia of a classless society. He also drank, heavily. “Capitalism made an animal out of man/ Marxism made an animal out of truth/ Shut up.” (1993, II, 369) Perhaps one of the most scandalous divides of our times has been the one between the living and the dead, the latent prohibition that the living should not be concerned with the dead based on the mere impossibility of the dead to be concerned with the living in the first place. What adds to this scandal is that this divide abuses anything that cannot return to us by subsuming it under the same futility. Hence death is no longer “loss” in the usual sense. It no more refers to the things we lost but to our “loss” (of time, money and well-being) as we insist to dwell on them. Death is a waste —of time. It is this waste that we find in the insouciance of Greek expenditure; the waste in dealing with a language that most of its historical part is no longer spoken (a dead language); the waste in translating a poet who is ex definitio untranslatable; the waste of his vision, his money, his life. The waste of dealing with anything that cannot return and that cannot bring in any returns . But it is also the waste of life that poetry itself presupposes, the waste of dealing with invisibility, with anything that is out of this world and thus invokes the fear of death that is in turn—and surprisingly— nowhere to be found. Instead of death, what is there, beyond the light, is the being without us (to recall the Lévinasian il y a ), the mumble of our own nothingness which constitutes the price to be paid for writing poetry under an evergreek light. To understand this to-and-fro, is to realize that poetry is something out of this world that nevertheless takes place in this world, by virtue of this world. But to ridiculously equate this to-and-fro with death as non-existence, is to exile poetry along with its own possibility from this same old world: I do not believe that poetry will ever disappear from this world. […] But I am also sure that it does not have many chances of playing, as you say, a redemptive role in our vertiginous technological future. Without being endangered as a creative need, it will be placed on the side of history. (2002, 32) It is mainly there that we would like to locate the meaning of Nikos Karouzos’s poetry today. If we are willing to include the Greek original it is because we consider that it will be both a waste of time for us to do so (since most of you cannot read Greek) and because it might induce you to the even larger waste of learning it. We would additionally be glad if this small introduction served as an equally wasteful, academically useless piece of reading, gesturing towards a taboo of investing in anything Greek—that is in anything dead among the living, in anything that will never come back and maybe was never here in the first place. This is the only way to reserve for ourselves the possibility of poetry and preserve the light of its promise. “To return: that is the miracle.” (1993, I, 17) Athens, Greece July 10, 2011 NOTES 1 “ Capitale (a Late Latin word based on caput “head”) emerged in the twelfth to thirteenth centuries in the sense of funds, stock of merchandise, sum of money or money carrying interest.[…] The word and the reality it stood for appear in the sermons of St. Bernardino of Siena (1380-1444) ‘… quamdam seminalem rationem lucrosi quam communiter capitale vocamus ’, ‘that prolific cause of wealth that we commonly call capital’” (Braudel, 1992, 232-233). 2 “A great man – a man whom nature has constructed and invented in the grand style – what is he? First : there is a long logic in all of his activity, hard to survey because of its length, and consequently misleading; he has the ability to extend his will across great stretches of his life and to despise and reject everything petty about him, including even the fairest, ‘divinest’ things in the world.” (Nietzsche, 1968, 505, §962) 3 Cf. Deleuze, 1986, 186-9. 4 “Return is the being of becoming, the unity of multiplicity, the necessity of chance: the being of difference as such or the eternal return.” (Deleuze, 189)5 In this 1982 interview Karouzos refers to the defeat of the communist movement in Greece after the civil war of 1946-1949 between the Governmental Army and the Democratic Army of Greece, the military division of the Greek communist party. Karouzos’s father was a member of the communist National Liberation front (EAM) members of which formed the mainl resistance movement (ELAS) in Greece during WWII. The poet was a member of the United Panhellenic Organization of Youth (EPON), which was a youth division of EAM. After the end of the war, ELAS was called to disarmament in view of the formation of a National Army. The members of EAM resigned from the government of national unity and a series of protests led to a 3 year civil war between ELAS and the Government Army. After the defeat of ELAS the Communist party was outlawed and many communists were exiled in deserted Greek islands. Karouzos, who took action in the Greek resistance and was active during the Greek civil war, was exiled in Icaria on 1947 and in Makronisos on 1953 where he was called two years earlier to do his military service. 6 “Existence in the world qua light, which makes desire possible, is then, in the midst of being, the possibility of detaching oneself from being. To enter into being is to link up with objects; it is in effect a bond that is already tainted with nullity. It is already to escape anonymity. In this world where everything seems to affirm our solidarity with the totality of existence, where we are caught up in the gears of a universal mechanism, our first feeling, our ineradicable illusion, is a feeling or illusion of freedom. To be in the world is this hesitation, this interval in existing, which we have seen in the analyses of fatigue and the present.” (Lévinas, 1988,43-4) 7from a TV interview. THE POETRY OF NIKOS KAROUZOS From Redwriter [ Ερυθρογρ?φος ], in Collected Works, Vol . II, Athens: Ikaros. 1993, 463-4. [Athens: Apopeira, 1990, 9-10.] JESUS ANTI-OEDIPUS* Why were we once saving till the fifth day the Paschal lamb? The scriptures say: with this victim’s meat we ought to cleanse all of our senses. To give life to the whitest wave miraculous odors in the extension of the chest. Ideals to death. For us to witness the illustrious dawns of Absinthe and for the soul to be a deeply carved ornament on the fore we named will. Then many deer running amidst the evergreen growth with watery hymns, then, the unintended angels descending with heights spiraling in their momentum offer themselves to the luminous Adventure. Whence the need for speech and our sufferings covered with flags like the glorified dead. An incorporeal finger pointing at the flamboyant and fragrant holocausts within the tired horizons and the exhausted breadths with joys of the mistletoe on fire and shivering all of the green-leaved love. Something would have chirped again had we not driven it away— maybe the ewe’s grass. Something would have called us to the eternal resurrection— maybe the grace of spring. But now our heart is fiercely blinded, withdrawn to the appearances of Hades. Silence and ice incessantly cover the Infant Spirit in thatched times. While the cherry trees are dreaming faintly glowing in absolute darkness there’s nothing the Babylonians can contemplate in labs with automatic colored lights. How to rejoice now in the fifth day of the lamb? We have forked the stars. We’ve gradually become supposedly sublime with plucked chimeras in our hands. Avenged relentlessly by science. *Though the poem appears in a 1990 collection, it was actually written in 1968. Hence the reader must be aware in not associating Karouzos’ Anti-Oedipus with the famous 1972 work of Deleuze and Guattari, given that the former precedes the latter. ΙΗΣΟΥΣ ΑΝΤΙ-ΟΙΔΙΠΟΥΣ Γιατ? κρατο?σαμε κ?ποτε ?ς την π?μπτη μ?ρα το πασχαλιν? πρ?βατο; Τα κε?μενα λ?νε: μ’ αυτο? του θ?ματος το κρ?ας ?πρεπε να καθαρ?σουμε ?λες τις αισθ?σεις. Για να δ?σουμε κ?μα στη ζω? λευκ?τατο θαυμ?σιες ευωδι?ς στην ?κταση του στ?θους. Ιδανικ? στο χ?ρο. Για να βλ?πουμε τα λαμπρ? χαρ?ματα του ?ψινθου και να ’ναι η ψυχ? στ?λισμα βαθυχ?ρακτο της πλ?ρης που την ε?παμε θ?ληση. Τ?τε πολλ?ς δορκ?δες τρ?χοντας αν?μεσα στην καταπρ?σινη φ?ση με τους υδ?τινους ?μνους, τ?τε, κατεβα?νοντας οι αθ?λητοι ?γγελοι με κυλινδο?μενο το ?ψος στην ορμ? τους χαρ?ζονται της αστραφτερ?ς Περιπ?τειας. ?θεν η μιλι? γι’ αυτ? χρει?ζεται και τα δειν? σκεπ?ζονται ωσ?ν τους τιμημ?νους νεκρο?ς με σημα?ες. Ασ?ματο δ?χτυλο δε?χνει τα φλογ?δη και μοσχοβ?λα ολοκαυτ?ματα στους κουρασμ?νους ορ?ζοντες στα εξουθενωμ?να πλ?τη καθ?ς αν?βουν οι χαρ?ς του νερα?δ?ξυλου και τρ?μει ολ?κληρη η πρασιν?φυλλη αγ?πη. Κ?τι θα κελαηδο?σε π?λι αν δεν το δι?χναμε— μπορε? της προβατ?νας το χορτ?ρι. Κ?τι θα μας καλο?σε στην απ?ραντη αν?σταση— μπορε? του ?αρος η χ?ρη. Μα η καρδι? μας ?γρια τυφλ?θηκε π?ρασε στα φαιν?μενα του ?δη. Σιγ? και π?γος αδι?κοπα σκεπ?ζει στους αχυρ?νιους καιρο?ς το Ν?πιο Πνε?μα. Την ?ρα που ονειρε?ονται οι βυσσινι?ς και λ?μπουν αμυδρ? μεσ’ στο απλ?τατο σκοτ?δι τ?ποτα δε στοχ?ζονται οι βαβυλ?νιοι στα εργαστ?ρια με τ’ αυτ?ματα χρωματιστ? φ?τα. Π?ς να χαρο?με πια την π?μπτη μ?ρα του προβ?του; Φουρκ?σαμε τ’ αστ?ρια. Γ?ναμε σιγ?-σιγ? δ?θεν υπ?ροχοι με μαδημ?νες χ?μαιρες στα χ?ρια. Μας ν?μεται σκληρ? η επιστ?μη. From: Redwriter [Ερυθρογρ?φος], in Collected Works, Vol. II, Athens: Ikaros. 1993, 472. [Athens: Apopeira, 1990, 18.] DIALECTΙCS OF SPRING Christ the straight angle; Christ the Pythagorean theorem. Christ the infinitesimal calculus from above the blessed Sets Christ. Christ the tessellation of massive particles Christ the zero mass. Hence we spray numbers and fields of lust. We are carabineers of diseased logic plus something— Observed means observer and Hekate The darkness luminous and light in the dark Astarte banqueters demons from today. ΔΙΑΛΕΚΤΙΚΗ ΤΟΥ ΕΑΡΟΣ Χριστ?ς η ορθ? γων?α· Χριστ?ς το πυθαγ?ριο θε?ρημα. Χριστ?ς ο απειροστικ?ς λογισμ?ς ?νωθεν ?λβια Χριστ?ς τα Σ?νολα. Χριστ?ς η ψηφιδογραφ?α στα μαζικ? σωμ?τια Χριστ?ς η μ?ζα μηδ?ν. ?ρα ψεκ?ζουμε αριθμο?ς και πεδ?α λαγνε?ας. Ε?μαστε τυφεκιοφ?ροι νοσο?σης λογικ?ς και κ?τι-- παρατηρο?μενο σημα?νει παρατηρητ?ς και Εκ?τη σκ?τος το π?μφωτο και φως εν τ? σκοτ?? η Αστ?ρτη συνδαιτημ?νες δα?μονες απ’ ?ρτι. From: Redwriter [Ερυθρογρ?φος], Athens: Apopeira, 1990, 18. [1993, II, 472]. CREDO (as we are used to say in Latin) Α I believe in one Poet expelled from heavens / fugitive from the god and vagabond, Empedocles / and here on earth / exile on the earth etc. of Baudelaire /. Β I believe in one Computer inside thunder and through matter. Γ Suffering undefiled / substantive / the Poet uplifts himself slow-burning suicidal implying lengthy sleeps. Δ Cutting down on prospective mistakes. Ε Of all things visible and invisible officiating the onion-peelings. Ζ The Poet has nothing / see the departed /. Η I believe in one Poet that says: madness I enjoy; he ridicules existence; let me light up from my mana. Θ Syntax he doesn’t care about when musicality commands him. Along with still more licenses, and Ts are played according to the concept sound anywhere. E.g. the winters here, he winters there; it will not come—I will not rest, etc. etc. Ι The Poet exercises thought until it’s stripped down. Κ And if he’s Greek he must always study the fineness of Attica, in light, mountains, fields and sea. For this fineness teaches language. Λ And if he’s deeply destined the Poet expresses the unexplainable of the explained; he happens to be a rightful heir to the scientist and his predecessor. Μ On the froth he does not last; the Poet blusters at the bottom of the pot. Ν Flamebred and never redeemed. Ξ The Poet must sometimes say: what a consumption of presence — be a bit lonely for a change! Ο The Poet is twilit. Π He is susceptible of deaths and resurrections. Ρ He looks from the corner of his eye and exists in a glance. Σ He follows behind the mother. Τ Eveningless when it comes to age. Υ I believe in one Poet who says: let the purities coincide. Until the Corinth of the Universe or even further. Φ In a higher despair. Χ In a brighter quintessence. Ψ In one sensation that lifts off. Ω Forgiving everyone. CREDO (ως ε?θισται να λ?με λατινιστ?) Α Πιστε?ω εις ?να Ποιητ?ν εκτ?ς ουρανο? / φυγ?ς θε?θεν και αλ?της, Εμπεδοκλ?ς / και επ? της γης / εξ?ριστος π?νω στη γη κ.λπ. του Βωδελα?ρου /. Β Πιστε?ω εις ?να Υπολογιστ?ν εντ?ς κεραυνο? και δια της ?λης. Γ Υποφ?ροντας ?χραντα / ουσιαστικ?ν / ο Ποιητ?ς ανατε?νεται βραδυφλεγ?ς αυτ?χειρας εξυπακο?οντας πολ?ωρους ?πνους. Δ Τα υποψ?φια λ?θη λιγοστε?οντας. Ε Ορατ?ν τε π?ντων και αορ?των ιερουργ?ντας την αποκρομμ?ωση. Ζ Ο Ποιτ?ς ?χει τ?ποτα / βλ?πε τους αναχωρ?σαντες /. Η Πιστε?ω εις ?να Ποιητ?ν που λ?ει: η τρ?λα μ’ αρ?σει· γελοιοποιε? την ?παρξη· ας αν?ψω απ’ τη μ?να μου. Θ Συνταχτικ? δεν το γνοι?ζεται στην προσταγ? της μουσικ?τητας. Μαζ? και μ’ ?λλες ακ?μη λευτερι?ς, και τα νυ πα?ζονται κατ? την ?ννοια ?χος οπουδ?ποτε. Π.χ. τον χειμ?να εδ?, το χειμ?να εκε?· δε θ? ’ρθει – δεν θα καταλαγι?σουμε, κ. λπ. κ.λπ. Ι Ο Ποιητ?ς γυμν?ζει τη σκ?ψη σε απογ?μνωση. Κ Κι αν ε?ναι ?λληνας οφε?λει να σπουδ?ζει π?ντοτε της Αττικ?ς τη λεπτ?τητα, σε φως, βουν?, χωρ?φια και θ?λασσα. Διδ?σκει γλ?σσα η λεπτ?τητα το?τη. Λ Κι αν ε?ναι βαθι? πεπρωμ?νος ο Ποιητ?ς εκφρ?ζει το ανεξ?γητο του εξηγητο?· τυγχ?νει ν?μιμος δι?δοχος του επιστ?μονα και προκ?τοχ?ς του. Μ Στον αφρ? δεν ?χει δι?ρκεια· στο πατοκ?ζανο μα?νεται ο Ποιητ?ς. Ν Φλογοδ?αιτος και ποτ? ξελυτρωμ?νος. Ξ Ο Ποιητ?ς κ?ποτε πρ?πει να λ?ει: μεγ?λη καταν?λωση παρουσ?ας – γενε?τε και λ?γο μοναξι?ρηδες! Ο Ο Ποιητ?ς ε?ναι αμφ?φλοξ. Π Επιδ?χεται θαν?τους και αναστ?σεις. Ρ Ακροθωρ?ζει και υπ?ρχει σε ξαφνοκο?ταγμα. Σ Ε?ναι ουραγ?ς της μητ?ρας. Τ Αν?σπερος απ? ηλικ?α. Υ Πιστε?ω εις ?να Ποιητ?ν που λ?ει: να συμπ?σουν οι αγν?τητες. Μ?χρι την Κ?ρινθο του Σ?μπαντος ? μακρ?τερα. Φ Σε αν?τερη απελπισ?α. Χ Σε φαειν?τερη πεμπτουσ?α. Ψ Σε μια α?σθηση που πτηνο?ται. Ω Συγχωρ?ντας τους π?ντες. From Large Sized Logic [ Λογικ? μεγ?λου σχ?ματος ], Athens: Erato, 1989, n.p. [1993, II, 521-3]. (shrink)

With STEM education garnering an increasing share of educational budgets and press, humanities teachers should consider how to respond to the growing power of math and science. Should humanists rea...

What the present work aimed to achieve is an assessment of the origin an d unity of Husserl s Logical Investigations. My approach was to take the history of its development as fundamental for the determination of its basic structure. Therefore, I proceeded to analyse Husserl s development between the Philosophy of Arithmetic and Logical Investigations with re spect to the fundamental issues in the justification of knowledge in mathematics and logic. In Husserl s own words, one of the concerns (...) that set him on the road to phenomenology was the clarification and analysis of the relation b etween the subjectivity of knowing and the objectivity of knowledge. Fro m my investigations it has, I hope, become apparent how this problem ori ginated in his earliest works and, through various influences and exchanges, led to his theory of intentionality in the first editio n of the Logical Investigations. The Logical Investigations is located between his Brentanist phase and t he ultimate development of transcendental phenomenology. It is the sedim ent of Husserl s logical investigations during the 1890s, which is the m ain period I analysed in the present work. Husserl himself often remarke s on the early origin of some of the issues he tried to deal with in the Logical Investigations. Still in his sketches for a new preface to the second edition of 1913, he took pains to point out the developmental his tory of the work from the Philosophy of Arithmetic onward. Regarding the Philosophy of Arithmetic, more often than not, Husserl remarks that it was just and elaboration of his Habilitationsschrift. Hence, following h is lead, we tried to embrace the whole period of his psychological and l ogical analyses from 1886/7 to 1900/01. Of course, I was certainly not the first, nor will I be the last, to be intrigued by Husserl s development in these years. Numerous books and articles have been written long before mine on precisely these issue s, often dealing with specific topics, such as the uneasy relation of psychology and psychologism in Husserl s work or fundamental inʂ 58;uences such as Bolzano s, which I therefore chose to leave aside. Not simply to duplicate or summarise such pre-existing scholarship, I tried to concentrate on the issues to which I felt I could contribute an orig inal insight, advancing the field. I would like to indicate ᤙ 7;ve points here, where I think I attained this goal: 1. The enduring relevance of Husserl s mathematical ba ckground. 2. Support for an early development of a theory of hig her order objects 3. A better evaluation of Frege s influence 4. A contextualisation of Schuhmann s thesis regarding the relevance of Twardowski for Husserl s notion of intentionality 5. The dependence of the unity of the Logical Investig ations on its historical development. Without understanding its developmental history we would misunderstand i ts internal coherence. In the first part we saw Husserl s early struggle to integrate the mathematical and psychological points of view on the philosophy of math ematics, a struggle that lasted from the Habilitationsschrift at least u p to and including his Doppelvortrag. The basic problem is the justi@ 257;cation of knowledge, in the case of mathematics, the justifica tion of knowledge in formal sciences, obtained with symbolic methods. Su ch problems regarding the subjectivity of knowing and the objectivity of knowledge guided the development of his position from Philosophy of Ari thmetic to Logical Investigations. In articulating his solution Husserl analysed the various relations betw een founding and founded layers of knowledge and whether and how one cou ld pass from on to the other. Already at the time of the Philosophy of A rithmetic he tried to account for higher order acts, relations and objec ts, the mature account of which would have to wait until the Logical Inv estigations and later. Among various influences on his progression towards phenomenology, Frege has been often considered to have provided the conversion to an ti-psychologism with his review of the Philosophy of Arithmetic. I think I have demonstrated that the review is almost entirely irrelevant in th is sense and that we should rather look at a much earlier influenc e on the Philosophy of Arithmetic. By showing that Brentano s conception of intentionality was already more sophisticated than until recently assumed, thanks to some recent public ations of unpublished material from Brentano s and Husserl s Nachlass, I think Schuhmann s thesis is right, but should be reinterpreted as being less radical than it would appear. Both Husserl and Twardowski were in& #64258;uenced by Brentano as his students. Following his and Meinong s l ead, they both elaborated a theory on intentionality, in connection with the other theories of intentionality in his school and the Brentano-Bol zano paradox. Furthermore, by providing a more continuous reading of Hus serl s development through the transcendental turn, I hope to have made clear that his later theory of the noema is not a return to a neo-Twardo wskian triadic position, but a reaffirmation, now in transcendental key, of his 1894 take on the matter. The Logical Investigations are uniquely determined by their historical c ontext in the middle of Husserl s development, falling almost exactly be tween the Habilitationsschrift and the Ideas. Due to their troubled hist ory, including changes in Husserl s earliest position around 1890, the f ailure of the second volume of the Philosophy of Arithmetic, various in& #64258;uences around 1894, and the subsequent reorientation and broadeni ng of his theories to a non-psychologistic logic and mathesis universali s, the Logical Investigations might at first seem to fall apart in two fundamentally disconnected books, the second one of which containin g six heterogeneous studies. It is my contention that it is exactly its troubled history that ties the Logical Investigations together, as Husse rl developed his logical investigations in the 1890s on the basis of a h andful thorny problems, including intentionality as centerpiece. From th e Habilitationsschrift to the Ideas it is the relation between subject a nd object, in all respects, ontological as well as epistemological, that guides his research. The Logical Investigations is a intermediate sedim ent of his struggles, containing an elaboration and improvement of his p osition in his early works and also pointing ahead towards the later pos ition of transcendental phenomenology as an implication and continuation of the solutions he proposes. Furthermore, I tried to address the problem that, while Husserl regarded his Logical Investigations as the breakthrough to phenomenology, many f undamental notions of the later transcendental phenomenology seem to be missing in the first edition of the Logical Investigations. The me thod of the reduction, the notion of a pure ego and a full account of th e noema are at most sketched or implied. Hence, I also looked ahead to t he further development of phenomenology after the Logical Investigations. As Husserl s influence has extended beyond the movement he found ed, I felt I could not bypass his significance for the currently d ominant analytical philosophy. Especially with respect to some of the co re topics of the Logical Investigations, but also earlier themes such as Husserl s semiotics, there is an interest in phenomenology from the ana lytic side. Nevertheless, precisely with regard to the unifying theme of intentionality, analytical philosophy often seems to miss the mark, and spectacularly so. I discussed Searle s influential, but in my opi nion, misguided and flawed approach, and I hope it is clear that I have chosen my method and approach in complete antithesis to his. The central contributions I was able to give, were only possible thanks to solid historical groundwork as necessary prerequisite for systematic analyses. Wherever possible, a reference to the original primary sources was provided, allowing the texts to speak for themselves and providing the reader with the critical instruments to evaluate my interpretations. As Husserl stood in a fruitful exchange with many other scholars, as st udent, colleague, friend and teacher, the intellectual context of his th oughts is essential to a correct understanding of his theories and aims. I hope to have found the right balance in the historical and the system atical aspects of my work to suit the interests of the reader and the re quirements of scholarship. (shrink)