Based on extensive research conducted by the authors, Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2, is designed to help classroom teachers understand, monitor, and guide the development of students' reasoning and sense making about core ideas in elementary school mathematics. It describes and illustrates the nature of these skills using classroom vignettes and actual student work in conjunction with instructional tasks and learning progressions to show how reasoning and sense making develop and how instruction can support students (...) in that development. Students who can make sense of mathematical ideas can apply those ideas in problem solving, even in unfamiliar situations, and can use them as a foundation for future learning. Without them, students are reduced to rote learning, often experiencing frustration and failure. But what do reasoning and sense making during learning and teaching look like? Each chapter of Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2 explores a different topic that young children encounter in mathematics, demonstrating with actual student work and classroom dialogue how their mathematical knowledge and reasoning ability move through "levels of sophistication" or learning progressions: After opening with a discussion of the nature of reasoning and sense making and their critical importance in developing mathematical thinking, chapter 1 examines how young students attempt to make sense of the concepts of place value and length measurement. Chapter 2 focuses on how early childhood instruction can engage students in mathematical reasoning while helping them construct a rich sense of number and operations. Chapter 3 identifies core algebraic ideas and shows how students can engage with these ideas in ways that not only deepen their understanding of arithmetic but also lays the foundation for the future study of algebra. Children's reasoning and sense making as they decompose and compose geometric shapes--including reasoning about area--is examined in chapter 4. The use of learning progressions to understand students' reasoning and to guide their sense making with appropriate teaching is also discussed. Not just a theoretical discussion, the book also provides specific suggestions for related instructional activities for each topic. Supplementary online resources can be accessed at NCTM's More4U website. Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2 will be a valuable and practical addition to your professional library. (shrink)

Traditionally, species have been treated as classes. In fact they may be considered individuals. The logical term “individual” has been confused with a biological synonym for “organism.” If species are individuals, then: 1) their names are proper, 2) there cannot be instances of them, 3) they do not have defining properties, 4) their constituent organisms are parts, not members. “ Species " may be defined as the most extensive units in the natural economy such that reproductive competition occurs among their (...) parts. Species are to evolutionary theory as firms are to economic theory: this analogy resolves many issues, such as the problems of “reality” and the ontological status of nomenclatorial types. (shrink)

Michael T. Ferejohn presents a new analysis of Aristotle's theory of explanation and scientific knowledge, in the context of its Socratic roots. Ferejohn shows how Aristotle resolves the tension between his commitment to the formal-case model of explanation and his recognition of the role of efficient causes in explaining natural phenomena.

A coherent treatment of the flow of ideas throughout Darwin's works, this volume presents a unified theoretical system that explains Darwin's investigations, evaluating the literature from a historical, scientific, and philosophical perspective.

In The Elusive God: Reorienting Religious Epistemology, Paul Moser argues that Jesus’s love commands have important implications for how philosophy should be done by Christian philosophers. He calls for a reorientation of the questions that philosophers pursue, requiring that questions lead to agape-oriented ministry. Yet Moser omits discussion of an important duty of philosophers—teaching. Once the duty of teaching is considered, this essay argues that few philosophers could meet Moser’s ideal. Instead of abandoning Moser’s project to reorient philosophy, though, this (...) essay takes it one step further and argues that many, though not all, Christian philosophers should leave academia to become clergy. Examination of these meta-pedagogical issues, including that of Christian calling and vocational choice, transitions to pedagogical speculation of what Moser’s demands might require in the classroom. Moser’s obedience mode of philosophy is then compared with competing models in the advocacy-neutrality classroom debate. (shrink)

_This sweeping discussion of the philosophy of evolutionary biology is based on the revolutionary idea that species are not kinds of organisms but wholes composed of organisms._.

Classifying is a fundamental operation in the acquisition of knowledge. Taxonomic theory can help students of cognition, evolutionary psychology, ethology, anatomy, and sociobiology to avoid serious mistakes, both practical and theoretical. More positively, it helps in generating hypotheses useful to a wide range of disciplines. Composite wholes, such as species and societies, are “individuals” in the logical sense, and should not be treated as if they were classes. A group of analogous features is a natural kind, but a group of (...) homologous features is not. Imposing hypotheses justified only on the basis of nominalist, realist, phenomenalist, or conceptualist metaphysics upon the neurophysiology of organisms or upon the causes of behavior exemplifies the “psychologist's fallacy” of William James. Levels should be distinguished from their members and from classes of levels, and the ontological status of entities ranked at levels should be made clear. It is important not to confuse such categories as substance and process with one another. Several genetical terms, such as “gene” and chromosome,” are even more equivocal than has been realized. Discussions about units of selection, behavior, and thinking suffer from the ambiguity of a “unit of” an entity. An important source of misunderstanding about natural selection is the habit of treating it as an “agent”: in an important sense, natural selection does not “act” at all. (shrink)

This study adapted and tested the efficacy of the Red-Light Purple-Light games for improving executive function skills in preprimary classrooms in Nairobi, Kenya. A cluster randomized controlled trial was used to evaluate the efficacy of the adapted RLPL intervention. Specifically, 24 centers were randomized to the RLPL or a wait-list control condition. Consistent with previous studies, participating classrooms delivered 16 lessons across an 8-week intervention period. A total of 479 children were recruited into the study. After exclusions based on child (...) age and data quality, 451 and 404 children had completed computerized assessments of EF skills at pre- and posttest assessments, respectively. Children in the RLPL centers did not demonstrate any improvements in EF skills relative to their peers in the wait-list control condition. Exploratory tests of moderators were also all null. Results are discussed with respect to measurement limitations and contextual factors that may explain the null results of RLPL on EF skills in young children in Kenya. (shrink)

After considering the life-long influence of poetry on Newman and his critical analysis of poetry, this study examines his poetic output during his Mediterranean voyage and concludes by considering both the spiritual implications and the literary observations of his famous poem “The Pillar of the Cloud.”.

Can an ugly experiment be a good experiment? Philosophers have identified many beautiful experiments and explored ways in which their beauty might be connected to their epistemic value. In contrast, the present chapter seeks out (and celebrates) ugly experiments. Among the ugliest are those being designed by AI algorithms. Interestingly, in the contexts where such experiments tend to be deployed, low aesthetic value correlates with high epistemic value. In other words, ugly experiments can be good. Given this, we should conclude (...) that beauty is not generally necessary or sufficient for epistemic value, and increasing beauty will not generally tend to increase epistemic value. (shrink)

Donne used Plato’s Lambda numbers to construct “A Litany.” Specifically, each number in the Lambda sequence ties not only to the concept of world-creation as outlined in Timaeus, but also to its notion of the circular nature of the world, of man returning to the monad.

이 연구에서 본인은 construal 이라는 상식적인 심리학적 개념에 대한 철학적 활용에 관하여 예시하고자 한다. Construal 이라는 것은 하나가 다른면에서 경험되어지는 심리적 상태이다. 가장 영향력 있는 철학적 활용으로는 이해관계에 근거한 construal로써 정서에 관한 Robert C. Roberts의 이론이여왔다. 하지만 본인은 이 개념은 아카라시아나 자기통찰 그리고 도교적 사고를 포함하는 몇 가지 다른 영역에서도 활용성을 가지고 있다고 주장하는 바이다. 전반적으로 이 연구가 이처럼 과소평가되는 개념에 대한 철학적 탐색이 더 이루어 질수 있는 자극이 되기를 바란다.

Joshua Greene has argued that the empirical findings of cognitive science have implications for ethics. In particular, he has argued (1) that people’s deontological judgments in response to trolley problems are strongly influenced by at least one morally irrelevant factor, personal force, and are therefore at least somewhat unreliable, and (2) that we ought to trust our consequentialist judgments more than our deontological judgments when making decisions about unfamiliar moral problems. While many cognitive scientists have rejected Greene’s dual-process theory of (...) moral judgment on empirical grounds, philosophers have mostly taken issue with his normative assertions. For the most part, these two discussions have occurred separately. The current analysis aims to remedy this situation by philosophically analyzing the implications of moral dilemma research using the CNI model of moral decision-making – a formalized, mathematical model that decomposes three distinct aspects of moral-dilemma judgments. In particular, we show how research guided by the CNI model reveals significant conceptual, empirical, and theoretical problems with Greene’s dual-process theory, thereby questioning the foundations of his normative conclusions. (shrink)

Within Luis Buñuel's classic surrealist film The Exterminating Angel is a philosophical motif which expresses, demonstrates, and develops two of Ludwig Wittgenstein's central concepts: language lays traps for the unwary that can lead to illogical thought and mind-bending quests; and any picture of the world is formed through cultural habits that cannot be rationally expressed but can be changed. This article argues that what we find in Buñuel's Angel is a “picture” that is at one level rational and habitual and (...) at another entirely absurd. These apparently rational preconceptions – the insular habits of privilege and the language that maintains it – produce a certain “aspect” which, when clung to, can entrap us. In this effort we thread a series of chance meetings into a web of encounters: of people at a dinner party, of a philosopher and a filmmaker, and perhaps most significantly, of games that form a totality of gamesmanship – a chance meeting of the game... (shrink)

Scientists imagine for epistemic reasons, and these imaginings can be better or worse. But what does it mean for an imagining to be epistemically better or worse? There are at least three metaepistemological frameworks that present different answers to this question: epistemological consequentialism, deontic epistemology, and virtue epistemology. This paper presents empirical evidence that scientists adopt each of these different epistemic frameworks with respect to imagination, but argues that the way they do this is best explained if scientists are fundamentally (...) epistemic consequentialists about imagination. (shrink)

In this article, I explore the encounter of the Mādhva philosopher Vyāsatīrtha with the works of the Navya-Naiyāyika Gaṅgeśa Upādhyāya. The article is based on original translations of passages from Vyāsatīrtha’s Nyāyāmr̥ta and Tarkatāṇḍava. Philosophically, the article focuses on the issue of empty-terms/nonexistent entities, particularly in the context of the theory of inference. I begin by outlining the origin of the Mādhva and Nyāya positions about these issues in their respective analyses of perceptual illusion. I then contrast the role of (...) Gaṅgeśa’s thought in the Nyāyāmr̥ta and Tarkatāṇḍava and show how Vyāsatīrtha responds to Gaṅgeśa’s ideas in different ways in those texts. I conclude with a discussion of how Vyāsatīrtha defends the Mādhva theory of “substrate-free” qualities against Gaṅgeśa in order to show that we can think and make valid inferences about nonexistent things. (shrink)

The structure of the brain and the nature of evolution suggest that, despite its uniqueness, language likely depends on brain systems that also subserve other functions. The declarative / procedural model claims that the mental lexicon of memorized word- specific knowledge depends on the largely temporal-lobe substrates of declarative memory, which underlies the storage and use of knowledge of facts and events. The mental grammar, which subserves the rule-governed combination of lexical items into complex representations, depends on a distinct neural (...) system. This system, which is composed of a network of specific frontal, basal - ganglia, parietal and cerebellar structures, underlies procedural memory, which supports the learning and execution of motor and cognitive skills, especially those involving sequences. The functions of the two brain systems, together with their anatomical, physiological and biochemical substrates, lead to specific claims and predictions regarding their roles in language. These predictions are compared with those of other neurocognitive models of language. Empirical evidence is presented from neuroimaging studies of normal language processing, and from developmental and adult- onset disorders. It is argued that this evidence supports the DP model. It is additionally proposed that “ language ” disorders, such as specific language impairment and non-fluent and fluent aphasia, may be profitably viewed as impairments primarily affecting one or the other brain system. Overall, the data suggest a new neurocognitive framework for the study of lexicon and grammar. (shrink)

Imagination is important for many things in science: solving problems, interpreting data, designing studies, etc. Philosophers of imagination typically account for the productive role played by imagination in science by focusing on how imagination is constrained, e.g., by using self-imposed rules to infer logically, or model events accurately. But the constraints offered by these philosophers either constrain too much, or not enough, and they can never account for uses of imagination that are needed to break today’s constraints in order to (...) make progress tomorrow. Thus, epistemology of imagination needs to make room for an element of epistemological anarchy. (shrink)

The Encyclopedia of Political Thought is the most comprehensive and rigorous treatment of significant political thinkers, political theories, concepts, ideas, and schools of thought. Comprises over 900 A-Z entries, including brief definitions, biographies, and major topics, written by a team of 700 contributors from around the world Explores key theories and theorists, including non-western perspectives, in tracing the evolution of political thought from antiquity to the present day Published in association with The Foundations of Political Theory, an organized section of (...) the American Political Science Association 8 Volumes www.encyclopediaofpoliticalthought.com. (shrink)

Sometimes we learn through the use of imagination. The epistemology of imagination asks how this is possible. One barrier to progress on this question has been a lack of agreement on how to characterize imagination; for example, is imagination a mental state, ability, character trait, or cognitive process? This paper argues that we should characterize imagination as a cognitive ability, exercises of which are cognitive processes. Following dual process theories of cognition developed in cognitive science, the set of imaginative processes (...) is then divided into two kinds: one that is unconscious, uncontrolled, and effortless, and another that is conscious, controlled, and effortful. This paper outlines the different epistemological strengths and weaknesses of the two kinds of imaginative process, and argues that a dual process model of imagination helpfully resolves or clarifies issues in the epistemology of imagination and the closely related epistemology of thought experiments. (shrink)

"Adaptation" has several meanings which have often been confused, including relations, processes, states, and intrinsic properties. It is used in comparative and historical contexts. "Adaptation" and "environment" may designate probabilistic concepts. Recognition of these points refutes arguments for the notions that: 1) all organisms are perfectly adapted; 2) organisms cannot be ill-adapted and survive or well-adapted and die; 3) adaptation is necessarily relative to the environment; 4) change in environment is necessary for evolution; 5) preadaptation implies teleology. Such notions are (...) associated with metaphysical ideas, and may affect the thinking of biologists. (shrink)

The choir of the collegiate church of Saint-Urbain, Troyes, has long been hailed as a masterpiece of Gothic architecture, and the skill of its designer attests to the advanced stage of sophistication that French architecture had attained by the third quarter of the thirteenth century. The supporting structure of the eastern half of the building, composed of an armature of emaciated mullions, sharpened moldings and gables, and spikelike buttresses, is thoroughly incorporated into the rich system of decorative membering, and the (...) glazing is so extensive that the edifice seems to stand only through a feat of architectural legerdemain. (shrink)