Elementary Science and Language Arts: Should We Blur the Boundaries?

Elementary school goals for instruction focus on developing literate readers and writers. It has been recommended that language arts strategies can help elementary teachers more effectively teach science. The terms “integrated, interdisciplinary, and thematic instruction” are defined and examples are given for using each in an elementary classroom. Definitions are provided comparing language arts and scientific literacy. Use of thematic instruction with an interdisciplinary focus is recommended to help meet both language arts and science goals and objectives as they relate to the National Science Education Standards and the National English Language Arts Standards. Recommendations are made for helping teachers effectively use language arts strategies to help develop science literacy, and science to provide purpose for reading and writing activities within thematic, interdisciplinary instruction often found in elementary schools.     

Technological integration and hyperconnectivity: Tools for promoting extreme human lifespans

Artificial, neurobiological, and social networks are three distinct complex adaptive systems (CASs), each containing discrete processing units (nodes, neurons, and humans, respectively). Despite the apparent differences, these three networks are bound by common underlying principles which describe the behavior of the system in terms of the connections of its components, and its emergent properties. The longevity (long‐term retention and functionality) of the components of each of these systems is also defined by common principles. Here, I will examine some properties of the longevity and function of the components of artificial and neurobiological systems, and generalize these to the longevity and function of the components of social CAS. In other words, I will show that principles governing the long‐term functionality of computer nodes and of neurons, may be extrapolated to the study of the long‐term functionality of humans (or more precisely, of the noemes, an abstract combination of “existence” and “digital fame”). The study of these phenomena can provide useful insights regarding practical ways that can be used to maximize human longevity. The basic law governing these behaviors is the “Law of Requisite Usefulness,” which states that the length of retention of an agent within a CAS is proportional to the agent's contribution to the overall adaptability of the system. © 2014 Wiley Periodicals, Inc. Complexity 20: 15–24, 2015     

Macros and modules in geometry

The paper highlights the importance of “macros” or modules for teaching and learning Geometry using Dynamical Geometry Software (DGS). The role of modules is analyzed in terms of “writing” and “reading” Geometry. At first, modules are taken as tools for geometrical construction tasks and as tools to describe and analyze these constructions. For proofs, decomposing a given geometrical statement may be supported by using prototypical pictures representing theorems of geometry (“modules”). Reading theorems into geometry and constructing proofs is still a major achievement of the student—which may be reached by using macros and modules as a major heuristic strategy     

The Mathematics Writer's Checklist: The Development of a Preliminary Assessment Tool for Writing in Mathematics

The use of writing as a pedagogical tool to help students learn mathematics is receiving increased attention at the college level ( Meier & Rishel, 1998 ), and the Principles and Standards for School Mathematics (NCTM, 2000) built a strong case for including writing in school mathematics, suggesting that writing enhances students' mathematical thinking. Yet, classroom experience indicates that not all students are able to write well about mathematics. This study examines the writing of a two groups of students in a college‐level calculus class in order to identify criteria that discriminate “;successful” vs. “;unsuccessful” writers in mathematics. Results indicate that “;successful” writers are more likely than “;unsuccessful” writers to use appropriate mathematical language, build a context for their writing, use a variety of examples for elaboration, include multiple modes of representation (algebraic, graphical, numeric) for their ideas, use appropriate mathematical notation, and address all topics specified in the assignment. These six criteria result in The Mathematics Writer's Checklist, and methods for its use as an instructional and assessment tool in the mathematics classroom are discussed.     

Artificial intelligence: Debates about its use and abuse

This paper is concerned with the question, “Is what a stored-program digital computer does thinking-in the full human sense of the term?” Several current controversies are examined, including the meaning and usefulness of the Turing test to determine “intelligence.” The Lucas controversy of the early 1960s is taken up, dealing with the philosophical issues related to the man-versus-machine debate, and Dreyfus' ideas against Machine Intelligence are explored. Searle's ideas in opposition to the validity of the Turing test are described, as are various interpretations of the Chinese room thought-experiment and its relation to real “thought”. Weizenbaum's opposition to the “information-processing model of man” is also developed. The paper concludes with a comparison of the 19th-century debates over Darwinian Evolution and those in this century over Artificial Intelligence.     

Cultural Influences on Children's Probabilistic Thinking

This study investigated selected cultural influences on probabilistic thinking of 11–12-year-old children in England. Language, beliefs and experience are shown to influence the children's “informal knowledge” of probability, i.e., the intuitive knowledge they bring to school and use in thinking about probabilistic situations presented in school. Some of the pupils' responses in interviews and in a questionnaire were consistent with the “outcome approach” and with the use of certain heuristics: “representativeness”; “availability”; “equiprobability.” A significant proportion of pupils revealed superstitions. Standard “random devices” such as dice were regarded by some children as subject to personal, religious or causative influences. In a comparison between two culturally-contrasted subgroups in the same school, we found significant differences in scores on probability tests, even when taking account of numerical and non-verbal ability. But the differences between the two groups could almost entirely be explained by differences in language ability.     

Some two-echelon style-goods inventory models with asymmetric market information

A “two-echelon” newsboy problem considers the interactive decisions between the “manufacturer” and the “retailer” – now recognized as two separate entities. Earlier papers on this problem assumed that the two parties share the same market information. We extend this problem by studying the situation in which the retailer has better market information than the manufacturer. Presented are several decision models that should be useful for guiding a manufacturer's decisions. Moreover, solutions to these models lead to various unexpected and interesting conclusions. For example, we found that improved retailer's market-knowledge always benefits the manufacturer and the system, though not necessarily the retailer himself. In contrast, improved manufacturer's knowledge benefits only the manufacturer himself at the expense of the retailer and of the system.     

Environmental literacy of undergraduate college students: Development of the environmental literacy instrument (ELI)

As the world population continues to increase and natural resources become limited, environmental education (EE) in universities play an essential role in developing environmentally literate. This study measured the environmental literacy (EL) levels (familiar knowledge, factual knowledge, attitude, behavior) of undergraduate college students. Measuring EL on a scale of 0–100%, undergraduate students scored 52%, indicating that they are not environmentally literate. Students had somewhat high attitudes (63%) but low levels of familiar knowledge (40%), factual knowledge (56%), and behavior (44%). College years are brief and formative; therefore, EE should be infused within university curricula in order to increase EL levels of students, who are future policy makers, voters, business people, and teachers.     

Disciplinary literacy in mathematics: One mathematician’s reading practices

Recent scholarship on disciplinary literacy calls for an emphasis on teaching discipline-specific language/literacy practices. An understanding of these practices is, therefore, essential to literacy instruction in secondary content areas such as mathematics. This case study examined one mathematician’s reading practices, with a focus on the strategies he used in text comprehension. Data collected include the mathematician’s think-alouds during reading, discussion of his reading think-alouds, and semi-structured interviews. These data were analyzed qualitatively through an iterative process involving multiple readings and identification and refinement of codes. The analysis revealed that the mathematician engaged in extensive reading and employed an array of strategies—rereading, close reading, monitoring and questioning, summarizing and paraphrasing, storying, drawing on prior knowledge and experience, evaluating and verifying, and note-taking and visualizing—to help him make sense of what he read. These findings provide important insights that can inform mathematics teachers’ efforts to support students’ mathematics reading/learning.     

A mathematical model of progressive literacy

We consider the two principal determinants of the dynamics of literacy in a developing country such as India: (a) a tendency of each family to improve or retain (but never retrogress) its literacy state with each successive generation, and (b) a differential in fertility, with number of off‐springs rising with decreasing literacy. The interplay of these contradictory trends is investigated in a mathematical model adapted and generalized from earlier work in the literature on modelling of social mobility and graded social systems. The model, besides being practically relevant, is exactly solvable and yields simple criteria and closed‐form solutions for different literacy distributions in terms of fertility and intergenerational transition proportions between male‐female “paired literacy states” of a society.     

“统计信息”与“信息高速公路”

本文从我国统计信息事业的现状，提出了关于第一类统计与第二类统计。同时指出统计信息事业的迅速发展与繁荣，首先必须实现两类统计的相互渗透；其二必须与计算机技术密切结合，以建立起各级各类统计信息的高速公路，使统计信息更好地为我国的科技、经济、社会的全面发展提供有效的服务。     

Fairness Norms Can Explain the Emergence of Specific Cooperation Norms in the Battle of the Prisoner's Dilemma

Cooperation norms often emerge in situations, where the long term collective benefits help to overcome short run individual interests, for instance in repeated Prisoner's Dilemma (PD) situations. Often, however, there are different paths to cooperation, benefiting different kinds of actors to different degrees. This leads to payoff asymmetries even in the state of cooperation, and consequently can give rise to normative conflicts about which norms should be in place. This norm coordination problem will be modeled as a Battle of the Sexes game (BoS) with different degrees of asymmetry in payoffs. I combine the PD and the BoS to the 3 × 3 Battle of the Prisoner's Dilemma (BOPD) with several asymmetric cooperative and 1 noncooperative equilibria. Game theoretical and “behavioral” predictions are derived about the kind of norms that are likely to emerge under different shadows of the future and degrees of asymmetry and tested in a lab experiment. The experimental data show that game theory fairly well predicts the basic main effects of the experimental manipulations but “behavioral” predictions perform better in describing the equilibrium selection process of emerging norms.     

Temporal Taylor’s scaling of facial electromyography and electrodermal activity in the course of emotional stimulation

High frequency psychophysiological data create a challenge for quantitative modeling based on Big Data tools since they reflect the complexity of processes taking place in human body and its responses to external events. Here we present studies of fluctuations in facial electromyography (fEMG) and electrodermal activity (EDA) massive time series and changes of such signals in the course of emotional stimulation. Zygomaticus major (ZYG; “smiling” muscle) activity, corrugator supercilii (COR; “frowning” muscle) activity, and phasic skin conductance (PHSC; sweating) levels of 65 participants were recorded during experiments that involved exposure to emotional stimuli (i.e., IAPS images, reading and writing messages on an artificial online discussion board). Temporal Taylor’s fluctuations scaling were found when signals for various participants and during various types of emotional events were compared. Values of scaling exponents were close to one, suggesting an external origin of system dynamics and/or strong interactions between system’s basic elements (e.g., muscle fibres). Our statistical analysis shows that the scaling exponents enable identification of high valence and arousal levels in ZYG and COR signals.     

Embodying mathematics and science: Microworlds as representations

This paper examines the category of open-ended exploratory computer environments that have been labeled “microworlds.” The paper reviews the ways in which the term “microworld” has been used in the mathematics and science education communities, and analyzes examples of specific computer microworlds. Two definitions of microworld are proposed: a structural definition that focuses on design elements shared by the environments, and a functional definition that highlights commonalties in how students learn with microworlds. In the final section of the paper, the notion that computer microworlds can be said to “embody” mathematical or scientific ideas is addressed, within the context of a re-evaluation of the general concept of representation.     

A survey of techniques in applied computational complexity

An attempt is made to introduce the non-expert reader to the many aspects of a relatively new and varied field which seems to be at the same time analysis, algebra and computer science. Computational complexity can be roughly described as the theory of optimizing finite and infinite algorithms for use on digital computers. Even for “simple” problems like the finding of a zero of a real function or even the evaluation of a polynomial, surprisingly deep techniques are necessary. A representative sample of the presently existing bibliography on the subject is included at the end.     

Noncommutative Generalizations of Theorems of Cohen and Kaplansky

This paper investigates situations where a property of a ring can be tested on a set of “prime right ideals.” Generalizing theorems of Cohen and Kaplansky, we show that every right ideal of a ring is finitely generated (resp. principal) iff every “prime right ideal” is finitely generated (resp. principal), where the phrase “prime right ideal” can be interpreted in one of many different ways. We also use our methods to show that other properties can be tested on special sets of right ideals, such as the right artinian property and various homological properties. Applying these methods, we prove the following noncommutative generalization of a result of Kaplansky: a (left and right) noetherian ring is a principal right ideal ring iff all of its maximal right ideals are principal. A counterexample shows that the left noetherian hypothesis cannot be dropped. Finally, we compare our results to earlier generalizations of Cohen’s and Kaplansky’s theorems in the literature.     

The power of various real-valued quantum queries

The computation of combinatorial and numerical problems on quantum computers is often much faster than on a classical computer in numbers of queries. A query is a procedure by which the quantum computer gains information about the specific problem. Different query definitions were given and our aim is to review them and to show that these definitions are not equivalent. To achieve this result we will study the simulation and approximation of one query type by another. While approximation is “easy” in one direction, we will show that it is “hard” in the other direction by a lower bound for the numbers of queries needed in the simulation. The main tool in this lower bound proof is a relationship between quantum algorithms and trigonometric polynomials that we will establish.     

Wisdom Beyond Rationality: A Reply to Ryan

We discuss Sharon Ryan’s Deep Rationality Theory of wisdom, defended recently in her “Wisdom, Knowledge and Rationality.” We argue that (a) Ryan’s use of the term “rationality” needs further elaboration; (b) there is a problem with requiring that the wise person possesses justified beliefs but not necessarily knowledge; (c) the conditions of DRT are not all necessary; (d) the conditions are not sufficient. At the end of our discussion, we suggest that there may be a problem with the very assumption that an informative, non-circular set of necessary and sufficient conditions of wisdom can be given.     

Teachers Describe Epistemologies of Science Instruction Through Q Methodology

Creating scientifically literate students is a common goal among educational stakeholders. An understanding of nature of science is an important component of scientific literacy in K‐12 science education. Q methodology was used to investigate the opinions of preservice and in‐service teachers on how they intend to teach or currently teach science. Q methodology is a measurement tool designed to capture personal beliefs. Participants included 40 preservice and in‐service elementary and secondary science teachers who sorted 40 self‐referential statements regarding science instruction. The results identified three epistemologies toward teaching science: A Changing World, My Beliefs, and Tried and True. Participants with the A Changing World epistemology believe evidence is reliable, scientific knowledge is generated in multiple ways, and science changes in light of new evidence. The My Beliefs epistemology reflects that scientific knowledge is subject to change due to embedded bias, science is affected by culture and religion, and evolution should not be taught in the classroom. The Tried and True epistemology views a scientific method as an exact method to prove science, believes experiments are crucial for scientific discoveries, absolute truth exists in scientific knowledge, and society and cultural factors can be eliminated from investigations. Implications for preservice teacher education programs and in‐service teacher professional development are addressed.