50 Years of Data Science

More than 50 years ago, John Tukey called for a reformation of academic statistics. In “The Future of Data Analysis,” he pointed to the existence of an as-yet unrecognized science, whose subject of interest was learning from data, or “data analysis.” Ten to 20 years ago, John Chambers, Jeff Wu, Bill Cleveland, and Leo Breiman independently once again urged academic statistics to expand its boundaries beyond the classical domain of theoretical statistics; Chambers called for more emphasis on data preparation and presentation rather than statistical modeling; and Breiman called for emphasis on prediction rather than inference. Cleveland and Wu even suggested the catchy name “data science” for this envisioned field. A recent and growing phenomenon has been the emergence of “data science” programs at major universities, including UC Berkeley, NYU, MIT, and most prominently, the University of Michigan, which in September 2015 announced a $100M “Data Science Initiative” that aims to hire 35 new faculty. Teaching in these new programs has significant overlap in curricular subject matter with traditional statistics courses; yet many academic statisticians perceive the new programs as “cultural appropriation.” This article reviews some ingredients of the current “data science moment,” including recent commentary about data science in the popular media, and about how/whether data science is really different from statistics. The now-contemplated field of data science amounts to a superset of the fields of statistics and machine learning, which adds some technology for “scaling up” to “big data.” This chosen superset is motivated by commercial rather than intellectual developments. Choosing in this way is likely to miss out on the really important intellectual event of the next 50 years. Because all of science itself will soon become data that can be mined, the imminent revolution in data science is not about mere “scaling up,” but instead the emergence of scientific studies of data analysis science-wide. In the future, we will be able to predict how a proposal to change data analysis workflows would impact the validity of data analysis across all of science, even predicting the impacts field-by-field. Drawing on work by Tukey, Cleveland, Chambers, and Breiman, I present a vision of data science based on the activities of people who are “learning from data,” and I describe an academic field dedicated to improving that activity in an evidence-based manner. This new field is a better academic enlargement of statistics and machine learning than today’s data science initiatives, while being able to accommodate the same short-term goals. Based on a presentation at the Tukey Centennial Workshop, Princeton, NJ, September 18, 2015.     

What Is STEM? A Discussion About Conceptions of STEM in Education and Partnerships

Educational reformation has proceeded slowly despite the many calls to improve science and mathematics for our students. The acronym STEM (science, technology, engineering, and mathematics) has been adopted by numerous programs as an important focus for renewed global competitiveness for the United States, but conceptions of what STEM entails often vary among stakeholders. This paper examines the conceptions of STEM held by faculty members from a public Research I institution in the middle of a regional “STEM movement.” Faculty members responded to two open‐ended questions: (1) What is STEM? and (2) How does STEM influence and/or impact your life? Although 72% of these faculty members possessed a relevant conception of STEM, the results suggest that they do not share a common conceptualization of STEM. Their conception is most likely based on their academic discipline or how STEM impacts their daily lives. STEM faculty members were likely to have a neutral or positive conception where non‐STEM faculty members often had negative feelings about STEM.     

Developing a reform mathematics curriculum program in Sweden: relating international research and the local context

This paper reports on a research-based mathematics curriculum program development project in Sweden, whose educational context is currently characterized by multiple reform initiatives. Current reforms include a repositioning of the teacher as central for students’ learning, but also a trend toward initiatives and teacher resources that are more directive than has been the case in the past 30 years. Collecting data from multiple sources, such as teacher log books, lesson observations and feedback meetings, we build on input from 11 elementary school teachers trying out our materials, including student texts and a teachers’ guide, during four trial rounds. We analyze how international research about curriculum programs and teachers’ use of these programs are interpreted and operationalized within the Swedish context. In particular, the two research questions guiding the study are: (1) “How do Swedish teachers interact with and reason about the reform-based classroom practices promoted by the curriculum program?” and (2) “How do Swedish teachers interact with and reason about their use of a teachers’ guide?” From our experiences in the Swedish educational context, we suggest the following contextual aspects to take into account when designing a curriculum program whose design is grounded in international research literature: characteristics of current classroom practices, teachers’ role in classrooms, the level of explicit/implicit support teachers are used to receiving, and teachers’ experiences using a teachers’ guide.     

No Peace in Our Time

Abstract

Forty young leaders were chosen to be profiled in this issue. In an effort to gain insight from them, they were each asked five questions: What are the major challenges for you as a young leader of the academy? What do you perceive as the major challenges ahead for higher education in the next two decades? Do you have a mentor(s), and if so, how has this helped you in your career? How are you learning to lead? What are your hopes for higher education in the next two decades?

From their responses several items emerged, including a great deal of concern about keeping higher education accessible and rethinking how learning can be prompted more widely. There was strong consensus that mentors had played a vital role in their development, and must continue to do so. Finally, there was strong agreement that preparation for national leadership required the opportunity to practice it, to make mistakes, to take risks, and to learn from their own “real world” choices.

The following profiles surely do not include all the young leaders of the academy, but this group clearly represents many of the strongest and the smartest. Our profound hope is that their numbers grow, as do their opportunities for learning through leading.     

Teachers' Understandings of Realistic Contexts to Capitalize on Students' Prior Knowledge

The theory of realistic mathematics education establishes that framing mathematics problems in realistic contexts can provide opportunities for guided reinvention. Using data from a study group, I examine geometry teachers' perspectives regarding realistic contexts during a lesson study cycle. I ask the following. (a) What are the participants' perspectives regarding realistic contexts that elicit students' prior knowledge? (b) How are the participants' perspectives of realistic contexts related to teachers' instructional obligations? (c) How do the participants draw upon these perspectives when designing a lesson? The participants identified five characteristics that are needed for realistic contexts: providing entry points to mathematics, using “catchy” and “youthful” contexts, selecting personal contexts for the students, using contexts that are not “too fake” or “forced,” and connecting to the lesson's mathematical content. These characteristics largely relate to the institutional, interpersonal, and individual obligations with some connections with the disciplinary obligation. The participants considered these characteristics when identifying a realistic context for a problem‐based lesson. The context promoted mathematical connections. In addition, the teachers varied the context to increase the relevance for their students. The study has implications for supporting teachers' implementation of problem‐based instruction by attending to teachers' perspectives regarding the obligations shaping their work.     

Students' Attitudes Toward Science as Predictors of Gains on Student Content Knowledge: Benefits of an After‐School Program

High‐quality after‐school programs devoted to science have the potential to enhance students' science knowledge and attitudes, which may impact their decisions about pursuing science‐related careers. Because of the unique nature of these informal learning environments, an understanding of the relationships among aspects of students' content knowledge acquisition and attitudes toward science may aid in the development of effective science‐related interventions. We investigated the impact of a semester‐long after‐school intervention utilizing an inquiry‐based infectious diseases curriculum (designed for use after‐school) on 63 urban students' content knowledge and aspects of their attitudes toward science. Content knowledge increased 24.6% from pretest to posttest. Multiple regression analyses indicated suggested that the “self‐directed effort” subscale of the Simpson–Troost Attitude Questionnaire—Revised best predicted increases in students' science content knowledge. The construct “science is fun for me” served as a suppressor effect. These findings suggest that future after‐school programs focusing on aspects of attitudes toward science most closely associated with gains in content knowledge might improve students' enthusiasm and academic preparedness for additional science coursework by improving student attitudes toward their perceptions of their self‐directed effort.     

Connecting Mathematics and Science in Undergraduate Teacher Education Programs: Faculty Voices from the Maryland Collaborative for Teacher Preparation

The study reported in this paper investigated perceptions concerning connections between mathematics and science held by university/college instructors who participated in the Maryland Collaborative for Teacher Preparation (MCTP), an NSF-funded program aimed at developing special middle-level mathematics and science teachers. Specifically, we asked (a) “What are the perceptions of MCTP instructors about the ‘other’ discipline?” (b) “What are the perceptions of MCTP instructors about the connections between mathematics and science?” and (c) “What are some barriers perceived by MCTP instructors in implementing mathematics and science courses that emphasize connections?” The findings suggest that the benefits of emphasizing mathematics and science connections perceived by MCTP instructors were similar to the benefits reported by school teachers. The barriers reported were also similar. The participation in the project appeared to have encouraged MCTP instructors to grapple with some fundamental questions, like “What should be the nature of mathematics and science connections?” and “What is the nature of mathematics/science in relationship to the other discipline?”     

Effective Professional Development and Change in Practice: Barriers Science Teachers Encounter and Implications for Reform

This study focused on two middle schools in the central US who participated in collaborative, sustained, whole‐school professional development in implementing inquiry as part of National Science Education Standards, or standards‐based instructional practices. Participants were involved in their second year of the professional development experience. The research question explored was, “What barriers do science teachers encounter when implementing standards‐based instruction while participating in effective professional development experiences?” Qualitative data collected in the form of teacher interviews and classroom observations were utilized and were analyzed using a barrier to reform rubric. Findings indicate that even with effective professional development, science teachers still encounter technical, political, and cultural barriers to implementation. More support is required for professional development efforts to be successful, such as resources and time, as well as administrative buy‐in and support. Findings also revealed that even the best intended professional development efforts do not reveal and address existing beliefs for all teachers. Implications for future science education reform stakeholders are discussed.     

Boundary Spanners as Bridges of Student and School Discourses in an Urban Science and Mathematics High School

A key to improving urban science and mathematics education is to facilitate the mutual understanding of the participants involved and then look for strategies to bridge differences. Educators need new theoretical tools to do so. In this paper the argument is made that the concept of “boundary spanner” is such a tool. Boundary spanners are individuals, objects, media, and other experiences that link an organization to its environment. They serve critical communicative roles, such as bridges for bringing distinct discourses together, cultural guides to make discourses of the “other” more explicit, and change agents for potentially reshaping participants' discourses. This ethnographic study provides three examples of boundary spanners found in the context of an urban public high school of science, mathematics, and technology: boundary media, boundary objects, and boundary experiences. The analysis brings to the foreground students' and teachers' distinct discourses about “good student identity,”“good student work,” and “good summer experience” and demonstrates how boundary spanners shaped, were shaped by, and sometimes brought together participants' distinct discourses. An argument is made for boundary spanners' practical and theoretical utility: practically, as a tool for enhancing meaning‐making between diverse groups, and theoretically, as a heuristic tool for understanding the reproductive and transformative aspects of urban science education.     

A Tractable and Expressive Class of Marginal Contribution Nets and Its Applications

Coalitional games raise a number of important questions from the point of view of computer science, key among them being how to represent such games compactly, and how to efficiently compute solution concepts assuming such representations. Marginal contribution nets (MC‐nets), introduced by Ieong and Shoham, are one of the simplest and most influential representation schemes for coalitional games. MC‐nets are a rulebased formalism, in which rules take the form pattern → value, where “pattern ” is a Boolean condition over agents, and “value ” is a numeric value. Ieong and Shoham showed that, for a class of what we will call “basic” MC‐nets, where patterns are constrained to be a conjunction of literals, marginal contribution nets permit the easy computation of solution concepts such as the Shapley value. However, there are very natural classes of coalitional games that require an exponential number of such basic MC‐net rules. We present read‐once MC‐nets, a new class of MC‐nets that is provably more compact than basic MC‐nets, while retaining the attractive computational properties of basic MC‐nets. We show how the techniques we develop for read‐once MC‐nets can be applied to other domains, in particular, computing solution concepts in network flow games on series‐parallel networks (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Consciousness as a state of matter

We examine the hypothesis that consciousness can be understood as a state of matter, “perceptronium”, with distinctive information processing abilities. We explore four basic principles that may distinguish conscious matter from other physical systems such as solids, liquids and gases: the information, integration, independence and dynamics principles. If such principles can identify conscious entities, then they can help solve the quantum factorization problem: why do conscious observers like us perceive the particular Hilbert space factorization corresponding to classical space (rather than Fourier space, say), and more generally, why do we perceive the world around us as a dynamic hierarchy of objects that are strongly integrated and relatively independent? Tensor factorization of matrices is found to play a central role, and our technical results include a theorem about Hamiltonian separability (defined using Hilbert–Schmidt superoperators) being maximized in the energy eigenbasis. Our approach generalizes Giulio Tononi’s integrated information framework for neural-network-based consciousness to arbitrary quantum systems, and we find interesting links to error-correcting codes, condensed matter criticality, and the Quantum Darwinism program, as well as an interesting connection between the emergence of consciousness and the emergence of time.     

Program equilibrium—a program reasoning approach

The concept of program equilibrium, introduced by Howard (Theory and Decision 24(3):203–213, 1988) and further formalised by Tennenholtz (Game Econ Behav 49:363–373, 2004), represents one of the most ingenious and potentially far-reaching applications of ideas from computer science in game theory to date. The basic idea is that a player in a game selects a strategy by entering a program, whose behaviour may be conditioned on the programs submitted by other players. Thus, for example, in the prisoner’s dilemma, a player can enter a program that says “If his program is the same as mine, then I cooperate, otherwise I defect”. It can easily be shown that if such programs are permitted, then rational cooperation is possible even in the one-shot prisoner’s dilemma. In the original proposal of Tennenholtz, comparison between programs was limited to syntactic comparison of program texts. While this approach has some considerable advantages (not the least being computational and semantic simplicity), it also has some important limitations. In this paper, we investigate an approach to program equilibrium in which richer conditions are allowed, based on model checking—one of the most successful approaches to reasoning about programs. We introduce a decision-tree model of strategies, which may be conditioned on strategies of others. We then formulate and investigate a notion of “outcome” for our setting, and investigate the complexity of reasoning about outcomes. We focus on coherent outcomes: outcomes in which every decision by every player is justified by the conditions in his program. We identify a condition under which there exist a unique coherent outcome. We also compare our notion of (coherent) outcome with that of (supported) semantics known from logic programming. We illustrate our approach with many examples.     

Agent‐based computational models and generative social science

This article argues that the agent‐based computational model permits a distinctive approach to social science for which the term “generative” is suitable. In defending this terminology, features distinguishing the approach from both “inductive” and “deductive” science are given. Then, the following specific contributions to social science are discussed: The agent‐based computational model is a new tool for empirical research. It offers a natural environment for the study of connectionist phenomena in social science. Agent‐based modeling provides a powerful way to address certain enduring—and especially interdisciplinary—questions. It allows one to subject certain core theories—such as neoclassical microeconomics—to important types of stress (e.g., the effect of evolving preferences). It permits one to study how rules of individual behavior give rise—or “map up”—to macroscopic regularities and organizations. In turn, one can employ laboratory behavioral research findings to select among competing agent‐based (“bottom up”) models. The agent‐based approach may well have the important effect of decoupling individual rationality from macroscopic equilibrium and of separating decision science from social science more generally. Agent‐based modeling offers powerful new forms of hybrid theoretical‐computational work; these are particularly relevant to the study of non‐equilibrium systems. The agent‐based approach invites the interpretation of society as a distributed computational device, and in turn the interpretation of social dynamics as a type of computation. This interpretation raises important foundational issues in social science—some related to intractability, and some to undecidability proper. Finally, since “emergence” figures prominently in this literature, I take up the connection between agent‐based modeling and classical emergentism, criticizing the latter and arguing that the two are incompatible. © 1999 John Wiley & Sons, Inc.     

Understanding kindergarten teachers’ perspectives of teaching basic geometric shapes: a phenomenographic research

Geometry is one of the disciplines children involve within early years of their lives. However, there is not much information about geometry education in Turkish kindergarten classes. The current study aims to examine teachers’ perspectives on teaching geometry in kindergarten classes. The researchers inquired about teachers’ in-class experiences in geometry and asked a series of questions such as “what are the benchmarks in your kindergarten class?”; “what kind of tools and materials you use to teach geometry in your class?”; “what shape do you teach first in your kindergarten class?”; “what do you expect to hear when you asked your students ‘what is square’?”; “how do you teach rectangular?”. The study utilized one of the qualitative research methods, namely phenomenography, to collect the data and analyze the data. The study involved with eight kindergarten teachers who work in different schools in central Kutahya, Turkey. The researchers collected data by conducting face-to-face half-structured interviews. The findings of this phenomenographic research showed that kindergarten teachers have some difficulties in teaching geometry and have lack of knowledge and skills in teaching geometry in kindergarten classes.     

Beginning Secondary Science Teachers' Conceptualization and Enactment of Inquiry‐Based Instruction

This study investigates the conceptions and use of inquiry during classroom instruction among beginning secondary science teachers. The 44 participants were beginning secondary science teachers in their first year of teaching. In order to capture the participants' conceptions of inquiry, the teachers were interviewed and observed during the school year. The interviews consisted of questions about inquiry instruction, while the observations documented the teachers' use of inquiry. All of the interviews were transcribed or coded in order to understand the conceptions of inquiry held by the teachers, and all of the observations were analyzed in order to determine the presence of inquiry during the lesson. The standard for assessing inquiry came from the National Science Education Standards. A quantitative analysis of the data indicated that the teachers frequently talked about implementing “scientific questions” and giving “priority to evidence.” This study found a consistency between the way new teachers talked about inquiry and the way they practiced it in their classrooms. Overall, our observations and interviews revealed that the beginning secondary science teachers tended to enact teacher‐centered forms of inquiry, and could benefit from induction programs focused on inquiry instruction.     

Hannah's Prior Knowledge About Chemicals: A Case Study of One Fourth‐Grade Child

Chemical principles are taught in elementary education across much of the United States because the National Science Education Standards include concepts about the nature of matter, states of matter, and changes in matter among other science concepts within the first to fifth grade levels. “Chemicals” is a word related to the nature of matter that is used not only in formal instruction, but also in everyday conversations. Children's prior knowledge about chemicals gained from everyday experiences will influence how they learn about chemical principles. The research described herein reveals insights into one child's conceptual structure related to the word “chemical,” which includes how she uses the word both inside and outside of school. Hannah was purposefully chosen for this case study because she exemplified “children's science.” Her understanding of chemicals as cleaners, in foods, and used for a purpose were primarily gained from everyday experiences. The implications of these findings are discussed with respect to both future research and elementary science education.     

HOW RAPID SHOULD EMISSION REDUCTION BE? A GAME‐THEORETIC APPROACH

Abstract In this paper, we search for multistage realization of international environmental agreements. To analyze countries' incentives and the results of their interactions, we mathematically represent players' strategic preferences and apply a game‐theoretic approach to make predictions about their outcomes. The initial decision on emissions reduction is determined by the Stackelberg equilibrium concept. We generalize Barrett's static “emission” model to a dynamic framework and answer the question “how rapid should the emission reduction be?” It appears that sharper abatement is desirable in the early term, which is similar to the conclusion of the Stern review. Numerical example demonstrates that abatement dynamics of the coalition and the free‐rider differ when discounting of the future payoffs increases. We show that without incentives from external organizations or governments, such pollution reduction path can actually lead to a decline in the agreement's membership size.     

Evaluating efficacy of environmental education programming

The Clark Fork Watershed Education Program (CFWEP) goals are: (a) increasing students’ understanding of the nature of ecological impacts within their watershed as related to historic mining damage; and (b) increasing students’ sense of stewardship of newly restored landscapes. Data from 2012 to 2016 were evaluated for student knowledge gains (46 trials representing 2,395 student pre‐surveys; 2,409 student post‐surveys). Data from 2013 to 2016 were evaluated for students’ attitudes toward science and disposition toward caring for the environment (38 trials representing 1,479 pre‐surveys; 1,460 post‐surveys). The results of this study support that the program’s goals are being achieved. Students achieved statistically significant gains on knowledge surveys with a 33.4% overall gain pre‐ to posttest (p < 0.0001). Students also moved toward greater positive responses in both attitudes toward science and disposition toward caring for the environment with Cohen’s d effect sizes of “medium effect” for caring toward the environment (d = 0.52) and “small effect” of positive disposition toward science (d = 0.24).     

Which is more fundamental: Outward peace or being true to our humanity?

How we perceive and define concepts should be a major concern for teachers and educators in general and for math teachers and educators in particular. This issue, however, is usually ignored or marginalised in curricula and classrooms, where textbooks form the major source of information, knowledge, meanings and definitions. The two words in the theme of this ZDM-issue—math and peace—are themselves good examples to explore. “What do we include in the math curriculum and what do we exclude, and why?” and “What do we mean by peace, and whose peace, and at what human and environmental cost?” are questions that the article raises and tries to point out how we should go about dealing with them. The article challenges the absolute meanings of concepts and stresses the importance of discussing meanings only within context. This concern requires giving teachers and students a greater say in the curriculum, to explore and discuss issues that affect their lives profoundly. The article challenges current values and goals, and suggests what it considers more fundamental values. In particular, it suggests that when there is conflict between peace and being true to our humanity, the latter should be given priority as a guiding value.