“Beyond an acronym,STEM is…”: Perceptions of STEM

Although STEM is at the forefront of many educational initiatives, little is known about various professionals’ perceptions of STEM. This mixed‐methods study surveyed 164 preservice teachers, inservice teachers, administrators, informal educators, and STEM professionals. Quantitative and qualitative questions on the survey elicited participants’ perceptions of STEM, STEM support, and STEM careers. Quantitative analysis revealed that profession influenced understandings of STEM, importance of STEM, support for STEM, and perceptions of STEM career opportunities. Qualitative analysis provided rich explanations for the differences in perceptions among professions. This study suggests that science teacher educators need to ensure preservice teachers have understandings of STEM and STEM careers, K‐16 educators need to emphasize the current importance of STEM, and administrators and policymakers need to align visions of STEM with curriculum and pacing guides so teachers feel supported in their STEM endeavors.     

Non-recursive functions,knots “with thick ropes,” and self-clenching “thick” hyperspheres

We introduce an approach to certain geometric variational problems based on the use of the algorithmic unrecognizability of the n-dimensional sphere for n ≥ 5. Sometimes this approach allows one to prove the existence of infinitely many solutions of a considered variational problem. This recursion-theoretic approach is applied in this paper to a class of functionals on the space of C^1.1-smooth hypersurfaces diffeomorphic to Sⁿ in Rⁿ⁺¹, where n is any fixed number ≥ 5. The simplest of these functionals k_v is defined by the formula k_v(Σⁿ) = (vol(Σⁿ))^1/n/r(Σⁿ), where r(Σⁿ) denotes the radius of injectivity of the normal exponential map for Σⁿ ? Rⁿ+l. We prove the existence of an infinite set of distinct locally minimal values of k_v on the space of C^1.1-smooth topological hyperspheres in Rⁿ⁺¹ for any n ≥ 5. The functional k_v naturally arises when one attempts to generalize knot theory in order to deal with embeddings and isotopies of “thick” circles and, more generally, “thick” spheres into Euclidean spaces. We introduce the notion of knot “with thick rope” types. The theory of knot “with thick rope” types turns out to be quite different from the classical knot theory because of the following result: There exists an infinite set of non-trivial knot “with thick rope” types in codimension one for every dimension greater than or equal to five.     

Incorporating Mathematics into the Science Program of Students Labeled “At‐Risk”

Twenty three at‐risk high school female students who had failed mathematics and science in a traditional school setting were the subjects of this study that integrated mathematics and science lessons over a period of four weeks. Using a combination of direct instruction, calculations, graphing, hands‐on projects, and discussion, the topic of mechanical advantage was studied, to find out how well students understood the topic. The study found that these students who initially knew very little about mechanical advantage, and who did not see any need to use mathematics in the study of science, indicated an increased understanding of mechanical advantage, and also seemed to realize that integrating mathematics and science enhanced learning.     

Correction to: “Transverse quadruple systems with five holes”

We correct an error found in Keranen, Kreher, J Combin Designs 15 (2007), 315–340. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 492–495, 2009     

The “weight” of models and complexity

This article introduces a way of measuring the intrinsic complexity of models. Unlike complication, complexity is an irreducible indication of the innate characteristics of models. Instead of a reductionist paradigm, complexity should be measured in a holistic way. This article redefines the relationship between models and data, and proposes the concept of the “weight” of models, that is, how “heavy” a model is. Based on this concept, this article further defines the complexity of a model to be its ability to distort the space configuration. Three complexity indices are proposed to quantify the extent to which the input space is distorted by a model. It is recognized that there is a lack of widely accepted definition or measure of model complexity. The answer provided by this article is an attempt to move the inquiry a step closer to that goal. © 2014 Wiley Periodicals, Inc. Complexity 21: 21–35, 2016     

“Natural Philosophy” as a Foundation for Science Education in an Age of High‐Stakes Accountability

Science curriculum and instruction in K‐12 settings in the United States is currently dominated by an emphasis on the science standards movement of the 1990s and the resulting standards‐based high‐stakes assessment and accountability movement of the 2000s. We argue that this focus has moved the field away from important philosophical understandings of science teaching and learning that have their roots in the history of both learning theory and scientific discovery. We offer a philosophical argument, as well as a model for implementation, grounded in the 19th century notion of “natural philosophy,” as well as Dewean progressivism and Piaget's notion of reconstruction through rediscovery, for the important place of the history of science in modern science education. We provide curricular examples of this model, as well as a discussion of how it might be implemented as part of teacher education. We focus our discussion on the elementary and middle school grades, because teachers at these levels tend to have more limited science content knowledge than their secondary school peers, making them more dependent upon curricular materials and thus more heavily influenced by curricular reforms.     

Visualizing the “heartbeat” of a city with tweets

Describing the dynamics of a city is a crucial step to both understanding the human activity in urban environments and to planning and designing cities accordingly. Here, we describe the collective dynamics of New York City (NYC) and surrounding areas as seen through the lens of Twitter usage. In particular, we observe and quantify the patterns that emerge naturally from the hourly activities in different areas of NYC, and discuss how they can be used to understand the urban areas. Using a dataset that includes more than 6 million geolocated Twitter messages we construct a movie of the geographic density of tweets. We observe the diurnal “heartbeat” of the NYC area. The largest scale dynamics are the waking and sleeping cycle and commuting from residential communities to office areas in Manhattan. Hourly dynamics reflect the interplay of commuting, work and leisure, including whether people are preoccupied with other activities or actively using Twitter. Differences between weekday and weekend dynamics point to changes in when people wake and sleep, and engage in social activities. We show that by measuring the average distances to a central location one can quantify the weekly differences and the shift in behavior during weekends. We also identify locations and times of high Twitter activity that occur because of specific activities. These include early morning high levels of traffic as people arrive and wait at air transportation hubs, and on Sunday at the Meadowlands Sports Complex and Statue of Liberty. We analyze the role of particular individuals where they have large impacts on overall Twitter activity. Our analysis points to the opportunity to develop insight into both geographic social dynamics and attention through social media analysis. © 2015 Wiley Periodicals, Inc. Complexity 21: 280–287, 2016