Scale and the evolutionarily based approximate number system: an exploratory study

ABSTRACT

Crosscutting concepts such as scale, proportion, and quantity are recognised by U.S. science standards as a potential vehicle for students to integrate their scientific and mathematical knowledge; yet, U.S. students and adults trail their international peers in scale and measurement estimation. Culturally based knowledge of scale such as measurement units may be built on evolutionarily-based systems of number such as the approximate number system (ANS), which processes approximate representations of numerical magnitude. ANS is related to mathematical achievement in pre-school and early elementary students, but there is little research on ANS among older students or in science-related areas such as scale. Here, we investigate the relationship between ANS precision in public school U.S. seventh graders and their accuracy estimating the length of standard units of measurement in SI and U.S. customary units. We also explored the relationship between ANS and science and mathematics achievement. Accuracy estimating the metre was positively and significantly related to ANS precision. Mathematics achievement, science achievement, and accuracy estimating other units were not significantly related to ANS. We thus suggest that ANS precision may be related to mathematics understanding beyond arithmetic, beyond the early school years, and to the crosscutting concepts of scale, proportion, and quantity.     

English,French and German summaries of major articles in this issue

Science has a role to play in the resolution of many of the issues deemed controversial in all societies. However, evidence of a lack of public confidence in science and scientists as effective problem‐solvers continues to accumulate. This paper speculates that this lack of confidence might in part be due to the way in which science educators present controversial issues. In particular, we argue that current approaches to teaching about controversy do not sufficiently acknowledge the nature of the issues themselves. The paper proposes a set of principles as the basis for a reconceptualization of the teaching of controversial issues and gives an example of how they might be applied.     

University vs. Research Institute? The Dual Pillars of German Science Production, 1950–2010

The world’s third largest producer of scientific research, Germany, is the origin of the research university and the independent, extra-university research institute. Its dual-pillar research policy differentiates these organizational forms functionally: universities specialize in advanced research-based teaching; institutes specialize intensely on research. Over the past decades this policy affected each sector differently: while universities suffered a lingering “legitimation crisis,” institutes enjoyed deepening “favored sponsorship”—financial and reputational advantages. Universities led the nation’s reestablishment of scientific prominence among the highly competitive European and global science systems after WWII. But sectoral analysis of contributions to science, technology, engineering, mathematics, and medical and health journal publications (1950–2010) finds that Germany’s small to medium-sized independent research institutes have made significant, growing contributions, particularly in publishing in higher impact journals proportionally more than their size. Simultaneously—despite dual-pillar policy implications—the university sector continues to be absolutely and relatively successful; not eclipsed by the institutes. Universities have consistently produced two-thirds of the nation’s publications in the highest quality journals since at least 1980 and have increased publications at a logarithmic rate; higher than the international mean. Indeed, they led Germany into the global mega-science style of production. Contrary to assumed benefits of functional differentiation, our results indicate that relative to their size, each sector has produced approximately similar publication records. While institutes have succeeded, the larger university sector, despite much less funding growth, has remained fundamental to German science production. Considering these findings, we discuss the future utility of the dual-pillar policy.

     

A Simple Unifying Measure of State Support for Postsecondary Education

Conflicting measures of state support for postsecondary education create confusion and misunderstanding that convolute debates about states’ postsecondary education funding. The use of multiple measures is largely unnecessary, though. A simple single measure is constructed that adequately quantifies both states’ postsecondary need and states’ ability to pay. Specifically, this study proposes measuring state support for postsecondary education as state postsecondary funding per high school graduate over the previous four years per dollar of per capita income.

The validity and intra-tester reliability of markerless motion capture to analyse kinematics of the BMX Supercross gate start

The aim of this study was to quantify the validity and intra-tester reliability of a novel method of kinematic measurement. The measurement target was the joint angles of an athlete performing a BMX Supercross (SX) gate start action through the first 1.2 s of movement in situ on a BMX SX ramp using a standard gate start procedure. The method employed GoPro® Hero 4 Silver (GoPro Inc., USA) cameras capturing data at 120 fps 720 p on a ‘normal’ lens setting. Kinovea 0.8.15 (Kinovea.org, France) was used for analysis. Tracking data was exported and angles computed in Matlab (Mathworks®, USA). The gold standard 3D method for joint angle measurement could not safely be employed in this environment, so a rigid angle was used. Validity was measured to be within 2°. Intra-tester reliability was measured by the same tester performing the analysis twice with an average of 55 days between analyses. Intra-tester reliability was high, with an absolute error <6° and <9 frames (0.075 s) across all angles and time points for key positions, respectively. The methodology is valid within 2° and reliable within 6° for the calculation of joint angles in the first ~1.25 s.     

Exploring criteria for successful query expansion in the genomic domain

Query Expansion is commonly used in Information Retrieval to overcome vocabulary mismatch issues, such as synonymy between the original query terms and a relevant document. In general, query expansion experiments exhibit mixed results. Overall TREC Genomics Track results are also mixed; however, results from the top performing systems provide strong evidence supporting the need for expansion. In this paper, we examine the conditions necessary for optimal query expansion performance with respect to two system design issues: IR framework and knowledge source used for expansion. We present a query expansion framework that improves Okapi baseline passage MAP performance by 185%. Using this framework, we compare and contrast the effectiveness of a variety of biomedical knowledge sources used by TREC 2006 Genomics Track participants for expansion. Based on the outcome of these experiments, we discuss the success factors required for effective query expansion with respect to various sources of term expansion, such as corpus-based cooccurrence statistics, pseudo-relevance feedback methods, and domain-specific and domain-independent ontologies and databases. Our results show that choice of document ranking algorithm is the most important factor affecting retrieval performance on this dataset. In addition, when an appropriate ranking algorithm is used, we find that query expansion with domain-specific knowledge sources provides an equally substantive gain in performance over a baseline system.

Assessing the integration of audience response system technology in teaching of anatomical sciences

The goals of our study were to determine the predictive value and usability of an audience response system (ARS) as a knowledge assessment tool in an undergraduate medical curriculum. Over a three year period (2006–2008), data were collected from first year didactic blocks in Genetics/Histology and Anatomy/Radiology (n = 42–50 per class). During each block, students answered clinically oriented multiple choice questions using the ARS. Students' performances were recorded and cumulative ARS scores were compared with final examination performances. Correlation coefficients between these variables were calculated to assess the existence and direction of an association between ARS and final examination score. If associations existed, univariate models were then constructed using ARS as a predictor of final examination score. Student and faculty perception of ARS difficulty, usefulness, effect on performance, and preferred use were evaluated using a questionnaire. There was a statistically significant positive correlation between ARS and final examination scores in all didactic blocks and predictive univariate models were constructed for each relationship (all P < 0.0001). Students and faculty agreed that ARS was easy to use and a reliable tool for providing real‐time feedback that improved their performance and participation. In conclusion, we found ARS to be an effective assessment tool benefiting the faculty and the students in a curriculum focused on interaction and self‐directed learning. Anat Sci Educ 2:160–166. © 2009 American Association of Anatomists.     

Behavioral variability is controlled by discriminative stimuli

Previous research has demonstrated that behavioral variability can be modified by reinforcers contingent on it, but there has been no convincing evidence of discriminative stimulus control over such variability. We therefore rewarded 20 rats for variable response sequences in the presence of one stimulus and provided equal rewards independently of sequence variability in the presence of a second stimulus. We found that sequence variability was significantly higher during the first stimulus than during the second, with the greatest difference occurring immediately following onset of the stimuli. Removing the discriminative stimuli caused levels of variability to converge. These experiments provide strong evidence that behavioral variability can be controlled by discriminative stimuli, which may be important for general theories of operant behavior and their applications.     

School-based bullying experiences as reflected by adults with visual impairments

The purpose of this study was to describe the reflections of adults with visual impairments regarding bullying experiences during their school-based education. An interpretative phenomenological analysis research approach was used and 11 participants (aged 20–35 years; seven women, four men) participated in this study. The sources of data were semi-structured audiotaped telephone interviews and reflective field notes. Thematic development was undertaken utilizing a three-step analytical process guided by the research approach. Based on the data analysis, three interrelated themes were constructed: (a) “It would be when they knew there weren't teachers watching”: bullying experiences in unowned and unstructured spaces; (b) “Going through the motions”: feelings about verbal, social, and physical victimization; and (c) “They had their own insecurities”: understanding the bullies and bystanders. The emerged themes provide a unique insight into the way in which those with visual impairments experienced bullying in schools and the meaning they ascribed to those experiences.