Think it over

This section of Resonance presents thought-provoking questions, and discusses answers a few months later. Readers are invited to send new questions, solutions to old ones and comments, to ‘Think It Over’, Resonance, Indian Academy of Sciences, Bangalore 560 080. Items illustrating ideas and concepts will generally be chosen.     

The Inveterate Tinkerer 14. ExperimentsWith Liquid Drops

In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. “Classroom” is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science.     

The inveterate tinkerer: Instability of Kolmogorov flow

In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. “Classroom” is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science.     

Pythagorean theorem from Heron’s formula: Another proof

In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. “Classroom” is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science.     

Classroom

In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. “Classroom” is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science.     

Classroom

In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. “Classroom” is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science.     

Crossword

The first part carries the answers to the crossword on cell that appeared in the October 2018 issue of Resonance while the second part contains a new crossword on nucleic acids.     

What Does it Mean to Assess Gifted Students’ Perceptions of Giftedness Labels?

Measuring gifted and talented (GT) students’ perceptions of their GT label might seem to be a relatively straightforward affair. Most of this research uses survey methods that ask GT students to complete Likert scale or open-ended response questionnaires about their perceptions of the label and then presents results in clear and quantifiable terms, such as “X % of students hold positive perceptions of the GT label.” However, our qualitative study of GT students in two middle school social studies classrooms presents findings that not only trouble, but prompt questions about simple proclamations regarding GT students’ perceptions of the GT label. What we found was that given the opportunity to share their thoughts at length, this group of GT students expressed a range of often contradictory perceptions about their GT label. Students expressed multiple interpretations and perceptions of the GT label, as well as both embraced the label and rejected the label.     

Inter-level Scaffolding and Sequences of Representational Activities in Teaching a Chemical System with Graphical Simulations

Chemistry knowledge can be represented at macro-, micro- and symbolic levels, and learning a chemistry topic requires students to engage in multiple representational activities. This study focused on scaffolding for inter-level connection-making in learning chemistry knowledge with graphical simulations. We also tested whether different sequences of representational activities produced different student learning outcomes in learning a chemistry topic. A sample of 129 seventh graders participated in this study. In a simulation-based environment, participants completed three representational activities to learn several ideal gas law concepts. We conducted a 2 × 3 factorial design experiment. We compared two scaffolding conditions: (1) the inter-level scaffolding condition in which participants received inter-level questions and experienced the dynamic link function in the simulation-based environment and (2) the intra-level scaffolding condition in which participants received intra-level questions and did not experience the dynamic link function. We also compared three different sequences of representational activities: macro-symbolic-micro, micro-symbolic-macro and symbolic-micro-macro. For the scaffolding variable, we found that the inter-level scaffolding condition produced significantly better performance in both knowledge comprehension and application, compared to the intra-level scaffolding condition. For the sequence variable, we found that the macro-symbolic-micro sequence produced significantly better knowledge comprehension performance than the other two sequences; however, it did not benefit knowledge application performance. There was a trend that the treatment group who experienced inter-level scaffolding and the micro-symbolic-macro sequence achieved the best knowledge application performance.     

Encouraging Students with Different Profiles of Perceptions to Pursue Science by Choosing Appropriate Teaching Methods for Each Age Group

This research aimed at identifying student profiles of perceptions by means of a clustering method using a validated questionnaire. These profiles describe students’ attraction to science and technology (S&T) studies and careers as a variable driven by school S&T self-concept and interest in school S&T. In addition to three rather predictable student profiles (confident enthusiast, average ambitious, and pessimistic dropout), the fourth fairly well-populated profile called confident indifferent was produced. Our second and third research questions allowed us to describe each profile in terms of the instructional methods to which their population was exposed (including the degree to which they were actively involved) and the instructional methods to which they would like more exposure. An analysis of the evolution of the profiles’ population over time is also presented. The results suggest that pedagogical variety and active involvement in the decision to pursue S&T are important. The perception of the utility and importance of S&T both in and out of school may also play an important role in these decisions. Minor pedagogical preferences were also found in certain age groups.     

Alienation in mathematics education: a problem considered from neo-Vygotskian approaches

In a recent article published in this journal, Williams (Educational Studies in Mathematics, 92, 59–72, 2016) offers a critique of neo-Vygotskian perspectives exemplified in recent work on the funds of knowledge and on cultural-historical activity theoretic perspectives. The critique has great value in that it asks interesting questions that often go unnoticed and fail to be discussed in mathematics education research—e.g., the question of alienation or the role of agency in Vygotsky’s notion of the zone of proximal development. Despite the great value of the questions raised, the critique fails because its idealist theoretical epistemological underpinning is at odds with Vygotsky’s thought and cultural-historical activity research in general. The critique falls short especially on the point of realizing the materialist dialectical method Vygotsky employed. The goal of this article is to address Williams’ critique by (a) revisiting the main argument of the critique, (b) articulating the departures of the critique from the materialist dialectical method, (c) conceptualizing development along the theoretical lines of the late (Spinozist-Marxian) Vygotsky, and (d) formulating a materialist dialectical approach to alienation. We conclude by summarizing three main problems of the critique.     

Teachers’ Use of Focus Questions in German Biology Classrooms: a Video-based Naturalistic Study

This study investigated the effects of teachers’ use of focus questions on students’ knowledge structures and classroom teaching-learning process by re-analyzing selected data from a quasi-experimental pre-post video study (Wadouh, 2007). Focus questions are content-related anchoring questions highlighting the key content taught in individual lessons (Forbes & Davis, 2010). In Wadouh’ study, students answered a knowledge test before and after the lesson on “blood and the circulatory system” and one lesson per teacher was videotaped to investigate teaching practices in grade 9 biology classrooms. Students also completed a post-unit concept mapping exercise and a motivation-interest questionnaire. In this study, 30 lesson videos selected from 47 were re-analyzed for teachers’ use of focus questions—no focus questions, non-specific or simple focus questions, and specific and challenging focus questions. Individual students’ scores in the concept mapping exercise were aggregated as students’ topic-related knowledge structure. Multilevel analyses revealed a significant positive effect of teachers’ use of specific and challenging focus questions on students’ topic-related knowledge structure. Furthermore, a comparative case analysis of the classroom teaching-learning process was conducted in four lessons where teachers used specific and challenging focus questions in two of the lessons and non-specific or simple focus questions in the other two lessons. The findings indicate that specific and challenging focus questions anchored lessons on students’ co-construction of scientific explanations by activating their pre-instructional ideas, whereas non-specific or simple focus questions anchored lessons on their accumulation of canonical scientific knowledge. This study’s limitations and implications for teacher education reform are discussed.     

Characterization of the mean velocity of a circular jet in a bounded basin

A circular jet has broad and important applications in practical engineering. Most research in this area has focused on a free jet, a wall jet or a vertical jet in a bounded domain. In this study, the mean velocities of circular offset jets were studied for four jet exit Froude numbers (Fr), three offset heights (S) (S/d=1, 2, 3) and three submergence ratios (ht/S) (surface jet, mixed jet, and submerged jet) in a bounded basin. Based on the results, we propose a velocity decay formula for a circular jet. The lateral velocity spread was more consistent with Gaussian and Cauchy–Lorentz distributions than the vertical velocity. Moreover, Fr had little effect on the decay of the mean velocity for a circular jet when Re>1×10⁴. The lateral and vertical spreads showed a quadratic relationship with the streamwise distance for different values of Fr at X/d<10. The positions of maximum mean velocity decay were independent of Fr and S/d when X/d<10. The spread rate was more uniform in the lateral direction than that in the vertical direction in a certain region for different S/d and ht/S. Therefore, the decay, spread, and maximum velocity position of the mean velocity for a circular offset jet can remain stable under different values of Fr, offset height, and submergence ratio.     

关于中心厄米特矩阵的广义反特征值问题

1　Introduction　AmatrixA∈Cn×missaidtobecentrohermitianifA =Jn AJm,andskewcentrohermitianifA =-Jn AJm,where Adenotetheconjugateofthema trixAandJlisthepermutationmatrixoforderlwithonesonthecrossdiagonal(bottomlefttotopright)andzeroselsewhere .ThehermitianToeplitzmatricesformanimportantsubclassofcentrohermi tianmatriceswhichoccurnaturallyindigitalsignalprocessingandotherareas ,seeforinstance[1] andreferencetherein .Thecentrohermitianandrelatedmatricesrecentlyplayanimportantroleinthesolu…     

Self Reflections of Undergraduate Students on Using Web-Supported Counterintuitive Science Demonstrations

Analysis of self-reflections of undergraduate education students in a project involving web-supported counterintuitive science demonstrations is reported in this paper. Participating students (N?=?19) taught science with counterintuitive demonstrations in local elementary school classrooms and used web-based resources accessed via wireless USB adapters. Student reflections to seven questions were analyzed qualitatively using four components of reflection (meeting objectives/perception of learning, dynamics of pedagogy, special needs accommodations, improving teaching) deriving 27 initial data categories and 12 emergent themes. Overall the undergraduates reported meeting objectives, engaging students in pedagogically relevant learning tasks including, providing accommodations to students with special needs, and gaining practice and insight to improve their own teaching. Additional research is needed to arrive at generalizable findings concerning teaching with web-supported counterintuitive science demonstrations in elementary classrooms.     

Points at Which Continuous Functions Have the Same Height

As an easy application of the intermediate value theorem, one can show that for any continuous function f: [0, 1] → ? with f (0) = f (1), there are points a, a + 1/2 both in [0, 1] such that f (a) = f (a + 1/2). In this note, we show that this property holds with 1/2 replaced by any number of the form 1/n for a positive integer n. More interestingly, we show that this is false for every number not of the form 1/n.     

On a Problem of Alaoglu and Erdős

Starting with an elementary problem that appeared in the Putnam mathematics competition, we proceed to discuss some techniques of transcendental number theory and prove the following result. If p, q, r are distinct primes and if c is a real number with the property that p^c, q^c, r^c are integers, then c must be a non-negative integer. The tools used are some linear algebra and complex analysis. The zero-density estimate method discussed here was used by Alan Baker to prove his celebrated theorem on linear forms in logarithms. The question as to whether we can replace three primes by two primes is an open question.     

Fecal Microbiota Succession of Piglets from Birth to Post-weaning by 454 Pyrosequencing Analysis

The objective of this study was to describe the fecal microbiota succession of piglets from birth to post-weaning by pyrosequencing. The dominant bacterial phyla were Bacteroidetes, Firmicutes, Proteobacteria, and Fusobacteria, although the composition of the fecal microbiota changed as the piglets grew. Bacteroides, Parabacteroides, Prevotella, Lactobacillus, unclassified Lachnospiraceae, Ruminococcus, Oscillospira, Phascolarctobacterium, and Desulfovibrio were the core genera in the feces of piglets and existed from birth to post-weaning. Bacteroides was the most abundant at birth; however, the proportion of Bacteroides decreased as the piglets aged, while the proportion of Prevotella increased until it became the most abundant genus at the post-weaning stage. Principal coordinate analysis indicated that the microbial communities of piglet fecal samples from birth to post-weaning could be separated into four groups according to the similarity of community composition. These corresponded to time points on day 0 (birth); day 7; days 14, 21, and 28 (pre-weaning); and day 35 (post-weaning). This study suggests that the development of the intestinal microbiota in the piglet is a gradual and sequential process. This methodology establishes a basis for broader studies to investigate the microbiota of the piglet intestinal tract.     

The Bondi Approach to the Lorentz

This article summarises a very elegant way of teaching the Lorentz transformation, which was introduced by Hermann Bondi (see Resonance, March 2016 for more about him). The starting point of this approach is that the best way of assigning space and time coordinates to a distant event is by radar, i.e., by transmitting and receiving light signals, and noting the times of departure and arrival. There is no need for the rigid rod. Bondi’s method, which he called the k-calculus, makes good use of the Doppler effect (hence the delta in the title). For students who have learnt special relativity in the standard way, this approach provides a different view of the subject.     

Making Space for Consuming Practices

This empirically driven paper is about workplace learning with specific focus on the ‘work’ of consuming practices. By consuming we refer to the eating, and the drinking, and (at times) to the smoking that workers, in most organisations, do on a daily basis. Indeed, it is the quotidian nature of consuming, coupled with its absence from workplace learning research that make them noteworthy practices to explore. In using the term practice we draw on the recent tranche of practice based theorisations: notably Schatzki (1996, Organization Studies, 26(3), 465-484, 2005, Organization Studies, 27(12), 1863-1873, 2006) and Gherardi (Human Relations, 54(1), 131-139, 2001, 2006, Learning Organization, 16(5), 352-359, 2009). The paper frames consuming practices as ‘dispersed’ (general) practices and, illustrated through empirical data from multiple projects, we progressively outline how these contribute to the learning of ‘integrative’ (specialized work) practices. Our overall aim is to (re)position consuming practices from prosaic, to having much relevance for research on workplace learning.