scholarly journals Two conceptions of fraction equivalence

2021 ◽  
Author(s):  
Pernille Ladegaard Pedersen ◽  
Mette Bjerre
Keyword(s):  
Conceptual Understanding ◽  
Mathematical Analysis ◽  
Past Research ◽  
Rational Numbers ◽  
The Other ◽  
Unified Framework ◽  
Future Directions ◽  
Equivalent Fractions

AbstractIn this study, we present a mathematical analysis distinguishing two conceptions of equivalence: proportional equivalence and unit equivalence. These two conceptions have distinct meanings in relation to equivalent fractions: one is grounded in proportionality, while the other is grounded in equal wholes. We argue that (a) the distinction of equivalence gives a unified framework of equal fractions that has not previously been described in the literature; (b) a conceptual understanding of both fraction equivalences is integral to understanding rational numbers; and (c) knowledge of both conceptions of equivalence is important for developing a conceptual understanding of fraction arithmetic. Past research has largely overlooked the distinction between the two types of equivalence. However, this may provide an important foundation for central topics that build on equivalence, and a better understanding of these two types of equivalence may support a more flexible understanding of fractions. Last, we propose future directions for teaching equivalence in mathematics.

Two Perspectives on Proportional Relationships: Extending Complementary Origins of Multiplication in Terms of Quantities

2015 ◽  
Vol 46 (1) ◽  
pp. 17-38 ◽  
Author(s):  
Sybilla Beckmann ◽  
Andrew Izsák
Keyword(s):  
Empirical Research ◽  
Mathematical Analysis ◽  
Measure Space ◽  
Space Versus ◽  
Past Research ◽  
Variable Number ◽  
The Other ◽  
Space Ratio

In this article, we present a mathematical analysis that distinguishes two distinct quantitative perspectives on ratios and proportional relationships: variable number of fixed quantities and fixed numbers of variable parts. This parallels the distinction between measurement and partitive meanings for division and between two meanings for multiplication—one rooted in counting equal-sized groups, the other in scaling the size of the groups. We argue that (a) the distinction in perspectives is independent from other distinctions in the literature on proportional relationships, including the within measure space versus between measure space ratio distinction; (b) the psychological roots for multiplication suggest the accessibility of the two perspectives to learners; and (c) the fixed numbers of variable parts perspective, though largely overlooked in past research, may provide an important foundation for central topics that build on proportional relationships. We also suggest directions for future empirical research.

scholarly journals The Future of Fat Grafting

2021 ◽  
Vol 41 (Supplement_1) ◽  
pp. S69-S74
Author(s):  
Summer E Hanson
Keyword(s):  
Adipose Tissue ◽  
Breast Reconstruction ◽  
Fat Grafting ◽  
The Other ◽  
Special Topic ◽  
Autologous Fat Grafting ◽  
Upper Arm ◽  
Future Directions ◽  
Autologous Fat ◽  
The Face

Abstract One of the earliest reported cases of autologous fat grafting (AFG) was by Neuber in 1893 and consisted of the transfer of small lobules of fat from the upper arm for cicatrical depression of the face. He advocated the use of smaller grafts, noting that pieces larger than the size of a bean would form cysts. In 1895, Czerny excised a lumbar lipoma and transplanted it to the chest for breast reconstruction. Since these early reports, the knowledge base around AFG has expanded exponentially, as illustrated by the other papers within this special topic. As we embark on the next phase of AFG in the clinical setting, there are several directions which are near-clinical translation. This paper discusses future directions in fat grafting that build on optimization of our current techniques as clinical indications expand, such as supplementing purified lipoaspirate and the associated regulatory burden, or deconstructing adipose tissue to selectively use adipose graft components for a variety of regenerative indications.

Humor Styles in Marriage: How Similar Are Husband and Wife?

2018 ◽  
Vol 122 (6) ◽  
pp. 2331-2347
Author(s):  
Meng-Ning Tsai ◽  
Ching-Lin Wu ◽  
Yu-Lin Chang ◽  
Hsueh-Chih Chen
Keyword(s):  
Confidence Interval ◽  
Multilevel Modeling ◽  
Married Couples ◽  
Past Research ◽  
The Other ◽  
Humor Styles ◽  
Cohen’S D ◽  
Humor Style ◽  
Valid Predictor ◽  
Cohen's D

Past research found that similar appreciation for humor exists between spouses, but it is not certain whether this similarity between spouses also exists in kindhearted or malicious humor. The present study investigated the similarity of Taiwanese married couples’ humor styles. Participants included 239 couples (mean age = 42.9 years) who had been married to each other for at least 10 years. We used a traditional Chinese edition of the Humor Styles Questionnaire to measure the humor style and clustered participants’ humor styles in order to examine the similarity between spouses. The results show that husbands have higher tendencies toward aggressive (Cohen’s d = 0.29, p < .01) and self-defeating (Cohen’s d = 0.35, p < .01) humor styles than wives. Results from multilevel modeling indicate that spouses’ aggressive ( p < .001, confidence interval = .17, .41) and self-defeating ( p < .01, confidence interval = .05, .30) humor styles acting as a valid predictor to the other spouses’ negative humor styles. Furthermore, the results show that personal humor styles could be categorized into four clusters: positive humor endorsers, negative humor endorsers, general humor endorsers, and humor deniers. According to the clusters within spouse pairs, results show that similarities in humor styles exist between spouses (χ2 = 16.73, p = .01). The current study finds that most couples have similar humor styles and that a high proportion of married couples share the same humor clusters.

scholarly journals Tracking the continuous dynamics of numerical processing: A brief review and editorial

2018 ◽  
Author(s):  
Thomas J. Faulkenberry ◽  
Matthias Witte ◽  
Matthias Hartmann
Keyword(s):  
Numerical Cognition ◽  
Mental Arithmetic ◽  
Special Section ◽  
Past Research ◽  
Number Processing ◽  
Hand Tracking ◽  
Single Digit ◽  
Future Directions ◽  
Numerical Processing ◽  
Computer Mouse

Many recent studies in numerical cognition have moved beyond the use of purely chronometric techniques in favor of methods which track the continuous dynamics of numerical processing. Two examples of such techniques include eye tracking and hand tracking (or computer mouse tracking). To reflect this increased concentration on continuous methods, we have collected a group of 5 articles that utilize these techniques to answer some contemporary questions in numerical cognition. In this editorial, we discuss the two paradigms and provide a brief review of some of the work in numerical cognition that has profited from the use of these techniques. For both methods, we discuss the past research through the frameworks of single digit number processing, multidigit number processing, and mental arithmetic processing. We conclude with a discussion of the papers that have been contributed to this special section and point to some possible future directions for researchers interested in tracking the continuous dynamics of numerical processing.

scholarly journals Digital culture

2021 ◽  
Author(s):  
Alberto Acerbi
Keyword(s):  
Digital Media ◽  
Cultural Evolution ◽  
Cultural Transmission ◽  
Past Research ◽  
Digital Culture ◽  
Cultural Dynamics ◽  
Cumulative Culture ◽  
Future Directions

Cultural evolution can provide a useful framework to understand how information is produced, transmitted, and selected in contemporary online, digital, media. The diffusion of digital technologies triggered a radical departure from previous modalities of cultural transmission but, at the same time, general characteristics of human cultural evolution and cognition influence these developments. In this chapter, I will explore some areas where the links between cultural evolution research and digital media seem more promising. As cultural evolution-inspired research on internet phenomena is still in its infancy, these areas represent suggestions and links with works in other disciplines more than reviews of past research in cultural evolution. These include topics such as how to characterise the online effects of social influence and the spread of information; the possibility that digital, online, media could enhance cumulative culture; and the differences between online and offline cultural transmission. In the last section I will consider other possible future directions: the influences of different affordances in different media supporting cultural transmission; the role of producers of cultural traits; and, finally, some considerations on the effects on cultural dynamics of algorithms selecting information.

scholarly journals PUBLICATION TREND ON TRAVEL PREFERENCES OF SENIOR TOURISTS FROM 2000 TO 2020

2021 ◽  
Vol 6 (26) ◽  
pp. 172-185
Author(s):  
Nurul Ain Farhana Zainordin ◽  
Syed Muhammad Rafy Syed Jaafar ◽  
Nurul Diyana Md Khairi
Keyword(s):  
Literature Review ◽  
The Other ◽  
Ageing Population ◽  
Market Segment ◽  
Future Directions ◽  
Tourism Research ◽  
Review Analysis ◽  
Future Direction ◽  
Insight Into

The ageing population is the crucial phenomenon that has led to the new market segment in tourism known as 'senior tourists.' A senior tourist is determined as an older traveller or grey tourist. The number of elderly keeps growing throughout time; hence, grey tourists will be relevant preferences, differing from the younger tourists. This paper aims to evaluate the relevant studies regarding travel preferences that involve senior tourists. The objective is to understand the publication trend behind the development of travel preferences for senior tourists. The findings suggest that the overall travel preferences among senior tourists studied include 12 aspects of travel preferences. Researchers tend to focus on the aspect of accommodation among senior tourists compared to the other elements. At the end of the review, this paper is set out to outline the literature review analysis to provide greater insight into the development of travel preferences among grey tourists in tourism research from 2000 to 2020. This paper's output offers future directions to explore the offer trends and future direction in tourism and behaviour literature.

Candidate Traits and Political Choice

2014 ◽  
Author(s):  
Bruce W. Hardy
Keyword(s):  
Past Research ◽  
Vote Choice ◽  
The Other ◽  
Character Traits ◽  
Future Research ◽  
Short Term ◽  
Presidential Candidates ◽  
Vote Preference ◽  
Research Ability ◽  
Personal Qualities

What role do presidential candidate character traits play in vote decisions? To some, the answer is obvious as campaigns, journalists, pundits, and voters frequently differentiate presidential candidates in terms of their personal qualities—traits are deemed important. On the other hand, past research suggests that, while candidate character traits are short term forces, they hold relatively limited in influence on vote preference. However, theoretical and methodological limitations may have hindered past research ability to detect the true influence of character traits in voter decisions. This author reviews past literature, offers a clear conceptualization of candidate character traits, presents ways in which trait may influence vote choice, and suggests areas for future research.

Current methods and future directions in avian diet analysis

The Auk ◽  
2021 ◽  
Author(s):  
Brandon D Hoenig ◽  
Allison M Snider ◽  
Anna M Forsman ◽  
Keith A Hobson ◽  
Steven C Latta ◽  
...  
Keyword(s):  
Stable Isotope ◽  
Food Webs ◽  
Stable Isotope Analysis ◽  
Dietary Habits ◽  
Isotope Analysis ◽  
Diet Analysis ◽  
Unified Framework ◽  
Future Directions ◽  
Laboratory Techniques ◽  
Prey Identification

Abstract Identifying the composition of avian diets is a critical step in characterizing the roles of birds within ecosystems. However, because birds are a diverse taxonomic group with equally diverse dietary habits, gaining an accurate and thorough understanding of avian diet can be difficult. In addition to overcoming the inherent difficulties of studying birds, the field is advancing rapidly, and researchers are challenged with a myriad of methods to study avian diet, a task that has only become more difficult with the introduction of laboratory techniques to dietary studies. Because methodology drives inference, it is important that researchers are aware of the capabilities and limitations of each method to ensure the results of their study are interpreted correctly. However, few reviews exist which detail each of the traditional and laboratory techniques used in dietary studies, with even fewer framing these methods through a bird-specific lens. Here, we discuss the strengths and limitations of morphological prey identification, DNA-based techniques, stable isotope analysis, and the tracing of dietary biomolecules throughout food webs. We identify areas of improvement for each method, provide instances in which the combination of techniques can yield the most comprehensive findings, introduce potential avenues for combining results from each technique within a unified framework, and present recommendations for the future focus of avian dietary research.

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