Model of Flexibility in the Conceptual Evolution of Multiplicative Comparison

Background: Proportionality is a paramount topic in students' mathematical literacy. In this topic, it is fundamental to understand the multiplicative comparison and the flexible use of the concepts of ratio and proportion. Objectives: To analyse the articulation between concepts, resolution strategies, and representations used by students, supported by numerical relationships and properties of operations to characterise a model of the conceptual evolution of multiplicative comparison. Design: Research based design. Setting and participants: Two mathematics teachers teaching 6th grade (11-12-year-old students) and their 38 (18 + 20) students during the lessons in which five assignments were explored. Data collection and analysis: The data includes the transcription of the video recordings of the classes and the students' written productions. The data were successively revisited and condensed to identify and illustrate the aspects that make up the model of the conceptual evolution of multiplicative comparison. Results: The construction of the concept of multiplicative comparison prevails in the work in two spaces of measurement and in the exploration of the multiplicative relationship between the corresponding quantities within each one. Resolution strategies are first non-quantitative and become quantitative, initially with additive and then multiplicative characteristics. The representations are based on the ratio as a fraction, on the double number line, and on the table of ratios, being supported by numerical relationships and properties of operations. Conclusions: The results elucidate, adjust, and illustrate a theoretical model related to the evolution of the multiplicative comparison in two spaces of measurement.

Impact of the Order of EAC and SOS During Instruction on Ratios

The purpose of this study was twofold. First, a set of instructional materials surrounding proportional reasoning with ratios (particularly the understanding of the multiplicative relationship between the quantities within the ratio, referred to as functional reasoning throughout this thesis) were created using the free online tool, Desmos, with a goal of determining the impact of the lesson materials on student understanding. The second goal was to explore the impact of the order in which two instructional strategies, Explicit Attention to Concepts (EAC) and Students’ Opportunity to Struggle (SOS), had on student understanding. The lesson materials consisted of 5 lessons. These 5 lessons had two forms: EAC then SOS or SOS then EAC. In each of these instructional groups, all EAC and SOS sections were identical in each of the five lessons, the difference between materials in each of these groups was the order in which the EAC and SOS sections occurred. Students’ understanding was assessed anonymously, and answers were scored dichotomously (i.e. correct or incorrect). There was a total of 22 items on the full assessment with 8 items addressing functional reasoning specifically. The major findings of this study include that the lesson materials led to an increase in understanding for both overall understanding and the sub-area of functional reasoning, and the EAC then SOS instructional group’s understanding of functional reasoning was higher than that of the SOS then EAC instructional group.

Epistemological Foundations of the Digital Technologies Used in Agriculture in Siberia

The authors substantiated the necessity for an epistemological approach to determining the main messages in the digitalization application by agricultural producers, taking into account natural and climatic, commodity-production and social factors.(Research purpose) To formulate the main messages when applying digital technologies in agricultural production, which determine epistemological approaches to their systematic use and allow increasing grain production by 2-3 times on the example of JSC Sokolovo.(Materials and methods) The authors applied a system analysis to agricultural production objects as to information field when describing them in the information space.(Results and discussion) The authors found that agricultural production objects were in an objective multiplicative relationship. Based on the results, a communication scheme between objects in agro-industrial production, reflecting their dialectical commonality was developed. They presented production objects as a resource characterized by a certain set of parameters and values. They showed the multiplicative nature of the resources relationship, describing the nature of the dependence by the method of passage to the limit. The authors identified general information requirements for solving the agriculture problems, crop production and for the means of processing this information in the amount of more than 2 petaflops. They established the necessary resolution for managing technical processes - less than 3 centimeters.(Conclusions) The authors proposed a paradigm for information support of technological processes in agricultural production. They confirmed the legitimacy of this approach to the paradigm formation by creating more than 20 databases. They gave examples of increasing the efficiency of grain production in the Novosibirsk region. The epistemological principles were based on the formulated six messages of information digital technologies, which made it possible to use them in more than 247 520 different combinations and apply to the whole farms variety, depending on their capabilities and desires.

Attention as a source of variability in decision-making: Accounting for overall-value effects with diffusion models

Research has demonstrated that value-based decisions depend not only on the relative value difference between options, but also on their overall value. In particular, response times tend to decrease as the overall value of the options increase. Standard sequential sampling models such as the diffusion model can account for this fact by assuming that decision thresholds or noise vary with overall value. Alternatively, attention-based models that incorporate eye-tracking data accommodate this overall-value effect directly as a consequence of the multiplicative relationship between attention and value magnitude. Using non-attentional diffusion models fit to data simulated with an attention-based model, we find that parameters related to decision thresholds or noise vary as a function of overall value, even though these were not features of the data generating process. We find additional evidence for misidentified parameters in a similar analysis using empirical data. Our results indicate that neglecting attentional effects can lead to mistaken conclusions about which decision parameters are sensitive to overall value.

Engagement with fat talk as a function of social comparison and body image concerns: Two replication studies support main effects but do not support an interaction effect.

Verbal denigration of personal body size and shape (“fat talk”) and engagement in social comparison has been linked to the development of body dissatisfaction and eating disordered behaviour. A key question is whether the relationship between these two predictors is additive or multiplicative, as the latter relationship would imply a far more serious impact on body dissatisfaction. A previous report has suggested a multiplicative relationship, and in two separate studies we replicated this study. In each study, female participants filled in fat talk, social comparison and body dissatisfaction measures. In the first study, 189 UK participants took part and in the second study, 371 US participants took part. Both studies found significant correlations between all three measures but no interaction effect, consistent with an additive not a multiplicative relationship. In a further test, we used a mini meta-analysis to combine the results of the two studies reported here with the results of the original study. Again, we found no evidence of an interaction. In conclusion, these studies show an additive relationship between fat talk and social comparison, suggesting their impact on body image is serious but not as serious as previously reported.

A Multiplicative Approach to Polyvictimization: A Study of Intimate Partner Violence Types as Risk Factors for Child Polyvictimization in South Korea

Drawing on a new typology of intimate partner violence (IPV), this paper tests the relationship between indicators of totalitarian and anarchic IPV and child polyvictimization incidence and severity. The paper argues for and utilizes a quantitative approach to study polyvictimization severity. Polyvictimization is operationalized as a multiplicative relationship between physical abuse and neglect in a random sample of 204 children from Kyunggi province, South Korea. The indicator of totalitarian IPV significantly predicted polyvictimization severity and incidence even when a traditional measure of intimate terrorism was held constant. The indicator of anarchic IPV significantly predicted polyvictimization severity but not incidence when a traditional measure of intimate terrorism was held constant. Implications are discussed.

The Benefits of Resiliency to Standard Market Impact Models

We leverage Kepler Cheuvreux client order database over the period October 2014 — October 2016 (349,442 trades corresponding to a EUR92.3bn turnover) to estimate new models of market impact. We find a multiplicative relationship between the market impact and the explanatory factors (the volatility, the trading period participation rate and the trading duration). Furthermore, the relationship between the participation rate and the duration on one side and the market impact on the other is concave, with the effect of the participation rate on the market impact scaling as a square root. We introduce a new indicator of resiliency, which measures the ability of the order book to resist the aggressive order flow in a given period. This indicator shows a positive correlation with the residuals of our standard model of market impact, clearly demonstrating that the more resilient the stock, the more resistant it is to market impact. Thus, we are able to calibrate an enhanced model of market impact using our indicator of resiliency, which improves the explanatory power of the model compared to standard approaches. Our resiliency indicator thereby exposes the relationship between the market impact at the meta-order scale and the market impact at the elementary trade scale.

Additive effects on the energy barrier for synaptic vesicle fusion cause supralinear effects on the vesicle fusion rate

The energy required to fuse synaptic vesicles with the plasma membrane (‘activation energy’) is considered a major determinant in synaptic efficacy. From reaction rate theory, we predict that a class of modulations exists, which utilize linear modulation of the energy barrier for fusion to achieve supralinear effects on the fusion rate. To test this prediction experimentally, we developed a method to assess the number of releasable vesicles, rate constants for vesicle priming, unpriming, and fusion, and the activation energy for fusion by fitting a vesicle state model to synaptic responses induced by hypertonic solutions. We show that complexinI/II deficiency or phorbol ester stimulation indeed affects responses to hypertonic solution in a supralinear manner. An additive vs multiplicative relationship between activation energy and fusion rate provides a novel explanation for previously observed non-linear effects of genetic/pharmacological perturbations on synaptic transmission and a novel interpretation of the cooperative nature of Ca2+-dependent release.

Argument Content and Argument Source: An Exploration

Argumentation is pervasive in everyday life. Understanding what makes a strong argument is therefore of both theoretical and practical interest. One factor that seems intuitively important to the strength of an argument is the reliability of the source providing it. Whilst traditional approaches to argument evaluation are silent on this issue, the Bayesian approach to argumentation (Hahn & Oaksford, 2007) is able to capture important aspects of source reliability. In particular, the Bayesian approach predicts that argument content and source reliability should interact to determine argument strength. In this paper, we outline the approach and then demonstrate the importance of source reliability in two empirical studies. These experiments show the multiplicative relationship between the content and the source of the argument predicted by the Bayesian framework.