Understanding Point and Slope in Linear Equations and Approximations: A Case Study

This article delves into an intervention designed to enhance a precalculus student’s understanding in constructing linear equations and in approximating function values. Before the intervention, the student primarily relied on the algebraic formula y2-y1/x2-x1 to determine slope, knew slope geometrically as Δy/Δx solely for integer values, and struggled to construct a linear equation without an explicitly shown y-intercept. Through the intervention, the student comprehended slope m as a unit rate and expanded this understanding to Δy = Δ for integer Δx by iterating m, Δ number of times. She also successfully used this newfound understanding to construct linear equations, including tangent line equations, and approximate function values. Nonetheless, she faced some challenges in comprehending Δy = Δ for non-integer Δ and in conceiving point as a multiplicative object with its coordinates representing covarying quantities. Further exploration is needed to validate these findings and address potential difficulties that students might face in grasping slope in the context of linear equations and approximations

Graphs of Two Variable Inequalities: Alternate Approaches to the Solution Test

In this article I suggest some alternatives to the solution test for the understanding of graphs of inequalities in two variables. Based on the work done with two groups of preservice secondary mathematics teachers, and by using the idea of variation and the framework of action and process conceptions of inequalities, I explain how graphs of inequalities can be viewed as a collection of rays or curves. I also explain the potential benefits of these alternative explanations in the solving of optimization problems and in the instruction of functions as a medium of one variable and two variable functions

A teacher's use of play to promote literacy learning in a prekindergarten classroom serving children from diverse language backgrounds

textThis study looked at both a teacher’s beliefs about the role of play and that teacher’s use of play in literacy learning serving children from diverse language backgrounds. Although several researchers have explored children’s literacy development in a play context, there is little research on this topic for children from diverse language backgrounds. In order to explore the role of play in literacy learning for children from diverse language backgrounds, I used a qualitative research approach to collect data from interviews, informal conversations, observations, and self-reflexive notes. In this study, the teacher believed play could be an ideal medium for ESL children who did not speak English fluently. Play gave them a relaxed and comfortable environment to practice a new language, English, without worrying about making mistakes. She understood play as a “concrete,” “hands-on,” “fun,” and “manipulative” activity that provides a relaxed and comfortable environment, becomes a good medium for integrated lessons, and gives a natural connection between the home language and English. She used play for a warm-up, games or tricks, integrated lessons, assessment, acting out characters, dramatic play, and block play in literacy learning for children from diverse language backgrounds. This study revealed that when a teacher believes that play takes an important role in children’s learning and development, she uses playful activities as potential teaching and learning mediums for ESL children’s literacy learning and development. In addition, the result supported that each teacher may have a unique understanding or practical notion of play in literacy learning, and it may strongly affect his/her classroom practices.Curriculum and Instructio

Effects of Consumer Ethnocentrism and Product Knowledge on Consumers’ Utilization of Country-Of-Origin Information

Information Byeong-Joon Moon, KyungHee University ABSTRACT -This article is concerned with the effects of consumer ethnocentrism and product knowledge on consumers' utilization of country-of-origin information for their product evaluation. The data suggest that, regardless of consumers' ethnocentrism, low-knowledge consumers' product attitude is more strongly influenced by country-of-origin perception than highknowledge consumers' product attitude. Effects of Consumer Ethnocentrism and Product Knowledge on Consumers' Utilization of Country-of-Origin Information Byeong-Joon Moon, KyungHee University 1 ABSTRACT This article is concerned with the effects of consumer ethnocentrism and product knowledge on consumers' utilization of country-of-origin information for their product evaluation. The data suggest that, regardless of consumers' ethnocentrism, lowknowledge consumers' product attitude is more strongly influenced by country-of-origin perception than high-knowledge consumers' product attitude. The data also show that, when domestic and foreign products are given as alternatives, regardless of consumers' knowledge, lowethnocentric consumers' product attitude is influenced by countryof-origin perception; however, high-ethnocentric consumers' product attitude is not influenced by country-of-origin perception

TRAF6 Mediates IL-1β/LPS-Induced Suppression of TGF-β Signaling through Its Interaction with the Type III TGF-β Receptor

Transforming growth factor-β1 (TGF-β1) is an important anti-inflammatory cytokine that modulates and resolves inflammatory responses. Recent studies have demonstrated that inflammation enhances neoplastic risk and potentiates tumor progression. In the evolution of cancer, pro-inflammatory cytokines such as IL-1β must overcome the anti-inflammatory effects of TGF-β to boost pro-inflammatory responses in epithelial cells. Here we show that IL-1β or Lipopolysaccharide (LPS) suppresses TGF-β-induced anti-inflammatory signaling in a NF-κB-independent manner. TRAF6, a key molecule in IL-1β signaling, mediates this suppressive effect through interaction with the type III TGF-β receptor (TβRIII), which is TGF-β-dependent and requires type I TGF-β receptor (TβRI) kinase activity. TβRI phosphorylates TβRIII at residue S829, which promotes the TRAF6/TβRIII interaction and consequent sequestration of TβRIII from the TβRII/TβRI complex. Our data indicate that IL-1β enhances the pro-inflammatory response by suppressing TGF-βsignaling through TRAF6-mediated sequestration of TβRIII, which may be an important contributor to the early stages of tumor progression

Systematic Review of Exposure to Bisphenol A Alternatives and Its Effects on Reproduction and Thyroid Endocrine System in Zebrafish

Bisphenol A (BPA), which is widely used for manufacturing polycarbonate plastics and epoxy resins, has been banned from use in plastic baby bottles because of concerns regarding endocrine disruption. Substances with similar chemical structures have been used as BPA alternatives; however, limited information is available on their toxic effects. In the present study, we reviewed the endocrine disrupting potential in the gonad and thyroid endocrine system in zebrafish after exposure to BPA and its alternatives (i.e., bisphenol AF, bisphenol C, bisphenol F, bisphenol S, bisphenol SIP, and bisphenol Z). Most BPA alternatives disturbed the endocrine system by altering the levels of genes and hormones involved in reproduction, development, and growth in zebrafish. Changes in gene expression related to steroidogenesis and sex hormone production were more prevalent in males than in females. Vitellogenin, an egg yolk precursor produced in females, was also detected in males, confirming that it could induce estrogenicity. Exposure to bisphenols in the parental generation induced a decrease in the hatchability associated with offspring generation. In zebrafish exposed to bisphenols, significant decreases in thyroxine concentrations and increases in thyroid-stimulating hormone concentrations were commonly observed. Alternative compounds used to replace a chemical of concern are believed to be less toxic than the original compound; however, several BPA alternatives appear to have similar or greater effects on the endocrine system in zebrafish. Since endocrine systems interact with each other, further studies are needed to assess the primary target of BPA alternatives among the endocrine axes

Simple Fabrication of Asymmetric High-Aspect-Ratio Polymer Nanopillars by Reusable AAO Templates

We present a simple method of utilizing anodized aluminum oxide (AAO) as a reproducible template for fabricating high-aspect-ratio uniformly bent polymeric nanopillars that can be used as a physical adhesive. It is shown how to achieve straight high-aspect-ratio nanopillars with concepts of the work of adhesion and lateral collapse between polymer pillars without serious damage to the master template. With the support of manufacturing polymeric nanopillars from the reusable AAO, a simple route to asymmetric dry adhesive nanopillars bent by residual stresses was demonstrated