Preservice teachers’ creation of dynamic geometry sketches to understand trigonometric relationships

Dynamic geometry software can help teachers highlight mathematical relationships in ways not possible with static diagrams. However, these opportunities are mediated by teachers' abilities to construct sketches that focus users' attention on the desired variant or invariant relationships. This paper looks at two cohorts of preservice secondary mathematics teachers and their attempts to build dynamic geometry sketches that highlighted the trigonometric relationship between the angle and slope of a line on the coordinate plane. We identify common challenges in the construction of these sketches and present examples for readers to interact with that highlight these issues. Lastly, we discuss ways that mathematics teacher educators can help beginning teachers understand common pitfalls in the building of dynamic geometry sketches, which can cause sketches not to operate as intended

Open law : technology in service of the rule of law

As law librarians we have ready access to the full range of legal materials - from free sources and powerful commercial legal databases, from medieval times to the modern day. We can have the entirety of primary law (and the secondary materials needed to decipher it) at our fingertips within seconds. For those without such access- which is the majority of the general public - what are their options? How do those who do not have access to the likes of Lexis and Westlaw, or even a library with printed legal materials, find legal information- and why is it important that they can? This article will consider these questions, covering the United Kingdom and the United States of America, with a particular focus on the issue of open law. First we will have a short historical overview of access to legal information; we will then turn to the reasons why wide and full access to legal information is important, and look at some examples of systems which aim at providing such access. Some of the issues with such systems are discussed, followed by a brief outline of an ideal open law system. We end with a look at the social and political elements needed to make the technology of open law systems work.</p

Suppressing intermittent flow patterns and reducing pressure loss in two-phase horizontal pipe flow using surfactants

The addition of small concentrations of surfactant to an air/water two-phase flow through a 2 inch Schedule 40 (0.052 m-id) smooth PVC pipe resulted in significant changes to the flow pattern map and pressure loss of the system. Sodium dodecylsulfate was added to an air/water two-phase flow at several concentrations at or below the critical micelle concentration. As the surfactant concentration increased, the amount of foam generated in the flow increased, and several flow patterns not previously reported were observed. There was a reduction in the conditions under which intermittent flow patterns developed. It is proposed that the ability of the foam to dissipate local pressure gradients caused the reduction in the occurrence of intermittent flow. Pressure loss was measured for two-phase air/water stratified flow with and without surfactant. Addition of surfactant reduced the pressure loss in two-phase flow at concentrations that have no effect on single-phase, water only pressure loss. It is proposed that the liquid surface is less easily deformed in surfactant-containing flows due to surface concentration gradients created by interfacial forces, resulting in lower interfacial friction

Applying Quantitative Reasoning to Clarify Arc Measurements

The importance of reasoning quantitatively is reflected in both mathematics education research and mathematical standards for K-12 students. In this article, we detail how a quantitative reasoning framework can be used to help differentiate two quantities we have found students often struggle with: arc length and the measure of a central angle. We argue that taking the time to define all four components of a quantity can support students’ understanding of theorems involving these quantities

Constructing Kites to Integrate Mathematics and Arts Concepts

This article describes a tetrahedral kite activity that was implemented with grade 9 students (age 14-15). We detail how the three-part lesson provided opportunities to integrate mathematics and art concepts, with potential to also weave in science and engineering ideas. The first part primed students to consider tetrahedral kites, their cultural and historical significance, and the materials needed for constructing the kite. The second part had students create a prototype using nets of tissue paper decorated with mark making techniques. The third part had students create a tetrahedron kite containing cultural and geographical mark making techniques on the tissue paper sides before flying the kites at a community event. We conclude the article with recommendations to help other teachers integrate mathematics and visual arts topics through tetrahedral kites

Students\u27 Perceived Utility of Precision Taught Calculus

The last decade of calculus research has showed students learn best when lecture is supplemented with thoughtful use of technology and group work; however, educators are given little direction of how they are to balance the already full first semester calculus class. Precision teaching is an instructional model that employs formative assessment to provide information on what topics are understood by students as well as indicate troublesome concepts. With this information, the instructor can adjust class time accordingly by incorporating supplemental activities most beneficial to students. The purpose of this interview study was to explore the perceived utility of precision teaching by eight students earning to see if further exploration of this topic was warranted. Although precision teaching requires more work for the instructor, students\u27 high perceived utility makes precision teaching a valuable method of undergraduate instruction because they claim to study more, understand material better, and earn higher grades

"The Goddess is Fat": The Emergence of Fat Dyke Liberation, 1970-1990

Following the emergence of second-wave feminism, lesbians within the feminist movement began to retaliate against the discrimination they felt for their sexuality and adopted lesbian feminism. Though this movement championed women, the reality was that it failed to address the myriad of women that identified as lesbians, instead choosing to focus on conventionally attractive, feminine-presenting, thin, white lesbians. Fat Liberation emerged across the United States in retaliation to the discrimination women of size felt within the movement, addressing larger topics such as diet-culture, disability activism, appropriate femininity, racial and ethnic discrimination, rape culture, and the belief that they were undesirable, and thus unlovable. Throughout the 1980s, this movement began to diversify and incorporate women outside of lesbian feminism in the fight against fatphobia as a tool against women's oppression.No embargoAcademic Major: Histor

Researching from a Distance: Using Live Web Conferencing to Mediate Data Collection

When faced with the challenge of limited resources and participants that span state and institutional borders, researchers still have technological options available to them for data collection. This presentation summarizes how I conducted video interviews with these types of participants using the internet software Elluminate. This presentation highlights the possibilities for research using this methodology and the critical aspects for successful implementation

Sustainability Education and Organizational Change: A Critical Case Study of Barriers and Change Drivers at a Higher Education Institution

Integrating sustainability within institutions of higher education can have a tremendous impact on students, faculty, and the larger community. Sustainability efforts also experience many barriers to implementation within higher education contexts. A change management perspective can help characterize these barriers and ways to overcome them. In this critical case study, we use a process model to examine the kinds of barriers Kennesaw State University (KSU) has faced regarding implementation of academic sustainability and to evaluate change drivers that can advance sustainability during a time of leadership change. The process model evaluates barriers and change drivers according to published frameworks, and provides a way for higher education institutions to identify the most difficult barriers, easily surmountable barriers, and areas where change drivers can have the most impact. At KSU, the process model identified the self-determination of middle-tier change drivers as the most important way to advance sustainable development in higher education institutions (SD in HEI) until new leadership emerges. The process model is iterative and modifiable, because the specific frameworks used in the process model may vary depending upon the needs of each HEI and stage of progression toward SD