Seeing Mathematics Through Different Eyes: An Equitable Approach to Use with Prospective Teachers

Teacher educators need to prepare prospective teachers by encouraging them to critically examine their current beliefs about the teaching and learning of mathematics while also providing opportunities for prospective teachers to develop an equity-centered orientation. Attending to these practices in teacher preparation programs may help prospective teachers observe actions that occur in classrooms and determine effective strategies that provide the opportunity to enhance all students’ access to high-quality mathematics instruction. As mathematics teacher educators, we must recognize what prospective teachers attend to as they direct their attention to various classroom events and how they relate the events to broader principles of teaching and learning. In this chapter, we investigate what prospective teachers attend to in a classroom vignette of a student who is above grade level in mathematics and exhibits disruptive behavior during instruction. Keeping everything constant in the vignette except the student’s race and sex, we examined prospective teachers’ responses when the student was an African American male, White male, African American female, and White female. By attending specifically to race and sex, we explored whether prospective teachers demonstrated (1) an equity-centered orientation toward mathematics instruction or (2) deficit views of students based on race, sex, or the intersection of the two. Using a constant comparative method, the data were coded and analyzed using the equity noticing framework. The results indicate that prospective teachers are beginning to attend to cultural influences and their responses reveal differences not only between races but also between males and female

What, how, who: Developing Mathematical Discourse

A collaborative classroom, an open-ended problem, and a what-how-who structure can build students’ reasoning skills and allow teachers to recognize all classroom contributions. With an increased focus on using social discourse to enhance students’ mathematical thinking and reasoning (NCTM 2014, Staples and King 2017), teachers are looking for discussion strategies that encourage middlelevel students to make sense of mathematical concepts. However, structuring these valuable discussions is complex. “Mathematical discourse should build on and honor student thinking, and provide students with opportunities to share ideas, clarify understandings, develop convincing arguments, and advance the mathematical learning of the entire class” (Smith, Steele, and Raith 2017, p. 123). In other words, teachers must carefully consider what tasks provide meaningful opportunities to explore ideas, generate hypotheses, and promote questions within a collaborative environment. Then, teachers need to consider how to structure the activity to encourage discussions and incorporate responses that contribute to understanding specific mathematical objectives. Additionally, teachers must select who will speak to “advance the mathematical storyline of the lesson” (NCTM 2014, p. 30). By intentionally focusing on these elements in mathematics instruction, middle-grades teachers can develop a classroom culture that not only emphasizes sense making but also values the intellectual capacity that students bring to the classroom (Gutiérrez 2013; Lemons-Smith 2008). In this article, we describe how teachers can promote meaningful discussions using the what-how-who structure while giving students opportunities to make sense of mathematical ideas within a social context

Maths Games: A Universal Design approach to mathematical reasoning

By incorporating math games into the classroom, through the principles of Universal Design teachers are able to address mathematical content, reasoning and problem solving, as well as tailoring games to address students\u27 individual needs

Analysis of the Effects of Sea Disposal on a One-Ton Container

Excess and obsolete stocks of chemical warfare material (CWM) were sea disposed by the United States between 1919 and 1970. One-ton containers were used for bulk storage of CWM and were the largest containers sea disposed. Disposal depths ranged from 300 to 17,000 feet. Based on a Type D container assembly drawing, three independent analyses (one corrosion and two structural) were performed on the containers to address the corrosion resistance from prolonged exposure to sea water and the structural response during the descent. Corrosion predictions were made using information about corrosion rates and the disposal environment. The structural analyses employed two different finite element codes and were used to predict the buckling and material response of the container during sea disposal. The results of these investigations are summarized below. Detailed reports on each study are contained in the appendices

Sliding into an equitable lesson

A kindergarten teacher uses Gutierrez\u27s four dimensions of equity to design and facilitate geometry instruction. Equitable instruction is reflected in how students are positioned in the classroom and how their identities evolve through purposeful interactions that value and recognize the intellectual capacity of each student (Gutiérrez 2013; Lemons-Smith 2008). These integral interactions occur when teachers and students exchange problem-solving strategies, discuss relations among various mathematical representations, and listen to the viewpoints of others (NCTM 2000; 2014)

Sustainability of Reforms, Both School and University Based

Further Reform in Teacher Preparation: School and University Based Abstract This study grew out of a five-year grant whose purpose was reform of teacher preparation programs. A Professional Development School (PDS) model was designed to support this work thus a university partnered with five elementary schools, a middle school, and a high school. At a transitional phase near the end of the grant, this study was designed to discover what teachers involved in the PDS thought should be kept in the programs and activities, what should be changed, and what should be added. Anonymous data was then compiled and analyzed to uncover categories and themes. Three main categories emerged in two of prompts (Keep and Add), which were program-based - professional development and activities. The prompt, Change, had only one category, which was also program-based. As the partnership moves forward this information has been vitally important to PDS sustainability

Progress on Gust Load Alleviation Wind Tunnel Experiment and Aeroservoelastic Model Validation for a Flexible Wing with Variable Camber Continuous Trailing Edge Flap System

This paper discusses a wind tunnel experiment of active gust load alleviation of a flexible wing which took place at University of Washington (UW) in 2019. The experiment performed under a NASA SBIR contract with Scientific Systems Company, Inc (SSCI). The objective of the experiment is to demonstrate active controls of the Variable Camber Continuous Trailing Edge Flap (VCCTEF) system for gust load alleviation and real-time drag optimization. The wind tunnel model is a 8.2% sub-scale Common Research Model (CRM) wing. The wing structure is designed to provide a substantial degree of flexibility to represent that of a modern high-aspect ratio wing. Eight active control surfaces are employed in the VCCTEF. A new gust generator system was designed and installed by UW under a sub-contract with SSCI. The first test entry started in July 2019 and ended in September 2019. During this test entry, many significant issues were found with the hardware and software. The significant issues with the servos prevented the test objective from being completed. A follow-up second test entry in 2020 is being planned. The wing system is being repaired by SSCI. This paper reports on the progress of this experimental effort and the aeroservoelastic (ASE) model validation which was conducted during the test entry

Two-level system with a thermally fluctuating transfer matrix element: Application to the problem of DNA charge transfer

Charge transfer along the base-pair stack in DNA is modeled in terms of thermally-assisted tunneling between adjacent base pairs. Central to our approach is the notion that tunneling between fluctuating pairs is rate-limited by the requirement of their optimal alignment. We focus on this aspect of the process by modeling two adjacent base pairs in terms of a classical damped oscillator subject to thermal fluctuations as described by a Fokker-Planck equation. We find that the process is characterized by two time scales, a result that is in accord with experimental findings.Comment: original file is revtex4, 10 pages, three eps figure