Examining preservice secondary mathematics teachers' ability to reason proportionally prior to and upon completion of a practice-based mathematics methods course focused on proportional reasoning

The purpose of this study was to examine preservice secondary mathematics teachers' understandings about proportional reasoning prior to and upon completion of a practice-based methods course focused on proportional reasoning, their opportunities to learn the intended content, and their ability to apply what was learned in a new setting. Ten teachers completed a pre/posttest and pre/post interview that was designed to explore their ability to reason proportionally. All classes were videotaped so as to examine teachers' opportunities to learn to reason proportionally and to utilize their understandings in a new setting. In addition, six teachers who were not enrolled in the course served as a contrast group and completed the pre/post instruments.The analysis of the data suggests that teachers learned important aspects of proportional reasoning from the course. Prior to the course, there were no differences between the understandings of the teachers enrolled in the course and those who were not. However, by the end of the course, teachers enrolled in the course utilized a broader range of solution strategies, significantly improved their capacity to distinguish between proportional and nonproportional relationships, and significantly enhanced their understanding of the nature of proportional relationships, while those in the contrast group did not.In addition, the analysis of the class sessions made salient that all of the mathematics that teachers learned during the course was made public during multiple classes and by multiple teachers. The analysis also revealed that even teachers who remained mostly silent during class discussions still learned the same mathematics that more the vocal teachers learned.The results of the analysis of class sessions from a subsequent course on algebra revealed that the teachers who participated in the proportional reasoning course drew upon their enhanced understandings of proportional relationships when appropriate. This result suggests that teachers had not merely memorized discrete facts about proportional relationships, but had developed flexible understandings that allowed them to access their knowledge as they explored different mathematical ideas. Finally, the results of the study suggest that practice-based teacher education courses can be fruitful sites for helping teachers develop mathematical knowledge needed for teaching

Maker Math: Exploring Mathematics through Digitally Fabricated Tools with K–12 In-Service Teachers

This paper reports on nine elementary, middle, and high school in-service teachers who participated in a series of workshops aimed at exploring the wonder, joy, and beauty of mathematics through the creation and application of digitally fabricated tools (i.e., laser-cut and 3D printed). Using the Technological Pedagogical and Content Knowledge (TPACK) framework to investigate technological, pedagogical, contextual, and content knowledge, researchers applied qualitative methods to uncover the affordances and constraints of teaching and learning math concepts with digitally fabricated tools and examined how the workshops supported broadening participation in mathematics by focusing on the connections between mathematical inquiry, nature, and the arts. Affordances include opportunities for hands-on learning, visual support at the secondary level, and real-world connections that go beyond the state standards. Barriers include purchasing a laser-cutter, ventilation and noise issues, time constraints, misalignment with school and district priorities, and a lack of administrative support. All participants indicated that they were interested in additional workshops focused on designing their own digitally fabricated mathematics tools that better align with their grade level(s) and standards

Vomocytosis of live pathogens from macrophages is regulated by the atypical MAP kinase ERK5

Vomocytosis, or non-lytic extrusion, is a poorly understood process through which macrophages release live pathogens that they have failed to kill back into the extracellular environment. Vomocytosis is conserved across vertebrates and occurs with a diverse range of pathogens, but to date the host signaling events that underpin expulsion remain entirely unknown. Here we use a targeted inhibitor screen to identify the MAP-kinase ERK5 as a critical suppressor of vomocytosis. Pharmacological inhibition or genetic manipulation of ERK5 activity significantly raises vomocytosis rates in human macrophages whilst stimulation of the ERK5 signaling pathway inhibits vomocytosis. Lastly, using a zebrafish model of cryptococcal disease, we show that reducing ERK5 activity in vivo stimulates vomocytosis and results in reduced dissemination of infection. ERK5 therefore represents the first host regulator of vomocytosis to be identified and a potential target for the future development of vomocytosis-modulating therapies

A multimodal imaging approach enables in vivo assessment of antifungal treatment in a mouse model of invasive pulmonary aspergillosis

Aspergillus fumigatus causes life-threatening lung infections in immunocompromised patients. Mouse models are extensively used in research to assess the in vivo efficacy of antifungals. In recent years, there has been an increasing interest in the use of non-invasive imaging techniques to evaluate experimental infections. However, single imaging modalities have limitations concerning the type of information they can provide. In this study, magnetic resonance imaging and bioluminescence imaging were combined to obtain longitudinal information on the extent of developing lesions and fungal load in a leucopenic mouse model of IPA. This multimodal imaging approach was used to assess changes occurring within lungs of infected mice receiving voriconazole treatment starting at different time points after infection. Results showed that IPA development depends on the inoculum size used to infect animals and that disease can be successfully prevented or treated by initiating intervention during early stages of infection. Furthermore, we demonstrated that reduction of the fungal load is not necessarily associated with the disappearance of lesions on anatomical lung images, especially when antifungal treatment coincides with immune recovery. In conclusion, multimodal imaging allows to investigate different aspects of disease progression or recovery by providing complementary information on dynamic processes, which are highly useful for assessing the efficacy of (novel) therapeutic compounds in a time- and labor-efficient manner

The Role of Clinical Information Technology in Depression Care Management

We examine the literature on the growing application of clinical information technology in managing depression care and highlight lessons learned from Robert Wood Johnson Foundation’s national program “Depression in Primary Care-Incentives Demonstrations.” Several program sites are implementing depression care registries. Key issues discussed about implementing registries include using a simple yet functional format, designing registries to track multiple conditions versus depression alone (i.e., patient-centric versus disease-centric registries) and avoiding violations of patient privacy with the advent of more advanced information technologies (e.g., web-based formats). Finally, we discuss some implications of clinical information technology for healthcare practices and policy makers.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44097/1/10488_2005_Article_4236.pd

Reflective Analysis as a Tool for Task Redesign: The Case of Prospective Elementary Teachers Solving and Posing Fraction Comparison Problems

Mathematical task design has been a central focus of the mathematics education research community over the last few years. In this study, six university teacher educators from six different US institutions formed a community of practice to explore key aspects of task design (planning, implementing, reflecting, and modifying) in the context of comparing fractions using reasoning and sense-making. By presenting results of their implementation of two tasks with 63 prospective elementary teachers across three institutions and their reflective analysis of the implementation, the authors highlight the importance of collecting and analyzing data and reflecting on this analysis to inform the redesign of tasks. The authors also found that considering different types of tasks (problem solving vs. problem posing) helps illuminate different aspects of prospective elementary teachers\u27 understanding, which can inform task redesign. Finally the authors contribute to the knowledge base on reasoning strategies for comparing fractions and prospective elementary teachers’ knowledge of these strategies

Greater Number of Larger Pieces: A Strategy to Promote Prospective Teachers’ Fraction Number Sense Development

Prospective teachers (PTs) need opportunities to develop fraction number sense, yet little research has explicated how this development occurs. Our research team collaboratively designed a task targeted at helping PTs develop fraction number sense through an exploration of fraction comparison strategies. This paper focuses on developing one particular strategy, which we call Greater Number of Larger Pieces (GLP). We argue that understanding this strategy has the potential to support PTs’ number sense, particularly in regards to the measure interpretation of fractions. Analysis of data from two iterations of this task (implemented by five mathematics teacher educators at five US institutions with 124 PTs) showed an improvement in the task’s ability to naturally elicit the GLP strategy from PTs. We share our task, results from each iteration, and discuss modifications that we believe led to increased usage of the GLP strategy

Algebra: A Challenge at the Crossroads of Policy and Practice

The authors review what is known about early and universal algebra, including who is getting access to algebra and student outcomes associated with algebra course taking in general and specifically with universal algebra policies. The findings indicate that increasing numbers of students, some of whom are underprepared, are taking algebra earlier. At the same time, other students with requisite skills are not given access to algebra. Although studies using nationally representative data indicate strong positive outcomes for students who take algebra early, studies conducted only in contexts where all students are mandated to take algebra in eighth or ninth grade provide mixed evidence of positive outcomes, with increased achievement when policies include strong supports for struggling students. The authors conclude with a call for studies that examine the relationship among algebra policies, instruction, and student outcomes to understand the mechanisms by which policies can lead to success for all students

Characterization and longitudinal monitoring of brain lesions in a mouse model of cerebral cryptococcosis by using in vivo IVM, MRI and MRS

status: publishe