Cultivating a Space for Critical Mathematical Inquiry through Knowledge-Eliciting Mathematical Activity

Learning mathematics becomes more effective when teachers leverage their students\u27 mathematical and everyday knowledge as resources for instruction. Thus, tasks that reveal these forms of knowledge would be especially useful to teachers. Unfortunately, such tasks are hard to find and even harder to create. Consequently, we developed a collection of mathematical tasks that we hoped would elicit “children’s multiple mathematical knowledge bases (i.e., the understandings and experiences that have the potential to shape and support children’s mathematics learning—including children’s mathematical thinking, and children’s cultural, home, and community-based knowledge)” (Turner et al., 2012, p. 68). These tasks proved to be productive and took on two forms, one of which called on students to provide mathematical and real-world justifications for decisions, and one of which used a community issue as a “contextual scaffold” for linking students’ community- and school-based knowledge

“I Got You”: Centering Identities and Humanness in Collaborations Between Mathematics Educators and Mathematicians

Existing literature widely reports on the value of collaborations between mathematicians and mathematics educators, and also how complex those collaborations can be. In this paper, we report on four collaborations that sought to address what mathematics is and who gets to do it. Drawing on the literature and from the careful and intentional work of the collaborators, we offer a framework to capture the richness of those collaborations – one that acknowledges the importance of acknowledging and welcoming the extensive personal and professional experience of each person involved in the collaboration – and a look at how collaborations built with that intentionality and acknowledgment can be impactful for students and institutions and be personally and professionally rewarding for the collaborators

Incidence and Clinical Significance of Inducible Atrial Tachycardia in Patients with Atrioventricular Nodal Reentrant Tachycardia

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72373/1/j.1540-8167.2001.00507.x.pd

Morphological and Functional Changes in the Retina after Chronic Oxygen-Induced Retinopathy

The mouse model of oxygen-induced retinopathy (OIR) has been widely used for studies of retinopathy of prematurity (ROP). This disorder, characterized by abnormal vascularization of the retina, tends to occur in low birth weight neonates after exposure to high supplemental oxygen. Currently, the incidence of ROP is increasing because of increased survival of these infants due to medical progress. However, little is known about changes in the chronic phase after ROP. Therefore, in this study, we examined morphological and functional changes in the retina using a chronic OIR model. Both the a- and b-waves in the OIR model recovered in a time-dependent manner at 4 weeks (w), 6 w, and 8 w, but the oscillatory potential (OP) amplitudes remained depressed following a return to normoxic conditions. Furthermore, decrease in the thicknesses of the inner plexiform layer (IPL) and inner nuclear layer (INL) at postnatal day (P) 17, 4 w, and 8 w and hyperpermeability of blood vessels were observed in conjunction with the decrease in the expression of claudin-5 and occludin at 8 w. The chronic OIR model revealed the following: (1) a decrease in OP amplitudes, (2) morphological abnormalities in the retinal cells (limited to the IPL and INL) and blood vessels, and (3) an increase in retinal vascular permeability via the impairment of the tight junction proteins. These findings suggest that the experimental animal model used in this study is suitable for elucidating the pathogenesis of ROP and may lead to the development of potential therapeutic agents for ROP treatment

Reconceptualizing Pedagogical and Curricular Knowledge Development through Making

While making is typically tethered to narratives of entrepreneurship and business, it can provide a gateway to meaningful interaction and deepened understanding of both content and pedagogy. In this article we provide descriptions of two courses—one each at the pre-service and in-service levels—that engage teachers in making and design practices that we hypothesized would inform their pedagogical and curricular thinking. With a focus on the design of new tools to support teaching and learning through the use of human-centered design practices and digital fabrication technologies, these courses have teachers exploring at the intersection of content, pedagogy, and making. Specifically, they inquire about theories of how people learn in interaction with physical tools and how these tools shape and guide content-specific thinking and learning. Several of their final projects are presented along with pedagogical and curricular inferences we made about them that suggest the promise of a making-oriented experience within teacher preparation and professional development

Making Sense of Qualitative Geometry: The Case of Amanda

This article presents a case study of a seven-year-old girl named Amanda who participated in an eighteen-week teaching experiment I conducted in order to model the development of her intuitive and informal topological ideas. I designed a new dynamic geometry environment that I used in each of the episodes of the teaching experiment to elicit these conceptions and further support their development. As the study progressed, I found that Amanda developed significant and authentic forms of geometric reasoning. It is these newly identified forms of reasoning, which I refer to as qualitative geometry, that have implications for the teaching and learning of geometry and for research into students\u27 mathematical reasoning