Assessing Understanding of Multiplication through Words, Pictures, and Numbers

The objective of this session is to engage mathematics teacher educators in a discussion of how to assess an understanding of the concept of multiplication as an operation and its relationships to other operations. The session will begin with a presentation of a previously published study assessing children’s understanding of multiplication as grouping and the relationship between multiplication and addition. The assessment asked a series of problems involving words, pictures, and numbers. The results of the study indicate that the types of problems asked were successful in providing evidence of children’s understanding of multiplication. The study also found that a group of third grade children had developed a better understanding of multiplication after just one multiplication unit from Investigations in Number, Data, and Space than a comparable group of fourth grade children had developed from an entire year of a traditional emphasis on memorizing multiplication facts. An interactive discussion of potential uses of this study and its assessment format in teacher education will follow the presentatio

Inclusive Design Studios: Rethinking the Instructor’s Role

The culture of the architectural design studio continues, in large part, to be based on centuries old traditions. Research on teaching, learning and bias suggest, however, that a rethinking of these traditions is long overdue if we aim to create inclusive learning environments and diversify our profession. Drawing on recent research on the cultivation of expertise, student motivation and stereotype threat, this essay considers how we might rethink design studio instruction. Studies on the development of expertise suggest a critical re-imagining of the instructor’s role in design studios. Research on student motivation suggests that many of the traditional practices of architectural education inevitably leave students unmotivated and need to be reconsidered. Finally, research on the ways in which stereotypes impact academic performance illuminate some of the roadblocks to diversifying our classrooms and profession. This essay shares evidence-based strategies to address these roadblocks and traditions to develop a more inclusive and effective design studio culture.&nbsp

Changing guards: time to move beyond Body Mass Index for population monitoring of excess adiposity

With the obesity epidemic, and the effects of aging populations, human phenotypes have changed over two generations, possibly more dramatically than in other species previously. As obesity is an important and growing hazard for population health, we recommend a systematic evaluation of the optimal measure(s) for population-level excess body fat. Ideal measure(s) for monitoring body composition and obesity should be simple, as accurate and sensitive as possible, and provide good categorisation of related health risks. Combinations of anthropometric markers or predictive equations may facilitate better use of anthropometric data than single measures to estimate body composition for populations. Here we provide new evidence that increasing proportions of aging populations are at high health-risk according to waist circumference, but not body mass index (BMI), so continued use of BMI as the principal population-level measure substantially underestimates the health-burden from excess adiposity

Paper 4: Assessing Understanding of Multiplication through Words, Pictures, and Numbers

The objective of this session is to engage mathematics teacher educators in a discussion of how to assess an understanding of the concept of multiplication as an operation and its relationships to other operations. The session will begin with a presentation of a previously published study assessing children’s understanding of multiplication as grouping and the relationship between multiplication and addition. The assessment asked a series of problems involving words, pictures, and numbers. The results of the study indicate that the types of problems asked were successful in providing evidence of children’s understanding of multiplication. The study also found that a group of third grade children had developed a better understanding of multiplication after just one multiplication unit from Investigations in Number, Data, and Space than a comparable group of fourth grade children had developed from an entire year of a traditional emphasis on memorizing multiplication facts. An interactive discussion of potential uses of this study and its assessment format in teacher education will follow the presentation

Action And Motivation: Measuring Perception Or Strategies?

It has been suggested that when judging the distance to a desirable object, motivated distortions of perceived distance occur, and that these distortions can be measured by actions, such as throwing a beanbag. The results of two new experiments suggest that reported variations in beanbag performance may instead depend on instructional effects, such as ones that emphasize proximity rather than accuracy. When the goal was to be closest to the target, underthrowing was observed, whether the target was intrinsically valuable or not. When the goal was to hit the target, however, throwing performance was unbiased

Introduction: Inclusive Design Pedagogies and Practices

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Bioreactor scalability: laboratory-scale bioreactor design influences performance, ecology, and community physiology in expanded granular sludge bed bioreactors

Studies investigating the feasibility of new, or improved, biotechnologies, such as wastewater treatment digesters, inevitably start with laboratory-scale trials. However, it is rarely determined whether laboratory-scale results reflect full-scale performance or microbial ecology. The Expanded Granular Sludge Bed (EGSB) bioreactor, which is a high-rate anaerobic digester configuration, was used as a model to address that knowledge gap in this study. Two laboratory-scale idealizations of the EGSB—a one-dimensional and a three- dimensional scale-down of a full-scale design—were built and operated in triplicate under near-identical conditions to a full-scale EGSB. The laboratory-scale bioreactors were seeded using biomass obtained from the full-scale bioreactor, and, spent water from the distillation of whisky from maize was applied as substrate at both scales. Over 70 days, bioreactor performance, microbial ecology, and microbial community physiology were monitored at various depths in the sludge-beds using 16S rRNA gene sequencing (V4 region), specific methanogenic activity (SMA) assays, and a range of physical and chemical monitoring methods. SMA assays indicated dominance of the hydrogenotrophic pathway at full-scale whilst a more balanced activity profile developed during the laboratory-scale trials. At each scale, Methanobacterium was the dominant methanogenic genus present. Bioreactor performance overall was better at laboratory-scale than full-scale. We observed that bioreactor design at laboratory-scale significantly influenced spatial distribution of microbial community physiology and taxonomy in the bioreactor sludge-bed, with 1-D bioreactor types promoting stratification of each. In the 1-D laboratory bioreactors, increased abundance of Firmicutes was associated with both granule position in the sludge bed and increased activity against acetate and ethanol as substrates. We further observed that stratification in the sludge-bed in 1-D laboratory-scale bioreactors was associated with increased richness in the underlying microbial community at species (OTU) level and improved overall performance

Imaging and Recording Subventricular Zone Progenitor Cells in Live Tissue of Postnatal Mice

The subventricular zone (SVZ) is one of two regions where neurogenesis persists in the postnatal brain. The SVZ, located along the lateral ventricle, is the largest neurogenic zone in the brain that contains multiple cell populations including astrocyte-like cells and neuroblasts. Neuroblasts migrate in chains to the olfactory bulb where they differentiate into interneurons. Here, we discuss the experimental approaches to record the electrophysiology of these cells and image their migration and calcium activity in acute slices. Although these techniques were in place for studying glial cells and neurons in mature networks, the SVZ raises new challenges due to the unique properties of SVZ cells, the cellular diversity, and the architecture of the region. We emphasize different methods, such as the use of transgenic mice and in vivo electroporation that permit identification of the different SVZ cell populations for patch clamp recording or imaging. Electroporation also permits genetic labeling of cells using fluorescent reporter mice and modification of the system using either RNA interference technology or floxed mice. In this review, we aim to provide conceptual and technical details of the approaches to perform electrophysiological and imaging studies of SVZ cells