Analyzing the Cognitive Demand of Enacted Examples in Precalculus: A Comparative Case Study of Graduate Student Instructors

The cognitive demand of mathematical tasks is an important aspect of analyzing the impact of instruction on student learning. The purpose of this study was to examine the instructional examples enacted by graduate student precalculus instructors in order to answer the following questions: What is the cognitive demand of the enacted examples? What does a high cognitive demand example look like when an instructor uses direct instruction? And how are examples drawn from the written curriculum enacted in different ways? Using both random and purposeful sampling of precalculus lessons, I conducted classroom observations as well as pre- and post-observation interviews with the instructors. A modified version of the Task Analysis Guide (Smith & Stein, 1998) was then used to categorize the cognitive demand of the instructional examples. As a result, I found that 25 out of the 93 examples (27%) I observed were enacted at a high level of cognitive demand. I also present vignettes that illustrate how three different instructors chose to enact the same example type at differing levels of cognitive demand

High Cognitive Demand Examples in Precalculus: Examining the Work and Knowledge Entailed in Enactment

Historically, pass rates in undergraduate precalculus courses have been dismally low and the teaching practices and knowledge of university instructors have been understudied. To help improve teaching effectiveness and student outcomes in undergraduate precalculus courses, I have studied the cognitive demand of enacted examples. The purpose of this dissertation is to examine the pedagogical work and mathematical knowledge entailed in the enactment of high cognitive demand examples in a three-part study. To answer my research questions, I conducted classroom observations as well as pre- and post-observation interviews with seven graduate student instructors at a large public R1 university in the Midwest and used grounded theory to analyze my data. In the first component of the dissertation, I examine what high cognitive demand examples look like and identify three roles that instructors take on when enacting high cognitive demand examples: modeling, facilitating, and monitoring. In the second component, I decomposed the work of enacting high cognitive demand examples into five teaching tasks: attending to the mathematical point, making connections, providing clear verbal explanations, articulating cognitive processes, and supporting student understanding. Finally, in the third component, I examined the mathematical knowledge for teaching entailed in enacting examples and found that there are five domains of knowledge that support the maintenance of cognitive demand: knowledge of connections, representations, unpacking, students, and sequencing. These findings suggest ways in which we can help novice instructors enact high cognitive demand examples by focusing on the work and knowledge entailed in maintaining the cognitive demand. Advisor: Yvonne La

Online Education: Transferring Personal Experiences to Professional Development

In this paper, we discuss how one candidate’s experience as she participated an online mathematics specialist program bolstered her confidence and ability to provide online professional development for her teachers. We include personal accounts by the mathematics specialist program instructors, the mathematics specialist candidate, and an elementary school teacher to illustrate how the experience of completing online graduate courses led to the candidate providing online learning opportunities for teachers. In particular, we highlight the importance of building relationships and using high-quality mathematical tasks in both the online preparation program and the online professional development. This case study provides evidence that exposure to online learning environments as a learner can help lower the barrier of entry for planning and providing online learning experiences as a teacher

Characterizing Mathematics Graduate Student Teaching Assistants’ Opportunities to Learn from Teaching

Exemplary models to inform novice instruction and the development of graduate teaching assistants (TAs) exist. What is missing from the literature is the process of how graduate students in model professional development programs make sense of and enact the experiences offered. A first step to understanding TAs’ learning to teach is to characterize how and whether they link observations of student work to hypotheses about student thinking and then connect those hypotheses to future teaching actions. A reason to be interested in these connections is that their strength and coherence determine how well TAs can learn from experiences. We found TAs can connect observations and future teaching, but that the connections vary in quality. Our analysis suggests future revisions to TA development programs, which we discuss in the conclusion

MicroRNA profiling reveals marker of motor neuron disease in ALS models

Amyotrophic lateral sclerosis (ALS) is a progressive neurodegenerative disorder marked by the loss of motor neurons (MNs) in the brain and spinal cord, leading to fatally debilitating weakness. Because this disease predominantly affects MNs, we aimed to characterize the distinct expression profile of that cell type to elucidate underlying disease mechanisms and to identify novel targets that inform on MN health during ALS disease time course. microRNAs (miRNAs) are short, noncoding RNAs that can shape the expression profile of a cell and thus often exhibit cell-type-enriched expression. To determine MN-enriched miRNA expression, we used Cre recombinase-dependent miRNA tagging and affinity purification in mice. By defining thein vivomiRNA expression of MNs, all neurons, astrocytes, and microglia, we then focused on MN-enriched miRNAs via a comparative analysis and found that they may functionally distinguish MNs postnatally from other spinal neurons. Characterizing the levels of the MN-enriched miRNAs in CSF harvested from ALS models of MN disease demonstrated that one miRNA (miR-218) tracked with MN loss and was responsive to an ALS therapy in rodent models. Therefore, we have used cellular expression profiling tools to define the distinct miRNA expression of MNs, which is likely to enrich future studies of MN disease. This approach enabled the development of a novel, drug-responsive marker of MN disease in ALS rodents.SIGNIFICANCE STATEMENTAmyotrophic lateral sclerosis (ALS) is a neurodegenerative disease in which motor neurons (MNs) in the brain and spinal cord are selectively lost. To develop tools to aid in our understanding of the distinct expression profiles of MNs and, ultimately, to monitor MN disease progression, we identified small regulatory microRNAs (miRNAs) that were highly enriched or exclusive in MNs. The signal for one of these MN-enriched miRNAs is detectable in spinal tap biofluid from an ALS rat model, where its levels change as disease progresses, suggesting that it may be a clinically useful marker of disease status. Furthermore, rats treated with ALS therapy have restored expression of this MN RNA marker, making it an MN-specific and drug-responsive marker for ALS rodents.</jats:p

Single-nucleus multi-omics of human stem cell-derived islets identifies deficiencies in lineage specification

Insulin-producing β cells created from human pluripotent stem cells have potential as a therapy for insulin-dependent diabetes, but human pluripotent stem cell-derived islets (SC-islets) still differ from their in vivo counterparts. To better understand the state of cell types within SC-islets and identify lineage specification deficiencies, we used single-nucleus multi-omic sequencing to analyse chromatin accessibility and transcriptional profiles of SC-islets and primary human islets. Here we provide an analysis that enabled the derivation of gene lists and activity for identifying each SC-islet cell type compared with primary islets. Within SC-islets, we found that the difference between β cells and awry enterochromaffin-like cells is a gradient of cell states rather than a stark difference in identity. Furthermore, transplantation of SC-islets in vivo improved cellular identities overtime, while long-term in vitro culture did not. Collectively, our results highlight the importance of chromatin and transcriptional landscapes during islet cell specification and maturation

Early JWST imaging reveals strong optical and NIR color gradients in galaxies at z∼2z\sim2 driven mostly by dust

Recent studies have shown that galaxies at cosmic noon are redder in the center and bluer in the outskirts, mirroring results in the local universe. These color gradients could be caused by either gradients in the stellar age or dust opacity; however, distinguishing between these two causes is impossible with rest-frame optical photometry alone. Here we investigate the underlying causes of the gradients from spatially-resolved rest-frame $U-V$ vs. $V-J$ color-color diagrams, measured from early observations with the James Webb Space Telescope. We use $1\, \mu m - 4\, \mu m$ NIRCam photometry from the CEERS survey of a sample of 54 galaxies with $M_* / M_\odot>10$ at redshifts $1.7<z<2.3$ selected from the 3D-HST catalog. We model the light profiles in the F115W, F200W and F356W NIRCam bands using \texttt{imcascade}, a Bayesian implementation of the Multi-Gaussian expansion (MGE) technique which flexibly represents galaxy profiles using a series of Gaussians. We construct resolved rest-frame $U-V$ and $V-J$ color profiles. The majority of star-forming galaxies have negative gradients (i.e. redder in the center, bluer in the outskirts) in both $U-V$ and $V-J$ colors consistent with radially decreasing dust attenuation. A smaller population (roughly 15\%) of star-forming galaxies have positive $U-V$ but negative $V-J$ gradients implying centrally concentrated star-formation. For quiescent galaxies we find a diversity of UVJ color profiles, with roughly one-third showing star-formation in their center. This study showcases the potential of JWST to study the resolved stellar populations of galaxies at cosmic noon.Comment: Updated to match published version, new Figure 5 and some text change

Rest-frame near-infrared sizes of galaxies at cosmic noon: objects in JWST's mirror are smaller than they appeared

Galaxy sizes and their evolution over cosmic time have been studied for decades and serve as key tests of galaxy formation models. However, at $z\gtrsim1$ these studies have been limited by a lack of deep, high-resolution rest-frame infrared imaging that accurately traces galaxy stellar mass distributions. Here, we leverage the new capabilities of the James Webb Space Telescope to measure the 4.4$\mu$m sizes of ${\sim}1000$ galaxies with $\log{\rm{M}_*/\rm{M}_\odot}\ge9$ and $1.0\le z \le 2.5$ from public CEERS imaging in the EGS deep field. We compare the sizes of galaxies measured from NIRCam imaging at 4.4$\mu$m ($\lambda_{\mathrm{rest}}\sim1.6\mu$m) with sizes measured at $1.5\mu$m ($\lambda_{\mathrm{rest}}\sim5500$A). We find that, on average, galaxy half-light radii are $\sim8$% smaller at 4.4$\mu$m than 1.5$\mu$m in this sample. This size difference is markedly stronger at higher stellar masses and redder rest-frame $V-J$ colors: galaxies with ${\rm M}_* \sim 10^{11}\,{\rm M}_\odot$ have 4.4$\mu$m sizes that are $\sim 25$% smaller than their 1.5$\mu$m sizes. Our results indicate that galaxy mass profiles are significantly more compact than their rest-frame optical light profiles at cosmic noon, and demonstrate that spatial variations in age and attenuation are important, particularly for massive galaxies. The trend that we find here impacts our understanding of the size growth and evolution of galaxies, and suggests that previous studies based on rest-frame optical light may not have captured the mass-weighted structural evolution of galaxies. This paper represents a first step towards a new understanding of the morphologies of early massive galaxies enabled by JWST's infrared window into the distant universe.Comment: Accepted to ApJL. 10 pages, 4 figures, 1 table with full size catalog in F150W and F444