A Case for Proof Making for Prospective Middle School Teachers

In this article, we discuss how we, as mathematics teacher educators, might help our prospective middle school teachers develop a disposition toward mathematics that involves making sound arguments and, more generally, making proofs about mathematical ideas. First, we illustrate what we mean by making sound mathematical proofs. We then use this definition to characterize what ninety-two prospective middle school teachers consider to be proof making, based on a survey that we administered in their first mathematics course. Following our findings, we discuss how we, as teacher educators, might realign our instruction to provide opportunities for prospective teachers to develop new understandings about proof making

Representation of others’ synchronous and asynchronous sentences interferes with sentence production

In dialogue, people represent each other's utterances in order to take turns and communicate successfully. In previous work Gambi, C., Van de Cavey, J., \& Pickering, M. J. (2015). Interference in joint picture naming. Journal of Experimental Psychology: Learning, Memory, and Cognition, 41(1), 1-21., speakers who were naming single pictures or picture pairs represented whether another speaker was engaged in the same task (versus a different or no task) concurrently, but did not represent in detail the content of the other speaker's utterance. Here, we investigate co-representation of whole sentences. In three experiments, pairs of speakers imagined each other producing active or passive descriptions of transitive events. Speakers took longer to begin speaking when they believed their partner was also preparing to speak, compared to when they did not. Interference occurred when speakers believed their partners were preparing to speak at the same time as them (synchronous production and co-representation; Experiment 1), and also when speakers believed that their partner would speak only after them (asynchronous production and co-representation; Experiments 2a and 2b). However, interference was generally no greater when speakers believed their partner was preparing a different compared to a similar utterance, providing no consistent evidence that speakers represented what their partners were preparing to say. Taken together, these findings indicate that speakers can represent another's intention to speak even as they are themselves preparing to speak, but that such representation tends to lack detail

Contraction of cross-linked actomyosin bundles

Cross-linked actomyosin bundles retract when severed in vivo by laser ablation, or when isolated from the cell and micromanipulated in vitro in the presence of ATP. We identify the time scale for contraction as a viscoelastic time tau, where the viscosity is due to (internal) protein friction. We obtain an estimate of the order of magnitude of the contraction time tau ~ 10-100 s, consistent with available experimental data for circumferential microfilament bundles and stress fibers. Our results are supported by an exactly solvable, hydrodynamic model of a retracting bundle as a cylinder of isotropic, active matter, from which the order of magnitude of the active stress is estimated.Comment: To be published in Physical Biolog

Adherens junctions remain dynamic

One of the four principal categories of cell-cell junctions that hold together and shape distinct tissues and organs in vertebrates, adherens junctions (AJs) form cell-cell contacts that connect transmembrane proteins with cytoskeletal actin filaments to provide architectural strength, aid in morphogenesis, and help to maintain proper tissue homeostasis. The classical organization of AJs, consisting of transmembrane cadherins and cytoplasmically attached β-catenins and α-catenins assembled together into a multiprotein complex, was once thought obligatory to craft a robust and stable connection to actin-based cytoskeletal elements, but this architecture has since been challenged and questioned to exist. In a stimulating paper published in a recent issue of BMC Biology, Millán et al. provide convincing evidence that in confluent vascular endothelial cells a novel dynamic vascular endothelial (VE)-cadherin-based AJ type exists that interacts with and physically connects prominent bundles of tension-mediating actin filaments, stress fibers, between neighboring cells. Stress fibers were known previously to link to integrin-based focal adhesion complexes but not to cell-cell adhesion mediating AJs. These new findings, together with previous results support the concept that different AJ subtypes, sharing the same transmembrane cadherin types, can assemble in various configurations to either increase barrier function and promote physical cell-cell adhesion, or to lessen cell-cell adhesion and promote cell separation and migration

Interference in Joint Picture Naming

In 4 experiments we showed that picture naming latencies are affected by beliefs about the task concurrently performed by another speaker. Participants took longer to name pictures when they believed that their partner concurrently named pictures than when they believed their partner was silent (Experiments 1 and 4) or concurrently categorized the pictures as being from the same or from different semantic categories (Experiment 2). However, picture naming latencies were not affected by beliefs about what one's partner said, as it did not matter whether participants believed their partner produced the same utterance, or an utterance that differed by ordering (Experiments 1 and 2) or lexical content (Experiments 3 and 4). These findings are consistent with the proposal that speakers represent whether another speaker is preparing to speak but not what they are preparing to say

Effectiveness of the International Phytosanitary Standard ISPM No. 15 on Reducing Wood Borer Infestation Rates in Wood Packaging Material Entering the United States

Numerous bark- and wood-infesting insects have been introduced to new countries by international trade where some have caused severe environmental and economic damage. Wood packaging material (WPM), such as pallets, is one of the high risk pathways for the introduction of wood pests. International recognition of this risk resulted in adoption of International Standards for Phytosanitary Measures No. 15 (ISPM15) in 2002, which provides treatment standards for WPM used in international trade. ISPM15 was originally developed by members of the International Plant Protection Convention to “practically eliminate” the risk of international transport of most bark and wood pests via WPM. The United States (US) implemented ISPM15 in three phases during 2005–2006. We compared pest interception rates of WPM inspected at US ports before and after US implementation of ISPM15 using the US Department of Agriculture AQIM (Agriculture Quarantine Inspection Monitoring) database. Analyses of records from 2003–2009 indicated that WPM infestation rates declined 36–52% following ISPM15 implementation, with results varying in statistical significance depending on the selected starting parameters. Power analyses of the AQIM data indicated there was at least a 95% chance of detecting a statistically significant reduction in infestation rates if they dropped by 90% post-ISPM15, but the probability fell as the impact of ISPM15 lessened. We discuss several factors that could have reduced the apparent impact of ISPM15 on lowering WPM infestation levels, and suggest ways that ISPM15 could be improved. The paucity of international interception data impeded our ability to conduct more thorough analyses of the impact of ISPM15, and demonstrates the need for well-planned sampling programs before and after implementation of major phytosanitary policies so that their effectiveness can be assessed. We also present summary data for bark- and wood-boring insects intercepted on WPM at US ports during 1984–2008

A randomised double-blind placebo-controlled feasibility trial of flavonoid-rich cocoa for fatigue in people with relapsing and remitting multiple sclerosis

The impact of flavonoids on fatigue has not been investigated in Relapsing and Remitting Multiple Sclerosis (RRMS). Objective: To determine the feasibility and estimate the potential effect of flavonoid-rich cocoa on fatigue and fatigability in RRMS. Methods: A randomised double-blind placebo-controlled feasibility study in people recently diagnosed with RRMS and fatigue, throughout the Thames Valley (ISRCTN: 69897291). During a six week intervention participants consumed a high or low flavonoid cocoa beverage daily. Fatigue and fatigability were measured at three visits (weeks 0, 3 and 6). Feasibility and fidelity were assessed through recruitment and retention, adherence and a process evaluation. Results: 40 pwMS (10 men, 30 women, age 44 ± 10 yrs) were randomised and allocated to high (n=19) or low (n=21) flavonoid groups and included in analysis. Missing data was 75%. There was a small effect on fatigue (Neuro-QoL: effect size {ES} 0.04; confidence interval {CI} -0.40-0.48) and a moderate effect on fatigability (six-minute walk test: ES 0.45; CI -0.18 - 1.07). There were seven adverse events (four control, three intervention), only one of which was possibly related and it was resolved. Conclusion: A flavonoid beverage demonstrates the potential to improve fatigue and fatigability in RRMS

Active Tension Network model suggests an exotic mechanical state realized in epithelial tissues.

Mechanical interactions play a crucial role in epithelial morphogenesis, yet understanding the complex mechanisms through which stress and deformation affect cell behavior remains an open problem. Here we formulate and analyze the Active Tension Network (ATN) model, which assumes that the mechanical balance of cells within a tissue is dominated by cortical tension and introduces tension-dependent active remodeling of the cortex. We find that ATNs exhibit unusual mechanical properties. Specifically, an ATN behaves as a fluid at short times, but at long times supports external tension like a solid. Furthermore, an ATN has an extensively degenerate equilibrium mechanical state associated with a discrete conformal - "isogonal" - deformation of cells. The ATN model predicts a constraint on equilibrium cell geometries, which we demonstrate to approximately hold in certain epithelial tissues. We further show that isogonal modes are observed in the fruit y embryo, accounting for the striking variability of apical areas of ventral cells and helping understand the early phase of gastrulation. Living matter realizes new and exotic mechanical states, the study of which helps to understand biological phenomena

Defective recognition of ATG8/LC3B by mutant SQSTM1/p62 implicates impairment of autophagy as a pathogenic mechanism in ALS-FTLD

Growing evidence implicates impairment of autophagy as a candidate pathogenic mechanism in the spectrum of neurodegenerative disorders which includes amyotrophic lateral sclerosis and frontotemporal lobar degeneration (ALS-FTLD). SQSTM1, which encodes the autophagy receptor SQSTM1/p62, is genetically associated with ALS-FTLD, although to date autophagy-relevant functional defects in disease-associated variants have not been described. A key protein-protein interaction in autophagy is the recognition of lipid-anchored ATG8/LC3 within the phagophore membrane by SQSTM1, mediated through its LC3-interacting region (LIR), and notably some ALS-FTLD mutations map to this region. Here we show that although representing a conservative substitution and predicted to be benign, the ALS-associated L341V mutation of SQSTM1 is defective in recognition of LC3B. We place our observations on a firm quantitative footing by showing the L341V-mutant LIR is associated with a ~3-fold reduction in LC3B binding affinity and using protein NMR we rationalise the structural basis for the effect. This functional deficit is realised in motor neurone-like cells, with L341V mutant EGFP-mCherry-SQSTM1 less readily incorporated into acidic autophagic vesicles than wild-type. Our data supports a model in which the L341V mutation limits the critical step of SQSTM1 recruitment to the phagophore. The oligomeric nature of SQSTM1 which presents multiple LIRs to template growth of the phagophore potentially gives rise to avidity effects which amplify the relatively modest impact of any single mutation on LC3B binding. Over the lifetime of a neurone impaired autophagy could expose a vulnerability which ultimately tips the balance from cell survival towards cell death