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This paper explores how in-service teachers enrolled in a graduate proof course interpret, understand, and use generic examples as part of their proving and justification activities. Generic examples, which are capable of proving and justifying with strong explanatory power, are particularly important for teachers considering teaching proof in their classrooms. The teachers in our study used generic examples to produce three types of proof: example-based arguments enhanced with generic language; incomplete generic examples; and complete generic examples. We found that teachers conflate generic examples and visual representations, prefer visual generic examples for teaching, and consider a generic example with symbolic representation to be more convincing than a generic example without. We conclude with implications for secondary school teaching, as well as suggestions for future professional development efforts. [ABSTRACT FROM AUTHOR]

Potassium (K+) ion channel activity is an important determinant of vascular tone by regulating cell membrane potential (MP). Activation of K+ channels leads to membrane hyperpolarization and subsequently vasodilatation, while inhibition of the channels causes membrane depolarization and then vasoconstriction. So far five distinct types of K+ channels have been identified in vascular smooth muscle cells (VSMCs): Ca+2‐activated K+ channels (BKCa), voltage‐dependent K+ channels (KV), ATP‐sensitive K+ channels (KATP), inward rectifier K+ channels (Kir), and tandem two‐pore K+ channels (K2P). The activity and expression of vascular K+ channels are changed during major vascular diseases such as hypertension, pulmonary hypertension, hypercholesterolemia, atherosclerosis, and diabetes mellitus. The defective function of K+ channels is commonly associated with impaired vascular responses and is likely to become as a result of changes in K+ channels during vascular diseases. Increased K+ channel function and expression may also help to compensate for increased abnormal vascular tone. There are many pharmacological and genotypic studies which were carried out on the subtypes of K+ channels expressed in variable amounts in different vascular beds. Modulation of K+ channel activity by molecular approaches and selective drug development may be a novel treatment modality for vascular dysfunction in the future. This review presents the basic properties, physiological functions, pathophysiological, and pharmacological roles of the five major classes of K+ channels that have been determined in VSMCs. [ABSTRACT FROM AUTHOR]

Asthma is an inflammatory disease of the airways of the lungs, which is characterized by airflow obstruction and bronchospasms. Glabridin is a major flavonoid, especially found in root of Glycyrrhiza glabra, and has several pharmacological activities, including antioxidant and anti-inflammatory effects. The anti-asthmatic effect and possible mechanism of glabridin, however, have not been revealed so far. The aim of this study is to investigate the effects and possible mechanisms of glabridin against ovalbumin (OVA)-induced airway hyperresponsiveness (AHR) and inflammation in mice. In male BALB/c mice, asthma was induced by intraperitoneal (i.p) injection of OVA mixed with 2 mg aluminium hydroxide on days 0, 14 and boosted with OVA aerosol challenge on days 21, 22, and 23. Mice were either treated with dexamethasone (i.p, 1 mg/kg) or glabridin (10, 20, and 30 mg/kg) from days 18–23. Pulmonary function parameters such as peak inspiratory flow, peak expiratory flow, tidal volume, expiratory volume, the frequency of breathing, enhanced pause values were evaluated by using whole-body plethysmography. Measurements were performed at baseline and following methacholine (50 mg/mL) challenges. In addition, white blood cells (WBC) count, total protein, and IgE levels were measured in bronchial alveolar lavage fluid (BALF), lung, and serum, respectively. Glabridin (20 or 30 mg/kg) significantly attenuated (p < 0.05) OVA-induced alteration in respiratory parameters. Elevated counts of total WBC, differential WBC (neutrophils, lymphocytes, monocytes, and eosinophils) in BALF and the total protein in lungs and BALF were significantly decreased (p < 0.05) by glabridin (20 or 30 mg/kg). It also significantly attenuated the increased serum IgE levels (p < 0.05). As glabridin reduces the level of serum IgE, the total protein and the count of WBC and improves respiratory function, it may be a novel therapeutic agent in asthma. [ABSTRACT FROM AUTHOR]

Bleomycin (BLM) is a chemotherapeutic agent that can cause pulmonary fibrosis. Little is known about the possible protective role of the CB2 receptor agonist, AM1241. We investigated the effects of CB2 receptor activation by AM1241 on BLM induced lung fibrosis in a rat model. BLM was administered via the trachea. Adult female Wistar rats were divided into five groups: saline (control group), BLM (BLM group), CB2 agonist (AM1241) + BLM (BLMA group), CB2 antagonist (AM630) and CB2 agonist (AM1241) + BLM (BLMA + A group), and vehicle (dimethylsulfoxide) + BLM (BLM + vehicle group). Hydroxyproline, collagen type 1, total protein, glutathione (GSH), malondialdehyde (MDA), interleukin (IL)-6 and tumor necrosis factor (TNF)-α levels were measured in lung fibrosis and control tissue using standard methods. We investigated the histopathology of lung tissue to determine the extent of fibrosis. We found significantly higher levels of hydroxyproline, TNF-α, IL-6 and total protein in the BLM group compared to the BLMA group. The level of GSH also was higher in the BLMA group compared to the BLM group. Inflammation and fibrotic changes were significantly reduced in the BLMA group. Our findings suggest that CB2 receptor activation provided protection against BLM induced pulmonary fibrosis by suppressing oxidative stress and increasing cytokines. [ABSTRACT FROM AUTHOR]

• The CAPS Framework presents the criteria, purposes, strategies, and affordances of example use. • There were significant correlations between strategies, affordances, and purposes. • Criteria, purposes and strategies differed across populations but affordances did not. • Students productively leveraged examples to gain insight and develop proofs. A persistent challenge in supporting students' proof activity is fostering the transition from less formal, empirical arguments to formal deductive arguments. A number of researchers have begun to investigate students' thinking with examples, addressing how example use can support conjecture understanding, exploration, and proof. We extend this line of work in presenting the CAPS (Criteria, Affordances, Purposes, and Strategies) Framework, a framework addressing students' choices, uses, strategies, and affordances gained with examples. Based on individual interviews with 38 participants from middle school through the undergraduate level, the CAPS Framework simultaneously addresses multiple aspects of students' example-based exploration and provides a way to analyze how these different aspects mutually inform one another as students conjecture and prove. We present the framework, exemplify its use through vignettes of student thinking, and share findings on how students' thinking with examples shifts across the populations of middle school, high school, and undergraduate students. [ABSTRACT FROM AUTHOR]

• We examined the nature of the successful and unsuccessful provers' example use. • We identified some distinctive characteristics of the successful provers' example use. • The purposes and strategies of example use influenced the affordances gained. • We highlighted a few factors that hindered the affordances gained from examples. Examples can be a powerful tool for students to learn to prove, particularly if used purposefully and strategically, but there is a pressing need to better understand the nature of productive example use. Therefore, we examined the characteristics of the successful and unsuccessful cases of proving in the context of a number theory task across the three student populations (middle school, high school, undergraduate), where by successful case we mean the ability to develop a viable justification that accounts for why the conjecture must be true. We present the characteristics of the successful and unsuccessful provers regarding the purposes, strategies, and affordances of example use, offer detailed accounts of a few illustrative cases of students' proving processes, and highlight a couple factors that seemed to have hindered the unsuccessful provers' ability to gain greater affordances from examples. We conclude with a discussion of the instructional implications of the results. [ABSTRACT FROM AUTHOR]