Success in algebra is considered to be the "gatekeeper" to postsecondary education and essential for many careers (National Mathematics Advisory Panel [NMAP], 2008). Mastering critical algebraic concepts, such as proportional reasoning and fractions, facilitates the learning of more advanced mathematical ideas. Many postsecondary degree programs require mastery of algebra content (Ketterlin-Geller & Chard, 2011).In recent years, nearly all states have established more rigorous mathematics requirements, including successful completion of Algebra 1, for high school graduation (American Diploma Project, 2004). Notably, students must learn mathematical topics, including fractions, prior to algebra instruction to be able to tackle the rigorous demands associated with this content area.Unfortunately, the National Assessment of Educational Progress (National Center for Education Statistics, 2013) indicated that about half of students in 8th and 12th grade lack the conceptual understanding and procedural knowledge that is critical for competence with fractions. Among fourth graders with and without disabilities, only about 31% could predict the first fraction in a pattern that was greater than 1, and only about 35% could solve a problem using operations with fractions. Among eighth graders, about 41% could solve a multistep problem involving fractions (National Center for Education Statistics, 2013). By comparison, according to the 2011 Trends in International Mathematics and Science Study, both fourth and eighth graders in East Asia countries outperformed those in the United States on mathematical reasoning, including fractions understanding and knowledge (Mullis, Martin, Foy, & Arora, 2012). Thus, for U.S. students, performance outcomes for fractions, including for students with academic difficulties, are alarming, given the importance of competence with fractions as part of the learning progression for algebra.As one of the critical foundations of algebra, conceptual understanding of fractions is considered an essential building block for successfully advancing in elementary and secondary mathematics. Conceptual understanding is defined as "implicit or explicit understanding of the principles that govern a domain and of the interrelations between units of knowledge in a domain" (pp. 346-347), whereas procedural understanding refers to "the ability to execute action sequences to solve problems" (Rittle-Johnson, Siegler, & Alibali, 2001, p. 346).

These results indicate that reversal of levobupivacaine-induced vasodilation by LE is mediated mainly through the attenuation of levobupivacaine-mediated inhibition of L-type calcium channel-dependent contraction and, in part, by inhibition of levobupivacaine-induced nitric oxide release. LE-mediated reversal of responses induced by local anesthetics may be related to their lipid solubility.

Systematically observing instruction for students with learning disabilities (LD) provides information regarding the quality of school-based interventions, allocation of instructional time, and other implementation variables associated with student outcomes. In this synthesis, observation studies of reading and mathematics instruction from 2000 to 2013 were identified through a systematic literature search. The purpose was to understand findings from observations of typical practice for students with LD during an era of increased exposure to evidence-based practices, educational policy reforms, and reports on reading and mathematics designed to influence instruction, and amid a period of increased academic expectations. Eleven studies focusing on academic instruction for students with LD were identified and reviewed. Cognitive strategy instruction, differentiated instruction, and opportunities for independent application (i.e., text reading, problem solving) were reported infrequently across the published observational research. However, findings provide some evidence of improved teacher use of effective instructional practices in several areas compared with earlier observation study syntheses. Implications for practice and areas for future research are discussed.

Key points Leptin is a potent respiratory stimulant. A long functional isoform of leptin receptor, LepRb, was detected in the carotid body (CB), a key peripheral hypoxia sensor. However, the effect of leptin on minute ventilation (VE) and the hypoxic ventilatory response (HVR) has not been sufficiently studied. We report that LepRb is present in approximately 74% of the CB glomus cells. Leptin increased carotid sinus nerve activity at baseline and in response to hypoxia in vivo. Subcutaneous infusion of leptin increased VE and HVR in C57BL/6J mice and this effect was abolished by CB denervation. Expression of LepRb in the carotid bodies of LepRb deficient obese db/db mice increased VE during wakefulness and sleep and augmented the HVR. We conclude that leptin acts on LepRb in the CBs to stimulate breathing and HVR, which may protect against sleep disordered breathing in obesity. Abstract Leptin is a potent respiratory stimulant. The carotid bodies (CB) express the long functional isoform of leptin receptor, LepRb, but the role of leptin in CB has not been fully elucidated. The objectives of the current study were (1) to examine the effect of subcutaneous leptin infusion on minute ventilation (VE) and the hypoxic ventilatory response to 10% O2 (HVR) in C57BL/6J mice before and after CB denervation; (2) to express LepRb in CB of LepRb‐deficient obese db/db mice and examine its effects on breathing during sleep and wakefulness and on HVR. We found that leptin enhanced carotid sinus nerve activity at baseline and in response to 10% O2 in vivo. In C57BL/6J mice, leptin increased VE from 1.1 to 1.5 mL/min/g during normoxia (P < 0.01) and from 3.6 to 4.7 mL/min/g during hypoxia (P < 0.001), augmenting HVR from 0.23 to 0.31 mL/min/g/ΔFnormalIO2 (P < 0.001). The effects of leptin on VE and HVR were abolished by CB denervation. In db/db mice, LepRb expression in CB increased VE from 1.1 to 1.3 mL/min/g during normoxia (P < 0.05) and from 2.8 to 3.2 mL/min/g during hypoxia (P < 0.02), increasing HVR. Compared to control db/db mice, LepRb transfected mice showed significantly higher VE throughout non‐rapid eye movement (20.1 vs. −27.7 mL/min respectively, P < 0.05) and rapid eye movement sleep (16.5 vs 23.4 mL/min, P < 0.05). We conclude that leptin acts in CB to augment VE and HVR, which may protect against sleep disordered breathing in obesity.