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The purpose of this paper is to offer a framework for interpreting students' understandings of and difficulties with mathematical ideas central to new directions in differential equations. These new directions seek to guide students into a more interpretive mode of thinking and to enhance their ability to graphically and numerically analyze differential equations. The framework reported here is the result of investigating in depth six students' understandings through a series of task-based individual interviews and classroom observations. The two major themes of the framework, the function-as-solution dilemma theme and students' intuitions and images theme, extend previous research on student cognition at the secondary and collegiate level to the domain of differential equations and reflect the increased recognition of situating analyses of student learning within students' learning environment. For new areas of interest such as differential equations, mapping out students' understandings of important mathematical ideas can be an important part of curricular and instructional design that seeks to refine and build on students' ways of thinking.

Review of: "A Colossal Hoax: The Giant From Cardiff That Fooled America," by Scott Tribble.

Review of: "Purebred & Homegrown: America's County Fairs," by Drake Hokanson and Carol Kratz.

This paper extends analyses of social interaction patterns that have been successful at characterizing elementary and secondary school classrooms to the learning and teaching of undergraduate mathematics. Using data from a classroom teaching experiment in differential equations as an example, we document the social and sociomathematical norms regarding explanation and discuss how these norms were constituted in this specific case. We focus on the social norms that students explain their thinking and try to make sense of other students' thinking and, for first-order differential equations, we document the sociomathematical norm that explanations be grounded in an interpretation of the rates of change. The analysis makes explicit certain social aspects of classroom environments that contribute to the conditions that make meaningful learning of mathematics possible.

To test the vision of Standards–based mathematics education, we conducted a comparative study of the effects of the Core-Plus Mathematics Project (CPMP) curriculum and more conventional curricula on growth of student understanding, skill, and problem-solving ability in algebra. Results indicate that the CPMP curriculum is more effective than conventional curricula in developing student ability to solve algebraic problems when those problems are presented in realistic contexts and when students are allowed to use graphing calculators. Conventional curricula are more effective than the CPMP curriculum in developing student skills in manipulation of symbolic expressions in algebra when those expressions are presented free of application context and when students are not allowed to use graphing calculators.

The paper reports on ongoing developmental research efforts to adapt the instructional design perspective of Realistic Mathematics Education (RME) to the learning and teaching of collegiate mathematics, using differential equations as a specific case. This report focuses on the RME design heuristic of guided reinvention as a means to locate a starting point for an instructional sequence for first-order differential equations and highlights the cyclical process instructional design and analysis of student learning. The instance of starting with a rate of change equation as an experientially real mathematical context is taken as a case for illustrating how university students might experience the creation of mathematical ideas. In particular, it is shown how three students came to reason conceptually about rate and in the process, develop their own informal Euler method for approximating solution functions to differential equations.

Objective of the study: The purpose of this case study was to observe the effects of a self-supported ultraendurance mountain cycling event on body composition, lower and upper body muscular endurance, anaerobic capacity, aerobic capacity and markers of clinical health. Materials and methods: A trained endurance cyclist competed in the self-supported ultra-endurance event known as the Tour Divide mountain bike race. The subject cycled the course route twice totaling approximately 8,835 total kilometers over the course of 44 days. Body composition, physical performance, and markers of clinical health were collected pre-race and up to 3-wk post-race. Results: Average total energy intake increased by 1,541 kcals during the race compared to pre-race food consumption. We observed an increase in carbohydrate (113%) and fat (12.85%) intake with a marked decrease in protein consumption (-28%). The subject lost a total of 8.4 kg over the course of the 44-d trek and remained 11.0 kg below pre-race body mass 3-wk post-race. The subject lost fat (7.2 kg) and fat-free mass (1.9 kg.) over the race period, resulting in a 6.4% decrease in body fat. The subject experienced a decrease in absolute VO2 peak, mean power, and peak power measured by a Wingate Anaerobic Capacity Test 96-hrs post-race. Upper and lower body muscular strength endurance performance decreased 96-hrs post-race -15-20 and -20%, respectively. Parameters of liver function, AST and ALT, were elevated immediately post-race (92 and 95%, respectively) and remained 46 and 58% above normative values 96-hrs post-race. Creatine kinase concentration also significantly increased 210% immediately following the race and remained elevated 24 (30%), 48 (46%) and 72-hrs (20%) post-race. Conclusions: We conclude that completing a 44-d extreme ultra-endurance mountain biking race results in a decrease in fat and fat free mass. Additionally, prolonged ultra-endurance performance facilitates decreases in aerobic capacity, anaerobic power, muscular strength endurance as well as increases in markers of muscle damage.

Background Obesity is associated with many negative health outcomes. Diet and exercise has been shown to reduce obesity and various other factors linked to poor health. One of the major concerns is the expense of diet and exercise programs. This study compared the cost effectiveness of four popular weight loss programs and controls in terms of weight loss success and outcomes. Methods

Effects of immediate and delayed nutrient timing following resistance exercise on changes in mixed muscle fractional synthesis rate (FSR) in post-menopausal women participating in a weight loss program M Byrd, S Simbo, YP Jung, B Sanchez, M Cho, CW Lee, B Lockard, C Baetge, K Levers, E Galvan, A Jagim, JM Oliver, R Dalton, B Bessire, K Horrell, T Leopold, M Koozehchian, D Khanna, K Shimkus, W Gapinsky, M Perez, J Hart, S Riechman, J Fluckey, M Greenwood, C Rasmussen, R Kreider

Background Extracts of Russian Tarragon (RT) have been reported to produce anti-hyperglycemic effects and influence plasma creatine (Cr) levels while supplementing with creatine monohydrate (CrM). The purpose of this preliminary study was to determine if short-term, low-dose aqueous RT extract ingestion prior to CrM supplementation influences whole body Cr retention, muscle Cr or measures of anaerobic sprint performance. Methods In a double-blind, randomized, and crossover manner; 10 recreationally trained males (20 ± 2 yrs; 179 ± 9 cm; 91.3 ± 34 kg) ingested 500 mg of aqueous RT extract (Finzelberg, Andernach, Germany) or 500 mg placebo 30-minutes prior to ingesting 5 g of CrM (Creapure®, AlzChem AG, Germany) twice per day for 5-days then repeated after a 6-week wash-out period. Urine was collected at baseline and during each of the 5-days of supplementation to determine urine Cr content. Whole body Cr retention was estimated from urine samples. Muscle biopsies were obtained for determination of muscle free Cr content. Participants also performed two 30-second Wingate anaerobic capacity tests prior to and following supplementation for determination of peak power (PP), mean power (MP), and total work (TW). Data were analysed by repeated measures MANOVA. Results Whole body daily Cr retention increased in both groups following supplementation (0.0 ± 0.0; 8.2 ± 1.4, 6.5 ± 2.4, 5.6 ± 3.2, 6.1 ± 2.6, 4.8 ± 3.2 g · d-1; p = 0.001) with no differences observed between groups (p = 0.59). After 3 and 5-days of supplementation, respectively, both supplementation protocols demonstrated a significant increase in muscle free Cr content from baseline (4.8 ± 16.7, 15.5 ± 23.6 mmol · kg-1 DW, p = 0.01) with no significant differences observed between groups (p = 0.34). Absolute change in MP (9 ± 57, 35 ± 57 W; p = 0.031), percent change in MP (2.5 ± 10.5, 6.7 ± 10.4%; p = 0.026), absolute change in TW (275 ± 1,700, 1,031 ± 1,721 J; p = 0.032), and percent change in TW (2.5 ± 10.5, 6.6 ± 10.4%; p = 0.027) increased over time in both groups with no differences observed between groups. Conclusions Short-term CrM supplementation (10 g · d-1 for 5-days) significantly increased whole body Cr retention and muscle free Cr content. However, ingesting 500 mg of RT 30-min prior to CrM supplementation did not affect whole body Cr retention, muscle free Cr content, or anaerobic sprint capacity in comparison to ingesting CrM with a placebo.

21 sedentary women (59.8±5 yr, 43.7±3% body fat, 31.0±3 kg/m2) followed Curves Complete® energy-restricted diet (30% C, 45% P, and 25% F) while participating in a circuit resistance-training (3 d/w...

The rising cost of higher education is one of the most vexing public policy challenges facing the United States and many other nations. At the same time, expanding access to higher education and promoting completion of degrees and related credentials of value is critical given the relationship between educational attainment and a host of individual and public returns on investment. Governments around the world struggle with the conundrum of how to expand educational access in a time of economic challenge and austerity measures designed to shrink national outlays in response to reduced tax revenues. These challenges have accelerated a two-decade global trend of shifting an increasing percentage of educational costs from governments to individual students and their families.

Too often powerful and beautiful mathematical ideas are learned (and taught) in a procedural manner, thus depriving students of an experience in which they create and refine ideas for themselves. As a first step toward improving the current undesirable situation in undergraduate mathematics education, this chapter describes several different modeling perspectives and their implications for teaching and learning.

Background Creatine monohydrate (CrM) has been proven to be the most effective form of creatine and is considered the gold standard. However, a number of different forms of creatine have been purported to be more efficacious than CrM. The purpose of this study was to determine if a pH balanced form of creatine (Kre-Alkayn (KA), All American Pharmaceutical, Billings, MT, USA) that has been purported to promote greater creatine retention and training adaptations with less side effects is more efficacious than CrM ingestion.

Background A number of commercial diet and exercise programs are promoted to help people lose weight and improve fitness. However, few studies have compared the effects of following different types of exercise and diet interventions on weight loss and/or changes in health and fitness markers. The purpose of this study was to compare the efficacy of a more structured meal plan based diet intervention and supervised exercise program that included resistance-exercise to a traditional point based diet program with weekly counseling and encouragement to increase physical activity.

Background A number of psychological interventions have been employed prior to and/or during exercise and weight loss interventions in an attempt to influence exercise adherence, compliance, and/or success. However, few studies have evaluated whether these types of efforts influence program efficacy. The purpose of this study was to determine whether having sedentary and overweight individuals experience the impact of losing weight on work capacity prior to initiation of an exercise and/or weight loss program would influence weight loss success.

Background Milk protein fractions and peptides have been shown to have bioactive properties. This preliminary study examined the potential mechanisms of action and clinical safety of novel milk protein peptide (MP). Findings A novel MP mixture inhibits the tyrosine kinase activity of epidermal growth factor receptor (EGFR), vascular endothelial growth factor receptor 2 (VEGFR2), and insulin receptor (IR) with IC50 of 9.85 μM, 7.7 μM, and 6.18 μM respectively. In vitro, this multi-kinase inhibitor causes apoptosis in HT-29 colon cancer cells, and in a C. elegans worm study, showed a weak but significant increase in lifespan. A six week double-blind, placebo-controlled study involving 73 healthy volunteers demonstrated that the MP mixture is safe to consume orally. All clinical blood markers remained within normal levels and no clinically significant side effects were reported. There was some evidence of improved insulin sensitivity, neutrophil-to-lymphocyte ratio (NLR), and quality of life assessment of role of physical function. Conclusions These data in combination with the observed in vitro anti-cancer properties warrant further clinical studies to investigate this MP mixture as a potential clinical nutrition intervention for improving the quality of life and clinical outcomes in cancer patients. Trial Registration NCT01412658

Background Phosphatidylserine (PS) is a phospholipid found in cell membranes of most animals and plants. PS has been shown to reduce stress and increase performance in runners, cyclists and golfers. The purpose of this study was to investigate the effects of a PS containing formulation on cognitive function, mood and endocrine response before and after intense resistance exercise. Methods 18 lower body, resistance trained, college aged males ingested 14 days of supplement (IQPLUS Focus, providing 400 mg of soy-derived PS) and a Placebo (PL), in a randomized, double-blind, placebo controlled, cross-over manner. Following 14 days of supplementation, participants performed an acute bout of lower body resistance training. Mood (Profile of Mood States, POMS) and cognitive function (Serial Subtraction Test, SST) were measured prior to, 5 minutes after, and 60 minutes after exercise. Venous blood samples were collected prior to, and 5, 15, 25, 40 and 60 minutes after exercise. Blood samples were analyzed for plasma cortisol and testosterone. Data were analyzed using repeated measures ANOVA. Results PS supplementation significantly reduced the time needed for a correct calculation on the SST by 20% (reduced by 1.27 s per calculation; PL: 6.4 s, PS: 5.13 s; p = 0.001), and reduced the total amount of errors by 39% (PL: 1.28 + .69, PS: .78 + .27, p = 0.53), and increased the amount of correct calculations by 13% (PL: 22.1 + 2.24, PS: 24.9 + 1.52, p = 0.07) prior to or in response to exercise compared to PL. Following exercise, there was no difference in SST scores between PS and PL. There were no significant changes in regards to mood or endocrine response to exercise as a result of PS supplementation. Conclusion PS supplementation significantly increased cognitive function prior to exercise. Improved cognitive function could benefit athletes and non-athletes alike. PS did not appear to affect mood or endocrine response prior to or following resistance exercise.

Background This study's purpose investigated the impact of different macronutrient distributions and varying caloric intakes along with regular exercise for metabolic and physiological changes related to weight loss. Methods One hundred forty-one sedentary, obese women (38.7 ± 8.0 yrs, 163.3 ± 6.9 cm, 93.2 ± 16.5 kg, 35.0 ± 6.2 kg•m-2, 44.8 ± 4.2% fat) were randomized to either no diet + no exercise control group (CON) a no diet + exercise control (ND), or one of four diet + exercise groups (high-energy diet [HED], very low carbohydrate, high protein diet [VLCHP], low carbohydrate, moderate protein diet [LCMP] and high carbohydrate, low protein [HCLP]) in addition to beginning a 3x•week-1 supervised resistance training program. After 0, 1, 10 and 14 weeks, all participants completed testing sessions which included anthropometric, body composition, energy expenditure, fasting blood samples, aerobic and muscular fitness assessments. Data were analyzed using repeated measures ANOVA with an alpha of 0.05 with LSD post-hoc analysis when appropriate. Results All dieting groups exhibited adequate compliance to their prescribed diet regimen as energy and macronutrient amounts and distributions were close to prescribed amounts. Those groups that followed a diet and exercise program reported significantly greater anthropometric (waist circumference and body mass) and body composition via DXA (fat mass and % fat) changes. Caloric restriction initially reduced energy expenditure, but successfully returned to baseline values after 10 weeks of dieting and exercising. Significant fitness improvements (aerobic capacity and maximal strength) occurred in all exercising groups. No significant changes occurred in lipid panel constituents, but serum insulin and HOMA-IR values decreased in the VLCHP group. Significant reductions in serum leptin occurred in all caloric restriction + exercise groups after 14 weeks, which were unchanged in other non-diet/non-exercise groups. Conclusions Overall and over the entire test period, all diet groups which restricted their caloric intake and exercised experienced similar responses to each other. Regular exercise and modest caloric restriction successfully promoted anthropometric and body composition improvements along with various markers of muscular fitness. Significant increases in relative energy expenditure and reductions in circulating leptin were found in response to all exercise and diet groups. Macronutrient distribution may impact circulating levels of insulin and overall ability to improve strength levels in obese women who follow regular exercise.

Background The Curves fitness program involves a 30-minute circuit training program. Women interested in losing weight can also follow a weight management program. The most recent version of the weight management program involves cycling between periods of moderate calorie restriction (1,200 – 1,500 kcals/d) followed by periods of higher caloric intake (2,200 kcals/d) in an attempt to prevent long term reductions in resting energy expenditure (REE). The purpose of this preliminary study was to examine the efficacy of this exercise and diet cycling program approach on weight loss, fat loss, and REE.

Background Making quick decisions and reducing the amount of errors at the beginning of a competition are crucial to the success in team sports and individual events. Phosphatidylserine (PS) has been shown to reduce stress and increase performance in runners, cyclists and golfers. A randomized, double-blind, placebo-controlled, cross-over pilot study was performed to evaluate the effect of PS supplementation on cognitive function prior to and following an acute bout of resistance training in 18 males aged 18-30.

Effects of high carbohydrate or high protein energy-restricted diets combined with resistanceexercise on weight loss and markers of health in women with serum triglyceride levels above or below median values Jonathan M Oliver, Julie Y Kresta, Mike Byrd, Claire Canon, Michelle Mardock, Sunday Simbo, Peter Jung, Brittanie Lockard, Deepesh Khanna, Majid Koozehchian, Chris Rasmussen, Chad Kerksick, Richard Kreider