A sense-making approach to proof: Strategies of students in traditional and problem-based number theory courses

This paper reports the results of an exploratory study of the perceptions of and approaches to mathematical proof of undergraduates enrolled in lecture-based and problem-based “transition to proof” courses. While the students in the lecture-based course demonstrated conceptions of proof that reflect those reported in the research literature as insufficient and typical of undergraduates, the students in the problem-based course were found to hold conceptions of and approach the construction of proofs in ways that demonstrated efforts to make sense of mathematical ideas. This sense-making manifested itself in the ways in which students employed initial strategies, notation, prior knowledge and experiences, and concrete examples in the proof construction process. These differences were also seen when students were asked to determine the validity of completed proofs. These results suggest that such a problem-based course may provide opportunities for students to develop conceptions of proof that are more meaningful and robust than does a traditional lecture-based course.     

Implementation of the EU Water Framework Directive in monitoring of small water bodies in Hungary, I. Establishment of surveillance monitoring system for physical and chemical characteristics for small mountain watercourses

The EU Water Framework Directives (WFD) prescribes to achieve a good status of surface waters by 2015. To keep this deadline of a new three level (surveillance, operational and investigative) monitoring system is required, including hydro-morphological, biological and chemical elements. The status of a water body should be related to the reference conditions, depending on surface water types. In Hungary, the standard monitoring network for surface water quality has been operated for rivers and large lakes; however no satisfactory information is available for small water bodies. Therefore, there is an urgent need to design a methodology to develop a monitoring network for small watercourses. For this purpose a slightly impacted mountain stream (Nagy Stream in Mátra Mountains), was selected and intensively monitored during three years (May 2002 → May 2005). Hydrological, biological and chemical parameters required by WFD were monitored in this program. Variability of parameters vs. time and space was also investigated. The minimum frequency of sampling was determined for chosen physico-chemical components to meet the WFD standards for confidence. It was found that the minimum frequency of sampling suggested by WFD in space and time may not be adequate for precise and accurate characterization of water quality.     

让物理演示实验进入各类选修课

介绍了一些在交叉学科中引进的易于操作的物理演示实验，并指出了物理演示实验的前景。     

浅谈高等数学习题课教学

探讨习题课教学应注意的问题．首先明确指出习题课的目的和意义,之后从重视对数学概念的理解运用、习题的选择、课堂互动等方面阐述如何提高课堂教学效率,以达到不断渗透数学思想、数学方法的目的,从而培养学生良好的思维品质．     

浅析ETA物理认知模型在中学物理习题教学中的应用

物理习题教学是中学物理教学的重要环节,能够帮助学生提高运用物理知识解决实际问题的能力.基于ETA物理认知模型,针对理论物理认知题型、实验物理认知到理论物理认知题型和应用物理认知题型3类题型的习题特点,总结出每类题型具体的应对策略.在习题教学过程中教师需要强化学生的物理基本知识和理论,帮助学生做好从实践到构建物理模型的过渡,引导学生做好理论与实际生活联系,为提升习题教学的有效性提供参考.     

专业课程融入课程思政模式初探——以“光学”为例

把思想政治教育贯穿人才培养体系,全面推进高校课程思政建设,发挥每门课程的育人作用是新时代中国特色社会主义高等教育的改革创新重要内容.学科专业课程作为课程思政建设的基本载体,需根据专业特色,发挥专业优势.以理工科专业课程光学为例,分析其悠久历史、探索历程和现代技术与思政要素在"个人-国家-社会"3个维度上的协同共振,构建浸润式光学课程思政模式,以供参考.     

Exercising QS: quantitative skills in an exercise science course

This study seeks to bring the discipline of exercise science into the discussion of Quantitative Skills (QS) in science. The author's experiences of providing learning support to students and working with educators in the field are described, demonstrating the difficulty of encouraging students to address their skills deficit. A survey of students’ perceptions of their own QS and of that required for their course, demonstrates the difficulties faced by students who do not have the prescribed assumed knowledge for the course. Limited results from academics suggest that their perceptions of students’ QS deficits are even direr than those of the under-prepared students.     

Evidence of Improvement in Various Impairments by Exercise Interventions in Patients with Knee Osteoarthritis: A Systematic Review and Meta-analysis of Randomized Clinical Trials

Purpose: To investigate improvement in various impairments by exercise interventions in patients with knee osteoarthritis (OA). Methods: We collected data on randomized controlled trials (RCTs) comparing the effects of exercise intervention with those of either nonintervention or psychoeducational intervention in patients with knee OA. Data on pain, stiffness, muscle strength, range of motion, flexibility, maximal oxygen uptake, and position sense were synthesized. The Grading of Recommendations Assessment, Development, and Evaluation system was used to determine the quality of the evidence. Results: Thirty-three RCTs involving 3,192 participants were identified. Meta-analysis provided highquality evidence that exercise intervention improves maximal oxygen uptake, and moderate-quality evidence that exercise intervention also improves pain, stiffness, knee extensor and flexor muscle strength, and position sense. The evidence that exercise intervention improves knee extension and flexion range of motion was deemed as undetermined-quality. Conclusion: In patients with knee OA, improvement in pain, stiffness, muscle strength, maximal oxygen uptake, and position sense with the use of exercise intervention can be expected. Although the quality of evidence of the effect of exercise intervention on range of motion was inconclusive, exercise intervention should be recommended for patients with knee OA to improve various impairments.     

Pricing American currency options in an exponential Lévy model

In this article the problem of the American option valuation in a Lévy process setting is analysed. The perpetual case is first considered. Without possible discontinuities (i.e. with negative jumps in the call case), known results concerning the currency option value as well as the exercise boundary are obtained with a martingale approach. With possible discontinuities of the underlying process at the exercise boundary (i.e. with positive jumps in the call case), original results are derived by relying on first passage time and overshoot associated with a Lévy process. For finite life American currency calls, the formula derived by Bates or Zhang, in the context of a negative jump size, is tested. It is basically an extension of the one developed by Mac Millan and extended by Barone‐Adesi and Whaley. It is shown that Bates' model generates pretty good results only when the process is continuous at the exercise boundary.     

“金课”背景下强化线性代数应用教学的实践与探索

线性代数课程具有高度的抽象性,再加上课时等多方面限制,使得学生学起来感觉非常枯燥.针对此问题,在线性代数课程中,适当增加应用的讲解,以增加学生对于相关知识应用的认知,提高学生综合利用线性代数知识解决问题的能力.通过调查问卷,分析了在线性代数课程中增加应用知识讲解的经验、存在的问题及应对措施.