• Title/Summary/Keyword: rate of change

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Students' Recognition and Representation of the Rate of Change in the Given Range of Intervals (구간에서의 변화율에 대한 인식과 표현에 대한 연구)

  • Lee, Dong Gu;Shin, Jaehon
    • Journal of Educational Research in Mathematics
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    • v.27 no.1
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    • pp.1-22
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    • 2017
  • This study investigated three $10^{th}$ grade students' concept of rate of change while they perceived changing values of given functions. We have conducted a teaching experiment consisting of 6 teaching episodes on how the students understood and expressed changing values of functions on certain intervals in accordance with the concept of rate of change. The result showed that the students did use the same word of 'rate of change' in their analysis of functions, but their understanding and expression of the word varied, which turned out to have diverse perceptions with regard to average rate of change. To consider these differences as qualitatively different levels might need further research, but we expect that this research will serve as a foundational study for further research in students' learning 'differential calculus' from the perspective of rate of change.

Secondary Mathematics Teachers' Perceptions of Rate of Change

  • Noh, Jihwa
    • East Asian mathematical journal
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    • v.33 no.4
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    • pp.431-451
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    • 2017
  • This is a descriptive study with the intent of providing a rich characterization of teachers' perceptions of rate of change. The nature of teachers' perceptions and differences among teachers were examined by collecting data through a survey on teachers' conceptions of rate of change in terms of learning goals, prerequisites, and beliefs about teaching and learning of rate of change, and an interview individually assessing teachers' concept images and definitions. The participating 13 teachers were selected to provide a range of similar and contrasting levels of experiences based on the teachers' educational background and the number of years they had been teaching. Findings and implications of this study are discussed.

Mediating Effects of Work-Family Balance on the Relationship of Role Recognition in the Family, Marital Intimacy and Job Satisfaction of Married Women: Using Latent Growth Curve Modeling and Autoregressive Cross-Lagged Modeling (기혼여성이 지각한 가족 내 역할 인식 및 부부친밀감과 직무만족도의 관계에서 일-가정양립 인식의 매개효과: 잠재성장모형 및 자기회귀교차지연모형 연구)

  • Han, Hye Rim;Lee, Ji Min
    • Family and Environment Research
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    • v.55 no.3
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    • pp.263-274
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    • 2017
  • The purposes of this study were to verify the longitudinal mediating effects of work-family balance on the relationship of role recognition in the family, marital intimacy and job satisfaction of married women, and to introduce longitudinal mediating effects by using latent growth curve modeling and autoregressive cross-lagged modeling. The subjects were married women from the third year data of the Korean Longitudinal Survey of Women and Family. Structural equational models were conducted with Amos ver. 21.0. The major findings are as follows. First, the result of the longitudinal mediating effects of latent growth modeling is the rate of change of work-family balance mediated between the rate of change of role recognition in the family and the rate of change of job satisfaction, and the rate of change of work-family balance mediated between the rate of change of marital intimacy and the rate of change of job satisfaction. Second, when using the autoregressive cross-lagged modeling, the more role recognition and marital intimacy of third year were the more work-family balance of fourth year, job satisfaction of fifth year. In both models, work-family balance mediated between role recognition in the family, marital intimacy and job satisfaction. Therefore, through this study, mediating effects of work-family balance can be found that there was a longitudinal effects.

The Rate of Change of an Energy Functional for Axially Moving Continua

  • Yang, Kyung-Jinn;Hong, Keum-Shik;Matsuno, Fumitoshi
    • 제어로봇시스템학회:학술대회논문집
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    • pp.2707-2712
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    • 2003
  • In this paper, with the utilization of a three-dimensional version of Leibniz’s rule, the procedure of deriving the time rate of change of an energy functional for axially moving continua is investigated. It will be shown that the method in [14], which describes the way of getting the time rate of change of an energy functional in Eulerian description, and subsequent results in [10, 11] are not complete. The key point is that the time derivatives at boundaries in the Eulerian description of axially moving continua should take into account the velocity of the moving material itself. A noble way of deriving the time rate of change of the energy functional is proposed. The correctness of the proposed method has been confirmed by other approaches. Two examples, one-dimensional axially moving string and beam equations, are provided for the purpose of demonstration. The results following the procedure proposed and the results in [14] are compared.

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Initial Rotor Position Detection of a Toroidal SRM Using the Rate of Change of Current (전류변화율을 이용한 토로이달 SRM의 초기위치 경출 방법)

  • Yang Hyong-Yeol;Lim Young-Cheol
    • The Transactions of the Korean Institute of Electrical Engineers D
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    • v.54 no.1
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    • pp.26-32
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    • 2005
  • Rotor position information is essential in the operation of the switched reluctance motor(SRM) drive for generation the phase current switching signals. When an incremental encoder is used as a rotor position sensor, the initial rotor position can not be detected. Some sensorless rotor position estimation methods also have the same problem. In these systems, to initially align the rotor, the forced alignment method has a delay and reverse rotation before the motor can start. Therefore it can not be acceptable for unidirectional drive systems. So the forced alignment method is not desirable in all drive systems and the research on the SRM drives should be directed to a system without rotor alignment. In this paper, a new detection method of initial rotor position using the rate of change of current is suggested. Firstly, di/dt versus θ/sub R/ reference table, which is the relation between the rate of change of current and rotor position, is generated and then the squared Euclidean distance method is used to estimate the rotor position based on the table. The simulated and experimental results are presented demonstrating the feasibility and accuracy of this method.

Heart Axis Rotation Due to Exercise

  • Lee, Tae-Jun
    • Journal of Preventive Medicine and Public Health
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    • v.4 no.1
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    • pp.1-18
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    • 1971
  • Eleven nonathletes and eleven athletes were exercised on a standardised Harvard step test, and the average rate of change in QRS amplitude in lead III of the electocardiogram associated with heart rotation and the average change in rate of heart beat were observed. 1. After the Harvard step exercise, the average rate of change in QRS amplitude in lead III of both groups increased. This was due to the clockwise rotation of the heart and was associated with respiratory movement. The diaphragm was inferred to remain for a while in a relatively more inspiratory position. 2. After the Halved step exercise, a high correlation between the recovery of the average rate of change in QRS amplitude in lead III and the average change in rate of heart beat was observed in the athletic group. 3. In the nonathletic group there was no significant correlation between the average rate of QRS amplitude change and the average rate of change of heart beat. 4. Athletes were assumed to be trained to ventilate quickly at their maximum ability, using deep descending movements of the diaphragm and other respiratory musclature. Consequently, the average in rate of heart beat also recovered quickly. 5. Nonathletes were inferred not to have been trained to adjust quickly to ventilate so efficiently with their diaphragm movement and other respiratory musculature, and are characterised by their longer time to complete recovery.

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Multi-level UnderVoltage Load Shedding Scheme Considering Rate of Change of Voltage for Voltage Stability (전압 변동률을 고려한 수도권 전압 안정화 다단계 부하차단 적용 방안)

  • Lee, Yun-Hwan;Kim, Tae-Gyun;Kim, Ji-Hun;Lee, Byong-Jun;Kang, Bu-Il;Cho, Jong-Man
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.58 no.12
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    • pp.2335-2341
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    • 2009
  • High technique growth of modem times and high industrial facility in consequence of buildings demand for electric power of an extensive scale with stability supply and maintenance of high quality. But, power system always have risk of network contingency. When power system break out disturbance, it circumstantially happen like uncontrolled loss of load developing from of cascading. Severely which would be raised wide area blackout, plan to prevent, which make stability through a little of load shedding and multi-level UnderVoltageLoadShdding should work. This paper presents target, sensitivity of bus voltage have choose appropriating load shedding location and load shedding decision making logic with considering rate of change of voltage have studied multi-level under voltage load shedding scheme. Calculation of rate of change of voltage applied method of least square. As a result, we are studied an dynamic analysis of 2008 summer peak data. We have been known that network analysis is a little development and developing UnderVoltageLoadShedding scheme.

Middle School Students' Understanding of Constant Rate of Change in Functional Situations Using SimCalc MathWorlds (SimCalc MathWorlds를 활용한 함수적 상황에서 드러나는 중학생들의 일정한 변화율에 대한 이해)

  • Ma, Minyoung
    • Journal of Educational Research in Mathematics
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    • v.27 no.3
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    • pp.599-614
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    • 2017
  • The purpose of this study is to compare and analyze middle school students' understanding of constant rate of change, in terms of observing, representing and interpreting dynamic functions in various ways using the SimCalc MathWorlds. For this purpose, parts of a class conducted for six students in the first grade of middle school were analyzed. The results suggested two implications for a class that used this program (SimCalc MathWorlds): First, we confirmed that the relationships between the two quantities that students notice in the same situation can be different. Second, the program helped students to develop a more comprehensive understanding of the meaning of the constant rate of change. The study also revealed the need to use technology in teaching and learning about functions, particularly to represent and interpret a given situation that involves the constant rate of change in various ways. Further, the results can contribute to developing contents and methods to teach functions using technology in consideration of students' different levels of understanding.

VISUAL CURVATURE FOR SPACE CURVES

  • JEON, MYUNGJIN
    • Honam Mathematical Journal
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    • v.37 no.4
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    • pp.487-504
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    • 2015
  • For a smooth plane curve, the curvature can be characterized by the rate of change of the angle between the tangent vector and a fixed vector. In this article we prove that the curvature of a space curve can also be given by the rate of change of the locally defined angle between the tangent vector at a point and the nearby point. By using height functions, we introduce turning angle of a space curve and characterize the curvature by the rate of change of the turning angle. The main advantage of the turning angle is that it can be used to characterize the curvature of discrete curves. For this purpose, we introduce a discrete turning angle and a discrete curvature called visual curvature for space curves. We can show that the visual curvature is an approximation of curvature for smooth curves.

Analysis on High School Students' Recognitions and Expressions of Changes in Concentration as a Rate of Change (변화율 관점에서 농도 변화에 대한 인식과 표현의 변화 과정에 대한 분석)

  • Lee, Dong Gun;Kim, Suk Hui;Ahn, Sang Jin;Shin, Jae Hong
    • Journal of Educational Research in Mathematics
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    • v.26 no.3
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    • pp.333-354
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    • 2016
  • The aim of the present study is twofold. One is to confirm a hypothesis that a student's rate concept influences her conceiving change of a function in the view of rate of change and the other is to build up foundations for understanding the transition process from her rate concept to the concept of rate of change when she investigates the change of concentration as an intensive quantity. We explored how three participating high school students recognized and expressed change of given functions by using their rate concept as a conceptual tool. The result indicates that a change in students' rate concept might have an effect on understanding how function values change in term of rate of change. We also expect that it could be a catalyst for further research for clarifying the relationship between students' rate concept and their development of a concept of rate of change as a foundation for learning calculus.