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Inhelder and Piaget (1958) studied schoolchildren’s understanding of a simple pendulum as a means of investigating the development of the control of variables scheme and the principle central to scientific experimentation. The time-consuming nature of the individual interview technique used by Inhelder has led to the development of a whole range of group test techniques aimed at testing the empirical validity and increasing the practical utility of Piaget’s work. The Rasch measurement techniques utilized in this study reveal that the Piagetian Reasoning Task III - Pendulum and the interview reveal the same underlying ability. Of particular interest to classroom teachers is the evidence that some individuals produced rather disparate performances across the two testing situations. The implications of the commonalities and individual differences in performance for interpreting children’s scientific understanding are discussed.

Phenomena associated with the present numerous opportunities for assessing higher order human capabilities related to and the of natural law. This paper illustrates how systematic , using phenomena, can provide a useful tool for classroom teachers and program planners. , a technique of teacher-facilitated student involving direct interaction between students and natural phenomena, is presented as a way to establish student competence in applying (e.g., conceptualizing variation due to error). This approach to can heighten student curiosity and provide a concrete referent for complementary cultural, historical, and scientific instruction. The role of in constructively shaping science education programs is considered.

The purpose of the present study was to test the hypothesis that student’s abductive reasoning skills play an important role in the generation of hypotheses on pendulum motion tasks. To test the hypothesis, a hypothesis-generating test on pendulum motion, and a prior-belief test about pendulum motion were developed and administered to a sample of 5th grade children. A significant number of subjects who have prior belief about the length to alter pendulum motion failed to apply their prior belief to generate a hypothesis on a swing task. These results suggest that students’ failure in hypothesis generation was related to abductive reasoning ability, rather than simple lack of prior belief. This study, then, supports the notion that abductive reasoning ability beyond prior belief plays an important role in the process of hypothesis generation. This study suggests that science education should provide teaching about abductive reasoning as well as scientific declarative knowledge for developing children’s hypothesis-generation skills.

Pendulums which swing in two dimensions simultaneously and are designed to leave a record of their motion are termed ‘harmonographs’. The curves which they draw are known, alternatively, as ‘Bowditch curves’ or ‘Lissajous curves’. A variety of designs of harmonographs have been invented over the years. These may be a ‘Y-suspended’ ‘simple’ pendulum, or they may be a complex ‘physical’ pendulum system. Harmonographs have been built as demonstration apparatus in physics (or mathematics) or as ‘art’ machines for enjoying the aesthetics of the curves produced.

In this article we use the pendulum as the vehicle for discussing the transition from classical to quantum physics. Since student knowledge of the classical pendulum can be generalized to all harmonic oscillators, we propose that a quantum analysis of the pendulum can lead students into the unanticipated consequences of quantum phenomena at the atomic level. We intend to illustrate how classical deterministic physical ideas are replaced by a point of view that contains both deterministic and probabilistic aspects. For example, the wave function contains probabilistic information but it evolves in time according to a fixed law, the Schrodinger equation. Discussion of the transition from classical to quantum thinking is historically grounded in the work of twentieth-century physicists who developed quantum ideas. We see application to current science in areas such as semiconductors, optics, GPS systems, and superconductivity. Our notion is that a scientifically-literate public should have a sense of the broad, conceptual schemes in modern physics, as well as those associated with classical physics. We discuss educational challenges and strategies connected to including quantum theory in a general education physics course. Our work would have other applications in college and secondary school settings.

A pendulum ‘engine’ with dynamic parameters can be created and pendulum functions manipulated and analyzed using interactive elements in Flash. The effects of changing the damping (convergence) properties, initial release angle and initial velocity conditions can be explored. The motions then can be digitized using the Flash Digitizer 1.1, exported and graphed. The powerful properties of actionscripting, coupled with the flexible interactivity of the Flash environment, allows for attractive and mathematically driven Flash movies. Along with the accessibility and interactive nature of the Web, and by contextualizing the history and mathematical applications of pendulum motions, this lesson becomes teacher and student-friendly for physics and mathematics classrooms.

In light of the established validity of pendulum as a topic in physics curricula (Matthews 2000), the study looked at the place of pendulum motion in the physics curriculum of the high school in Israel. The data is available through presenting results of the nationwide matriculation examination in its units of Mechanics and Research Laboratory for the Advanced Placement program (several thousands students). Although the assessment questions and problems mainly tested students’ performance, and less their understanding of the subject, the study, by discussing these problems and questions, allows a perception of the extent to which the pendulum topic is addressed in High School physics instruction. The results can support a discussion on the nature of the requirements and values encouraged by the particular educational system and the strengths and weaknesses of the adopted educational policies.

When we refer to scientific knowledge, we, implicitly or explicitly, refer to its three components, namely its conceptual framework, its methodological principles and its cultural aspects. The pendulum is a topic of science teaching and learning where all three of these aspects can be examined with the aim of gaining a holistic appreciation of the transformation of a natural phenomenon into a phenomenon of the physical sciences and how this can then be recontextualized into a topic of school science learning. The main objective of this study is to examine whether this richness of the pendulum as a topic of teaching is revealed in the school science textbooks in Greece and Cyprus, for both primary and secondary education. We will use an analytical mapping instrument in order to determine, whether the pendulum is introduced at some grade level and, if so, in what context. We will then use an interpretive instrument, which relies on taxonomy of science curricula into traditional, innovative and constructivist programs, in order to attach meaning to the analysis. Finally, we will formulate a series of proposals in relation to the educational value of the simple pendulum at the Greek and Cypriot gymnasium level.

This paper describes life-span development of understanding about pendulum motion and effects of school science. The subjects were 2,766 people ranging from kindergartners up to 88 years senior citizens. The conflict and consensus between children and their parent’s understanding of pendulum motion were also analyzed. The kindergartner’s understanding, mostly non-scientific, made a marked developmental change to another type of non-scientific understanding by the time they reach G 4. Parents with scientific understanding do not presumably nurture scientifically minded children, even though about half of them can apply scientific conceptions that shorter pendulums swing faster, and the amplitude and speed of pendulum motion do not depend on its weight. There seems to be another type of developmental change from scientific understanding to non-scientific understanding around their fifties. It is suggested that the scientific understanding in the public about pendulum motion become predominant due to the educational intervention through school science.

As part of a first-year college Introductory Physics course, I have students construct an Excel® spreadsheet based on the differential equation for pendulum motion (we take a pendulum having a light bar rather than a string, so it can go ‘over the top’). In extensive discussions with the students, I find that forcing them to make the spreadsheet , entering velocities as position differences divided by time, etc., leads to a firmer grasp of basic calculus concepts. And, the instant graphical response of the finished product gives a sense of accomplishment as well as a lot of fun while building intuition about pendulum motion.