Peter Garik

Student misconceptions in signals and systems and their origins

We report on our investigation of student misconceptions and their origins within the Signals and Systems module taught in the Department of Aeronautics and Astronautics at the Massachusetts Institute of Technology. This study is a sequel to an earlier paper in which we discussed our findings on student conceptions and reasoning regarding the behavior of linear, time-invariant electrical circuits. In this paper, we report our findings on student understanding of the fundamental topics involved in the study of continuous-time linear, time-invariant systems. During spring term 2003, we conducted clinical interviews for our data gathering. Fifty-one students enrolled in Signals and Systems volunteered to take part in this study. In our analysis, we identified the typical student difficulties and misconceptions, and the mathematical cognitive resources underlying these misconceptions. In this paper, we report on our results and how they could inform the development of instructional material and methods that support student learningWe report on our ongoing investigation on student misconceptions and their origins within the signals and systems module taught in the Department of Aeronautics and Astronautics at the Massachusetts Institute of Technology. Signals and Systems, as taught in Aeronautics and Astronautics at MIT, consist of two parts. The first part, offered in the Fall semester, covers introductory linear circuits; the second part, offered in the Spring semester, covers the analysis of generic continuous-time linear time-invariant systems. During Fall 2002, we conducted clinical interviews to assess student understanding of introductory linear circuits. Fifty-four sophomore students enrolled in Signals and Systems volunteered to take part in this study. The interview transcripts were analyzed, physical and mathematical misconceptions were identified, and their sources were examined based on diSessa s theory of intuitive knowledge, and Chi and Slotta s ontological categorization. In this paper, we report on our results and suggest how this understanding can be used to develop more effective pedagogical instruments designed to enhance student learning.

Learning Fractals by “Doing Science”: Applying Cognitive Apprenticeship Strategies to Curriculum Design and Instruction

Science research professionals originated an education innovation project that adapts the mentoring model of graduate study in science to the high school, closely coupling experiment and computer visualization models devised originally for science research in natural or random fractals. Educational researchers who joined the project helped to interpret the effort in terms of “cognitive apprenticeship,” a teaching paradigm already known in the cognitive research literature. This article traces the evolution of the materials informed by this paradigm and the results of two sequential trials of a fractal dimension unit in a suburban high school. In the 2nd‐year trial, students began to act as independent investigators and the teacher gradually and spontaneously adopted the role of mentor.

Student Misconceptions in Signals and Systems and their Origins — Part II

We report on our investigation of student misconceptions and their origins within the Signals and Systems module taught in the Department of Aeronautics and Astronautics at the Massachusetts Institute of Technology. This study is a sequel to an earlier paper in which we discussed our findings on student conceptions and reasoning regarding the behavior of linear, time-invariant electrical circuits. In this paper, we report our findings on student understanding of the fundamental topics involved in the study of continuous-time linear, time-invariant systems. During spring term 2003, we conducted clinical interviews for our data gathering. Fifty-one students enrolled in Signals and Systems volunteered to take part in this study. In our analysis, we identified the typical student difficulties and misconceptions, and the mathematical cognitive resources underlying these misconceptions. In this paper, we report on our results and how they could inform the development of instructional material and methods that support student learning

An Object-Based Modeling Tool for Science Inquiry

A major challenge of future secondary and undergraduate science instruction will be to help students learn to formulate, at an appropriate level of representation, mathematical models of physical phenomena for use with a computer simulation engine. Students will learn to investigate the behavior of these models and test their validity and scope of application. In order to make this leap in instruction to teaching model formulation, we have to confront the fact that students typically find it very difficult to express problems in the standard formal mathematical representations. The symbolic language of differential equations, for example, is very far removed from students’ mental models of the objects and object interactions involved in problem situations. Another kind of representation language—mathematically equivalent and mechanically translatable to differential equations, but more natural and accessible to students—is needed to provide them with initial experiences in problem formulation. The transition to the standard formal language can be made later, after they have acquired the relevant insights. This chapter describes a modeling tool for expressing phenomena directly in terms of the characteristic interactions among the objects involved. This object-based representation facilitates the introduction of modeling ideas and activities in science education. At the same time, it offers science researchers a productive new approach for investigating complex phenomena.

Report on a Boston University Conference December 7-8, 2012 on "How Can the History and Philosophy of Science Contribute to Contemporary US Science Teaching?".

This is an editorial report on the outcomes of an international conference sponsored by a grant from the National Science Foundation (NSF) (REESE-1205273) to the School of Education at Boston University and the Center for Philosophy and History of Science at Boston University for a conference titled: How Can the History and Philosophy of Science Contribute to Contemporary US Science Teaching? The presentations of the conference speakers and the reports of the working groups are reviewed. Multiple themes emerged for K-16 education from the perspective of the history and philosophy of science. Key ones were that: students need to understand that central to science is argumentation, criticism, and analysis; students should be educated to appreciate science as part of our culture; students should be educated to be science literate; what is meant by the nature of science as discussed in much of the science education literature must be broadened to accommodate a science literacy that includes preparation for socioscientific issues; teaching for science literacy requires the development of new assessment tools; and, it is difficult to change what science teachers do in their classrooms. The principal conclusions drawn by the editors are that: to prepare students to be citizens in a participatory democracy, science education must be embedded in a liberal arts education; science teachers alone cannot be expected to prepare students to be scientifically literate; and, to educate students for scientific literacy will require a new curriculum that is coordinated across the humanities, history/social studies, and science classrooms.

Understanding Naïve Reasonings in Signals and Systems: A Foundation for Designing Effective Instructional Material

Student naïve reasonings in an undergraduate engineering course, signals and systems, were investigated in order to provide the groundwork for designing effective instructional material. Students majoring in aerospace engineering at the Massachusetts Institute of Technology were interviewed to probe their reasoning about different signals and systems topics, particularly in their analysis of continuous-time, linear, time-invariant systems using the fundamental properties of LTI systems and linear systems tools. In this paper, we present central naïve reasonings that were identified related to the concepts of linearity, time-invariance, and convolution. We then discuss how these findings support instructors in designing effective instructional materials for signals and systems, such as concept questions for use in interactive lectures, guides for recitation sessions targeted to address student conceptual problems, and exam questions that accurately diagnose student conceptual problems.