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Buffalo State PHY 690 - A Hands-on Introduction

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Introduction to Vectors 1A Hands-on Introduction to Displacement and Velocity Vectorsand Vector Operations through the Use of an Inexpensive“Never Fall” Wind-Up ToyGwen Saylor, Department of Physics, State University of New York – Buffalo State College, 1300 Elmwood Ave, Buffalo, NY 14222 [email protected] Acknowledgements: This paper is submitted in partial fulfillment of the requirements necessary for PHY690: Masters Project at SUNY – Buffalo State College under the guidance of Dr. Dan MacIsaac.Introduction to Vectors 2Abstract: This paper presents a set of hands-on activities to be used as an introduction to vector quantities and vector commutation. In these activities students are introduced to basic vector arithmetic through the analysis of the motion of a “Never-Fall” wind up toy. With inexpensive equipment students can visualize the head to tail method of vector addition, determine the horizontal and vertical components of vectors and observe the combination of two concurrent parallel or perpendicular vectors. The importance of the sequencing of these concepts early within in the curriculum is discussed in context of research into the teaching and learning of vectors. These activities introduce students to the characteristics of vector quantities while supporting skills required for vector operations. Through guided activity worksheets students will be exposed to the terminology used frequently on the New York State Regents Physics examrelated to vectors.Introduction to Vectors 3Introduction: Vector concepts and vector operations are a central part of the New York States Physics Core Curriculum. Any in depth discussion of motion, forces or field behavior requires knowledge of vector quantities. Experienced physics teachers know that many of the characteristics of vectors that seem obvious to individuals with a background in physics are not at all obvious to many first time physics students. In the same way that physics education has focused on modifying instruction to explicitly address student misconceptions related to forces through the Force Concept Inventory introduced by Hestenes, Wells and Swackhamer (1992), physics instructors must also take steps to address student preconceptions with vector quantities The Vector Knowledge Test, administered to introductory college level physics courses comprised of primarily science majors, revealed that nearly half of the students who reported prior exposure to vectors from high school physics or math entered the class with no useful knowledge of basic vector skills (Knight, 1995). In probing student preconceptions about vectors, Aguirre presented seven vector characteristics that require explicit instruction (Aguirre and Erickson, 1984). A common theme to the seven characteristics outlined in Aguirre’s research is the role of the reference frame in understanding vectors and the independence of each component vector. Through interviews withstudents regarding three experimental situations, Aguirre (1988) discovered a number of student preconceptions that require explicit instruction but are often viewed as implicit by instructors. Specific recommendations from the analysis of the Vector Knowledge Test (Knight, 1995) suggest vectors should be introduced over a course of several weeks prior to introduction of projectiles or Newtonian mechanics. Subsequent investigations using diagnostic testing of introductory college students noted that students demonstrated some intuitive knowledge of vectors but lacked the ability to apply skills such as tip-to tail and parallelogram methods of vector addition (Nguyen and Meltzer, 2003).Many physics textbooks present vectors during a unit on forces and then transition quickly toother quantities such as velocity, acceleration, momentum and displacement. From a students’ viewpoint “adding velocity arrows appears very different from adding displacement arrows, and acceleration arrows are totally incomprehensible” (Arons, 1997, p107). Displacement vectors insome scenarios are successive rather than concurrent. As a result displacement vectors are the simplest starting point; however, as instructors transition from displacement vectors to force vectors students are bound to get confused unless the nature of each of these quantities is discussed (Roche, 1997). Care must be taken in curriculum planning to allow adequate discussion and exploration with the addition of each new vector quantity. Students who grasp the idea of vectors as they relate to velocity have significant difficulty translating those skills to acceleration. Shaffer and McDermott found in a survey on introductory physics students, graduate students and physics TA’s, that the ability to correctly draw and label a velocity vectorIntroduction to Vectors 4was markedly greater than the number of students who were able to correctly draw and label an acceleration vector (Shafer and McDermott, 2005). I propose that isolating the initial introduction of vector skills and vector characteristics to non-accelerated motion will help students overcome the prevalent misconceptions documentedin aforementioned research. By devoting instructional time to establishing the characteristics of vectors within the context of non-accelerated motion students can gain comfort with vector operations and confront common misconceptions without the compounding difficulty of other complex topics such as projectiles and mechanics. Vectors are an abstract concept for students. A few simple examples at the outset of a discussion are not sufficient to address the level of student difficulty with basic vector skills. The activities presented in this document limit the introduction of vector quantities and vector operations to displacement and velocity scenarios in order to provide explicit instruction of vector characteristics. As instructors introduce new concepts, reference to these common learning experiences can accompany discussion of differences and similarities between quantities. The two activities, “Activity One: Ladybug Transit” and “Activity Two: Ladybug on a Conveyor Belt” presented in this document attempt to provide instructional tools that make vector characteristics both explicit and highly visual for learners. The motion of the equipment, while not modeled after Aguirre’s design (1988) is similar in intent to two of the experimental situations presented; however, on a more simplistic and


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Buffalo State PHY 690 - A Hands-on Introduction

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