Introduction to Vectors A Hands on Introduction to Displacement and Velocity Vectors and Vector Operations through the Use of an Inexpensive Never Fall Wind Up Toy Gwen Saylor Department of Physics State University of New York Buffalo State College 1300 Elmwood Ave Buffalo NY 14222 gsaylor acsdny org 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 1 Introduction to Vectors Abstract 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 exam related to vectors 2 Introduction to Vectors Introduction 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 with students 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 to other 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 in some 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 vector 3 Introduction to Vectors was 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 documented in 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 cost effective scale The ability to reason with vectors and apply vector operations in problem solving is essential to understanding of topics such as
View Full Document
Unlocking...