Introduction to Vectors 11 Introduction I to Vectors I 2 4b l1rd L j f A Hands on Introduction to Displacement Velocity Vectors and Frame of Reference through the Use of an Inexpensive Toy Gwen Saylor Department QP a f RiB8 1ttH9 Wind I WQrizgptal GriV of Physics State University of New York Buffalo State College IF 1b d to vector Ih paper presents a set 0 f hands on actIVltIe t J Abstract T Y e lise as an mtrodllctIOn terminology common in the New York State Regents Ph ics curriculwn through a focus on displacement and velocity vectors Vith inexpensive equipment student are able to visualize the tip to tail method of vector addition deter line the horizontal and vertical components of vectors and observe the combination of two COl lIrrent parallel or perpendicular vectors Students observe the motion of a toy all a mov g grid to establish the concept of frame of reference for relative motion The terminology d level of difficulty are geared toward a Iligh school Regents class Through guided activity IVO sheets student groups explore scenarios that frequently appear on the New York State Regen Pi4 IVam related to vectors 1300 Elmwood Ave Buffalo NY 1422 SaYIOr acSdny or i I If f1 7 Acknowledgements This paper is submitted in partial fulfillment of the requirements necessary for PHY690 Masters Project at SUNY Buffalo State College wlder the guidance of Dr Dan Maclsaac D0 A 11 i Jro 5 L Jtr1 r L a fjj f 0 I rl1 v 0 C Introduction n4k i IT e J I t ct Vectors are a HPl w 1 sktlW8 fill t Introduction I tN sf hlilCS C L eo Ie r 7 Students I ave greater dIfficulty problem solving throughout the entire year This paper summarizes a method for i vectors early m the Regents PhYSICScumculum a ce erated motIon ts PhYSICSCore CUfflculum oper erposltIon off tces 0 tt at C I 1 r e J eo C r Y motion of the toys and apply Prio ge to the York of vectors t Co r nt 4 c I Throughout the year dents a confromed with problems that require combining parallel or perpen ICU ors quantities and resolving vectors into horizontal and vertical components Students are also tasked to graphically solve for the resultant oftlVo vectors using lIther head to tail or parallelogram 01 the vertIcal axes methods for scaled vectors that are not necessanly I t e the honzontal k While questIons i 1 If vector presentations S J alIgned to I 1 at f from the kinematics unit geometry and algebra that lead to of vectors m over the course of the year are linlited solely to those presented on past Regents Physics exams In order for a student to transition from the basic level of functionality listed in Key Ideas 5 1a c in Table o mastery of skills and concepts in the remainder of the curriculmn learners must be able t aemonstrate the following skills and wlderstanding p 71 7 J7 rlJ Jlf t M During activity two Ladybug on a conveyor belt students observe student worksheet are occasIOnally above the dIfficulty of the students may develop misconceptions It rt f c J or Is rf ctI t m the Regents cUfflculwn they are deSIgned to confront common mlsconceptlOns challenges as students develop a greater understandmg skills that appl the combination of concurrent parallel or perpendicular vectors using a moving toy and a moving grid to model two dimensional motions By observingthetoy relative to the grid and relative to Define terms such as dIsplacement velOCIty resultant equilibrallt and componenJ s Establish the relatIonship between compone ctood the concept of addItIve lllverse Arons 1995 the resultant vectors Itfi dmg g 107 f e r Define the meanmg ofa negatIve vectors m re aMn to the honzontal and vertIcal axes Understand that vector quantItIes are not fixed to a locatIOn Brown 1993 Rrylew the fixed frame students WIll learn that both path and velOCIty are dependent on the frame of reference Se t I D r by graphical meth ods and introduces the equations necessary for the analytical commlltation C I The The two tIv S p this docwnf t ACtIVIty One Ladybug TranSIt and AchvltyTwo Lad aConveyorBelt p mstructIonaltools makevector characteristics both expl it an ighly vis or learners Each activity mducted in tbe space of a student desktop ing aCh group member Students observe the components A v or lI t ft 1 t h e J L t Co C Activity One Ladybug Transit a1YSwsstudents to resolve vectors into horizontal and vertical JY momentum and fO Ie C of vector quantitIes and vect r 0 I P acement and velOCIty scenanos wbile romotIng 0 proJecttl 4 r The mtroductlon that are appropnate Q l 3 I c tIf wIth vectors than IS reflected mmany lugh school cumculums ure to address the central role of vectors in problem solving early on in the curriculum lea s sludellt diilictUty wIth ltles mtroduce the vector SkIlls and vector tenmnology I to Vectors J 4 r k I O l 1 In the same way that physics education has focused on modifying instruction to explicitly GUIded quesl10ns are used throughout the actIVitIes to support concept development address student misconceptions related to forces through the Force Concept Inventory introduced vocabulary acqUISItIon and skill application by Hestenes Wells and Swackhamer Vectors in the New York State Regents Physics Curriculum student preconceptIons With vector quantIl1es The Vector Know edge lest mll1lstered to introductory college level physics courses comprised of primarily science ma rs revealed that The following chart See Table 1 summarizes the portions of the Standards from Mathematical 1992 physics instructors must al so t steps to address nearly half of the students who reported prior exposure to vectors from hi h sc 001 physics or Analysis and Scientific Inquiry that relate to vectors in the New York State math entered the class with no useful knowledge Physics Core Curriculwn of basic vec r skill Knight 1995 High J S fh Q f r l re e e 1l0 In probing student preconcepti6 ns characteristics slvl lr that require explicit instruction Aguirre and Erickson clude the folio d It e t II r J re et COr D v Ot Oll tL t c 5 11 1984 mg i are independent 1 offrame IA If 9 vo v 0 LJ 0 I C t S of reference rS r W V O J A common theme I J research is the role of the reference frame in Vector components act sequentially rather than simultaneously Time is different for the resultant path than for the components CU fler independence of each component vector Based on interviews and that students commonly held preconceptions regarding vectors Speed and displacement J p4 about vectors Agwrre presented seven vec lr to the seven characteristjo s outlined
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