A Simple Instrument to Assess Students Ability to Relate Representations in Kinematics For Submission to the STANYS Bulletin Maurice Hayon Dept of Physics SUNY Buffalo State College 1300 Elmwood Ave Buffalo NY 14222 mhayon1 gmail com ABSTRACT This article focuses on the importance development structure and delivery of a formative assessment tool that I created called Relating Representations in Kinematics RRK When teaching physics we constantly remind the students that there are generally four different ways to represent motion verbally V mathematically M graphically G and diagrammatically dot diagrams D These four representations are emphasized in the New York State Physical Setting Core Curriculum The RRK tests students on their ability to differentiate between these representations and students ability to transfer information from one representation to another The RRK can also be used as an activity to help students practice relating and interpreting motion Acknowledgement This manuscript was prepared in partial fulfillment of requirements for PHY690 Masters Project at SUNY Buffalo State College under the guidance of Professor Dan MacIsaac Introduction According to Standard 1 of the NYS Physical Setting Physics Core Curriculum students are required to be able to distinguish relate and interpret symbolic verbal and mathematical information New York State Education Department a 2008 Symbolic information in kinematics refers to both graphical and diagrammatical descriptions of motion Research also shows that students must know how to relate one interpretation of motion to another in order to master their understanding of kinematics The thinking involved in making the translations to and from graphs help register the concepts of 1 kinematics Arons 1997 Apparently students who could correctly translate from one kinematics graph to another also had the best overall understanding of kinematics graphs Beichner 1994 In my years of experience as a physics teacher at Baldwin Senior High School I ve noticed that students naturally have trouble relating between the different representations of motion Most of my students can correctly solve a simple mathematical problems since they ve had years of practice in their math classes However linking symbolic information to a mathematical problem becomes a major hurdle I developed Relating Representations in Kinematics RRK as a worksheet activity to address the students shortcomings in making that connection After the success of the activity I altered it slightly and used it as a formative assessment tool There are other assessment tools that are effective and well researched in testing specific areas in kinematics such as the Test of Understanding of Graphs in Kinematics TUG K Beichner 1994 and the Force Concept and Motion Evaluation FCME Sokoloff Thornton 1998 Although these are excellent assessment tools they did not address the concerns I ve experienced with my students For the TUG K the emphasis is more on the graphical motion Although students must still relate between graphing and other representations for some questions every question regards a graph and there are no questions that deal with dot diagrams The FCME contains questions in kinematics but the focus is more on Newtonian physics and dynamics which is beyond the scope of this topic The RRK can also be used as an in class activity where students can work in groups to solve each question The characteristics of the questions in the RRK qualify 2 them as Context Rich Problems Context Rich Problems n d If students are seeing these questions for the first time they will not be able to solve it but can collaboratively share ideas to arrive to a conclusion Groups can use computer programs such as Logger Pro 3 0 with sonar devices cameras or other sensors to achieve real life data to compare it to a problem that they are working with If those materials are not present students can also use computer simulations from websites such as PhET http phet colorado edu simulations to model actual movement Structure of the RRK This assessment tool is only four questions long but each question includes a combination of relating interpretations For example question 3 has the sequence Graphical Verbal Mathematical Diagrammatical GVMD Students must analyze a velocity vs time graph and qualitatively sketch the acceleration and position vs time graphs to complete the graphing section of the question It is important to note that the graphs in the RRK are aligned horizontally since questions in the New York State Regents Exam frequently place motion graphs of different quantities next to each other rather than on top of each other New York State Education Department b 2008 Students must then take the graphical information and explain the motion verbally The next step is to use the verbal part of the question to answer a mathematical problem Finally students are asked to draw dot diagrams to represent the same motion Since students must graph something three times there are five problems per question So there are actually 20 problems for this assessment and the students should take approximately 45 minutes to complete it 3 Mathematically there should be 24 different ways to arrange these four representations however most of the combinations repeat itself for example a G V M D b G V D M Although the combination is different students are relating a verbal representation from the graphical for both questions This route will yield a 120 problem assessment which is very excessive for obvious reasons such as time constraint and test exhaustion Therefore the sequence for the assessment was constructed as 1 D M V G 2 V D G M 3 G V M D 4 M G D V This sequence ensured that the students would be assessed on every possible way to relate the representations with the minimum amount of questions so that it was possible to use this assessment as a full period exam Question 1 DMVG The RRK was developed to begin with a dot diagram that represents a jogger running at a constant velocity Students are to use their general constant velocity equation d vt in order to solve the problem Any inclusion of acceleration in a student s answer for this problem is a clear indication of his lack of conceptual understanding of acceleration 4 For the verbal representation students must mention constant velocity The grader should not accept constant speed unless it is accompanied by constant direction The dot diagram clearly shows that the
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