A Simple Instrument to Assess Students’ Ability to Relate Representations in Kinematics2. Beichner, R.K. (1994, August). Testing student interpretation of kinematics graphs. American Journal of Physics, 62(8) 750-762.A Simple Instrument to Assess Students’Ability to Relate Representations in KinematicsFor Submission to the STANYS BulletinMaurice Hayon, Dept. of Physics, SUNY-Buffalo State College, 1300 Elmwood Ave, Buffalo, NY 14222 < [email protected]>ABSTRACTThis 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.AcknowledgementThis manuscript was prepared in partial fulfillment of requirements for PHY690: MastersProject 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 1kinematics]," (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 notaddress the concerns I’ve experienced with my students. For the TUG-K, the emphasis ismore 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 noquestions 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 2them 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 canalso 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.3Mathematically, there should be 24 different ways to arrange these four representations, however, most of the combinations repeat itself—for example:a) G, V, M, Db) 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 isvery excessive for obvious reasons such as time constraint and test exhaustion. Therefore, the sequence for the assessment was constructed as:1. D, M, V, G2. V, D, G, M3. G, V, M, D4. M, G, D, VThis 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: DMVGThe RRK was developed to begin with a dot diagram that represents a jogger running at a constant velocity.
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