1. Robert W. Arts, Ph.D.* Professor of Education & Physics University of Pikeville Pikeville, KY Using a Universal Qualitative Analysis Writing Assignment (UQAWA) to Stimulate and Assess Critical Thinking in the Physics Classroom Presented at the Spring Meeting of the Kentucky Association of Physics Teachers Bowling Green, KY, March 17, 2012 *Based on work by Dan Bowman at Ferrum College

2. Abstract The ability to use equations to relate quantities relevant to a given problem qualitatively is a form of critical thinking that is crucial to a student’s success in the sciences. This skill is important both in deciding how to tackle a problem as well as in determining if the results of a calculation are reasonable. However, this skill is difficult to teach and assess with traditional methods. Universal Qualitative Analysis Writing Assignments (UQAWAs) are an attempt to address this difficulty.

3. What is a UQAWA? A Universal Qualitative Analysis Writing Assignment (UQAWA) is a method of both assessing and enhancing a certain aspect of your critical thinking skills, namely, the ability to –1. determine which physical quantities are relevant to understanding a given physical situation; –2. determine which equations relating those quantities are relevant to understanding the situation; –3. use those equations to qualitatively describe how the physical situation will play out.

4. Using Equations Qualitatively For example, if you’re asked why a block of lead is heavier than an equal-sized block of aluminum, you should know first that the densities, masses and volumes of the two blocks are the relevant quantities. Next you should recall that density ½ is the ratio of mass m over volume V : Hence, for blocks of equal volume V, the mass of the lead block is m Pb = ρ Pb V while the mass of the aluminum block is m Al = ρ Al V. So, the fact that ρ Pb > ρ Al makes the mass of the lead block greater, and hence it feels heavier.

5. The Skills 1. Identify the relevant physical quantities –These are the vocabulary of the propositions. 2. Identify the relevant equations relating these quantities –Note: Using standard critical thinking terminology, these yield the propositions from which a valid argument must be constructed. (A proposition is the idea expressed in a declarative sentence; it must be either true or false.) 3. Construct a valid argument. –Note: Again, in standard terminology, an argument is a list of two or more propositions one of which (called the conclusion) is intended to follow from the others (called premises). A valid argument is one in which the conclusion follows necessarily from the premises.

6. Traditional Methods 1. Standard textbook problems (a.k.a. “story problems”) –Students must identify relevant physical quantities and the equations relating them. These are neither evaluated nor assessed explicitly in most cases (“partial credit” can be an explicit evaluation). Ideally, they should also use equations qualitatively to construct a valid argument about what they expect to happen. However, this is neither evaluated nor assessed. Furthermore, the extent of the mathematics involved often discourages this (i.e., they are in a hurry to get the problem “done” and move on to the next one). 2. “Back of envelope” calculations –These are in many ways the same as the standard textbook problems, however, the mathematics here is simpler, which encourages deeper thought to occur. Still, it is not usually assessed because doing so is difficult. 3. “Fermi” problems –These are more about estimation and unit conversion. These problems definitely get at the three skills but at a lower level. Also, unless the students write out their arguments, it is difficult to assess these skills.

7. More… 4. Conceptual questions, usually multiple choice or short answer –Students must use all three skills, and are evaluated on whether or not they do so successfully, but this is usually a poor assessment tool since it is hard to look at the skills on an individual basis. 5. Conceptual essay questions –These get at all of the pieces, but they can be difficult to use for assessment purposes without a rubric. Also, students seem to be at a loss for how to support their arguments using equations unless the practice is demonstrated repeatedly. 6. UQAWAs –The goal here is to provide a framework for the conceptual essay that guides the student through the process, coupled with a rubric to assess the various skills.

8. The Format Each UQAWA has four sections: –Description of Phenomenon This is the physical situation that will be asked to be explained. This is in their own words. It should be concise; short, but containing all of the relevant information that is to be explained. –Relevant Quantities This is a list of the relevant physical quantities. All of the quantities referred to in any explanations are be listed here. For each quantity, its name is listed, the symbol is indicated, its SI units are shown, and a brief description of its meaning is presented.

9. The Format Continued… –Relevant Equations This is a list of the equations relevant to describing the phenomenon. All of the equations referred to in explanations are listed here. –Explanation of Phenomenon This is the meat of the assignment. Here students use the quantities and equations identified to qualitatively explain the phenomenon described in the first section. There should be a clear, logical, causal explanation of the phenomenon describing how each relevant quantity affects the next by means of one of the relevant equations. Labeled sketches of the situation are encouraged.

10. For Our Trivial Example

11. Scoring

12. Scoring Details (example)

13. Actual Sample Assignment UQAWA - Light & Optics Spring 2009 Write a UQAWA that uses Snell's law to explain the difference between a double convex (converging) and a double concave (diverging) lens. Recall that a UQAWA by its nature is "qualitative." Therefore, while numerical values are not necessary in the completion of the UQAWA, it does not exclude the inclusion of labeled figures and diagrams!!

14. Actual Submission (partial)

17. Thank You ! Any Questions? RobertArts@upike.edu