More mathematics in a conceptual physics course: formula appreciation activities

1. More mathematics in a conceptual physics course: formula appreciation activities Conceptual Physics Courses • Are gaining more popularity as high school and college-level courses for non-science majors. • Do not have mathematics prerequisites. • Use minimal amount of mathematics. Some preliminary results of the analysis • In the bar-chart: The Likert-scale 5 item survey responses are clustered as Negative (strongly disagree, disagree), Neutral, and Positive (agree, strongly agree). • Overall pre- and post survey items responses show evidence of more prominent attitude and anxiety changes in the experimental group. Some of the interesting survey item responses are presented below: Vazgen Shekoyan Queensborough Community College, CUNY Overview Motivation • Most of QCC students have a) high science and mathematics anxieties (both before and after taking college level courses) as well as negative attitudes and beliefs about science. b) low levels of basic math preparation (some students have to repeat a Remedial Math course several times in order to get a Pass grade and get access to college level courses). • Up to one-third of students taking QCC Conceptual Physics course are Elementary Education Majors, who have • the highest levels of science and math anxieties; • are likely to avoid teaching science as future elementary school teachers and transfer their science and math anxieties and beleifs to their students. of our students have Q15: I like the equations in science courses Conceptual physics courses are typically offered to non-science majors as a fulfillment of laboratory science degree requirements. These courses do not have mathematics prerequisites and use minimal amount of mathematics. Is it worthwhile adding more mathematics in conceptual physics courses? How would it affect students’ science attitudes and anxieties? I have devised and incorporated mathematical activities (formula appreciation activities) in a Conceptual Physics course offered at Queensborough Community College (QCC). Most of the activities were comprised of a) making sense of formulas by examining limiting cases, and b) identifying proportionalities between variables in the formulas. I have evaluated the implications of the implementation on students’ science attitudes and anxieties in a quasi-experimental control-group design study. In this poster I will present examples of such activities and discuss the implications of the implementation. Step 3: Looking for limiting cases • A sample task: Step 2: Identifying proportionalities in formulas Consists of 3 phases: • Phase 1: Proportionality Discovery activity with circles • Phase 2: Generalization of the proportionality rule • Phase 3: Identifying proportionalities in physics formulas; practice exercises and problems Q5: You could say that my anxiety in physics is due to my fear of math Main Research Questions • How would adding “formula appreciation” activities into a Conceptual Physics class affect students physics and math anxieties? • How would it affect their learning attitudes towards physics? • In particular, how would it affect their beliefs about the role formulas play in understanding and learning physics? Phase 1: Proportionality Discovery activity with circles • Available equipment: strings, scissors, rulers and graph paper with drawn circles of various sizes. • Experimental discovery (C=circumference; A=area of a circle): • The hypothesis is then tested with measurement on bigger circles. Phase 2: Generalization of the proportionality rule Description of the Study Q8: I do not expect physics equations/formulas to help my understanding of ideas; they are just for doing calculations The Course and Intervention: • PH 101: Principles of Physics is a one-semester conceptual physics course (3 lecture hours, 2 lab hours). • Textbook: “Conceptual Physics”, P. Hewitt, 11th edition. • In the experimental sections I have incorporated the “formula appreciation” activities in the lecture and few homework assignments. • Two parallel section of PH101 served as experimental and control groups during both Fa13 and Sp14 semesters. • Both experimental and control groups had the same lecture instructor, same labs, and similar homeworks before the intervention Step 2 completion (the first half of the semester). • Control group mathematics encounter: basic formulas defined (e.g., v=d/t, a=f/m); Plug and Chug exercises; proportionality ideas introduced only in Newton’s II law coverage, simple algebra used in the lab component of the course (plug and chug, %error calculations, plotting graphs and finding slopes). • Due to intervention the experimental group covered about 15% less new material. Formula Appreciation Intervention “Formula Appreciation” intervention steps • Step 1: Playing with formulas • to help students being at ease with formula manipulation • Step 2: Identifying proportionalities in formulas • to help them make sense of formulas by finding the relationships between variables in simple physics formulas/equations • Step 3: Looking for limiting cases • additional steps of making sense of formulas • checking correctness of formulas/equations by considering limiting cases Q9: In physics, it is important to make sense out of formulas before I can use them correctly Phase 3: Identifying proportionalities in physics formulas and problem solving • Proportionality identification practice: Example1: The table in the next page shows proportionalities in different formulas. Fill-in the blank spaces. • Proportionality identification exercises: Q1: If the net force on a sliding block is somehow tripled, by how much does the acceleration increase? Q2: You are given a glass with half the radius of Jane’s glass. Note that both glasses have same depths. Jane drank the whole glass. You want to drink exactly as much wine as she drank. How many glasses of wine do you need to drink with your glass to make it happen? Q3: How many times more stopping distance is required to stop a car if it was 3 times as fast? Step 1: Playing with formulas • Presented to students as a formula manipulation game • Instructors need to make sure to justify the “rules of the game” by bringing simple numerical examples so that the rules are not perceived as “fake”. Rules of a game: • Both sides of the equality sign can be multiplied, divided (except for 0), added and subtracted by same number/symbol on both sides of equation/formula • Your task is to play with provided formulas until they are modified into the “ t= something” form. • Sample task 1: 4t+5=17. Following the rule of the game, bring the equation to the form t = … • Sample task 2:a-3t=c. Following the rule of the game, bring the equation to the form t = … Data Collection • The experimental group – 53 students, control group – 40 students. • Pre and post attitude surveys in both groups. The survey is comprised of cluster of questions on • Physics and Math anxieties • Selected CLASS questions related to the role of formulas/equations. • Math mastery pre and post surveys • Demographic, academic experience, and physics & math confidence level survey. Q10: In physics, mathematical formulas express meaningful relationships among measurable quantities Acknowledgments • I would like to thank Sunil Dehipawala, David Lieberman and Tak Cheung for interesting discussion and for help with the implementation of the study. • The study was supported by 2013 QCC Challenge Pedagogy grant.