or Putting the Cart before the Horse Teaching Data Analysis in the Undergraduate Physics Laboratory, or Putting the Cart before the Horse Dr. Natalia Krasnopolskaia Department of Physics, University of Toronto 2017 CAP Congress Queen’s University

1. Main problems with data analysis (DA) in UG labs In this talk, the “DA” denotes “measurement technique + data analysis + uncertainty calculation”. The problems are common for traditional laboratory and active learning based classes. During the first lab sessions in their 1st year Physics labs, students have zero background in measurement technique, data analysis and uncertainty calculation. Poor basic knowledge makes students’ self-preparation with recommended readings inefficient. Usually, no time is allotted in the 1st and 2nd year lectures, labs or tutorials for introduction to measurement techniques and data analysis. Theoretical concepts of math courses, e.g. probability and statistics, are not psychologically associated by junior students with data analysis required in the lab reports in physics.

2. My experience in teaching DA in UG labs My experience is based on teaching the traditional UG labs to the 1st-, 2nd-, 3rd- and 4th- year students of Physics Specialists, Physics Major and Engineering Science Programmes in 2007-17. Enrolment ̴ 200. …………………………………………………………………………………………………………………………………… The basic source recommended by me to any level of the UG physics laboratory is “Data Reduction and Error Analysis for the Physical Sciences” by P.R. Bevington and D.H. Robinson, 3rd ed., McGraw Hill, 2003. The other recommended reading is “An Introduction to Error Analysis: The Study of Uncertainties in Physics Measurements” by J.R. Taylor, 2nd ed., University Science Books, 1997.

3. Evolution of my methods of teaching DA in the 1st year Physics (Mechanics in the fall term). 2007-08, 2008-09 (a lab coordinator): Error Test = a 20-minute computer base assignment. II. 2009-10 (a lecturer and a lab coordinator): one hour of introduction to DA at the 2nd lecture. 2010-11, 2011-12, 2012-13 (a lecturer and a lab coordinator): during the first week of classes, three one-hour lectures devoted to DA. IV. 2013-14 (a lab coordinator): Error Test on Blackboard plus 0.5-hour tutorial by TAs in groups (beginning of the 1st and 2nd session).

4. Lecturing DA in the 1st year Mechanics (fall term) Lectures in DA were based on a discussion of the real lab experiments. No theory preceding the real example was given. I put the cart before the horse. Compulsory experiments taken as examples were: “Acceleration Due to Gravity on the Air Track”. The PASCO motion sensor returns linear acceleration down the track, and students measure the height and the length of the track to calculate the angle. “Newton’s 3rd Law”. Student calculate a difference between readings of PASCO sensors on two colliding trucks and analyze a histogram of the distribution of the differences about zero. “Dynamics of Rotational Motion”. The PASCO rotary motion sensor measures angular acceleration of a disk with attached load that produces torque. Students plot torque vs. acceleration and apply linear fit to find the moment of inertia as a slope.

4. Lecturing DA in the 1st year Mechanics (fall term) significance of an experiment in science; reading uncertainty, accuracy and precision; uncertainty and a number of significant figures; direct and indirect measurements; propagation of errors in an equation g=ah/l; 6) significance of a number of measurements; 7) normal distribution and scope of its application; 8) mean, standard deviation, uncertainty of the mean; 9) choosing a proper physical model; 10) the best fit (linear regression), uncertainties of the slope and y-intercept; 11) chi-squared criterion; the other goodness of fit criteria (residuals); 12) significance of the error bars in a diagram. Lecture 1. “Acceleration Due to Gravity on the Air Track”. a Δa h Δh l Δl g Δg Lecture 3. “Newton’s 3rd Law”. Lecture 3. “Dynamics of Rotational Motion”.

5. Evolution of my methods of teaching DA for the 2nd year Engineering Science students The course consists of 4 sections: Waves, Modern Physics, Quantum Physics and Thermal Physics. The labs cover all topics in two semesters. The curriculum does not include hours for lecturing the DA topics. 2014-15, 2015-16: notes on error analysis posted to Blackboard and the course web site. 2016-17: two-hour lecture at the beginning of the fall term with following one-hour exercise to demonstrate the acquired knowledge. This takes one out of four lab sessions scheduled for the fall term. 2017-18 (planned): 2.5-hour lecture/tutorial with interactive component and following exercise. 7

Simulated Data Analysis assignment that requires 6. Teaching DA in the Advanced Physics Laboratory (3rd and 4th year students of Physics Specialists, Physics Majors and Engineering Science Programmes) 2007-17: Three-hour introduction in data acquisition techniques data analysis and uncertainty calculation. Simulated Data Analysis assignment that requires choosing a model; programming, preferably in Python; fitting with a number of suggested functions (Gaussian, Cauchy, Moyal) on a linear background; calculating at least three goodness of fit criteria; concluding on the best fit and the best model.

7. Surveys and feedback (students) 1st year students (Engineering Science students, 2013-14) Q: How did you learn data analysis? (208 responses) 2nd year students (Engineering Science students, 2016-17) Q: How would you like to learn data analysis? (162 responses) 3rd and 4th year (Advanced Physics Laboratory, 2016-17) Q: Was the Simulated Data Analysis assignment helpful?(54 resp) Q: How would you like to learn data analysis? With lecture notes and tutorials - 56 % Studying examples from the past years Error Test - 43 % Lecture/tutorial at the 1st lab session each year - 56.3% On-line course with quizzes and self-tests each year - 33.3 % On-line materials posted to a web page - 26.5 % YES - 87 % ; NO - 23% (because I had to learn Python first) Introduction talk at the beginning of the lab course - 95 % Recommended readings suffice the course requirements - 5%

MERITS AND LEARNING OUTCOMES 8. Merits and demerits of allocating hours for teaching data analysis in Physics courses MERITS AND LEARNING OUTCOMES Students begin treating data analysis and uncertainty calculation as a natural part of Physics course. Students start analyzing data efficiently and accurately. We have reasonable expectations for the lab reports content. Students clearly understand the instructors’ expectations regarding the lab report. Later, it is easier for students to learn and memorize sophisticated mathematical material with real examples of the real experiments’ data obtained in the Physics course. An opportunity of consulting the lecture/tutorial notes is great; the notes are more concentrated than any book.

DEMERITS AND ADDITIONAL PROBLEMS 8. Merits and demerits of allocating hours for teaching data analysis in Physics courses DEMERITS AND ADDITIONAL PROBLEMS Allocating hours for Data Analysis requires change to a curriculum of a course. Not significant, however… If DA is included in lectures, some “physics” topics will be eliminated from lectures (I skipped the 1-D Kinematics). Or the hours of the lab sessions/practicals will be shared between teaching DA and the hands-on activities. If DA is introduced as a separate course (e.g. an on-line one), it requires an instructor with good knowledge of experiments of the current physics course and previous physics courses taken by the students of this class.

9. Results and Summary Either we have very modest expectations of students’ progress with DA in the labs, or we are teaching data analysis in a lecture/tutorial class, or during a lab session. Students don’t understand necessity of thorough analysis of uncertainties until you show in detail the procedure and your expectations. This class should be interactive. TAs/ Lab Demonstrators indicate a big difference in the quality of lab reports and marks with and without classes on uncertainty analysis and data acquisition techniques. Every next year students remember very little from their previous year DA skills in physics labs. It looks like teaching data analysis and measurement techniques should be included in the curriculum at the beginning of physics course annually.

Questions? Thank you!