# Enhancing Student Understanding of 1D and 2D Motions:

### The Role of Sequencing Topics, Kinesthetic Experience, Video Analysis and Analytic Mathematical Modeling

**Priscilla Laws**

For the past 25 years or so the new field of Physics Education Research (PER) has provided university, college and high school teachers with new insights into learning difficulties encountered by introductory physics students. During this time members of the *Activity Based Physics Group* have been developing curricular materials based on the outcomes of PER. Most of the Group’s materials employ computer tools that include data collection, display and analysis software along with sensors and video images of real phenomena. These new curricular materials and computer tools are activity-based and flexible. They can be used to create interactive lecture sessions, guided inquiry tutorials in recitation sections, and guided laboratory observations. Elements of the set of curricular materials, known as the *Activity Based Physics Suite,* ^{1}can be used in many teaching environments from large university lecture and lab courses to small high school classes. Suite materials have been classroom tested and proven to help students overcome many of the learning difficulties identified by PER.

The *Activity Based Physics Suite* materials were described briefly, and then the rest of the talk focused on *Workshop Physics*, an innovative curriculum first introduced at Dickinson College in 1989. ^{2} In *Workshop Physics* a carefully designed sequence of collaborative activities replaces formal lectures, recitation sessions and laboratories.

The *Workshop Physics Activity Guide*, ^{3} consisting of four guided inquiry modules, was developed between 1987 and 1993 for use in a laboratory setting where about 24 students meet for 2 hours 3 times each week. Students work in collaborative groups to learn physics by predicting, observing and analyzing data from real phenomena. Students often use computer tools for sensor and video based data-collection and analysis.

Both conceptual learning and the development of facility with the use of analytic mathematical equations to describe physical phenomena are central themes in *Workshop Physics* courses. Thus, the role of pre- and post-testing to measure learning gains in these areas was discussed, along with two commonly used instruments for measuring conceptual and mathematical learning in the mechanics portion of the course: the *Force and Motion Conceptual Evaluation* (FMCE) ^{4} and the *Mathematical Modeling Conceptual Evaluation* (MMCE).^{5}

In addition, the speaker presented some examples of kinesthetic activities developed to help students understand Newtonian mechanics. These included: (1) walking in front of a motion detector to create real time graphs; (2) measuring the motion of a bowling ball pushed steadily by a student holding a baton; (3) pulling a student along a level floor with a constant force with and without sliding friction; and (4) measuring centripetal force while a student on a 2D cart undergoes uniform circular motion. ^{6}

Next an approach to reorganization of the mechanics topics was described. This *New Mechanics* sequence ^{7} is embodied in several of the *Activity Based Physics Suite* materials including *Workshop Physics*, *RealTime Physics* and *Interactive Lecture Demonstrations*. This new sequence involves the treatment of both 1D kinematics and 1D dynamics before any 2D motions are considered. This means that projectile motion is not introduced until after students have studied 1D kinematics and Newton’s Second Law for linear motion.

After summarizing some of the *Workshop Physics* activities that contribute to conceptual mastery, the speaker showed Pre- and Post-test data for the FMCE Examination presented in E.F. Redish’s book on *Teaching Physics with the Physics Suite* cited earlier. ^{8}

Although most of the presentation dealt with conceptual development strategies used in the *Workshop Physics* curriculum, it ended with a summary of a new approach called *Analytic Mathematical Modeling* that has been developed to enable students to relate analytic equations to physical phenomena. ^{9} Homework assignments were developed that require students to use Logger *Pro* software ^{10} to obtain data from video segments of real phenomena and determine the equation that models that data. ^{11}

Unpublished data on Pre- and Post-test gains on the Mathematical Modeling Conceptual Evaluation (MMCE) were compared for *Workshop Physics* students at Dickinson College and those in a traditionally taught calculus-based course at another university where analytic mathematical modeling was not introduced. The Dickinson students did significantly better on their recognition of the physical significance of coefficients for both linear and quadratic functions.

The speaker concluded that "Curricular materials based on the outcomes of physics education research, when coupled with student use of computer based investigative tools, can have a tremendous impact on student learning in introductory physics courses."

**References**

1. Redish, E.F*.,Teaching Physics with the Physics Suite* (John Wiley & Sons, New York, 2003).

2. http://physics.dickinson.edu/~wp_web/wp_homepage.html

3. Laws, P.W*., Workshop Physics Activity Guide*, Modules 1-4 w/ Appendices (John Wiley & Sons, New York, 2004). 855 pp.

4. Sokoloff, D.R. & Thornton, R.K., *American Journal of Physics*, **66**, pp. 338-352 (1998).

5. The MMCE, FMCE and other assessment examinations can be downloaded from http://physics.dickinson.edu/~wp_web/wp_resources/wp_assessment.html

6. Pfister, H. & Laws, P.W., "Kinesthesia-1: A One-Dimensional Kinesthetic Apparatus to Teach Mechanics," *The Physics Teacher***,** Vol. 33, April 1995

7. Laws, P.W., "A New Order for Mechanics," J. Wilson, Ed. Proceedings of the Conference on Introductory Physics Course, (Wiley, 1997) pp. 125-136

9. Laws, P.W., Teese, R.B., Willis, M.C. and Cooney, P.J. "Physics with Video Analysis (Vernier, 2009), Appendix C.

10. http://www.vernier.com/soft/lp.html

11. http://physics.dickinson.edu/~wp_web/wp_resources/wp_coursedocuments.html#Homework

*Priscilla Laws is Research Professor of Physics at Dickinson College. Since 1986, she has dedicated herself to the development of activity-based curricular materials and computer software to enhance student learning in introductory physics courses. This work has included several publications that are part of the Activity-Based Physics Suite. She has received a number of awards for educational innovations and software development. The most notable include the Charles A. Dana award for Pioneering Achievement in Education (1994), the Robert A. Millikan Medal from the American Association of Physics Teachers (1996), and the International Commission on Physics Education (ICPE) Medal in recognition of distinguished contributions to Physics Education (2008).
*

Disclaimer- The articles and opinion pieces found in this issue of the APS Forum on Education Newsletter are not peer refereed and represent solely the views of the authors and not necessarily the views of the APS.