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.
Some preliminary results of the analysis
Vazgen Shekoyan
• Do not have mathematics prerequisites.
• Use minimal amount of mathematics.
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
a) the highest levels of science and math anxieties;
b) 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
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?
Queensborough Community College, CUNY
Overview
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 2: Identifying proportionalities in formulas
Step 3: Looking for limiting cases
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
• A sample task:
Formula Appreciation Intervention
• 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
Step 1: Playing with formulas
• The hypothesis is then tested with measurement on bigger
circles.
Phase 2: Generalization of the proportionality rule
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.
 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”.
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.
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.
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 = …
Q5: You could say that my anxiety in physics is due to my fear of math
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):
Description of the Study
“Formula Appreciation” intervention steps
• Step 1: Playing with formulas
 to help students being at ease with formula manipulation
• 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:
• 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?
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.
Q8: I do not expect physics equations/formulas to help my
understanding of ideas; they are just for doing calculations
Q9: In physics, it is important to make sense out of formulas before I can
use them correctly
Q10: In physics, mathematical formulas express meaningful
relationships among measurable quantities