A few years ago we began to revamp our introductory physics course for life science students.1 We knew that this cohort would be less prepared and less adventurous mathematically than engineering, physical science, or mathematics majors. Moreover, from our own experience and the mathematics education literature,2-4 we knew that trigonometry would be particularly challenging. Based on these circumstances, we decided to systematically probe the following questions: What is the range of students' initial knowledge with respect to trigonometry? Is reviewing trigonometric concepts valuable and/or necessary? Can students see the trigonometric equations describing oscillations as conveying an idea, in addition to being a tool to get “the answer”?
REFERENCES
1.
D. C.
Meredith
and J. A.
Bolker
, “Rounding off the cow: Challenges and successes in an interdisciplinary physics course for life science students,”
Am. J. Phys.
80
, 913
–922
(Oct. 2012
).2.
D. M.
Bressoud
, “Historical reflections on teaching trigonometry,”
Math. Teach.
104
, 106
–112
(2010
).3.
K.
Weber
, “Students' understanding of trigonometric functions,”
Math. Educ. Res. J.
17
,91
–112
(2005
).4.
K. C.
Moore
, “An investigation into pre-calculus students' conceptions of angle measure,”
Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education Conference Proceedings (SIGMAA on RUME)
(Feb. 2009
).5.
P. G.
Hewitt
, “Equations as guides to thinking and problem solving,”
Phys. Teach.
49
, 264
(May 2011
).6.
B. L.
Sherin
, “How students understand physics equations,”
Cognition Instruct
. 19
(4
), 479
–541
(2001
).7.
Ibid, p. 491.
8.
Ibid, p. 499.
9.
In later versions, we changed to using 2π/T instead off, as it was more intuitive (and one less new variable to understand).
10.
For another example of a small mathematical point with a significant conceptual underpinning, see
K.
Hayes
and M. C.
Wittmann
, “The role of sign in students' modeling of scalar equations,”
Phys. Teach.
48
, 246
–249
(April 2010
).11.
See TPT Online at http://dx.doi.org/10.1119/1.4862119 for copies of our worksheet and pre/post-test.
12.
National Governors Association Center for Best Practices, Council of Chief State School Officers
, “Common Core State Standards for Mathematics”
(National Governors Association Center for Best Practices, Council of Chief State School Officers
, Washington, D.C.
, 2010
).13.
We dropped rotational motion because there are not a lot of biological systems that move in full circles with constant angular acceleration or velocity.
14.
A. B.
Arons
, A Guide to Introductory Physics Teaching
(Wiley
, New York
, 1990
), pp. 3
–5
.© 2014 American Association of Physics Teachers.
2014
American Association of Physics Teachers
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