Traditional school laboratory exercises on a system of moving objects connected by strings involve deriving expressions for the system acceleration, a = (∑F )/m, and sketching a graph of acceleration vs. force. While being in the form of rational functions, these expressions present great opportunities for broadening the scope of the analysis by using a more sophisticated math apparatus—the concept of limits. Using the idea of limits allows for extending both predictions and explanations of this type of motion that are—according to Redish—essential goals of teaching physics. This type of analysis, known in physics as limiting case analysis, allows for generalizing inferences by evaluating or estimating values of algebraic functions based on its extreme inputs. In practice, such transition provides opportunities for deriving valid conclusions for cases when direct laboratory measurements are not possible. While using limits is common for scientists, the idea of applying limits in school practice is not visible, and testing students’ ability in this area is also rare.

1.
The College Board
,
AP® Physics 1 and 2 Inquiry-Based Lab Investigations: A Teacher’s Manual
, https://secure-media.collegeboard.org/digitalServices/pdf/ap/ap-physics-inquiry-based-lab-manual.pdf, p.
61
, accessed Oct. 17, 2016.
2.
Edward F.
Redish
, “
Analysing the competency of mathematical modelling in physics
,” (
University of Maryland
,
2016
), https://arxiv.org/ftp/arxiv/papers/1604/1604.02966.pdf, accessed Oct. 17, 2016.
3.
Edward F.
Redish
, “
Problem solving and the use of math in physics courses
,” arXiv preprint physics/0608268 (
2006
), https://arxiv.org/ftp/physics/papers/0608/0608268.pdf, accessed Feb. 27, 2017.
4.
James
Stewart
,
Lothar
Redlin
, and
Saleem
Watson
,
Precalculus
(
Nelson Education
,
Toronto
,
2016
), p.
54
.
5.
M.
Honey
,
G.
Pearson
,
H.
Schweingruber
(eds.),
STEM Integration in K-12 Education: Status, Prospects, and an Agenda for Research
(
National Academies Press
,
Washington, DC
,
2014
).
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