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Mathematical vs. Conceptual Understanding: Where Do We Draw The Line?
written by
Homeyra R. Sadaghiani and Nicholas Aguilera
This research involved high school physics students and how they learn to understand Newton's laws as they relate to falling bodies and projectile motion. Students in introductory, algebra-based, high school physics classes were evaluated based on their prior knowledge through a pretest, designed to assess their initial comprehension of the motion of falling bodies and projectiles. Groups were divided and taught separately with an emphasis on either mathematical derivation of equations, followed by brief conceptual discussions, or on thorough conceptual analysis, followed by a brief mathematical verification. After a post-test was given, an evaluation of the responses and explanations of each group of students was used to determine which method of instruction was more effective. Results indicate that after the conceptual group and math groups achieved similar scores on the pretest, the conceptual group obtained a slightly higher normalized gain of 25% on the post-test, compared to the mathematical group's normalized gain of 16% (unpaired two-tailed t-test P value for post-test results was 0.1037) and, while within standard deviations, also achieved higher overall scores on all post-test questions and higher normalized gains on all but one post-test question. Further, most students, even those in the mathematically-instructed group, were more inclined to give conceptually-based responses on post-test questions than mathematically-based ones. In the context of this topic, the dominating difficulty for both groups was in analyzing two-dimensional projectile motion and, more specifically, the behavior of each one-dimensional component of such motion.
Physics Education Research Conference 2012
Part of the PER Conference series Philadelphia, PA: August 1-2, 2012 Volume 1513, Pages 358-361
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Record Link
<a href="https://www.per-central.org/items/detail.cfm?ID=12852">Sadaghiani, Homeyra, and Nicholas Aguilera. "Mathematical vs. Conceptual Understanding: Where Do We Draw The Line?." Paper presented at the Physics Education Research Conference 2012, Philadelphia, PA, August 1-2, 2012.</a>
AIP Format
H. Sadaghiani and N. Aguilera, , presented at the Physics Education Research Conference 2012, Philadelphia, PA, 2012, WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12852&DocID=3384).
AJP/PRST-PER
H. Sadaghiani and N. Aguilera, Mathematical vs. Conceptual Understanding: Where Do We Draw The Line?, presented at the Physics Education Research Conference 2012, Philadelphia, PA, 2012, <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12852&DocID=3384>.
APA Format
Sadaghiani, H., & Aguilera, N. (2012, August 1-2). Mathematical vs. Conceptual Understanding: Where Do We Draw The Line?. Paper presented at Physics Education Research Conference 2012, Philadelphia, PA. Retrieved March 27, 2023, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12852&DocID=3384
Chicago Format
Sadaghiani, Homeyra, and Nicholas Aguilera. "Mathematical vs. Conceptual Understanding: Where Do We Draw The Line?." Paper presented at the Physics Education Research Conference 2012, Philadelphia, PA, August 1-2, 2012. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12852&DocID=3384 (accessed 27 March 2023).
MLA Format
Sadaghiani, Homeyra, and Nicholas Aguilera. "Mathematical vs. Conceptual Understanding: Where Do We Draw The Line?." Physics Education Research Conference 2012. Philadelphia, PA: 2012. 358-361 Vol. 1513 of PER Conference. 27 Mar. 2023 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12852&DocID=3384>.
BibTeX Export Format
@inproceedings{
Author = "Homeyra Sadaghiani and Nicholas Aguilera",
Title = {Mathematical vs. Conceptual Understanding: Where Do We Draw The Line?},
BookTitle = {Physics Education Research Conference 2012},
Pages = {358-361},
Address = {Philadelphia, PA},
Series = {PER Conference},
Volume = {1513},
Month = {August 1-2},
Year = {2012}
}
Refer Export Format
%A Homeyra Sadaghiani %A Nicholas Aguilera %T Mathematical vs. Conceptual Understanding: Where Do We Draw The Line? %S PER Conference %V 1513 %D August 1-2 2012 %P 358-361 %C Philadelphia, PA %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12852&DocID=3384 %O Physics Education Research Conference 2012 %O August 1-2 %O application/pdf
EndNote Export Format
%0 Conference Proceedings %A Sadaghiani, Homeyra %A Aguilera, Nicholas %D August 1-2 2012 %T Mathematical vs. Conceptual Understanding: Where Do We Draw The Line? %B Physics Education Research Conference 2012 %C Philadelphia, PA %V 1513 %P 358-361 %S PER Conference %8 August 1-2 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12852&DocID=3384 Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications.
Citation Source Information
The AIP Style presented is based on information from the AIP Style Manual. The AJP/PRST-PER presented is based on the AIP Style with the addition of journal article titles and conference proceeding article titles. The APA Style presented is based on information from APA Style.org: Electronic References. The Chicago Style presented is based on information from Examples of Chicago-Style Documentation. The MLA Style presented is based on information from the MLA FAQ. Mathematical vs. Conceptual Understanding: Where Do We Draw The Line?:Know of another related resource? Login to relate this resource to it. |
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