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The Linear Motion as a Scenario for Addressing Relations Between a Function and Its Derivative

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2015 ASEE Annual Conference & Exposition


Seattle, Washington

Publication Date

June 14, 2015

Start Date

June 14, 2015

End Date

June 17, 2015





Conference Session

Mathematics Division Technical Session 3

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Page Count


Page Numbers

26.1556.1 - 26.1556.13



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Paper Authors


Eliud Quintero Tecnologico de Monterrey (ITESM)

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PhD in Innovative Education by the Monterrey Institute of Technology and Higher Education (ITESM). Degree in Mathematics by UANL, in Monterrey, Mexico. Interested in research areas such as educational technology for the learning of mathematics, teaching - learning of calculus, visualization, analysis of multimodal production of signs.

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Patricia Salinas Tecnologico de Monterrey (ITESM)

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Full time Professor at Mathematics Department in Campus Monterrey, Tecnológico de Monterrey.
Educational researcher with interest in the integration of technology for the learning of Mathematics.
With a Bachelors Degree in Mathematics and 2 Masters Degrees, in Education with Mathematics Specialization. PhD in Mathematics Education since 2011. Member of the National System of Researchers SNI 1, CONACYT, México.
Co-author of several textbooks for the teaching and learning of Calculus.

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  The linear motion as a scenario for addressing relations between a function and its derivative.The motion of an object over a horizontal straight line has been the scenario supporting thedevelopment of a first Calculus course in a private university in northern Mexico. This courseused specially the continuous dynamic SimCalc MathWorlds® software to interact with amathematical content traditionally treated as an application of differential calculus. We refer toestablish relationships between the properties of a function and its derivative. The (positive /negative) sign of the derivative values is related to the behavior (increasing / decreasing) of thefunction; and the behavior (increasing / decreasing) of the derivative is related to the behavior(concave upward / downward) of the function graph. To promote learning in the classroom ofthese relationships, we have designed a didactic sequence with the use of the software, studentsmanipulate the dynamic elements of it, to be able to identify and establish qualitativerelationships between graphs of a function and its derivative. A study has been conducted inwhich 65 engineering students of about 18 years old from three classroom groups participated.As part of the method, a diagnostic assessment to the three groups was applied. The didacticsequence was then implemented integrating the SimCalc environment during 2 weeks. Finally,we designed and implemented an assessment instrument by which the appropriation of thenamed mathematical relationships was valued. The instrument design includes the design ofitems in a multiple-choice format, including three different situations: in the context of linearmotion, in other real contexts and without an associated real context. The research questionleading the study we present in this paper is: To what extent the linear motion context, throughthe mediation of SimCalc, supports students to apply qualitative relationships between a functiongraph and its derivative graph in other contexts with real meaning or without it? The findingsshow that the learning of students appropriated in the context of motion can be transferred tosituations without a real context, but does not occur in the same way in other contexts differentfrom the motion. This result helps to improve the proposal already practicing in our institutionand valuing the use of digital technologies for the learning of Calculus.

Quintero, E., & Salinas, P. (2015, June), The Linear Motion as a Scenario for Addressing Relations Between a Function and Its Derivative Paper presented at 2015 ASEE Annual Conference & Exposition, Seattle, Washington. 10.18260/p.24893

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