Conference Session

Mathematics Division Technical Session 4

Collection

2015 ASEE Annual Conference & Exposition

Authors

Peter Goldsmith P.Eng., University of Calgary

Tagged Divisions

Mathematics

operator, applied in postfix notation. To obtain the transferfunction of this system, one assumes that the initial conditions of the input and output signals arezero and applies the Laplace transform to both sides of this differential equation to giveU(s)a(s) = Y (s)b(s), where U(s) and Y (s) are the Laplace transforms of u(t) and y(t),respectively, and s is a complex variable. This yields the transfer function Y (s)/U(s) = a(s)/b(s),which may be multiplied by a particular transformed input U(s) to find the correspondingtransformed output Y (s).Transfer functions are appealing in that they model dynamic systems as rational functions that canbe added, multiplied, and inverted to reduce networks of interconnected subsystems. However,the educational

Conference Session

Mathematics Division Technical Session 3

Collection

2015 ASEE Annual Conference & Exposition

Authors

Eliud Quintero, Tecnologico de Monterrey (ITESM); Patricia Salinas, Tecnologico de Monterrey (ITESM)

Tagged Topics

Diversity

Tagged Divisions

Mathematics

. Revista Latinoamericana de Investigación En Matemática Educativa, 12(3), 355– 382. 5. Noss, R., Hoyles, C., Mavrikis, M., Geraniou, E., Gutierrez-Santos, S., & Pearce, D. (2009). Broadening the sense of “dynamic”: A microworld to support students’ mathematical generalisation. ZDM—The International Journal on Mathematics Education, 41(4), 493–503. doi:10.1007/s11858-009-0182-8 6. Salinas, P., Quintero, E., & González-Mendívil, E. (2014). An environment to promote a visual learning of Calculus. In H. R. Arabnia, A. Bahrami, L. Deligiannidis, & G. Jandieri (Eds.), Proceedings of the International Conference on Frontiers in Education: Computer Science and Computer Engineering (pp. 425–429). Las

Conference Session

Mathematics Division Technical Session 3

Collection

2015 ASEE Annual Conference & Exposition

Authors

Christine Lindstrøm, Oslo and Akershus University College

Tagged Divisions

Mathematics

and one requiring a written explanation). An example of a problem in thecategory of basic mathematics (numeracy) is the following (problem 1): “10% of the boys and10% of the girls at school play soccer. How many percent of all students in the school playsoccer? A) 5%, B) 10%, C) 15%, D) 20%, E) Cannot answer.” A problem from scientificmathematics (calculations with scientific notation and units) is (problem 2) “Complete thecalculation: s = vt = 3.0 ⋅ 108 m/s ⋅ 2.0 ⋅ 10-5 s = ”.The same mathematics test was used as pre- and post-test. The pre-test was administered inclass during the first week of first semester, before the physics course had started, and thepost-test was administered in the second week of second semester, which was the

Conference Session

Mathematics Division Technical Session 3

Collection

2015 ASEE Annual Conference & Exposition

Authors

Ruth Rodríguez-Gallegos, Tecnologico de Monterrey (ITESM); Rafael Ernesto Bourguet-Diaz, Tecnologico de Monterrey (ITESM)

Tagged Topics

Diversity

Tagged Divisions

Mathematics

the second part of the session, the last 45 minutes, the student is asked to observe for a secondtime the software so that they can adapt it to the studied situation in class. They first studied thesystem of two tanks, but now salt is added to the incoming flow. Now what we are concernedabout is the variable Amount of Salt in the tank S(t) [The figure below is an example of 1 tankwith water mixed with salt]. dS = IS- OS;S(t = 0) = S0 dt dS

Conference Session

Mathematics Division Technical Session 1

Collection

2015 ASEE Annual Conference & Exposition

Authors

Janet Callahan, Boise State University; Judith A. Garzolini, Boise State University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

orientation.Recruitment of participants was additionally conducted using the Louis Stokes Alliance forMinority Participation (LSAMP) program at Boise State, through personal interaction, email andthe LSAMP website.The second major recruitment strategy is focused on continuing students and occurs followingend of spring and fall semester, after running a “DFW” report (students who receive a grade ofD, F or W) on STEM students in Intermediate Algebra (IntAlg), College Algebra (ColAlg),Trigonometry (Trig) or Calculus I (CalcI). These are invited to receive an ALEKS license overwinter or summer break. One final and recent method of recruitment has been more directive,being linked as a requirement for incoming students who qualified for a NSF S-STEMscholarship. Nine

Conference Session

Mathematics Division Technical Session 3

Collection

2015 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University; Gabriela C. Gualpa, Quinnipiac University

Tagged Divisions

Mathematics

. Page 26.1396.2APOS Theory In this section, APOS theory and the relevant literature that is employed to evaluate thequestion and the corresponding interviews to discern the students’ conceptual function knowledgeare explained. The philosophy of mathematics affected engineering and mathematics education in theundergraduate curriculum in the 1990s. Piaget‘s schemes idea in the 1970’s, and its developmentwith detailed explanations by Piaget and Garcia in the 1980’s, influenced researchers ofundergraduate engineering and mathematics education curriculum in the 1990’s. Students’conceptual view of the function was defined by Breidenbach, Dubinsky, Hawks, and Nichols in1992, which relied on Piaget’s study of functions in 1977 (Piaget, Grize

Conference Session

Mathematics Division Technical Session 1

Collection

2015 ASEE Annual Conference & Exposition

Authors

Angela Minichiello, Utah State University; Ted Campbell, Utah State University; Jim Dorward, Utah State University; Sherry Marx, Utah State University

Tagged Divisions

Mathematics

efforts to change instruction in STEM education.Acknowledgements This paper is based on research funded by the National Science Foundation under Awardnumber DUE 1245194. Any opinions, findings, conclusions or recommendations expressed inthis material are those of the author(s) and do not necessarily reflect the views of the NationalScience Foundation.This research is conducted under our university IRB protocol 4532.References[1] Association of American Universities (AAU). (2006). National Defense Education and Innovative Initiative: Meeting America’s Economic and Security Challenges of the 21st Century. Washington, DC.[2] Beach, A., Henderson, C., & Finkelstein, N. (2012). Facilitating change in undergraduate STEM education

Conference Session

Mathematics Division Technical Session 2

Collection

2015 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

26.213.2Cooley et al. (2007) In this study a quotient function is given in its algebraic form andparticipants are asked to employ their calculus knowledge to determine the graph of thecorresponding function. Written and video recorded oral interview responses of participantsare analyzed by using the APOS theory.APOS Theory and LiteratureThe philosophy of mathematics influenced researchers in mathematics and engineeringeducation in the undergraduate curriculum in the 1990s. Piaget‘s schemes idea in the1970’s, and its development with detailed explanations by Piaget and Garcia in the 1980’s,influenced researchers of undergraduate mathematics education curriculum in the 1990’s.Students’ conceptual view of the function was defined by Breidenbach, Dubinsky

Conference Session

Mathematics Division Technical Session 2

Collection

2015 ASEE Annual Conference & Exposition

Authors

Khalid El Gaidi, Royal Institute of Technology (KTH); Tomas Ekholm, Royal Institute of Technology (KTH)

Tagged Divisions

Mathematics

where affordances for conceptualunderstanding are designed into the course and not only left to the student to attain in future oncethey have reached mathematical maturity through procedural struggle.References [1] Pisa 2012 results in focus. http://www.oecd.org/pisa/keyfindings/pisa-2012-results-overview.pdf, 2012. [2] E. Bergqvist. Types of reasoning required in university exams in mathematics. Journal of Mathematical Behavior, 26(4):348–370, 2007. [3] B. S. Edwards and M.B. Ward. Surprises from mathematics education research: Students (mis) use of mathematical definitions. The Mathematical Association of America [Monthly 111], 2004. [4] P. Winkelman. Perceptions of mathematics in engineering. European Journal of Engineering

Conference Session

Mathematics Division Technical Session 2

Collection

2015 ASEE Annual Conference & Exposition

Authors

Patricia Salinas, Tecnologico de Monterrey (ITESM); Eliud Quintero, Tecnologico de Monterrey (ITESM); Pablo Guillermo Ramirez, Tecnologico de Monterrey (ITESM); Eduardo González Mendívil, Tecnologico de Monterrey (ITESM)

Tagged Divisions

Mathematics

perception. Yin, Song, Tabata, Ogataand Hwang11 have developed a framework of Participatory Simulation for Mobile Learningusing Scaffolding. We find in their approach the opportunity to explore the new learning eventsthat are arising with the use of digital technology in Mathematics Education. Page 26.792.11References 1. Salinas, P., González-Mendívil, E., Quintero, E., Ríos, H., Ramírez, H., & Morales, S. (2013). The development of a didactic prototype for the learning of mathematics through augmented reality. Procedia Computer Science, 25(81), 62–70. doi:10.1016/j.procs.2013.11.008 2. Salinas, P., Quintero, E., & González

Conference Session

Mathematics Division Technical Session 4

Collection

2015 ASEE Annual Conference & Exposition

Authors

Judith A Komar, Colorado Technical University; Tonya Troka, Colorado Technical University

Tagged Divisions

Mathematics

, participants in the Conference to Improve College algebra, held at the U. S. MilitaryAcademy, 5 indicated that traditional college algebra courses are not working because they aretaught using outdated content. The conclusions from the conference also indicated that collegealgebra has high D, F, and W rates. The concerns regarding college algebra nationwide arefurther compounded by the fact that college algebra is one of the largest enrollment courses inthe United States. According to the most recent Conference Board of Mathematical Sciences(CBMS) survey conducted in the fall of 2010, college algebra has the largest course enrollmentof all the introductory math courses.6 There is a nationwide call to improve the results in collegealgebra. CTU has

Conference Session

Mathematics Division Technical Session 4

Collection

2015 ASEE Annual Conference & Exposition

Authors

Virgil U. Pierce, University of Texas, Pan American; Javier Angel Kypuros, University of Texas, Pan American

Tagged Topics

Diversity

Tagged Divisions

Mathematics

bridge program was1.8 on a 4.0 scale, compared with a 1.55 from the general Calculus 1 classes. However thechance that a random sample of 16 students from Calculus 1 had a GPA of 1.8 or higher is 26%,so again we cannot conclude that this change was statistically significant.Figure 3 shows the grade in Calculus 1 in Fall 2014 for students who successfully completed thesummer bridge program versus the time they spent on task in the summer program. Again wefind little to no correlation, however it is interesting that there is a cluster of “B”s at the upperend of the time scale. Figure 4 shows the grade in Calculus 1 in Fall 2014 for students who

Conference Session

Mathematics Division Technical Session 2

Collection

2015 ASEE Annual Conference & Exposition

Authors

Doug Bullock, Boise State University; Janet Callahan, Boise State University; Susan E. Shadle Ph.D., Boise State University

Tagged Divisions

Mathematics

andGeneral Statistics. Two instructors of Linear Algebra have already run a course using commonhomework. And the group that oversees our multi-section Scientific Computing course isconsidering a similar approach. If successful, these efforts would achieve full coordination of theentire suite of service courses across every STEM or related discipline.Acknowledgments The authors would like to acknowledge the assistance of Jude Garzolini in conducting the humansubjects study. This material is based upon work supported by the National Science Foundationunder Grant Nos. DUE-0856815 (Idaho STEP), DUE-0963659 (I^3), and DUE-1347830(WIDER). Any opinions, findings, and conclusions or recommendations expressed in thismaterial are those of the author(s) and do

Conference Session

Mathematics Division Technical Session 4

Collection

2015 ASEE Annual Conference & Exposition

Authors

Ravi T. Shankar, Florida Atlantic University; Jean Lapaix, Florida Atlantic University; Charles Perry Weinthal; Don Ploger, Florida Atlantic University; Malissa Augustin, Florida Atlantic University; Santiago Aguerrevere

Tagged Divisions

Mathematics

Conference Session

Mathematics Division Technical Session 1

Collection

2015 ASEE Annual Conference & Exposition

Authors

Michael P. Hennessey, University of St. Thomas

Tagged Divisions

Mathematics

) fromdirectors of graduate studies at several well-known R1 engineering graduate schools, especiallyones offering Ph.D.’s in both electrical and mechanical engineering, since those are theundergraduate programs that St. Thomas offers (3 requests in total). Unfortunately, none ofthem responded! That said, based on the author’s academic experience over many years alongwith discussions with other faculty members (including several from the MathematicsDepartment), the following core topics were selected: (1) vector integral Calculus, (2) anintroduction to Fourier series, (3) an introduction to partial differential equations, (4) anintroduction to complex analysis, and (5) conformal mapping and applications. Note that a highpercentage of the material builds

Conference Session

Mathematics Division Technical Session 1

Collection

2015 ASEE Annual Conference & Exposition

Authors

Gunter Bischof, University of Applied Sciences Joanneum, Graz; Andreas Zwölfer, University of Applied Sciences Joanneum, Graz; Domagoj Rubeša, University of Applied Sciences Joanneum, Graz

Tagged Topics

Diversity

Tagged Divisions

Mathematics

Thomas Goldfinch, “The Influence of University Entry Scores on Performance in Engineering Mechanics”, 20th Australasian Association for Engineering Education Conference, Adelaide, SA, Dec 6-9, 20094. Sarah Tumen, Boaz Shulruf, and John Hattie, “Student pathways at the university: patterns and predictors of completion”, Studies in Higher Education, 33(3), 233-252, 20085. Nancy J. McCormick and Marva S. Lucas, “Exploring mathematics college readiness in the United States”, Current Issues in Education, 14(1), 20116. Eileen Goold and Frank Devitt, “The role of mathematics in engineering practice and in formation of engineers”, SEFI 40th annual conference: Mathematics and Engineering Education, Thessaloniki, 20127