Conference Session

Mathematics Division Technical Session 1

Collection

2016 ASEE Annual Conference & Exposition

Authors

Rebecca Bourn, University of Wisconsin - Milwaukee; Sarah Baxter, University of St. Thomas

Tagged Divisions

Mathematics

Calculus, which most certainly covers this topic, but the problem“feels” different to students in the later course because the notation and setting have changed andthe purpose is specific to statistics rather than the more abstract concepts of the area of a two-dimensional region and anti-derivatives.Previous WorkIn recent years the authors have been exploring ways to reframe course assignments to provide agreater variety of application and visualization avenues to enhance critical thinking and promptstudent reflection. The objective is to provide multiple levels of connections that promotestudents’ cognitive retention. Preliminary work1 presented a methodology for using large scale,Fermi-type estimation problems to try to encourage students to

Conference Session

Mathematics Division Technical Session 2

Collection

2016 ASEE Annual Conference & Exposition

Authors

Aaron Brakoniecki, Boston University; Michael Ward, Boston University; Gretchen Fougere, Boston University

Tagged Divisions

Mathematics

of the reflection when theengineering students and the beginning teachers reflected on the engineering design process theyimplemented during the activity. They compared this to the mathematical practice standards theyare expected to implement throughout their classrooms. What occurred during this discussionwere many connections among the different aspects of these two descriptions. They sawconnections between the mathematical expectations to make sense of the problem and theengineering process of identifying the needs and constraints. They linked the mathematicalstandards of reasoning abstractly and constructing viable arguments to the engineering processesof developing possible solutions and selecting promising solutions. With the

Conference Session

Mathematics Division Technical Session 4

Collection

2016 ASEE Annual Conference & Exposition

Authors

Eliza Gallagher, Clemson University; Lisa Benson, Clemson University; Geoff Potvin, Florida International University

Tagged Divisions

Mathematics

qualitative in nature, and our chosen research methods reflectthat. Rather than conduct a quasi-experimental design with a selection of GTAs participating incase analysis and others not, we instead used mixed qualitative and quantitative methods tocollect and analyze data solely from participants who experienced the use of case analysis in theirfirst semester of graduate school. This paper focuses in particular on two quantitative measures(survey data and student performance) and on two qualitative measures (case discussion recordsand reflective writings). We give a summary of the data within each of those four categoriesseparately. However, the nature of the research questions is such that a more significant analysisinvolves integration of those

Conference Session

Mathematics Division Technical Session 2

Collection

2016 ASEE Annual Conference & Exposition

Authors

Muteb M. Alqahtani, Rutgers University; Arthur Belford Powell, Rutgers University

Tagged Divisions

Mathematics

Foundation, DRK-12 program, under awardDRL-1118888. The findings and opinions reported are those of the authors and do not necessarily reflect the viewsof the funding agency.For example, a line segment can be used as a radius to create a circle. These objects can bedragged around the screen, which allows the users to observe the consequences of their draggingto understand the relations among the different objects. Users act on geometric objects and DGEsreact to their actions in a manner that corresponds to engineered infrastructure that responds tothe theory of geometry [8, 9]. This co-active relationship between the environment and usersallows users to monitor and reflect on their activity. In an instrument-mediated activity in DGE,the environment

Conference Session

Mathematics Division Technical Session 1

Collection

2016 ASEE Annual Conference & Exposition

Authors

Guenter Bischof, Joanneum University of Applied Sciences; Thomas Singraber B.Sc., Joanneum University of Applied Sciences; Christian J. Steinmann, HM&S IT-Consulting; Marton Szabo-Kass B.Sc., Joanneum University of Applied Sciences; Stefan Woerndl B.Sc., Joanneum University of Applied Sciences

Tagged Divisions

Mathematics

oppositedirections. Then the simulation was started within the highest-order integration scheme andthe positions of the particles were stored after each time step. From these data a movie wascreated as described above. In the following figures (Figures 10 to 14) snapshots are shown,which were taken at different evolutionary phases of wave phenomena that occurred in thecourse of the numerical simulation.The snapshot in Figure 10 shows two wave fronts that have already established and propagatetowards each other. Both regions confined by the wave fronts show already a rich internalstructure that is caused by several reflections at the boundaries (Dirichlet boundary conditionsproduce fixed end wave reflections) and by interference.Figure 10: Array of 261206

Conference Session

Mathematics Division Technical Session 3

Collection

2016 ASEE Annual Conference & Exposition

Authors

Larry G. Richards, University of Virginia; Susan K. Donohue, University of Virginia

Tagged Divisions

Mathematics

Solar Car Figure 6: Pulling a Load with a Solar CarEach team prepares a summary sheet showing a sketch of their design, a bill of materials (theparts they used with the cost of each), the total cost of their design, and how much weight theircar was able to pull. After the competition, the entire class reflects on the results and discusseswhat worked and what did not.After completing this ETK, the students have learned about solar cells, motors, and tirematerials, but they have also learned about the engineering design process, and how to constructa vehicle to perform a task. They also learned how to measure the values of variables, theimportance of consistent procedures for making measurements, how to compute

Collection

2016 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

memory, step-by-step instructions on how to perform theoperation...When an action is repeated and the individual reflects upon it, he or she can make an internalmental construction called a process which the individual can think of as performing the same kindof action, but no longer with the need of external stimuli...An object is constructed from a process when the individual becomes aware of the process as atotality and realizes that transformations can act on it...A schema is an ... individuals collection of actions, processes, objects, and other schemas whichare linked by some general principles to form a framework in individual's mind... Baker, Cooley and Trigueros (2000) applied APOS theory to understand undergraduatestudents’ conceptual

Conference Session

Mathematics Division Technical Session 4

Collection

2016 ASEE Annual Conference & Exposition

Authors

Virgil U. Pierce, University of Texas, Rio Grande Valley; Javier Angel Kypuros, University of Texas, Rio Grande Valley; Shirley J. Mills, University of Texas, Rio Grande Valley

Tagged Topics

Diversity

Tagged Divisions

Mathematics

at improving entering students’ college readinessand mathematics placement. The small scale intervention, A Bridge to Calculus, is intended toimprove students’ placement from College Algebra into Calculus 1. The target population forthis effort are students with high school experience in a Calculus course but whose performanceon placement exams does not reflect this experience. At our institution this is a significantnumber of students and the goal of the project is to develop methods to address and acceleratestudents in this category. The course design, to take advantage of the students’ prior experience,emphasizes practice and mastery using a modified emporium course design and the ALEKSsoftware1. This intervention runs as a summer course

Collection

2016 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University

Tagged Divisions

Mathematics

classification; Intra, Inter and Trans to investigate how first year calculusstudents construct the concept of chain rule. Their attempt to use the APOS theory resulted ininsufficiency by itself therefore they included the schema development idea of Piaget et al. (1989).Clark et al. (1997) used triad classification after realization of not being able to apply the APOStheory. Similar to Clark et al. (1997) APOS theory appears to be inappropriate for evaluating theresearch question in this work because students' responses didn't reflect a proper setting to applythe APOS theory; therefore, participating students' responses are analyzed by using the schemadevelopment idea. The Triad classification in this setting is as follows:• Intra Stage: Students

Conference Session

Mathematics Division Technical Session 3

Collection

2016 ASEE Annual Conference & Exposition

Authors

Doug Bullock, Boise State University; Kathrine E. Johnson; Janet Callahan, Boise State University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

(3) face-to-face but taught in parallel with the online section. 600 500 400 300 Other 200 Reform 100 0Figure 2: Calculus I enrollment by semester.Total students “captured” by the reform project, as a percent of enrollment is shown in Figure 3.It appears to be stabilizing in the low to mid 70’s, which currently reflects the portion of calculusthat Boise State University has chosen to offer as honors, online, or face-to-face but parallel toonline. 100% 90% 80% 70% 60% 50% 40

Conference Session

Mathematics Division Technical Session 3

Collection

2016 ASEE Annual Conference & Exposition

Authors

Edmund Tsang, Western Michigan University; Kenneth David Domingue, Western Michigan University ; Sarah Gray Hagen, Western Michigan University; Rebecca A. Scheffers, Western Michigan University; Lenore Yaeger; Katherine Fox, Western Michigan University

Tagged Divisions

Mathematics

reflect the academic training of one of this paper’sauthors, which included a B.S. degree in mechanical engineering, a Ph.D. in metallurgy, andpost-doctoral experience in solid state physics. Table 2 shows a week-by-week class schedule ofENGR 1002 and the engineering topics:Table 2. A Weekly Class Schedule of ENGR 1002 and Engineering TopicsWeek Class Schedule Engineering Topics CommentsWeek 1 Course Overview and Engineering units and unit Address a common student Units Conversion mistake: (ab)x≠abx or axb but = axbxWeek 2 Algebraic Expression Definition and algebraic