Conference Session

Mathematics Division Technical Session 3

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Emre Tokgoz, Quinnipiac University; Elif Naz Tekalp; Hasan Alp Tekalp

Tagged Divisions

Mathematics

. APOS theory is initiated with Piaget’stheory of reflective abstraction [17] and got expanded to K16 mathematics education and RUME in recent years. Itwas applied in 1997 to mathematical topics for analyzing combined math knowledge of a student in a specificsubject [1]. Action, process, object, and schema are the mental structures proposed as a part of the APOS theory tofollow developmental stages of the learners. The main goal of this theory is to observe and categorize mentalstructures through observations of learners’ mental mechanisms; it is important to understand the totality ofknowledge and its’ reflection in applications.In the relevant APOS literature, learners’ conceptual view of the function was studied in [3] by relying on

Conference Session

Mathematics Division Technical Session 2

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Emre Tokgoz, Quinnipiac University; Samantha Eddi Scarpinella , Quinnipiac University; Michael Giannone, Quinnipiac University

Tagged Divisions

Mathematics

reflects upon an action when the action is repeated and he or she can make an internal mental construction called a process by which the individual can think of as performing the same kind of action without an external support...  An object is results from individual’s awareness of the process’ totality and realizes that transformations can act on it...  A schema is a linkage of collected actions, processes, objects, and other schemas that help to form a framework by using general principles in individual’s mind...APOS theory can be appropriately applied to the collected research data due to the involvementof certain mathematical concepts such as limits, derivatives, and asymptotes. The participants ofthis

Conference Session

Mathematics Division Technical Session 1

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Rebecca Machen, University of Colorado Boulder; Wysheka Austin, Clemson University; Matthew K. Voigt, Clemson University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

malintent, thatassociate people of color with negative concepts, even though most people self-report havingminimal to no bias (Greenwald et al., 1998). These unintentional beliefs, often referred to asracial microaggressions, communicate hostility toward people of color. Pierce (1974)conceptualized microaggressions as subtle, cumulative mini-assaults. Sue and colleagues (2007)define microaggressions as "brief and commonplace daily verbal, behavioral, or environmentalindignities, whether intentional or unintentional, that communicate hostile, derogatory, ornegative racial slights and insults toward persons of color" (p. 271). The current literatureexpands the definition of microaggressions to include "acts that reflect superiority, hostility

Conference Session

Mathematics Division Technical Session 3

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Salvador Mayoral, California State University, Fullerton; Antoinette Sherrise Linton, California State University, Fullerton; Hassan Yousefi, California State University, Fullerton; Jidong Huang, California State University, Fullerton

Tagged Divisions

Mathematics

1 Percentage of students repeating lower-division Math and Physics CoursesFor students who pass their lower-division courses and continue pursuing a STEM field, thisdoes not often translate into success in math-intensive engineering courses. Figure 2 shows thepercent repetition rate for various lower and upper-division ECS courses. Many courses acrossECS consist of repetition rates above 20%. This alludes to students not retaining the materiallearned in their previous pre-requisite courses, and consequently, students continue to repeatcourses and extend their graduation date as reflected in the graduation trends in 4, 5, 6-yeargraduation rates, shown in Figure 3. Although the 4-year graduation rate has consistently stayedat 5% since 2009

Conference Session

Mathematics Division Technical Session 2

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Mary Katherine Watson, The Citadel; Tara Hornor, The Citadel; William J. Davis P.E., The Citadel; Simon Thomas Ghanat P.E., The Citadel

Tagged Divisions

Mathematics

research strategy enabled both statistical analysis ofparticipants’ quantitative ratings, as well as individual student’s rich personal reflections on theirown experiences and leadership development to be compared with other participants [20, 21].Our study adheres to an approved Institutional Review Board (IRB) protocol.Participant DemographicsOur first cohort of ExCEL scholars consisted of six male students, with two identifying asHispanic/Latino. Scholars varied in terms of their math preparedness, with two previouslycompleting Advanced Placement (AP) Calculus, one completing honors Calculus, and threecompleting Precalculus. Upon entry to The Citadel, scholars’ average score on a math placementexam was 66.7%, with scores ranging from 47.1% to

Conference Session

Mathematics Division Technical Session 2

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Blair J. McDonald P.E., Western Illinois University; Susan C. Brooks, Western Illinois University - Quad Cities

Tagged Divisions

Mathematics

other essential topics with which students often struggle. Suchinteractions among students and peer mentors aid in improving student attitudes and their senseof belonging at the institution.Having Dr. Brooks attend the statics class as a student caused a great deal of reflection on Dr.McDonald’s part. It quickly became clear that many mathematical processes were only lightlytouched upon, in favor of dwelling on ‘this is how you work the problem’ discussions. Having amathematician in the audience makes one pay attention to how mathematics is presented andapplied. Engineers often take mathematical shortcuts without providing much in the way ofexplanation; this was quickly pointed out!One of the first opportunities that engineering students have

Conference Session

Mathematics Division Technical Session 1

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Patricia A. Ralston, University of Louisville; Campbell R. Bego, University of Louisville

Tagged Topics

Diversity

Tagged Divisions

Mathematics

college, so we can more easilyimplement evidence-based practices with potential to improve retention, of which there are several.Recently, we have focused on implementing formative assessment, which has been shown to improveretention of at-risk students and under-represented minorities [3], [4]. This paper presents and reflects onthe implementation of formative assessment in our Calculus I course for engineering students.Theoretical Framework: Formative assessmentFormative assessment is an instructional technique in which teachers quickly assess students during oroutside class for minimal reward/penalty, with emphasis on improving learning. Formative assessmenthelps both students and teachers to identify knowledge gaps and misconceptions, and

Conference Session

Mathematics Division Technical Session 1

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Tyler James Sullivan, Clemson University; Matthew K. Voigt, Clemson University; Naneh Apkarian, Arizona State University; Antonio Estevan Martinez IV, UC San Diego & San Diego State University; Jessica Ellis Hagman, Colorado State University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

effects with care, and the surveyasked students to reflect back to the beginning of the term.Implications and Non-Implications We end by emphasizing some implications of this work, and perhaps more importantly,some non-implications of this work. First, we see an important implication in the hiring of morediverse faculty. In order for students to experience positive MRMEs, there is a need for morefaculty that can serve as role models based on a variety of social markers and personal identities.To draw on the vaccine metaphor, we emphasize that while increasing instructor diversity amongmultiple

Conference Session

Mathematics Division Technical Session 2

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Allen J. Antoine Jr, Rice University Office of STEM Engagement; Carrie A. Obenland, Rice University; Roger Ramirez, Rice University; Christopher Barr, Office of Research, Rice University; Matthew Cushing, Rice University; Carolyn Aitken Nichol, Rice University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

workshop but rather a year-long teacherprofessional development program that provides teachers with 100 contact hours to acquire andapply new knowledge and reflect on their teaching practices. Several studies emphasizecontinuous PD that occurs periodically throughout the school year to best support teachers asthey make adjustments to their lessons and teaching practices. [17,18,19,20]. In addition to PDduration, teachers in AMP! learn how to shift their current lessons to include more effectivestrategies such as inquiry-based and team based lessons [21,22]. Inquiry based teaching can bedescribed as an open communication between teachers and students to freely ask questions topromote conceptual understanding and puts an emphasis on lesson