Conference Session

Using Applications and Projects in Teaching Mathematics

Collection

2012 ASEE Annual Conference & Exposition

Authors

Gunter Bischof, Joanneum University of Applied Sciences, Graz, Austria; Christian Steinmann, Joanneum University of Applied Sciences, Graz, Austria

Tagged Divisions

Mathematics

25.642.3equations is obtained when considering an incompressible flow of a Newtonian fluid. Liquidsare often regarded as incompressible because they require such high pressure to compressthem appreciably. However, it is quite legitimate in many applications to consider even agaseous medium such as the atmosphere to be incompressible, in which case theincompressible flow assumption typically holds well at low Mach numbers up to about 0.3.The behavior of a viscous incompressible fluid is governed by the simplified Navier-Stokesequation, which can be written as ∂v 1 + ( v ⋅ ∇) v = − ∇P +ν ∆v , ∂t ρand by the continuity equation

Conference Session

Techniques in Improving Mathematics Education in STEM Curricula

Collection

2012 ASEE Annual Conference & Exposition

Authors

Erin Shaw, University of Southern California; Zachary Boehm, University of Southern California; Hussain Badruddin Penwala, University of Southern California; Jihie Kim, University of Southern California

Tagged Divisions

Mathematics

10 No time 6 8 4 One 1-5 Hours 6 2 Two 4 5-10 Hours 0 Three/Four 2 10-15 Hours 0 Games Texting Phone Page 25.661.4 Figure 2a,b. Types of devices owned by students and number of hours spent

Conference Session

Using Computers, Software, and Writing to Improve Mathematical Understanding

Collection

2012 ASEE Annual Conference & Exposition

Authors

N. Jean Hodges, Virginia Commonwealth University, Qatar

Tagged Divisions

Mathematics

to do so.One teaching strategy shown by researchers since the 1960s and 1970s to be an effective learningand thinking tool is writing. Writing enables the writer to capture otherwise random thoughts byplacing them on a writing surface where they become concrete and thus more readily examined andmanipulated. Consequently, writing should be an effective tool for enabling math students to retainthe mathematical principles being developed in the classroom as well as for aiding them to improvetheir critical thinking abilities needed for applying their mathematical understandings to problems ofthe modern world.By incorporating writing that emphasizes critical thinking into the math classroom, this study seeksan answer to two questions: (1) how can

Conference Session

Techniques in Improving Mathematics Education in STEM Curricula

Collection

2012 ASEE Annual Conference & Exposition

Authors

Yonghui Wang, Prairie View A&M University; Jian-ao Lian, Prairie View A&M University; Yonggao Yang, Prairie View A&M University

Tagged Divisions

Mathematics

Algebra and Calculus I. For each course a certain amountof time will be set aside for students to reinforce the concepts they just learned during the normallecture time. The learning modules are designed to be user friendly in order to attract students’attention to math learning instead of texting in classrooms. The benefits of this pedagogyinclude: 1) interactive modules make students actively involved in the math learning process; 2)the unlimited randomly generated questions and examples give students more opportunities onpracticing and reinforcing the concepts they just learned; 3) the quick answer checking functionhelps students build confidence by immediately identifying their learning progress; and 4) themobility of the modules ensures that

Conference Session

The Transition from Secondary to College Mathematics

Collection

2012 ASEE Annual Conference & Exposition

Authors

Helen M. Doerr, Syracuse University; Andria Costello Staniec, Syracuse University; AnnMarie H. O'Neil, C.S. Driver Middle School

Tagged Divisions

Mathematics

designprinciples that guided the development and implementation of these programs, followed by adiscussion of the lessons learned.Programmatic Changes in MathematicsWe developed and implemented three changes in the mathematics program for engineeringstudents: (1) a revision of the summer bridge program mathematics course; (2) the creation of amodified pre-calculus course for students who would otherwise have been placed in a collegealgebra course; and (3) the implementation of a Calculus I course for students who had not takencalculus in high school. In each of the sections that follow, we describe the engineering studentsfor whom the change was targeted and our specific goals for the changes we implemented.The Summer Bridge ProgramThe summer bridge

Conference Session

Using Applications and Projects in Teaching Mathematics

Collection

2012 ASEE Annual Conference & Exposition

Authors

Julie Gainsburg, California State University, Northridge

Tagged Divisions

Mathematics

’ dispositions with abackwards approach: It rests on the assumption, grounded in my prior research, that the ultimatemathematical disposition of engineers, that of skeptical reverence, is a productive and desirableone for future engineers and other professionals. It then targets individuals at various stages ofthe transition between school and engineering work and explores their evolving perceptions ofthe relationship between mathematics and engineering.MethodsThis study focused on the 12 participants who were selected to represent early engineer-development stages: two students in each of Years 1 and 2 of the undergraduate civil-engineeringprogram at California State University, Northridge: three students in each of Years 3 and 4 inthis program, some

Conference Session

Using Computers, Software, and Writing to Improve Mathematical Understanding

Collection

2012 ASEE Annual Conference & Exposition

Authors

John Schmeelk, Virginia Commonwealth University, Qatar

Tagged Divisions

Mathematics

. Then we obtain the familiar and very important 2 i 1result to many applications: the cosine of the angle between the two vectors, x and y,satisfies the equation, cos()=xy/( x y ). We know the maximum value for the cosineoccurs when the two vectors coincide, giving a value, cosine(0)=1. This is an importantobservation in edge detection and will later be explained. We now evaluate the values ofthe grey levels between neighboring pixel locations. This will be determined byintroducing the partial derivative formulas, f ( x, y) f ( x  x, y)  f ( x, y)  lim

Conference Session

Techniques in Improving Mathematics Education in STEM Curricula

Collection

2012 ASEE Annual Conference & Exposition

Authors

Jennifer Vandenbussche, Southern Polytechnic State University; Christina R. Scherrer, Southern Polytechnic State University

Tagged Divisions

Mathematics

% Other 54.5% 53.1% Total students completing the survey 22 32 Table 1: Self-reported demographicsDemographics of the College Algebra sectionsThe students took a survey within the first few weeks of class that contained questions about Page 25.150.6their background. The survey was adapted from a student pre-survey used on a project entitled,“Developing statistical indicators of the quality of undergraduate mathematics education,”headquartered at the Office for Mathematics, Science and Technology Education

Conference Session

The Transition from Secondary to College Mathematics

Collection

2012 ASEE Annual Conference & Exposition

Authors

Galen E. Turner III, Louisiana Tech University; Kelly B. Crittenden, Louisiana Tech University; James D. Nelson, Louisiana Tech University; Heath Tims, Louisiana Tech University

Tagged Divisions

Mathematics

Ftotal = k f 2We find empirically that k ranges between 6 and 9 for the College of Engineering and Science atLouisiana Tech university for each year starting in 2000. Figure 1. shows the f-index for 2007-08, here k =6. Page 25.165.3 f-index for 2007-08 14 12Number of Students 10 8 6 4 2 0 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Conference Session

The Transition from Secondary to College Mathematics

Collection

2012 ASEE Annual Conference & Exposition

Authors

Sabina Jeschke, RWTH Aachen University; Olivier Frédéric Pfeiffer, Technische Universität Berlin; Omar Musa Hasan, American University of Mdaba; Erhard Zorn, Technische Universität Berlin

Tagged Divisions

Mathematics

take the mathematics of the first semester before they enroll atthe university5. Page 25.175.2Mathematics Bridge CourseIn order to facilitate the transition from high school to university the Department of Mathematicsof our university offers a four-week bridge course before each semester. In this coursemathematics on the level of an advanced high school course is repeated. The course consists of adaily two-hour lecture and a two-hour exercise. Before the summer semester regularly 200-300and before the winter semester 800-1000 freshmen participate in this course (see figure 1).Because of financial reasons recitations classes in small groups

Conference Session

Techniques in Improving Mathematics Education in STEM Curricula

Collection

2012 ASEE Annual Conference & Exposition

Authors

John R. Reisel, University of Wisconsin, Milwaukee; Marissa Jablonski, University of Wisconsin, Milwaukee; Ethan V. Munson, University of Wisconsin, Milwaukee; Hossein Hosseini, University of Wisconsin, Milwaukee

Tagged Divisions

Mathematics

different times: 9:00-9:50 am, 1:00-1:50 pm, and6:30-7:20 pm. The sections were designed to concentrate on specific math courses, and studentswere to register for the appropriate section based on their math course. Five new peer mentorswere hired while two mentors remained from the year before to share their experiences and serveas role models for the new hires. Most incoming freshmen registered for the course and since itwas a part of their schedule, the majority attended throughout the semester. Having the class as apart of their weekly schedule, coupled with introducing a grade for the course based uponparticipation, increased attendance. Nearly all students who participated in the study groupsattended more than 2/3 of the meetings.However

Conference Session

Using Computers, Software, and Writing to Improve Mathematical Understanding

Collection

2012 ASEE Annual Conference & Exposition

Authors

Jorge A. Samayoa, Galileo University and Purdue University; Carlos Humberto Zelada, Galileo University

Tagged Divisions

Mathematics

collecting interesting data, such as most visitedtopics, demographics, and traffic intensity per hour. We use traffic intensity per hour as a way ofhow to use MediaWiki as a supplementary educational tool.1 Introduction1.1 Wikis in EducationA wiki is a well known tool for collaborative environment, the concept was developed by WardCunningham in 1995. Later, in 2001, Ward Cunnignham and Bo Leuf 5 define the nature of thewiki as an interface that allows users to edit and create any page in the wiki, without the need toinstall external plugins to the web browser. Wikis are commonly used as a tool for creatingcontent in collaboration with others and to serve as a source of information. Also, this web toolallows users to discuss and share their

Conference Session

The Transition from Secondary to College Mathematics

Collection

2012 ASEE Annual Conference & Exposition

Authors

Alex Feldman, Boise State University; Doug Bullock, Boise State University; Janet Callahan, Boise State University

Tagged Divisions

Mathematics

school, resulting in lack of knowledge retention by thetime they enter the university and eventually enroll in a required mathematics course. Page 25.1433.2When a student is placed in a class that is too easy it is a waste of time and resources, but the 1situation will often right itself after one semester. If a student is placed in a class that is toodifficult there are two serious deleterious effects: 1. The student may perform poorly, and fail the course or earn a grade damaging to the student’s grade point average. There is a documented connection between first year GPA and

Conference Session

Using Computers, Software, and Writing to Improve Mathematical Understanding

Collection

2012 ASEE Annual Conference & Exposition

Authors

Bipin K. Pai, Purdue University, Calumet

Tagged Divisions

Mathematics

25.1435.2groups when their performances are compared to account for the fact that one of the groups didnot have the opportunity to participate in the online quizzes or online discussions, especially ifcredit is given for such online activities. The Numerical Methods course taught in Summer 2011was offered as a hybrid course rather than a totally online course for several reasons including(1) the fact that although it was the second time that this course was offered as an online course,it was actually the first time that this course had online quizzes and online discussions, (2) theclass met at least once a week face-to-face in order to answer questions that students for somereason chose not to ask online, and (3) the instructor was uneasy about

Conference Session

Using Applications and Projects in Teaching Mathematics

Collection

2012 ASEE Annual Conference & Exposition

Authors

Hassan Moore, University of Alabama, Birmingham

Tagged Divisions

Mathematics

. Whenever numerical answers are required, find the exact values using a calculator. A certain amount of collaboration is acceptable in doing this project, but reports must be written individually. Thus, when writing your report, make sure that it is clearly different from reports of others and reflects your own thoughts for solving the problems. Reports that are virtually identical to others will not receive credit.In project 1, students are asked to use their knowledge of solving first-order ordinary differentialequations to tackle basic ideas in rocket science through the examination of the Jules Vernecatapult idea and single-stage rockets. The second project explores ideas in mechanicalvibrations with the concept of

Conference Session

Using Applications and Projects in Teaching Mathematics

Collection

2012 ASEE Annual Conference & Exposition

Authors

David I. Spang, Burlington County College; Kathleen Spang, Middlesex Boro High School

Tagged Divisions

Mathematics

approach, the formalized incorporation of applications will have somecommon elements:1) The application must have some readily identifiable significance, both in terms offunctionality and economic benefit, and the underlying and reliant principles must be readilyidentifiable and well understood.2) The underlying and reliant principles must be summarized in plain language andcommunicated with a simple figure or table, where appropriate.3) The application and principles must have significance to an emerging student, both in futureacademic courses (on the undergraduate and graduate levels) and in likely career experiences.4) The introduction and development of the application must follow a sound pedagogicalapproach (i.e. the inclusion of Bloom’s

Conference Session

The Transition from Secondary to College Mathematics

Collection

2012 ASEE Annual Conference & Exposition

Authors

Bert Pariser, Technical Career Institutes

Tagged Divisions

Mathematics

address is http://nlvm.usu.edu/en/nav/topic_t_3.html.A group of High School Teachers who were taking a course in teaching mathematics using UtahState University Software were having difficulty. They asked me to explain how it was possibleto use this software to actually teach the Pythagorean Theorem. In other words “How does thesolution of the puzzle prove the Pythagorean Theorem?” After my discussion with the teachers,it was clear to me that the concept of using manipulates motivated them to ask questions. Thisled me to believe that students would be similarly motivated by these manipulates. Page 25.1256.2The puzzle is set up as shown in Figure 1