Conference Session

Innovative Instructional Strategies and Curricula

Collection

2010 Annual Conference & Exposition

Authors

Jayathi Raghavan, Embry-Riddle Aeronautical University, Daytona Beach; Hong Liu, Embry-Riddle Aeronautical University, Daytona Beach

Tagged Divisions

Mathematics

undergraduate program in Computational Mathematics hasbeen recently approved. The trend seems to be that most of the students wishing to pursue thedegree program are engineering students interested in pursuing a dual major. The challengesfaced by the department are 1) to offer these dual majors an integrated curriculum that wouldtake advantage of their engineering background and 2) to offer a curriculum which will enablethem to complete the degree within one additional year without compromising the integrity ofthe program. In this paper, the authors discuss in detail their Computational Mathematicscurriculum and the modification of the curriculum for the dual majors.IntroductionComputational Mathematics is a multidisciplinary field that applies the

Conference Session

Computers and Software in Teaching Mathematics

Collection

2010 Annual Conference & Exposition

Authors

Bertram Pariser, Technical Career Institute, Inc.; Cyrus Meherji, Technical Career Institute, Inc.

Tagged Divisions

Mathematics

8342 342.75 1931 78 20.67 1967 905 35.00 2003 10454 417.25 Page 15.1241.5Figure 1 Data of the Dow Jones Averages and the Price of Gold from 1896 to 2008Figure 2 is a graph of the Dow Jones Industrial Average and the Price of Gold from 1896 to2008 The price of gold increase from $37.40 to $589.50 an increase of 970% while the DowJones Industrial Average increased $838.92 to $963.99 an increase of 15%. 1970 838.92 37.40 1971 890.20 43.55 1972 1020.02 65.00 1973 850.86 111.75 1974 616.24 193.00 1975 852.41 140.75 1976 1004.65 134.63 1977 831.17 165.15 1978 805.01 226.40 1979 838.74

Conference Session

Integrating Mathematics, Science, and Engineering

Collection

2010 Annual Conference & Exposition

Authors

Elton Graves, Rose-Hulman Institute of Technology

Tagged Divisions

Mathematics

∞ −n π t n2π 2t Ux, t = ∑ Ane 9 C n sin nπx  = 6 ∑ Bne− 9 sin nπx  6 n=1 n=1 Setting t = 0 and Ux, t = 6x − x 2 we arrive at Page 15.1263.3 ∞ n2π 20 6x − x 2

Conference Session

Computers and Software in Teaching Mathematics

Collection

2010 Annual Conference & Exposition

Authors

Cynthia Young, University of Central Florida; Michael Georgiopoulos, University of Central Florida; Tace Crouse, University of Central Florida; Alvaro Islas, University of Central Florida; Scott Hagen, University of Central Florida; Cherie Geiger, University of Central Florida; Melissa Dagley-Falls, University of Central Florida; Patricia Ramsey, University of Central Florida; Patrice Lancey, University of Central Florida

Tagged Divisions

Mathematics

. Page 15.548.2© American Society for Engineering Education, 2010   EXCEL in Mathematics: Applications of Calculus  Abstract Nationally only 40% of the incoming freshmen STEM majors are successful in earning aSTEM degree [1]. The University of Central Florida (UCF) EXCEL program is an NSF fundedSTEP (Science, Technology, Engineering and Mathematics Talent Expansion Program) whosegoal is to increase the number of UCF STEM graduates. One of the activities that EXCEL hasidentified as essential in retaining students in science and engineering disciplines is thedevelopment and teaching of special courses at the freshman level, called

Conference Session

Innovative Instructional Strategies and Curricula

Collection

2010 Annual Conference & Exposition

Authors

Murray Teitell, DeVry University, Long Beach; William Sullivan, DeVry University

Tagged Divisions

Mathematics

to the academic and career goals of thestudent. This began the active learning process. An example of “The Frame” is illustrated in Figure 1. The student has an interest in howdiseases spread. The student’s career goal was to go into a biomedical field. The studentresearched the process and found a set of differential equations that model the spread of diseasefor a particular and general case.5,6Figure 1. “The Frame” utilized in the context of the spreading of disease. Susceptible βI Infected g Recoveredβ = transmission rate, B = birth rate, d = death rate, R0 = reproductive rate (rate that infectedpersons cause new infected persons), g = recovery rate, S, I and R are the populations of thethree

Conference Session

Innovative Instructional Strategies and Curricula

Collection

2010 Annual Conference & Exposition

Authors

Kingsley Reeves, University of South Florida; Bill Blank, University of South Florida; Victor Hernandez-Gantes, University of South Florida; Maniphone Dickerson, University of South Florida

Tagged Divisions

Mathematics

learning. Forexample, one exercise enables students to build upon previously acquired knowledge related tocounting techniques and the concept of statistical independence and, through self-discovery,derive the probability mass function for the binomial distribution. Data were collected from botha control group and a treatment group. Preliminary results regarding the efficacy of such anapproach are presented.1. IntroductionThe need for a strong engineering workforce in the United States has been affirmed by severalnational studies including some sponsored by both the National Science Foundation and theNational Academy of Engineering1-3. Existing research on learning and teaching offerspedagogical approaches that have proven to be effective in

Conference Session

Integrating Mathematics, Science, and Engineering

Collection

2010 Annual Conference & Exposition

Authors

John Heublein, Kansas State University, Salina; Kenneth Barnard, Kansas State University, Salina

Tagged Divisions

Mathematics

teaching experience is used qualitatively inobserving student mathematics preparations and motivation changes over time. From experience,we have also tried different pedagogy methods, have agreement that the current “millennial”students are visual learners with technical shrewdness, and prefer active engagement activities.Limitations of study: We have a small faculty, N = eight, in the K-State at Salina aviationdepartment, therefore the data survey collected is very small and lacks validity. Having said that,these two faculty members have broad based observation level experience, as well as depth ofexperience. The faculty survey (Attachment #1) supports the stated hypothesis.Review of the literature:There has been an abundance of discussion and

Conference Session

Innovative Instructional Strategies and Curricula

Collection

2010 Annual Conference & Exposition

Authors

Robert Homolka, Kansas State University, Salina; Greg Stephens, Kansas State University, Salina

Tagged Divisions

Mathematics

tournaments and the College World Series two times andat the professional level (National League) a couple of times. Throughout this lengthy career, Igathered numerous stories to share (See Appendix A). Here are three abbreviated sample storiesused: 1. The pitching coach at WSU, while objecting to my strike zone, kicked dirt on the entire plate. He proceeded to uncover a two inch space down the middle of the plate and commented that was my strike zone! What percentage of the plate did he uncover? 2. While umpiring a major league game, Davey Johnson the manager of Cincinnati, questioned why a pitch was not called a strike which would have resulted in strike three. The batter hit the next pitch for a home

Conference Session

Students' Abilities and Attitudes

Collection

2010 Annual Conference & Exposition

Authors

Geoff Wright; Peter Rich, Brigham Young University; Keith Leatham, Brigham Young University

Tagged Divisions

Mathematics

computer programming. Coincidently the 2008 – 2009 employment and labor report by the U.S. Bureau of Labor Statistics predicts the need for engineers with programming experience will be one of the careers with the largest numerical increase and demand. This research outlines: 1) the need for engineering in k-12 environments, 2) analyzes the reasons for which schools have had a difficult time fully integrating engineering into school curriculum, 3) proposes a mixed content and pedagogical approach to teaching engineering and programming based on a hands-on inquiry approach, and 4) outlines additional benefits of using a blended content approach such as this (e.g., improved student

Conference Session

Integrating Mathematics, Science, and Engineering

Collection

2010 Annual Conference & Exposition

Authors

Brad Hunt, Norwood High School; Regina Lamendella, Lawrence Berkeley National Laboratory; Sara Garrison, Norwood City Schools; Andrea Burrows, The University of Cincinnati; Mike Borowczak, The University of Cincinnati; Anant Kukreti, The University of Cincinnati

Tagged Divisions

Mathematics

the effort to develop the post-test for the lesson. Awell-defined template is used by the Fellow to create the lesson, which can be disseminated onthe project’s website soon after its implementation. This template consists of the followingblocks: 1) Summary – goal to be achieved by students; 2) Objectives – skills to be acquired bystudents; 3) Standards to be addressed; and 4) Lesson Information – Grade Level, Subject Area,Duration, Setting, Materials Needed, Background Knowledge, Lesson Plan(s) details, andAdditional Resources (learning objects, timelines, assessment rubrics, surveys, etc.). Item 4includes detailed information provided via hotlinks. The Fellow submits the final lesson to theGrant Coordinator for checking and approval before

Conference Session

Issues and Solutions in Mathematics Education

Collection

2010 Annual Conference & Exposition

Authors

Gisela Gomes, Universidade Presbiteriana Mackenzie; Janete Bolite Frant, Universidade Bandeirante; Arthur Powell, Rutgers University

Tagged Divisions

Mathematics

aspectsstudents emphasized in their work and interviews. Aspects of mathematical Student 1 Student 2 thinking Knowledge base Linear regression; Matrix; Gauss method for equations; graphs of equations; geometry; functions concept of variables Problem solving strategy Raise conjectures; Raise conjectures; verify verify conjectures and conjectures and refine if it refine if it would be the would be the case. case. Refining the problem; Compare old

Conference Session

Computers and Software in Teaching Mathematics

Collection

2010 Annual Conference & Exposition

Authors

Zohra Manseur, SUNY Oswego; Adrian Ieta, SUNY Oswego; Rachid Manseur, SUNY-Oswego

Tagged Divisions

Mathematics

generalcurriculum that together constitute a complete degree program: 1. General education requirements – these courses provide a broad college education in the arts, humanities, social sciences, natural sciences, mathematics, and computer science. 2. Cognates – these are the courses in areas that provide essential preparation for the study of engineering. These consist of courses in mathematics, chemistry, biology, physics, and computer science. 3. Core – Core courses in engineering provide the education and training needed for the professional practice of engineering. 4. Electives – These are typically choice courses mostly in engineering or the cognate subjects that allow students to acquire deeper knowledge in a

Conference Session

Students' Abilities and Attitudes

Collection

2010 Annual Conference & Exposition

Authors

Chih Hsien Huang, MingChi University of Technology

Tagged Divisions

Mathematics

AC 2010-725: AN INVESTIGATION OF ENGINEERING STUDENTS' ATTITUDESTOWARD CALCULUS IN TAIWANChih Hsien Huang, MingChi University of Technology Page 15.168.1© American Society for Engineering Education, 2010 An Investigation of Engineering Students' Attitudes toward Calculus in TaiwanAbstractThe purpose of this study was to investigate engineering students in Taiwan to (1) assess theirattitudes toward calculus, (2) determine the difference in attitudes scores between males andfemales and (3) assess the relationship between students, attitudes toward calculus and theircalculus achievement. Attitude was measured in cognitive, affective, and

Conference Session

Students' Abilities and Attitudes

Collection

2010 Annual Conference & Exposition

Authors

Maria Terrell, Cornell University Math Dept.; Robert Terrell, Cornell University; Lisa Schneider, Cornell University

Tagged Divisions

Mathematics

: (1) Development of the first draft of the MAI, (2) Pilot testing the MAI,and (3) Preliminary analysis of the pilot test data.To develop the MAI, faculty of second- and third-year engineering courses were surveyed abouthow key concepts and techniques from single variable differential and integral calculus are usedin intermediate-level engineering courses. Based on their feedback, as well as feedback fromadvanced undergraduate engineering students, an initial set of test items was developed. Theresulting MAI consists of five open-ended questions with eleven sub-questions. The test isdesigned to be administered during one hour in paper-and-pencil format.The MAI was administered during the first week of the Fall 2009 semester as a pre-test to

Conference Session

Issues and Solutions in Mathematics Education

Collection

2010 Annual Conference & Exposition

Authors

Dianne Raubenheimer, North Carolina State University; Hatice Ozturk, North Carolina State University; Alina Duca, NCSU

Tagged Divisions

Mathematics

performance, pre-requisiteknowledge and skills. Page 15.239.2IntroductionThe mathematics knowledge and skills gap encountered by undergraduate engineering studentswhen they enter engineering courses requiring the use of mathematics abilities which weretaught in the three semester calculus sequence has been well documented 1, 2, 3. However, there is'widespread agreement among academics and practicing engineers that a good grounding inmathematics is essential for engineers' 4. The challenge facing the engineering instructor is howto bring all students up to mathematical mastery level as quickly as possible at appropriate pointsduring the semester when

Conference Session

Issues and Solutions in Mathematics Education

Collection

2010 Annual Conference & Exposition

Authors

Andrew Grossfield, Vaughn College of Aeronautics

Tagged Divisions

Mathematics

: variable, limit, polynomial, inverse function and function.Students embarking on a study of algebra must confront the word variable, usually defined as aletter representing a member of a set. In a study of rectangles, the length, width, area andperimeter, all belong to the set of positive real numbers. Can an area be added to a length? Canthe students be blamed for being confused?Variables are symbols representing measureable properties of systems. The concept is anotational device for writing the laws of these systems. Consider the set of rectangles as oursystem to study. The laws are relationships of the system, in this case: 1) The area of any rectangle is the product of its length and width and 2) the perimeter is twice the sum of

Conference Session

Issues and Solutions in Mathematics Education

Collection

2010 Annual Conference & Exposition

Authors

Andrew Grossfield, Vaughn College of Aeronautics

Tagged Divisions

Mathematics

to use if the table is not too long and the desired values of theindependent variable are listed. A table description of the function A = ρ R2 is shown inTable 1. 2 R A=ρR 0 0 1 A= ρ= 3.14159 2 A = 4 ρ = 12.56637 3 A = 9 ρ = 28.27433 4 A = 16 ρ = 50.26548 5 A = 25 ρ = 78.53982 6 A = 36 ρ = 113.09734Table 1Another format for describing functions is called a

Conference Session

Innovative Instructional Strategies and Curricula

Collection

2010 Annual Conference & Exposition

Authors

John Schmeelk, Virginia Commonwealth University Qatar Branch; Jean Hodges, Virginia Commonwealth University Qatar Branch

Tagged Divisions

Mathematics

teaching of MATH 131 at VCUQatar.This study, the fifth in a series examining ways to motivate learning of contemporary mathamong VCUQatar’s design students, summarizes the preceding studies and extracts from themobservations and recommendations that may be adapted to transform other analytical coursesinto culturally-appropriate studies.The Evolution of MATH 131The Journey. Year 1 (2005-2006, “Making Connections Among Culture, Personality, and ContentIn Analytical Courses”).3 MATH 131 at VCUQatar began with a textbook, graphic calculator,white board, and markers. Several lectures delivered each textbook topic. VCUQatar was afemale-only institution of mostly Qataris, who were difficult to motivate into studying andunderstanding the math