Multi-Course Alignment for First-Year Engineering Students ...
Transcript of Multi-Course Alignment for First-Year Engineering Students ...
Paper ID #9852
Multi-Course Alignment for 1st Year Engineering Students: Mathematics,Physics, and Programming in MATLAB
Caroline Liron, Embry-Riddle Aeronautical Univ., Daytona Beach
Caroline Liron is an Assistant Professor in the Engineering Fundamentals Department, at Embry-RiddleAeronautical University (ERAU), where she has been teaching since 2005. She obtained her bachelor’sin aeronautics and space from EPF, Ecole d’Ingenieur (France), and her M.S. in aerospace engineeringfrom ERAU. She currently teaches Introduction to Programming for Engineers. She is involved in devel-oping and maintaining the hybrid version of that class, and researching improvements methods to teachprogramming to incoming freshmen using new technologies.
Dr. Heidi M Steinhauer, Embry-Riddle Aeronautical Univ., Daytona Beach
Heidi M. Steinhauer is the Department Chair of the Freshman Engineering Department and is an As-sociate Professor of Engineering at Embry-Riddle Aeronautical University. Steinhauer holds a Ph.D. inengineering education from Virginia Tech. She has taught Spatial Visualization Development, Engineer-ing Graphics, Introduction to Engineering Design, Automation and Rapid Prototyping, and has developedseveral advanced applications of 3D modeling courses. She is the co-advisor of the only all-women’s BajaSAE Team in the world. Her current research interests center around the development and assessment ofstudents’ spatial visualization skills, effective integration of 3D modeling into engineering design, andwomen’s retention in engineering.
Dr. Jayathi Raghavan, Embry-Riddle Aeronautical Univ., Daytona BeachDr. Bereket Berhane, Embry Riddle Aeronautical University
c©American Society for Engineering Education, 2014
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Multi-Course Alignment for 1st Year Engineering Students:
Mathematics, Physics, and Programming in MATLAB
Background
Historically, siloed courses utilizing traditional, deductive, teaching methods have struggled to
effectively promote conceptual understanding. Gains students achieve are usually modest and not
statistically significant; generally students are able to increase their factual knowledge only.
These modest gains are predicated on students having either no preconceptions or correct but
incomplete ones. However, students who have incorrect preconceptions do poorly as they must
change their existing cognitive structure.1 Inductive teaching methods better enable students to
achieve a permanent change to their cognitive structures. Students also have a difficulty
transferring learning horizontally through their courses.
Purpose
First year students struggle to synthesize concepts across Programming for Engineers, Calculus I,
and Physics I courses.2 While calculus and physics are tools to be utilized by engineers to solve
problems, our students are often unable to see that the knowledge presented in the mathematical
and physics context can be transferred to solving engineering problems. Students also tend to
view programming as an isolated component of engineering. They should understand instead that
programming is yet another tool to verify results and to solve more complex problems, reducing
risks of algebraic errors.3
Design/Method
Three faculty members linked their classes to create a STEM (science, technology, engineering,
and mathematics) small-learning-community (SLC). The same set of students is registered for
the three linked courses: Calculus I, Physics I, and Introduction to Programming using
MATLAB. In addition, these same three faculty members also taught one or two non-SLC
sections of the same course; these were the control groups. Students were randomly selected
from the incoming newly admitted students to be within the SLC.
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Table 1 describes the topics taught in each course. As a start, only the topics highlighted in bold
were chosen to be developed across all three classes: graphs and functions, integration, related
rates, vectors, free body diagrams, Newton’s laws of Motion, center of mass and its motion.
Table 1: Description of Calculus I, Physics I and Programming Courses
Course Description
Calculus I Graphs and functions; differentiation and integration of algebraic and
elementary trigonometric functions; related rates; applications of first
and second derivatives.4
Physics I Vectors and scalars quantities; geometrical optics, kinematics; free body
diagrams, Newton’s Laws of Motion, work, work-energy, conservation
of energy, conservation of momentum, center of mass and its motion. 4
Introduction to
Programming for
Engineers
Software design and development: specification, requirements, design,
code, and test; scripts, data-types, input and outputs, flow-control,
functions, arrays, files and plotting.
An overarching idea behind the SLC is to help students realize that the topics of Calculus I,
Physics I, and Programming are most effective when used together in engineering. These
concepts in engineering applications are not siloed and nor should the coursework be. Therefore
to address this conceptual misalignment, all three faculty developed mini-projects, or specific
assignments incorporating concepts from each of the three disciplines. All three faculty
collaboratively developed the real-world application problems that required leveraging
knowledge horizontally across all three courses.
The bold faced common themes were then mapped to provide a framework in the development
of the interdisciplinary mini-projects. It was critical to ensure the mini-projects developed
aligned the appropriate topics across all three courses. Table 2 presents the final mapping of the
common course topics and the developed themes of the mini-projects.
Table 2: Mapping of MATLAB topics to Calculus I and Physics I mini-projects
Calculus I Physics I
Flow-control (loops) Integral of a function Calculate slopes during a trajectory
Arrays, plotting Related rates Vector Fundamentals, Cable
Tension, Trajectory Analysis
Files Center of mass of an aircraft
This paper will present the development of and the results from the MATLAB course. Other
specific mini-projects given in Calculus I and Physics I classes are to be presented in future
papers. The next section will present two of the mini-projects developed for the MATLAB
course in detail.
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At the start of the semester, students are just beginning to learn many of the theorems of
Calculus I and Physics I and are not ready to solve these types of problems in either course. It
was determined that MATLAB’s plotting capability is a tool that could be presented earlier in
the programming course to help solve these Calculus I and Physics I class problems, thereby
providing students with additional exposure to the material as presented from a programming
context.5 This was the guide for the development of the two mini-projects discussed in this paper
that integrated MATLAB, Calculus I and Physics I knowledge.
Mini-Project #1: Cable Tension (Vectors, Plotting, Free Body Diagrams)
During week four of Physics I, students learn to solve for the magnitude of forces acting on an
object such as tensions in cables holding a weight (Figure 1).
Figure 1. Typical freshman Engineering Physics I problem.
After drawing the free-body diagram as shown in Figure 2, the projections of the vectors on the x
and y-axis help apply Newton’s second law of motion* to solve for the tension in each cable.
Figure 2. Physics solution of forces, using free body diagrams and Newton’s law (week four).
* sum of all forces on a non-moving object is equal to zero
�� ��
�
�� ��
�� ��
�
��cos(�2) ��cos(�1) �
����������= 0
+�� cos(�2) − �� cos(�1) = 0
�� =�� cos(�1)cos(�2)
Mathematical Solution
(Newton’s law)
Therefore: ��
Free Body Diagram
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In parallel during the same week, in the MATLAB programming course, a plotting method can
be implemented in replacement of a free-body diagram to solve for the tension in each cable.
There are various advantages to solving the same problem during the same week:
• Student see different methods
• It reinforces the fact that engineers use the same knowledge across all classes
• It reinforces the topic itself, by having student practice the same problem multiple times
• The knowledge of one topic is spread over more time
The first exam in MATLAB is shown in Figure 3 (Refer to Appendix A for the complete
example of Mini-Project #1). Due to the one hour time constraint, students are not required to
draw the free-body diagram to determine the equations. The final linear equations are given to
the students in the exam write-up but instead of algebraically solving them, students are asked to
find the tensions in the cables using a graphical method. The intersection of the two lines lets
students determine tension1 on the x-axis and tension2 on the y-axis on Figure 4.
A weight W (in Newton) is attached to the ceiling by the mean of two cables, as shown here. Calculate
the tension �� and �� (in Newton) using graphical analysis only.
Don’t panic: the equations have been solved for you, and therefore the problem can be solved
graphically. By solving the physics, �� can be expressed as a function of �� by two equations. These
equations are linear equations of the form�(�) = ∗ � + ":
Equation 1: ��(��) = #$%(&')#$%(&() ∗ ��
Equation 2: ��(��) = − %)*(&')%)*(&() ∗ �� ++
%)*(&()
Assuming both angles and the weight are known by the user, develop a program that can solve the
tensions for any similar setup by plotting both equations above and reading (��, ��) on the intersection
of these lines. The cable used can handle a maximum tension of 62N. Will it break? When complete, fill
Figure 3. Exam 1 (week four) - Solving graphically for tension forces in cables.
�� ��
�
�� ��
Page 24.920.5
Figure 4. Graphical Solution. The intersection easily lets students
determine the cable tensions T1 and T2.
Mini-Project #2: Trajectory Analysis (Vectors, Plotting, Equations of Motion)
Students are often uncertain and uncomfortable with polynomial equations and that uncertainty
leads to algebraic errors and poor results. Polynomial equations typically appear when students
learn about equations of motion, specifically with projectile trajectories. Plotting the two curves
with MATLAB allows students to visually solve for the (x,y) coordinates of their intersections,
thus answering actual physics concepts of trajectories.
For example, students typically know that a projectile thrown at a 45° angle will travel the
furthest distance. However, if there is a sloped hill, some students mistakenly believe that 45° is
still the angle that will lead to the furthest distance travelled. In the following lab example, the
curve is a polynomial of the second degree. Yet, the graphical approach applied here is identical
to the cable tension that finds the intersection of the curves and solves for physics property of the
trajectory as shown in Figures 5 and 6. (Refer to Appendix B for the complete example of Mini-
Project #2)
T1
T2
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Problem2 (name your file projectileHillImpact.m) – no step needed, most are done for you anyways!
A projectile is thrown on a hill (see figure). Knowing the two angles (angle of throw �. and angle of the
hill �/) and the initial velocity 01 of the projectile, solve graphically for the coordinates (x, y) of the
impact.
Equations: Both height and distances are function of time.
234526(6) = 016748(�.) −1
29.816^2
=476>8?36� � 016 cos�.�
The time interval that should be studied is from 0 seconds to �
@.A�01sin�.� seconds.
Figure 5. MATLAB Lab: Graphically solving the intersection of linear and polynomial equations.
Figure 6. Teaching student to plot trajectories and determine
intersections of curves graphically.
One benefit of writing code is its re-usability. A follow-up lab shown in Figure 7 based on the
same trajectory problem provided students with the opportunity to implement the crucial
re-usability aspect of a program, while again re-enforcing the fact that 45° is not always the angle
that will lead to the furthest distance travelled.
�. �/
(�, ��?
height (m)
distance (m)
height travelled vs. distance
x
y
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Problem3 (name your file: GuessProjectile2.m)
Use the solution provided online for Lab4, problem2 (please fix your code from Lab4 so that it works
properly before continuing!). For the entire problem set 01 = 30FG . Update the script so that the angle
of the throw �. can be entered by the user. By using the code repeatedly, and guessing on the value of
the throw angle, determine what throw gives the longest straight distance on the hill for each of the
following angles of hills.
�/�HH Guesses you tried, and x ‘visually’
read on the plot: angle (max x)
�.I��J for maximum
distance (best guess)
(extra credit – determine
graphically)
Max Distance (meters)
5° 20° (44.5m), 30° (68m), 45° (83m),
50° (83m), 60° (76m), so it’s between
45° and 60°… 55° (80.92m), 50°
(83.715m), 45° (83.7144m), 53°
(82.3727)
50 sqrt(83.715^2+7.324^2) =
84.0348
25°
30°
45°
Figure 7. Practicing the “re-usability” aspect of a program on a physics application.
Later in the semester, students learn the theoretical process to derive then solve these systems of
equations in Physics I and Calculus I. Having solved the problem graphically using MATLAB
provides students with the increased confidence in their ability to solve problems
mathematically.
Assessments & Results
To assess the impact of the SLC on student’s learning, assessments were made through two
satisfaction surveys (Hybrid Survey (Appendix C), and Social Media Integration Survey
(Appendix D)) and grade analysis. Both surveys were created by the author. The Social Media
Integration Survey has been used every semester since Fall 2012. All students in SLC and
non-SLC sections were given surveys at the end of the semester. Some of the results are
presented here.
Height (m)
distance (m)
Height travelled vs. distance
max distance �.
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The results of the surveys and the grade analysis are dependent on whether the student attended
classes continuously. The surveys were done in class on the very last day. While most students
were present, not only had some students withdrawn or stopped attending during the semester
but others were simply absent the last day. The overall class enrollment progression is shown in
Table 3.
Table 3: Enrollment statistics
Enrolled First
Day
Withdrew
or
Enrolled but no longer
attending classes
or
Removed from campus
roster
Students
active at end
of semester
Absent on
day surveys
administered
Non-SLC 52 7 (13%) 45 6
SLC 37 4 (11%) 33 2
For question 12 of the Hybrid Survey, “To what extent would you use MATLAB to solve a
mathematical or physics problem?”, more students from the non-SLC, 31% (non-SLC) vs. 23%
(SLC) would absolutely program a solution regardless of the level of complexity (Figure 8). This
may be due to the fact the non-SLC was not controlled for class level. It is nice to notice that
regardless of the complexity of the problem, 87% of students (non-SLC) and 97% (SLC) would
venture to program the solution (Table 4). One student from the SLC wrote that he would use
MATLAB only “If I had to re run the numbers more than twice”, which is exactly what has been
emphasized all semester: one major benefit of a program is its re-usability.
Figure 8. Will of students (non-SLC and SLC) to use programming for
mathematical or physics problems.
57
14
1
12
1
8
13
2
7
It would never come
to mind
Possibly, if the
problem was simple
Possibly, whether the
problem is simple or
complicated
Absolutely, if the
problem was simple
Absolutely, whether
the problem was
simple or
complicated
To what extent would you use MATLAB to solve a mathematical or physics
problem?
non-SLC (S=39) SLC (S=31)
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Table 4: Percentage of students would possibly or absolutely use programming
No Possibly Absolutely (Possibly & Absolutely)
Non-SLC (S=39) 13% 54% 33% 87%
SLC (S=31) 3% 68% 29% 97%
Questions 2, 3 and 4 of the same Hybrid Survey were given to only the SLC students to evaluate
the overall program success and identify the areas for improvement. An overwhelming majority
(85%) enjoyed being part of the SLC. However, while still a majority, a smaller amount felt it
helped learn better (67%), and enjoy their first semester at Embry-Riddle Aeronautical
University more than if they had not been in a SLC (70%) (Figures 9, 10, and 11).
Figure 9. Did students enjoy being part of the SLC?
Figure 10. Learning impact of being in the SLC.
Figure 11. Impact of being in the SLC on the aspect of enjoying college life.
1216
40 1
Strongly agree Agree Neither yes or
no
Disagree Strongly
disagree
You enjoyed being part of the Small Learning
Community (S = 33)
9
13
8
2 1
Strongly agree Agree Neither yes or
no
Disagree Strongly
disagree
I believe being part of the learning community
helped me learn better in class (S = 33)
914
8
0 2
Strongly agree Agree Neither yes or
no
Disagree Strongly
disagree
I believe being part of the Small Learning
Community made me enjoy my first semester better
than if I had not been part of a community. (S = 33)
Page 24.920.10
All students were also given a Social Media Integration survey. The highest number of
matriculated freshman occurs during the fall semester; the past two fall semesters were used to
measure the level of social integration of students. In the Fall of 2012, the SLC was not
available.
Students were asked on a Likert scale of 1 to 4 (1=not at all, 2=a little, 3=integrated, 4= very
well integrated), how much they felt part of both the Embry-Riddle Aeronautical University
community and the engineering community. Students in the Fall 2013 semester felt a higher
level of social integration in both categories (see Table 5). This may be due to the SLC students
bonding quicker with each other due to their multiple shared classes. Unfortunately, this survey
did not allow filtering the SLC from the non-SLC students.
Table 5: Level of integration (Fall 2012 and Fall 2013), with and without SLC experience
To what extend do you feel part
of the Embry-Riddle
Community?
To what extend do you feel
part of the ENGINEERING
Community?
Fall 2012 (without SLC)
(S=93) 2.75 (s.d.= 0.85) 2.37 (s.d.= 0.81)
Fall 2013 (with SLC)
(S=72) 2.82 (s.d.= 0.77) 2.49 (s.d.= 0.85)
Additional Findings
Collaborative Environment: The students in the SLC sections were more comfortable with each
other and were collaborative while working the in-class problems. They helped each other and
were more at ease asking for help from their fellow classmates in solving the problems. Students
in the non-SLC tended to solve the problems on their own and some of them were very reluctant
to ask for help or to form groups.
Increased Persistence: Students in the SLC completed 13% more assignments than non-SLC
students and they performed better across the major grade categories of the class as shown in
Table 6. It is believed the increased sense of community in the SLC section directly impacted
student performance. While students in the SLC may have been more apt of working together, no
more excessive collaboration (cheating) was discovered in the SLC classes. However, students
encouraged each other to complete assignments ahead of time thus giving them more time to
improve and do better on each assignment by over 10% (Table 7).
Table 6: Completion rates in major categories of the class for the MATLAB class
Averages Assignments Mini-Projects Quizzes Exams Final Projects
Non-SLC (S=50) 80% 71% 87% 96% 84%
SLC (S=35) 93% 79% 93% 99% 90%
Page 24.920.11
Table 7: Averages in major categories of the MATLAB class
Averages
(weight)
Assignments
(20%)
Quizzes
(10%)
Exams
(40%)
Final Projects
(20%)
Non-SLC (S=50) 76% 76% 74% 60%
SLC (S=35) 89% 84% 78% 69%
Increased Class Participation: As the students of the SLC were more familiar with each other,
they asked and answered more questions in class than the non-SLC. This made the course more
enjoyable both from the student’s point of view but also from the faculty perspective. Due to the
more outspoken, interactive, and energetic environment of the SLC students, stronger classroom
management was required. Only the confident students in the non-SLC sections were
comfortable enough to ask questions. However these were infrequent and often done outside of
class.
Increased Faculty Satisfaction: All three faculty observed that it was more enjoyable to teach the
SLC sections, as the students related well with others. They did not hesitate to interact with
professors in discussions beyond the scope of the class. Some students opened up about their
families, their interests, and their weekend activities. Some also asked about internships, and
future work opportunities. While this did happen in the non-SLC sections, it was much more
frequent with the SLC students.
Grade Distribution
At Embry-Riddle Aeronautical University, Early-Alert (third week) and Mid-Term (seventh
week) evaluations are completed to identify students who received satisfactory (S),
unsatisfactory (U), or unsatisfactory with excessive absence (UX) grades. Final semester grades
between the SLC and the non-SLC group were also compared to measure the impact of the
program.
During the week of Early-Alert, 51 students were still enrolled in the non-SLC sections, and 37
were enrolled in the SLC. One student who had withdrawn from the non-SLC section was no
longer enrolled and had left the school for personal reasons. A significantly higher number of the
SLC students had a Satisfactory evaluation as compared to the non-SLC (Table 8). In this
MATLAB class, this represented a current grade above or equal to 75%.
By the week of Mid-Term, two students withdrew from the SLC and from the University for
personal reasons. In order to get a satisfactory at the Mid-Term in the MATLAB class, students
needed a current average greater or equal to 70% and a grade on exam2 greater than or equal to
70%. The material taught had increased in complexity, thus lowering the threshold at 70% vs.
75% in the Early-Alert. Table 8 shows that still more SLC students were doing satisfactory in the
class than in the non-SLC. However, the overall Satisfactory percentage fell similarly in both
SLC and non-SLC.
Page 24.920.12
Table 8: Early-alert and Mid-term comparison in the MATLAB programming class
Early-Alert S U UX Withdrew
Non-SLC (S=52) Early-Alert 77% 21% 0% 2%
Mid-Term 65% 29% 4% 2%
SLC (S=37) Early-Alert 87% 8% 5% 0%
Mid-Term 76% 19% 0% 5%
The MATLAB non-SLC sections included students already in upper level math and physics.
Only 14 students (27%) in the non-SLC were also taking Calculus I and Physics I in separate
sections. In Table 9, it is interesting to compare the Early-Alert for those 14 students with the
SLC students, and note a 22% difference in Satisfactory. Possible reasons may be different
alignment of course content with faculty teaching non-SLC sections of Calculus I and Physics I,
or the lack of bonding that motivates students to study and progress together. However, if
comparing only the controlled non-SLC with the SLC, Table 9 shows an increase of Satisfactory
in the controlled non-SLC to the point of being very similar to the SLC results. By this time,
students have been at school for seven weeks, thus the bonding of all students might be reflected
here.
Table 9: Early-Alert and Mid-Term for the SLC and controlled non-SLC
Early-Alert S U UX Withdrew
Controlled Non-SLC (S=14)
(Calculus I and Physic I)
Early-Alert 64% 36% 0% 0%
Mid-Term 79% 21% 0% 0%
SLC (S=37) Early-Alert 87% 8% 5% 0%
Mid-Term 76% 19% 0% 6%
The comparison final grade distribution in Table 10 shows a significant reduction in failure. The
high failure rate in the non-SLC section is due to students who were enrolled but chose to no
longer attend class mid-way through the semester, and currently 5 students (10%) who have
Incompletes (I) due to on-going academic integrity procedures. While the number of A’s is not
significantly different, it is interesting to note the increase in B’s and C’s in the SLC students.
Table 10: Grade distribution in the MATLAB class
A B C D/F/I/W
Non-SLC (S=52) 15% 15% 14% 56%
Controlled Non-SLC (S=14)
(Calculus I and Physics I) 22% 7% 14% 57%
SLC (S=37) 19% 35% 19% 27%
Page 24.920.13
At the end of the semester, one student had withdrawn from the university (no GPA available)
both in the SLC and non-SLC, while one student had withdrawn from the SLC from the
MATLAB course but remained at the university. The GPA comparison shows a semester GPA
higher by 0.31 for the SLC sections compared to the non-SLC (Table 11). There is an even
greater difference between the SLC and the Controlled Non-SLC.
Table 11: End of semester GPA comparison of all groups
Semester GPA Average
(out of 4)
Non-SLC (S=51) 2.23 (s.d. = 1.01)
Controlled Non-SLC (S=14)
(Calculus I and Physics I)
2.17 (s.d. = 0.95)
SLC (S=36) 2.54 (s.d. = 0.84)
Challenges
Several challenges repeatedly appear in all sections. The lack of pre-requisite knowledge for
Calculus I is a significant challenge. Although students do take a math placement test, it is clear
that some pre-requisite are lacking. While the students are considered to be “Calculus I ready”,
they are not. An actual Calculus I ready class should benefit even more from a Calculus I,
Physics I and programming community environment.
Although the SLC section showed great ease and comfort in relating to each other, it is not sure
that the community spirit was shared by all of them. There were identifiably about four students
who chose to be outside the circle and participated in class only upon faculty insistence. More
discussion with all participating faculty on addressing such students is needed. Some students
will self-isolate, and determining how to successfully handle these students continues to be a
challenge.
Future Improvements
To continue improving the SLC experience, several points are considered.
Additional interdisciplinary mini-projects will be developed collaboratively with all three faculty
members. The collaboration in the work, the cross-referencing of the topics, and the delivery
timing during the semester is crucial for the students to fully gain the advantage of this teaching
method.
Page 24.920.14
The surveys at the end of the semester need to be able to filter the SLC from the non-SLC, but
also the control for math and physics experience for the non-SLC. This will allow for a more
meaningful comparison of the results.
If possible, the non-SLC needs to be a true control group. These non-SLC students should also
only be enrolled in Calculus I and Physics I. This is a challenge for registration. At the same
time, a better advertising of the SLC opportunity is required, with possibly a simple letter sent to
the students during registration process before the semester starts.
Longitudinal math, physics, and statics data will be collected for the students who participated in
the STEM SLC and compared to students who did not to see potential long term impact.
Conclusion
The STEM SLC students significantly performed better in the MATLAB class as the passing rate
is 73% vs. 44% in the non-SLC. The fact that the students in the SLC met daily together in their
classes created not only a bond of friendship, but of work ethic as well. They motivated each
other on a daily basis in addition to the faculty reminding them of their work daily. This
impacted their attendance, their participation, and the completion rate of the overall work.
The association of all topics across all three classes made the classes more connected. Students
did not feel they had three segregated classes, but possibly saw it as one class only. The mini-
projects, although specific to each faculty, connected the topics from all three faculty
simultaneously. Students in the SLC participated well in all mini-projects and considered all
three faculty when asking for help regardless of the problem.
The Spring 2014 will continue to introduce mini-projects in all three classes and the monitoring
of the current SLC and future SLC sections will take place.
1. Goris, T. V., & Dyrenfurth, M. J. “Students’ Misconceptions in Science, Technology and Engineering”, in ASEE
Illinois/Indiana Section Conference proceeding, Purdue University, West Lafayette, IN, 2010.
2. Rebello, S, and L. Cui. “Retention and Transfer of Learning from Math to Physics to Engineering” Proceedings
of the 2008 American Society for Engineering Education Annual Conference & Exposition, Pittsburgh, PA, June
22-25, 2008.
3. Rencis, J.J. and Grandin, H.T., “Mechanics of Materials: an Introductory Course with Integration of Theory,
Analysis, Verification and Design,” 2005 American Society for Engineering Education Annual Conference &
Exposition, Portland, OR, June 12-15, 2005.
Page 24.920.15
4. Pembridge, J., and Verleger, M., “First-Year Math and Physics Courses and their Role in Predicting Academic
Success in Subsequent Courses”, in ASEE Annual Conference and Exposition, Atlanta, GA, June 23-26, 2013.
5. Herniter, Marc E., Scott, David R., Pagasa, Rakesh, “Teaching Programming Skills with MatLab”, Computers in
Education Journal, 2001.
Page 24.920.16
Appendix A: Mini-Project #1
Name: _______________________________________ Section: _____ Practice for Exam1/Extra Credit
Assignment
Topics: MATLAB, variables, scripts, vectors, plotting, input/output
Take 3 full minutes to read the ENTIRE cover sheet first.
SUBMIT script file (NO ZIP) before the end of the class time. Turn in cover sheet.
A weight W (in Newton) is attached to the ceiling by the mean of two cables, as shown here. Calculate
the tension �� and �� (in Newton) using graphical analysis only.
Don’t panic: the equations have been solved for you, and therefore the problem can be solved
graphically. By solving the physics, �� can be expressed as a function of �� by two equations. These
equations are linear equations of the form ��� = ∗ � + ":
Equation 1: ����� =#$%&'�
#$%&(�∗ ��
Equation 2: ����� = −%)*&'�
%)*&(�∗ �� +
+
%)*&(�
Assuming both angles and the weight are known by the user, develop a program that can solve the
tensions for any similar setup by plotting both equations above and reading ��, ��� on the intersection
of these lines. The cable used can handle a maximum tension of 62N. Will it break? When complete, fill
in the table (5pts):
Angle 1
(degrees)
Angle 2
(degrees)
W (Newton) T1 (Newton)
2 decimals
T2 (Newton)
2 decimals
Break?
45 37 90
30 60 70
Using the full 7 steps taught in this class, and only the material taught in this class at this time, develop a
program that is easily reusable to solve the problem.
Step1(5pts):
Step2:
�� ��
�
�� ��
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Step3: (Equations given already)
Step4: (Assume values from scenario1 (line 1 in the table))
Step5: (solve graphically – hence no step5 needed)
Step6: not applicable
Step7a (comments) and 7b (place directly on the script file).
Requirements for the program itself:
- (12pts) prompt the user for the values of ��, ��, �.
- (15pts) define all vectors that can plot equation1 and 2
- (10pts) plot correctly, using colors, markers and line specifications AS SHOWN in the videos.
- (15pts) label the plot properly and fully
(7pts – other random errors!)
Within script:
name/section/description (3pts)
commands to clean up previous execution of MATLAB codes (3pts)
comments (which is considered the algorithm) (5pts)
spacing of code (5pts)
appropriate variable names (no single letters) (5pts)
semi-colon hiding intermediate calcuations (5pts)
Step7c (5pts): Verify mathematically your solution seems accurate.
(T1, T2)?
��M�
��M�
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Appendix B: Mini Project #2
Name:
Section:
Lab04: Vectors and Plotting
Code. Zip. Submit. 11:59pm Print. Staple in order. Bring to next lab.
Problem1 (name your file aircraftWind.m)
The path of an aircraft is changed due to winds. The pilot had travelled 50km west, then 35km south-
west, then an additional unknown straight distance. However, the pilot came back to the original
straight-line path, 200km from the original spot. Calculate the vector’s components for the missing
straight distance using vector analysis.
Complete Step1 to Step3 to completely understand the different vectors involved, one for each
distance. Step2 should be to scale. In the script file, define each vector separately by hardcoding their
component. Then solve for the components of the missing distance.
Problem2 (name your file projectileHillImpact.m) – no step needed, most are done for you anyways!
A projectile is thrown on a hill (see figure). Knowing the two angles (angle of throw �. and angle of the
hill �/� and the initial velocity 01 of the projectile, solve graphically for the coordinates (x, y) of the
impact.
Equations: Both height and distances are function of time.
ℎ345ℎ66� = 016748�.� −1
29.816^2
=476>8?36� = 016 cos�.�
The time interval that should be studied is from 0 seconds to �
@.A�01sin�.� seconds.
Requirements of the code:
- Hardcode the 3 givens as separate variables.
�. �/
�, ��?
height (m)
distance (m)
height travelled vs. distance
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- The equation of the line for the hill should be calculated within the script, based on the angle of
the hill.
- Plots should be as complete as on the tutorial video. (title, grid, labels, legend)
Just like in Lab2, reuse your code by changing the hardcoded values to answer the following questions:
Scenario # Angle Hill (degrees) Angle Throw
(degrees)
Initial Velocity
(m/s)
(x,y) impact?
1 30 45 20
2 10 50 20
3 45 60 20
Rubric:
Cover sheet complete & stapled properly: 10pts
Problems: 30pts + 15pts for correct results
Reminder: make sure to have within the script file, in order:
1. (2pts) first and last name
2. (2pts) section number
3. (4pts) description of the problem (10 words maximum)
4. (2pts) the two commands that erase the command window and the workspace
5. (5pts) comments throughout the code
6. (5pts) spacing (skipping lines between major paragraphs)
7. (5pts) variables names that are WORDS that describe the content. Absolutely do not
use single letter.
8. (5pts) semi-colons hiding all intermediate calculations; only the final result counts!
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Appendix C: Hybrid Survey
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Appendix D: Social Media Integration
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