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Improving Student Performance in Calculus
Dabney W. Dixon
Rebecca Rizzo, Mark Grinshpon, Erol Akbas,
Jeremy Brazas, and Markus Germann
DWF vs. Number of Students, Fall 2009
0%
10%
20%
30%
40%
50%
60%
70%
0 1000 2000 3000 4000 5000 6000
Number of students
Pe
rce
nt
Math 2211
Math 2212
DWF Rates of Major Courses
1. These data are the number of tries for Calc I (2211) in 2007.
2. 30% of the people try a second time.
3. Of those, 70% of people try a third time.
4. There is some difference in the ABC/DF/W percentages as a function of the number of tries, but
these are not too large and may not be interpretable.
5. One way of thinking of this (based on 2007 numbers) is that the University pays for teaching
approximately 325 people Calc I. Of these, approximately 120 succeed on the first try. Sixty
students try a second time, of which 20 succeed. Of the original 325 people, 185 never
succeed. This teaching consumes resources. If the student stays to get a grade, completion of
the course with a D or an F lowers their GPA, without moving them forward in their studies or
career.
Math 2211 in 2007
The Dreaded 3.0 Cliff
http://depts.washington.e
du/obgyn/clerkship/imag
es/CliffEdgeSign.jpg
http://www.johnsmyth.ie/blog/gallery/silverstrand/silver-strand-1a.jpg?w=840
Four Credit Hour Courses Suppose you have the average (left) and number of credit hours (top) and get the indicated grade in a single 4 credit hour course. What happens to
your GPA? If the cells are in red, it is less than 3.0.
3 Getting a B in a four credit course 2 Getting a C in a four credit course
15 30 45 60 15 30 45 60
3.5 3.39 3.44 3.46 3.47 3.18 3.32 3.38 3.41
3.4 3.32 3.35 3.37 3.38 3.11 3.24 3.29 3.31
3.3 3.24 3.26 3.28 3.28 3.03 3.15 3.19 3.22
3.2 3.16 3.18 3.18 3.19 2.95 3.06 3.10 3.13
3.1 3.08 3.09 3.09 3.09 2.87 2.97 3.01 3.03
3.0 3.00 3.00 3.00 3.00 2.79 2.88 2.92 2.94
2.9 2.92 2.91 2.91 2.91 2.71 2.79 2.83 2.84
2.8 2.84 2.82 2.82 2.81 2.63 2.71 2.73 2.75
2.7 2.76 2.74 2.72 2.72 2.55 2.62 2.64 2.66
1 Getting a D in a four credit course 0 Getting an F in a four credit course
15 30 45 60 15 30 45 60
3.50 2.97 3.21 3.30 3.34 2.76 3.09 3.21 3.28
3.40 2.89 3.12 3.20 3.25 2.68 3.00 3.12 3.19
3.30 2.82 3.03 3.11 3.16 2.61 2.91 3.03 3.09
3.20 2.74 2.94 3.02 3.06 2.53 2.82 2.94 3.00
3.10 2.66 2.85 2.93 2.97 2.45 2.74 2.85 2.91
3.00 2.58 2.76 2.84 2.88 2.37 2.65 2.76 2.81
2.90 2.50 2.68 2.74 2.78 2.29 2.56 2.66 2.72
2.80 2.42 2.59 2.65 2.69 2.21 2.47 2.57 2.63
2.70 2.34 2.50 2.56 2.59 2.13 2.38 2.48 2.53
The Effect of the HOPE Scholarship on Graduation
61%
21%
67%
42%
0%
20%
40%
60%
80%
HOPE - HOPE HOPE - NoHOPE
No HOPE -HOPE
No HOPE - NoHOPE
2013 HOPE Statistics FTFT Freshman entering Fall 2007
0%
20%
40%
60%
80%
HOPE - HOPE HOPE - No HOPE No HOPE - HOPE No HOPE - No HOPE
71%
41%
59%
30%
9
What majors take Calculus I? Initial Data Analysis
Fall 2009
Why are so many Biology majors taking Calculus I? It is neither required nor
recommended.
http://2.bp.blogspot.com/-DhdfDrgQQvo/Udh4L3o3F6I/AAAAAAAAg5A/UsRZQY_nUfU/s1600/Urban+Legend+1.png
Calculus is Needed for Medical School
11
Medical School!
12
FOR BIOLOGY STUDENTS signed up for Math 2211 • Email sent 6 weeks and 2 weeks before the start of the semester to all Biology and
majors signed up for Calculus. • Text agreed upon by Biology and Math. Dear Student, According to our records, you are planning to take Calculus I (Math 2211) next semester. The highest level of mathematics required for the Biology major is Math 1113 (Precalculus). Calculus I is a very rigorous elective and we ask that you read the information below carefully. Calculus is required for most pharmacy schools. It is rarely required for dental schools. In the past, many medical schools required calculus, but times are changing. At present, few schools have this requirement. If this is a concern of yours, we recommend that you determine if calculus is actually required for the schools to which you will be applying. Many medical schools now require statistics. A useful list may be found at http://www.swarthmore.edu/Documents/slife/pre_med/Math_Req_for_Medical_School.pdf.
0%
5%
10%
15%
20%
25%
30%
35%
40%
Sp09 Fa09 Sp10 Fa10 Sp11 Fa11 Sp12 Fa12 Sp12
Biology Majors as a Percentage of Overall Calculus I Enrollment
Biology
Majors
Total
Enrollment
Sp09 131 367
Fa09 164 477
Sp10 122 445
Fa10 106 450
Sp11 65 323
Fa11 83 409
Sp12 86 358
Fa12 72 372
Sp12 40 329
First Day PowerPoint
Email to Biology Majors
Calc Life Sci Advisors
The Debye length is the measure of a charge carrier’s net electrostatic effect in solution, and how far those electrostatic effects persist.
↔
↔
↔↔
Words Math
Sketch Graph
16
Calculus for the Life Sciences
Dabney Dixon, STEM
Professor
•Ph.D., Massachusetts
Institute of Technology
•Office Phone: 404-413-5508
•Email: [email protected]
Rachel Belinsky, M&S
Lecturer
•Ph.D. Mathematics (Functional
Analysis), Leningrad University,
Russia
•Office phone: 404-413-6449
•Email: [email protected]
Robert Clewley, M&S
Assistant Professor
•Ph.D., Applied Mathematics,
Dept. of Engineering
Mathematics, University of
Bristol, UK
•Office phone: 404-413-6420
•Email:
Valerie Miller, M&S
Associate Professor
•Ph.D., Mathematics, University of
South Carolina
•Office phone: 404-413-6421
•E-mail: [email protected]
Mark Germann, Biophysical
Chemistry
Professor
•Ph.D., University of Calgary
•Office Phone: 404-413-5561
•Email: [email protected]
Donald Edwards, NI & Biology
Regents' Professor
•Ph.D., Yale University
•Office Phone: 404-413-5394
•Email: [email protected]
Michael Stewart, M&S
Assistant Professor
•Ph.D., Electrical Engineering, University
of Illinois – Urbana
•Office phone: 404-413-6433
•Email: [email protected]
Carol Myers, M&S
Lecturer
•M.Ed. Mathematics Education,
Georgia State University
•Office phone: 404-413-6406
•Email: [email protected]
Mariana Montiel, M&S
Assistant Professor
•Ph.D., Mathematics, University of
New Hampshire
•Office phone: 404-413-6414
•Email: [email protected]
Department of Mathematics
David J. Dwyer
Professor, Chair
•Ph.D., Purdue University; complex
analysis, actuarial science
•Telephone: 812-488-2632
•Email: [email protected]
Mark E. Gruenwald
Professor
•Ph.D., Northern Illinois University;
functional analysis, computer science
•Telephone: 812-488-2959
•Email: [email protected]
21
Paradigm Shift in Pedagogy
What (concept)
How (technique)
Why (motivation/ application)
What (concept)
How (technique)
Why (motivation/ application)
From To
Rebecca Rizzo
The “Pizza for Calculus” Summer
Rebecca Rizzo
23
Calculus for the Life Sciences Preview Lunches
Where are the pictures?
24
25
26
Now you’re speaking my
language!
Dr. Rizzo: After my chain rule lesson (and showing the Lion King slide), a student candidly came up to me at the end of class and said, 'At first I was worried about this class ... then I saw the Lion King slide. After that, I knew it wouldn't be so bad.'
27
Dr. Rizzo: After Dr. Yi Jiang's talk on Mathematical Biology, I asked if the talk validated the need for Calculus. One student said candidly, "Well, for as boring as I think this material is, I now can see the use of the material and the need to learn the techniques of Calculus in order to understand and explain the science."
Yi Jiang Mathematical Biology
What Students Are Saying
• I like that it is an applied course.
• I can ‘see’ when it is appropriate to use the mathematics .
• More concept-based rather than ‘mathy’.
• Specialized within my major. I am in class with other students studying the same major
• Flexibility in how the material is covered.
29
One comment from the Fall 2012 instructor evaluation: “Calculus for the Life Sciences makes up where some of the other more generic classes fall short: it's able to incorporate
knowledge of higher-level mathematics into meaningful insight about how it can be and is used in the area of interest (in this case biology, chemistry, and the like). This insight and
discussion into direct applications goes quite a ways in answering the "Why are we learning this?" question that often plagues math education, and further, it engages the
students. Judging the class off that merit…it decidedly deserves recognition.”
What Instructors Are Saying
• Fun to teach and feels successful teaching the course
• Great to use applications to drive the mathematical concepts.
• High student rating on Teacher Effectiveness. Average 4.85 (out of 5)
• Due to increased exposure, Math 2201 students have become more comfortable in recognizing when to apply the concepts of limits, differentiation, and integration within a given situation.
The textbook for Math 2201 and Math 2202 is Calculus for Life Sciences, (Bittinger, Brand, Quintanilla, Pearson, 2006, ISBN-10: 0321279352 ISBN-13: 9780321279354). Math 2201 covers Chapters #1 - #5. Math 2202 covers chapters #6 - #10. If you are taking Math 2202 after you took Math 2211, please purchase the textbook and read the sections highlighted in blue in the first list. These sections (subjects) are not covered in Math 2211 and will be used in Math 2202 in some of the coming sections. At the end of the document you will also find a sample syllabus for Math 2201 and exercises in the textbook assigned as homework in Math 2201. The syllabus for Math 2202 will be given to you by the instructor in the first week of the semester.
Going from Calculus to Calculus for the Life Sciences?
The Debye length is the measure of a charge carrier’s net electrostatic effect in solution, and how far those electrostatic effects persist.
↔
↔
↔↔
Words Math
Sketch Graph
Perception Counts
Erol Akbas
http://upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Bacterial_growth_en.svg/2000px-Bacterial_growth_en.svg.png
http://cosmoscon.files.wordpress.com/2012/02/softsoap-soap-31.jpg
Jeremy Brazas
Interactivity and Hands-on Exploration
http://upload.wikimedia.org/wikipedia/commons/e/ee/Kotmale_footbridge_2006-09-03.jpg
How to Build a Bridge to
Success
Rob Clewley
40
Creative Inquiry Modules
• This project sought to replicate the highly successful Creative Inquiry model employed for teaching core Calculus courses at Clemson University
• A module was created and presented in one section during Summer 2012
• Students were required to complete a project based on the module
• The project counted as 6% of the students’ overall course grade
• The module did not have a significant effect on student grades
• Student attitudes toward the module were not positive (due to the fact that no other section required the project)
Rebecca Rizzo
41
WeBWorK
• Piloted in Calculus for the Life Sciences I in Fall 2012
• Used for online homework
• Proved unwieldy
Mark Grinshpon
Concept Maps https://rachelkrejci.files.wordpress.com/2010/02/nctm-final.jpg
Weekly Meetings with TAs and SI Leaders
0%
20%
40%
60%
80%
100%
1 2 3 4 5 6 7 8 9 10 11 12
% A
tte
nd
ing
Week
Weekly Meeting Attendance Spring 2012
• Two Mathematics faculty met with calculus TAs and SIs once a week
• Meetings were used to discuss course content from the week and to provide teaching tips
• Meeting attendance was not mandatory
• Faculty felt the meetings were helpful and have proposed that these meetings be made a part of calculus TA and SI job descriptions
http://www.nps.gov/noca/planyourvisit/images/Thunder_Creek_Bridge_1.jpg
Calculus Supplemental Instruction
Fall, 2014
• 784 students (Calculus I, II and Calculus for the Life Sciences I)
• Average 39 session hours for each SI leader • 12 SI leaders • $1500 each • Total outlay: ~ $18,000
• 137 students (17%) attended ≥ 5 times • $131/student attending
• For those who attended, average GPA = +0.34
compared to those who did not • Many fewer SI students withdrew
• Content knowledge and higher GPA help career • Some students will keep their HOPE with the
higher course GPA • Total W is about 13% or 103 students – this is two
sections that have to be taught again. Tuition more than covers the staffing, but there is a social cost to students and faculty
• Community building • SI leaders are more accomplished in their
disciplines
SI No-SI
GPA 3.00 2.66
DWF 11% 30%
DF 10% 13%
W 1% 17%
• Total visits by students: 600 • Average of approximately 43 visits per
day • Individual students who visited the
MAC: 311 • The average duration of a visit to the
MAC: approximately 90 minutes
Selected Math Assistance Complex Attendance Two-week period October 27 – November 7, 2014
Visits by individual courses: MATH 0099 – 17 visits MATH 1070 – 12 visits MATH 1101 – 87 visits MATH 1111 – 14 visits MATH 1113 – 19 visits MATH 1220 – 17 visits MATH 2201 – 31 visits MATH 2201 – 9 visits MATH 2211 – 161 visits MATH 2212 – 89 visits MATH 2215 – 41 visits Other classes – 103 visits
Mark Grinshpon, Donald Harden
48
Graded Homework
• Eight graduate students from the Department of Mathematics and Statistics are hired each semester to grade the weekly homework, each serving one course section
• Between 9 and 12 homework assignments are assigned during the semester, depending on the instructor
• Each homework assignment consists of 10-12 problems, three of which are selected by the instructor to be graded
• Students typically have a week to complete the homework, which includes the material being covered in class that week
Graded Homework: A Significant Help
A B C D F
Fa 2011 25% 19% 24% 11% 21%
Fa 2012 33% 19% 16% 10% 21%
0%
5%
10%
15%
20%
25%
30%
35%
Test 1
Graded Homework
A B C D F
Fa 2011 17% 21% 21% 17% 24%
Fa 2012 33% 21% 19% 10% 18%
0%
5%
10%
15%
20%
25%
30%
35%
Test 2
Fall 2011 ABC – 61% DFW – 39%
Fall 2012 ABC – 74% DFW – 26%
Focusing on mastery: Up to 30% of missed points for an exam
that is reworked
Catches erroneous schema in the mathematical thoughts of students
Flexible coordinator
who provides resources
and support
Courses created in
D2L
Calculus/Pre-calculus
coordination
Mini-grants allow
exploration
http://www.gcc.edu/PublishingImages/Academics/Mathematics/(1)%20Department%20of%20Mathematics.jpg
Faculty Interaction is Key
Time for some Calculus I help!? Fall 2010 Walk-in Help Sessions Schedule
Come to all or part of any session, anytime throughout the semester
Monday Tuesday Wednesday Thursday Friday
8-9 Dr. Miller-COE764 (8:30-9:45) Dr. Miller-COE764 (8:30-9:45)
Dr. Miller-COE764 (8:30-9:45)
9-10 Dr. Miller-COE764 (8:30-9:45) Prof. Meyers-COE754 Gaurav Kumar-GCB327 Jason Han, Kell Hall122 (9-1)
MAC-Kell Hall122 (9:30-5) Dr. Miller-COE764 (8:30-9:45) Prof. Meyers-COE754 Jason Han, Kell Hall122 (9-1)
MAC-Kell Hall122 (9:30-5)
Dr. Miller-COE764 (8:30-9:45)
10-11 Jason Han-Kell Hall122 (9-1) MAC-Kell Hall122 (9:30-5) Emmanuel Thomas-Sparks423 Dr. Advart-COE756
Jason Han, Kell Hall122 (9-1)
Dr. Advart-COE756 Jason Han-Kell Hall122 (10-1)
MAC-Kell Hall122 (10-1)
11-12 Jason Han-Kell Hall122 (9-1) Heesun Lee-GCB523
MAC-Kell Hall122 (9:30-5) Dr. Clewley-PSC812
Jason Han, Kell Hall122 (9-1) Gaurav Kumar-ALC431 (10:50-11:50) Heesun Lee-GCB523 Dr. Timsina-COE786
Jason Han-Kell Hall122 (10-1) Dr. Clewley-PSC812
Dr. Timsina-COE786 MAC-Kell Hall122 (10-1)
12-1 Jason Han-Kell Hall122 (9-1) Dr. Grinshpon-Kell120
MAC-Kell Hall122 (9:30-5) Emmanuel Thomas-GCB301 Dr. Grinshpon-Kell120
Jason Han, Kell Hall122 (9-1) Dr. Miller-COE764 (1:30-2:30) Dr. Timsina-COE786 (1:30-2:30)
Jason Han-Kell Hall122 (10-1) Dr. Grinshpon-Kell120 Emmanuel Thomas-GCB301
MAC-Kell Hall122 (10-1)
1-2 Dr. Miller-COE764 (1:30-2:30) Dr. Timsina-COE786 (1:30-2:30)
MAC-Kell Hall122 (9:30-5)
MAC-Kell Hall122 (9-5) Dr. Miller-COE764 (1:30-2:30) Dr. Timsina-COE786 (1:30-2:30)
MAC-Kell Hall122 (9:30-5)
Heesun Lee-GCB320 (1:40-2:40)
2-3 Dr. Miller-COE764 (1:30-2:30) Dr. Timsina-COE786 (1:30-2:30)
MAC-Kell Hall122 (9:30-5) Dr. Grinshpon-COE752 (2-3:45)
MAC-Kell Hall122 (9-5) MAC-Kell Hall122 (9:30-5) Dr. Grinshpon-COE752 (2-3:45)
Heesun Lee-GCB320 (1:40-2:40) Gaurav Kumar-ALC224 (2:45-3:45)
3-4 Maria Shorina-Kell Hall122 (3-5) Dr. Grinshpon-COE752 (2-3:45) Dane Allen-GCB318 (2:50-3:50)
Maria Shorina-Kell Hall122 (3-5) Dr. Grinshpon-COE752 (2-3:45) Dane Allen-GCB318 (2:50-3:50) Maria Shorina-Kell Hall122 (3-5)
Gaurav Kumar-ALC224 (2:45-3:45)
4-5 Linda DeCamp-GCB503 (4:20-5:20) Maria Shorina-Kell Hall122 (3-5) Vivek Mishra-GCB223 (4:40-5:40)
Maria Shorina-Kell Hall122 (3-5)
Maria Shorina-Kell Hall122 (3-5) Vivek Mishra-GCB223 (4:40-5:40)
5-6 Vivek Mishra-GCB223 (4:40-5:40)
Vivek Mishra-GCB223 (4:40-5:40)
6-7 Vivek Mishra-GCB321 (6:15-7:15)
7-8 Linda DeCamp-GCB503 (7:30-8:20) Linda DeCamp-GCB503 (7:30-8:20)
And for more practice: The Math Assistance Complex (MAC) (122 Kell Hall)
The range of a football thrown
with initial velocity vo is:
and
The Calculus I Senior Coaching Staff Fall 2010
Dr. Carol Myers
COE 754
MW 9:00am-10:00am
Dr. Tirtha Timsina
COE 786
WF 11-12pm, MW 1:30-2:30pm
Dr. Rob Clewley
PSC 812
TR 11:00am-12:00pm
Dr. Mark Grinshpon
COE 752
TR 2:00pm-3:45pm
Kell 120
MTR 12-1:10pm
Dr. Valerie Miller
COE 764
MWF 8:30am-9:45am
MW 1:30pm-2:30pm
Vivek Mishra
GCB 223
TR 4:40-5:40pm
GCB 321
T 6:15-7:15pm
Heesun Lee
GCB 523
MW 10:55-1:55am
GCB 320
F 1:40-2:40pm
Linda DeCamp
GCB 503
M 4:20-5:20pm
&
MW 7:30-8:20 pm
Dane Allen
GCB 318
TR 2:50-3:50pm
Emmanuel Thomas
Sparks 432
T 9:50-10:50am
GCB 301
TR 11:50am-2:50pm
Jason Han
MAC
MW 9:00am-1:00pm
TR 10:00am-1:00pm
Dr. Christian Avart
COE 756
TR 10:00am-11:00am
The Calculus I Junior Coaching Staff Fall 2010
Maria Shorina
MAC
M 11:00am-1:00pm
TR 1:00pm-5:00pm
W 9:00am-1:00pm
Gaurav Kumar
M 9:00-10:am GCB 327
W 10:50-11:50 ALC 432
F 2:45-3:45 ALC 224
Planning on Taking Calculus?
Math 2201 and 2202: Calculus for the Life Sciences I and II Appropriate for students in Biology, Chemistry, Neuroscience and Psychology
Math 2211 and 2212: Calculus I and II Required for majors in:
• Actuarial Science • Computer Science • Geology • Mathematics and Statistics • Physics and Astronomy
Math 1220: Survey of Calculus The course to take if you need/want only one semester of calculus
Math 1112
Math 1111
Math 1113
First Day PowerPoint
Supplemental Instruction
Serious Attention
Graded Homework
Calculus for the Life Sciences
http://briansrunningadventures.com/wp-content/uploads/2014/03/qualityvsquantity11.jpg
Calculus of One Variable I
36%
20% 18% 12%
8% 14%
26%
22% 20%
14%
12%
12%
38%
58% 61%
73% 80%
74%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
FY2010 FY2011 FY2012 FY2013 FY2014 FY2015
% o
f St
ud
en
ts
Fiscal Year
MATH2211
ABC
DF
W/WF
Prerequisites
Mark Grinshpon
60
http://www2.seminolestate.edu/rr
apalje/PreCalculus%20and%20Tr
ig/PreCal44.gif
Who is taking Pre-calculus?
• 1/3 of students take Calculus • 1/3 of students take no more
math • 1/3 of students take Algebra-
based Physics; they need another semester of math, but not necessarily Pre-calculus
A key future effort in Georgia?
• Flexible coordinator that provides resources and support
• Create course templates in D2L
• Continue interaction among instructors
• Allow flexibility in instructor approaches
• Redo exams (up to 30%)
• Use graded homework
• Study guides and sample tests
• Any student to any help source
– Faculty office hours
– Supplemental Instruction
– Math Assistance Complex
• Honors sections
• Social media (Facebook and D2L) • Remind Biology majors that Calculus
is not required • Calculus for the Life Sciences • Educate medical school advisors • Give examples of faculty who use
calculus in their research • Involve science faculty • Math/Graph/Data/Word/Sketch • Withdraw students not attending
first two weeks administratively • Continue piloting books and other
resources • STEM mini-grants
• Calculus/Pre-calculus coordination • Why – What – How pedagogy • What is the effective limit of
changes in Calculus alone?
Calculus
Dabney Dixon, [email protected]
62
Collaborative (Teams)
Experimental (Resources)
Data-driven (Resources)
Whole student (many factors)
Incremental (Time)
With thanks to:
Rebecca Rizzo
Markus Germann
Mark Grinshpon
Valerie Miller
Erol Akbas
Jeremy Brazas
Erica Li Donald Harden
Savannah White
FOR BIOLOGY STUDENTS signed up for Math 2211 If you decide that calculus is important for you, please take Calculus for the Life Sciences (Math 2201 and 2202). These courses cover essentially the same material as in the classic Calculus sequences, but focus on the use of calculus in chemistry and biology. If you think that a one semester calculus course is best for you, and a 1000 level course is appropriate, Survey of Calculus (Math 1220) may be a good choice for you. If you wish to take Calculus, we urge you to organize your time in two ways. First, make sure that you have a light schedule the semester you take Calculus. Second, schedule plenty of study time and plan on using tutorial resources to help you learn the material. Attending faculty office hours, and going both to Supplemental Instruction and the Math Assistance Complex (MAC) should help you significantly in understanding the material and thereby doing well in the course. We make these suggestions out of the concern that difficulty in Calculus can distract you from your other studies and lower your GPA. This has implications for your future career plans and may have financial implications if you have a scholarship. Because calculus is a four credit course, it is particularly important that you do well (your GPA is weighted by credit hour). Best wishes for your studies.
65
Collaborative Experimental
Data-driven Whole student
Incremental
Calculus of One Variable II
23% 16% 13% 12% 12% 12%
28%
25%
20%
14% 15% 15%
48%
60% 66%
74% 72% 73%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
FY2010 FY2011 FY2012 FY2013 FY2014 FY2015
% o
f St
ud
en
ts
Fiscal Year
MATH2212
ABC
DF
W/WF
Calculus for the Life Sciences I
7% 11%
15% 9%
7%
10%
84% 83% 76%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
FY2013 FY2014 FY2015
% o
f St
ud
en
ts
Fiscal Year
MATH 2201
ABC
DF
W/WF
Calculus for the Life Sciences II
8% 2% 0%
8%
4% 12%
83% 93%
88%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
FY2013 FY2014 FY2015
% o
f St
ud
en
ts
Fiscal Year
MATH 2202
ABC
DF
W/WF
*Fall and Spring Semesters Only
Multivariate Calculus
13% 12% 5% 8%
12% 11%
17% 13%
13%
16%
17% 15%
70% 73%
82% 76%
70% 73%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
FY2010 FY2011 FY2012 FY2013 FY2014 FY2015
% o
f St
ud
en
ts
Fiscal Year
MATH 2215
ABC
DF
W/WF
Survey of Calculus
9% 10% 9% 14% 17% 16%
18% 26%
20%
20%
32% 27%
72% 65%
71% 66%
50% 55%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
FY2010 FY2011 FY2012 FY2013 FY2014 FY 2015
% o
f St
ud
en
ts
Fiscal Year
MATH 1220
ABC
DF
W/WF
71
Calculus for the Life Sciences
Rebecca Rizzo
Markus Germann
72
Collaborative
Experimental
Data-driven
Whole student
Incremental
1. There is some difference in the ABC rates as a function of department.
2. Interestingly, the highest ABC rates are in the “undecided” and “other” categories – perhaps
because the students in these categories are especially interested in calculus.
3. It is perhaps unexpected that math majors have the lowest ABC rate.
4. The ABC rates for BIO, CHM and CSC are around 30%. Math 2211 is not required for
Biology. Math 2211 is required for Chemistry and Computer Science.
Math 2211 in 2007
75
Calculus for the Life Sciences
Jeremy Brazas
76
Graded Homework and Group Work
• In Fall 2012, both instructors gave weekly graded homework assignments
• In Fall 2013, Dr. Rizzo moved to a homework journal which she walks around the room and checks at the beginning of class
• One of the biggest student requests has been for more social engagement
• Group work allows the students teach one another
• Instructors monitor student progress and reteach concepts to groups and to the entire class as necessary
77
Office Hours and Phone Calls
• Both instructors felt that student visits to their office hours were important to student success
• Dr. Akbas called students who made less than an 80 on the first test
• Other efforts were made to engage students, including a Calculus for the Life Sciences Facebook page, which continues to be utilized by students
• In the bottom photo, a Calculus for the Life Sciences I student is explaining a problem to a Calculus I student during Dr. Rizzo’s office hours
78
The First Week of Class
• The “First Day” PowerPoint
• Opportunities for help are emphasized
• Students who don’t come the first week are dropped administratively
Finding derivatives using the
chain rule: Effect of rainfall on predators and prey:
• The population of lions, L, in Africa greatly depends on the population of their prey, P, which consists mainly of large mammals with a preference for zebras, impalas, wildebeest, buffalo, and warthogs.
• The extension of vegetation, V, affects the population of prey, which feed on the vegetation. The vegetation, and the vegetation if effected by the amount of rainfall, r.
These dependencies can be: L = f(P), P = g(V ) and V = h(r).
80
How does major affect performance?
Initial Data Analysis Fall 2009
Motivation: Derivative as a rate of change
Rate of change: A measure of how fast is one quantity changing as another quantity changes? (input/output)
http://wonkroom.thinkprogress.org/wp-content/uploads/2009/03/co2_growth_rate.PNG
Motivation: Using derivative to optimize
Optimization: using this idea of rate of change to determine maximum or minimum output on a given interval.
http://www.mcs.anl.gov/~more/dfo/images/noisy_quadratic_surf.png
http://www.brynmawr.edu/math/people/vandiver/BiologicalapplicationstoincorporateintoCalculus.htm
Suppose data was collected on an African wildlife preserve and the functions f, g, h were approximated as follows:
• L = f(P) = 0.5P2
• P = g(V) = 2V
• V = h(r) = r1/2
• Compute the rate of change in the population of lions with respect to the rainfall, dL/dr. (Adapted from [1].)
• (ask for each of the three equations, what does it look like graphed)
These dependencies can be expressed: L = f(P) Lion population is a function of prey population P = g(V) Prey population is a function of vegetation density V = h(r) Vegetation density is a function of rainfall
http://upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Bacterial_growth_en.svg/2000px-Bacterial_growth_en.svg.png
http://cosmoscon.files.wordpress.com/2012/02/softsoap-soap-31.jpg
Erol Akbas
Erol Akbas
Lessons Learned
• Students want the social engagement
– In the classroom as group work (studying/working problems together in class)
– Extension of the classroom (Facebook)
• Students reached out to each other for help, organized study groups; and now Fall 2012 students are engaging with Spring 2013 students.
ABC, DF and W Percentages for Various Ways of Entering Calc 2211
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Fall 2008
COMT (177)
Transfer 1113
(37)
GSU 1113
(106)
AP 1113 (14)
ABC
W
DF
• Grades in Pre-calculus have less predictive ability than the Compass test has for grades in Calculus
• Students finishing Pre-calculus can take the test once (paid for by GSU) to be sure that they are ready for Calculus
• Budgeted for three years • No takers
95
Collaborative Experimental
Data-driven Whole student
Incremental
What Math is Needed for Medical School? (Bryn Mawr)
The information in this table was compiled from the 2015 edition of the Medical School Admissions Requirements (MSAR) published by the Association of American Medical Colleges (AAMC; www.aamc.org) and from a July 2014 review of individual medical school websites. Only schools with specific requirements are listed in this
table.
97
Dan Deocampo Geosciences
Deepwater
Horizon Oil Spill
Assuming the rate of leakage decreased linearly from 62000 to 53000 barrels per day during the time interval stated above, write a function f (t) for the daily rate of leakage in terms of time. Use this function to write and compute a definite integral for the total amount of oil that leaked out. The NYT article cited above gave a total of nearly 5 million barrels. Does your estimate agree? Eric Towne, Bates College
98
Tutoring Support for Precalculus Concepts: Online and In Person
• Tutors were hired to create and give a five minute presentation on an essential precalculus topics once a week at the beginning of class
• Control and experimental sections were
taught by the same professor
• Students were then given a worksheet to practice the concept
• Tutors were available during and after class to help the students
• The online experimental group was given a series of twelve online quizzes using MyMath Test
• Analysis of course data did not show a significant effect on students’ test grades or final course grades Sutandra Sarkar
99
Tutoring Support for Precalculus Concepts: ALEKS
• Assessment and LEarning in Knowledge Spaces (ALEKS) is a Web-based, artificially intelligent assessment and learning system
• Used to check and build students’ algebra and precalculus skills
• Required for 3 of the 8 sections taught in Fall 2012
• Counted as 6% of overall course grade
• Initial data analysis did not show that
ALEKS had a significant effect on students’ course grades
• A second experiment is being conducted this semester using a different ALEKS product
Sutandra Sarkar
Math
Sketches
Words Tables
Graphs
Math
Sketches
Words Tables
Graphs
What is the Real Issue?
