Moving Toward a More Effective Learning
Environment in First Year Calculus
Javier Garza, Tarleton State University
March 30, 2012
Deeper
understanding/Learn
21
More confident
2
Make a good grade
Prepared for Calculus
II/Physics
Real world problem
solving/practical use
Do better than last time I
took it
Meet the challenge/tried
my best
19
Richer passion for math
2
10
Independence
9
Do well on tests/final
Specific topics
N=32
1
2
Attend class
"Earn a grade that I'm not
ashamed of"
"I have not created a hatred
for math"
2
Graduation
1
5
Improve study habits
Meet other students
interested in math
2
1
4
Refresher
1
4
Fun
1
Learn to Learn
"Calculus isn't scary
anymore"
"If I don't fall asleep during
class"
3
Help other students
1
"I hope to be noticed on how
I feel about math"
It helps me to be a better
teacher
1
1
1
1
1
1
Beginning of Semester Survey
•17 questions
•Responses: CRD Group (N=65)* and Calculus I Group (N=15)
* 78 in CRD logged in to survey though only 65 provided consistent responses.
•1 = Strongly Agree 2 = Agree 3 = Neutral 4 = Disagree 5 = Strongly Disagree
•Of 78 in CRD group, 63 (84%) were enrolled in RDG 301 (Intro. to Children’s Lit)
•A/D Gap is the difference between % reporting 1 or 2 and % reporting 4 or 5
CRD
Cal I
Cal I
Cohort (F11) (Sp 12)
(F11)
I think this course will be intellectually
stimulating.
Mean
Agree/Disagree
Gap
1.88*
+82
1.53
+93
This is my first time to take this course.
Mean
Agree/Disagree
Gap
1.68***
+82
3.2
-7
1.75**
+75
Only a course grade of “A” in this course
is acceptable to me.
Mean
Agree/Disagree
Gap
+76
2
+60
1.24**
+100
CRD Cal I
Cohort (F11)
(F11)
I can contribute valuable thoughts and
ideas to a discussion in this area of study.
Mean
Agree/Disagree
Gap
1.92*
+82
2.53
+46
The requirements of this course scare
me.
Mean
Agree/Disagree
Gap
2.94*
+1
3.53
-40
I do not need this course content in
everyday life.
Mean
Agree/Disagree
Gap
4.09*
-81
3.73
-60
I find this subject area to be interesting.
Mean
Agree/Disagree
Gap
1.75**
+86
2.2
+73
I think this course will be fun.
Mean
Agree/Disagree
Gap
2.02*
+74
2.47
+53
Cal I
(Sp
12)
90
80
y = 0.58x + 15.153
R² = 0.7317
70
60
50
40
30
20
10
0
0
20
40
60
80
100
120
Fall 11 Fall 11 Fall 11 Sp 12
Test 1 Test 2 Test 3 Test 1
Sp 12
Test 2
Sp 12
Test 3
N
33
29
28
25
25
23
Avg
73.4
65
61.6
75.3
70.2
77.0
StDev
19.1
21
26.4
18.2
13.8
14.3
Arum, R., & Roksa, J. (2011). Academically adrift: Limited learning on college
campuses. Chicago, IL: The University of Chicago Press.
• 45 percent of students "did not demonstrate any significant improvement in
learning" during the first two years of college.
• 36 percent of students "did not demonstrate any significant improvement in
learning" over four years of college.
Deslauriers, L., Schelew, E., & Wieman, C. (2011). Improved learning in a
large-enrollment physics class. Science 332(6031), 862-864.
Abbr. Abstract: We measured the learning of a specific set of topics and objectives when
taught by 3 hours of traditional lecture given by an experienced highly rated instructor and 3
hours of instruction given by a trained but inexperienced instructor using instruction based on
research in cognitive psychology and physics education. The comparison was made between
two large sections (N = 267 and N = 271) of an introductory undergraduate physics course. We
found increased student attendance, higher engagement, and more than twice the learning in
the section taught using research-based instruction.
Merrow, J. (2005). Declining by degrees: Higher education at risk [Motion
picture]. United States: Learning Matters, Inc.
“The lecture method is a process whereby the lecture
notes of the instructor get transferred to the notes of
the students without passing through the brains of
either”.
Eric Mazur: Confessions of a Converted Lecturer
Schneps, M. H., & Sadler, P. M. (1988). A private universe:
misconceptions that block learning [ Motion picture].
United States: Corporation for Public Broadcasting.
Available at
http://www.learner.org/vod/vod_window.html?pid
=9.
Carlson, M. P., & Rasmussen, C. (Eds.). (2008). Making the
connection: research and teaching in undergraduate
mathematics education (MAA Notes #73). Washington,
DC: Mathematical Association of America.
Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs,
values and goals. Annual Review Psychology, 53, 109-132.
Finkel, D. L. (2000). Teaching with your mouth shut. Portsmouth,
NH: Boynton/Cook.
Newcombe, N. S., Ambady, N., Eccles, J., Gomez, L., Klahr, D.,
Linn, M., Miller, K., & Mix, K. (2009). Psychology’s role in
mathematics and science education. American Psychologist,
64(6), 538-550.
Nilson, L. B. (2010). Teaching at its best (3rd ed.). San Francisco,
CA: Jossey-Bass.
Schoenfeld, A. H. (1992). Learning to think mathematically:
Problem solving, metacognition, and sense-making in
mathematics. In D. Grouws (Ed.), Handbook for Research on
Mathematics Teaching and Learning (pp. 334-370). New York:
MacMillan.
This is not about “change” for the sake of change
My goal is to provide students a transformational experience subsequent to
which they believe themselves to be independently equipped and
empowered to “do” mathematics and to engage in meaningful
mathematical dialogue with others, and are intrinsically inclined to
engage in the struggles of problem solving.
Indicators of success:
•
•
•
•
•
•
•
Students attend class (based upon intrinsic interest);
Students complete the homework with a high level of mastery
Students constructively engage in cooperative/collaborative
learning activities
Students perform well on exams
Students take more mathematics coursework
Students are successful in “subsequent coursework”
Students are interested in independent study
Classroom – Justify their attendance;
encourage, empower, equip
Office – Inviting
Home – Learning and evolution toward
independence
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Utilized Enhanced WebAssign for online
homework (10% of grade; objective questions),
integrating dynamic content and support features
Required written homework assignments (10% of
grade; problems requiring justification)
Provided daily course calendar (comfort through
explicit demonstration of course design)
Provided grader with rubric for grading written
homework (intentional, constructive feedback)
Tailored solutions (Stewart) provided for exam
practice problems
Replaced curves with extra credit serving as final
exam review
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Administered beginning of semester and endcourse (after grades assigned) survey online;
compared results to those of other classes
Developed and administered Calculus Concept
Inventory (mention Goldstein) at beginning and
end of course
Reviewed math education research (Carlson) to
bone up on common misconceptions among
calculus students and develop activities (example,
bottle problem)
Spent over a week to shore up prerequisite
knowledge (in particular, notion of function)
Rigidly enforced no-late homework policy
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Recorded item-by-item results for each student
on each test to inform opportunities for
emphasis next semester.
Sent email to every individual student several
times a semester to notify of progress and
express support/concerns as needed
Scheduled office hours based upon student
availability rather than my convenience.
Recommitted to use of CAS (Mathematica) to
facilitate dialogue and enhancement of
conceptual understanding
Provide more in-class opportunities for students to make
connections between multiple representations of
calculus concepts and discuss (Teach with my mouth
shut)

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


Example: Provide function graphs on grids and ask them to
sketch derivatives by estimating derivative values
Provide simple (constant, linear) function graphs on grids
and ask them to complete a table providing area under the
graph on interval [0,t]. Make connection between definite
integral and antiderivative.
Directed learning activity connecting prior knowledge of
relationship between graphs of f(x) and f(x)+k, and the family
of antiderivatives of a function
Provide direction fields for y’=f(x) and ask them to sketch y;
make connection to antiderivatives.
Provide table that facilitates their understanding of inherent
structure of chain rule application
28. The course improved my understanding of the subject area.
36. It was necessary for me to effectively utilize my graphing calculator to successfully solve
problems in the course.
1.18
1.3
5. Having a solid background in this area will be useful for me in the future.
1.36
8. I think this course was intellectually stimulating.
1.36
41. The instructor was sufficiently accessible via email.
1.36
45. The tests served as good assessments of my mastery of Calculus concepts.
22. I demonstrated an assertiveness in exchanging ideas that is different from my previous
behavior.
43. The Supplemental Instruction leader served as an effective source of academic support for
me this semester.
37. It was necessary for me to effectively utilize Mathematica to successfully solve problems in
the course.
4. I will need this course content in everyday life.
17. Uses the same sort of activities that any other teacher would use.
24. My experiences resulted in differences in how I analyzed, discussed, and shared ideas with
others.
23. I had an experience in which dialogue with my teacher or peers resulted in a change in my
ideas or beliefs.
42. The mathematics clinic served as an effective source of academic support for me this
semester.
1.36
2.27
2.27
2.36
2.45
2.55
2.55
2.73
2.82
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Assist Supplemental Instruction leader in
developing activities
Change daily MO so that students are expected
to complete problems requiring lower level
thinking skills independently, outside of class,
without benefit of prior coverage (evolution)
“Uncover material”: More effectively utilize
class time to enrich conceptual understanding,
make connections, facilitate dialogue
Learn while listening more and “telling” less
Integrate in-class presentations at board
Thank you!!
garza@tarleton.edu