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```					             T.I.M.E.S.
Training Intuition in Mathematics
for Engineering Success

Results of a Two-Year Pilot Study

Investigators:
Dr. Phillip Mlsna   Dr. Janet McShane
Maya Lanzetta       Jennifer Maynard
Chester Ismay       Sarah Brown
Observations
• Engineering professors commonly have
noticed many students struggle in lower-
division engineering classes.

• One emergent theme is poor mathematics
preparation.

possible to improve student performance
and retention levels?
2
Motivation
Students frequently have underdeveloped
mathematical skills, which can lead to:

–   Difficulty adjusting to collegiate expectations
–   Hardships & frustration in understanding the
material
–   Change of major away from engineering
–   Leaving the university

Freshmen seem to be particularly sensitive!
3
Consequences of Poor
Mathematics Preparation
•   Inability to properly carry units through
calculations
•   Heavy reliance on calculators and computers for
even very simple computations
•   Blind trust in the correctness of answers that
emerge from a calculator
•   Inability to make rough numerical estimates
•   Inability to detect nonsense answers
•   Inability to visualize or plot common functions
•   Inability to decompose a task into a logical series
of detailed steps
4
Our Approach

• Identify and concentrate upon a limited set
of mathematics skills
•   Administration of a pre-test to identify
students with poor skills in targeted areas
•   Include all freshman engineering courses
•   Use guided modules in the areas of
deficiency to increase students’ comfort
and skill
•   Self-paced practice; test for mastery
5
Building the TIMES Pilot

• Identify specific subject areas of difficulty
• Acquire professor and course participation
• Construct a pretest
• Create modules guided by GTAs
• Develop instruments to measure mastery
• Administer end of course evaluation
• Obtain an overall measure (grade in class)
• Provide frequent feedback to students and
professors
6
Targeted Skill Areas

• Fractions
• Unit Conversions & Calculations
• Graphing
• Solving systems of equations
• Estimation & Problem Solving
• Exponentials and Logarithms

7
Fractions
•   Simplify:   9 7

5 15

•   Solve:
3    7
x  1
4    8
•   Simplify:
x          x 3
 2
x  6 x  9 x  5x  6
2

8
Unit Conversion

• Set up the expression to convert 25
miles per hour to meters per second

• Convert 3,500 milligrams/centiliter to
grams per milliliter.

9
Graphing

Graph:
4
»A. y  x  3
3

»B. f ( x)  x 2  3

10
Systems of Equations

Solve:

3x  5 y  7

2 x  3 y  11

11
Problem Solving & Estimation

Emily wants to buy carpeting for her dorm
room. The room has two closets, which
will not be carpeted. The room, excluding
the closets, is 16 3/4 ft long by 11 2/5 ft
wide.
– Estimate how much carpeting Emily will need
and explain how you arrived at this estimate.
– How much carpeting will Emily actually need?

12
Exponentials & Logarithms

Given that log b x  n means b n  x ,
complete the following:
•A. 1  log   10   ______

•B.   Evaluate          log 5 (125 )

13
Implementation

• Acquiring instructor participation to
hour) and incorporation of TIMES into
•   Administration of a pre-test to identify
students with poor mathematical
skills in freshman level engineering
classes (EE 110, EE 188, EGR 186,
CENE 150)
14
Breakdown of Students by Course

Course   Fall   Spring   Fall   Spring   Overall
2006   2007     2007   2008
EE 110   54     0        69     0        123

EE 188 88       56       87     78       309

EGR      122    77       167    108      474
186
CENE     51     26       75     45       197
150
Total    315    159      398    231      1103
15
Implementation
• Frequent feedback to instructors &
students regarding student progress
•   Regularly scheduled sessions with
individualized tutoring by GTAs
•   Guided modules in the areas of
deficiency to increase students’
comfort and skill.
•   A final assessment of mastery in the
area(s) of difficulty
16
Percentage of Students Needing Help

Course        Fall      Spring   Fall     Spring   Overall
2006      2007     2007     2008
Fractions     72        23      98        66      187
(22.9%)   (14.5%) (24.6%)   (28.6%) (17%)
Unit          78        43      125       92      338
Conversion
(24.8%)   (27.0%) (31.4%)   (39.8%) (30.6%)
Graphing      77        24      35        36      172
(24.4%)   (15.1%) (8.8%)    (15.6%) (15.6%)
Systems of    161       45      108       72      386
Equations
(51.1%)   (28.3%) (27.1%)   (31.2%) (35.0%)
Exponentials & 67       21      104       68      260
Logarithms
(21.3%)   (13.2%) (26.1%)   (29.4%) (23.6%)
Problem       140       66      82        83      371
Solving &
(44.4%)   (41.5%) (20.6%)   (35.9%) (33.6%)
Estimation
Total         315       156      398      231      1103
Students Needing Help by Topic
(Overall)

• Fractions: 17.0%
• Unit Conversion: 30.6%
• Graphing: 15.6%
• Systems of Equations: 35.0%
• Problem Solving & Est.: 33.6%
• Exponentials & Logarithms: 23.6%

18
Key Conclusion 1

The percentage of freshman
students who exhibit difficulty
with one or more of the six
target topics is quite high
(nearly 75%).

19
Participation of Students
Fall 2006   Spring    Fall 2007   Overall
2007

Needed &           4          44        69         117
Participated    (1.3%)     (27.7%)   (17.3%)     (13.4%)
Needed &         251          64       208         523
Did not        (79.1%)     (40.3%)   (52.3%)     (60.0%)
participate
Did not           60          51       121         232
need            (19%)      (32.1%)   (30.4%)     (26.6%)
Total            315        159        398        872
number
Results
(Participation, Overall)
• Students who needed help &
participated: 13.4%

• Students who needed help & did not
participate: 60.0%

• Students who did not need help:
26.6%
21
Key Conclusions 2

• Voluntary participation results in low
turnout.
•   Students attend meetings more often
when it is required as part of their grade.
•   Students are very unlikely to follow
through with the training modules unless
this activity is a required part of their
course.

22
D/F/W in Engineering Course
Based on Need & Participation

Fall     Spring       Fall     Overall
2006       2007       2007
D/F             0.0%      20.45%     4.35%      10.26%
participated    (0/4)      (9/44)    (3/69)     (12/117)

D/F Did not     15.54%    21.88%      41.25%     16.83%
participate    (39/251)   (14/64)    (35/208)   (88/523)
D/F/W given     23.92%     31.48%     21.66%     24.22%
need           (61/255)   (31.48%)   (60/277)   (155/640)
D/F/W given    8.33%      15.69%      12.40%     12.07%
no need        (5/60)      (8/51)    (15/121)   (28/232)
23
Results
(D/F/W with respect to need & participation)

•   Students who received a D/F given they needed
help & participated: 10.26%
•   Students who received a D/F given they needed
help & did not participate: 16.83%
•   Students who received a D/F/W given they
needed help: 24.22%
•   Students who received a D/F/W given they did not
need help: 12.07%

24
Key Conclusion 3

The pre-test has proven to be a good
predictor of student success in their
engineering course even though the
material tested is not explicitly a
course component.

25
Analyzing the Data:
–Needed & Participated
2.86
–Needed & Not Participated
2.53
–Did Not Need
3.02
–Overall
2.75
99% Confidence Intervals for
Differences of Average GPAs
Lower                 Upper
Overall vs. N & P             -0.31                  0.09
Overall vs. N & NP*            0.02                  0.42
Overall vs. DNN*              -0.47                 -0.07
N & P vs. N & NP*              0.13                  0.53
N & P vs. DNN                 -0.36                  0.04
N & NP vs. DNN*               -0.69                 -0.29

•   Overall (GPA: 2.75)
•   N &P = Needed help & participated (GPA: 2.86)
•   N & NP = Needed help & did not participate (GPA: 2.53)
•   DNN = Did not need help (GPA: 3.02)
•   * Indicates statistically significant differences between the
groups.
27
Key Conclusion 4

TIMES participation has
demonstrated a measurable and
statistically significant
improvement in student
engineering courses.

28
Student Feedback
(From Participants)

• “The modules were very well written
and explained the material very
clearly.”
•   “The material was confusing.”
•   “I learned new things. I can solve
problems that I couldn’t before.”
•   “I would have passed if I could use
my calculator.”
29
Feedback
(Students who needed help, but did not participate)

•   “I only needed a few minutes of self review to
remember how to do the math.”
•   “I knew what to do. I just was caught by surprise
•   “Too busy / forgot / not very good information.”
•   “My schedule was extremely busy.”
•   “The schedule for the meetings did not fit my
schedule.”
•   “My math level is far beyond this TIMES test. I felt
this was a blatant waste of my time.”

30
The Changing TIMES

Modules are now installed on VISTA:
–modules are available to print in case
meeting times conflict with student
schedules
–deadlines for each module are set at
specific intervals to encourage students
to master basic skills early in the
semester
31
Future TIMES

Two year pilot study was funded by
Hewlett and LCE grants.

Sustaining TIMES requires:
–Departmental approval
–Funding for two part-time GTAs

32
Possible Subjects for
Expansion

• Physics
• Chemistry
• Biology
• Mathematics
Steps Needed To
Expand TIMES
• Specify the subject areas of difficulty
• Professor input and the courses needing
to be targeted
•   Designing a Pretest
•   Constructing Modules for Targeted Areas
•   Instruments to measure mastery of
material
•   End of course evaluation
•   Overall measure (i.e. grade in class)
34
Summary
•   A large percentage of freshman students exhibit
difficulty with one or more of the six target topics.
•   Students are very unlikely to follow through with
the training modules unless this activity is a
required part of their course grade.
•   The pre-test has proven is a good predictor of
student success in the course even though the
material tested is not explicitly a course
component.
•   TIMES participation has demonstrated a
measurable and statistically significant
improvement in student performance in their
Issues for Further Study
• Based on our design, we are unable to
distinguish whether students who
participated were simply more motivated
or whether TIMES was the driving force.
•   Does TIMES assist students in their
mathematics classes?
•   Does TIMES assist with Engineering
retention rates?
•   Does student self-perception affect
participation and is it reliable?
36
Questions???

37

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