A strategy to reduce the blank answers on math tests at first engineering courses

A strategy to reduce the
blank answers on math
tests at first engineering
courses
Susana Nieto (1,2) sni@usal.es
Higinio Ramos (1) higra@usal.es
(1) Applied Mathematics Department
(2) Institute of Educational Sciences
UNIVERSITY OF SALAMANCA

Context
 Engineering students at the
Polytechnic School of
Zamora (University of
Salamanca).
 Math subjects at the first
courses.
2
S. Nieto, H. Ramos, 2016

Context
 Students having special difficulties
handling math subjects:
◦ Increasing group of students from Vocational
Training Modules.
◦ Poor basic knowledge about mathematics
even in students from scientific or technical
Bachelors.
◦ Not only in Spain [1-2, 6-7], similar situation in
other European countries [3-5]
3S. Nieto, H. Ramos, 2016

Context
 Persistence along time of these
deficiencies.
 Poor mathematical skills + low level of
confidence about their capability of
passing mathematical subjects = “vicious
circle”.
Bad experiences
in examinations
Poor mathematical
performance
Low level of
self-confidence

Context
 It generates a increasing group of
repeating students (1)= high dropping
rate.
CALCULUS (Mechanical Engineering) 2015-2016
Students who have not taken any call
for midterms or final exams 10,9%
Students who have not taken
the final exam 27,2%
the second-chance examination 31,5%

Context
 It generates a increasing group of
repeating students (II)= bad results at
examinations
Students who passed
the mid-term exams 18,2%
Students who passed
the final exam 30,9%
Students who passed
the second-chance examination 5,2%

Context
 In our experience, a big amount of
questions at the written examinations of
mathematics remain unanswered
 Maximum 7 over 10.
Average of blank answers
on the final exam 3,68
on the second-chance exam 3,33

Context
 Diagnosis:
◦ Bad results at examinations come from
the students’ bad performance , but also
from the big number of blank questions.
◦ Students tend to abandon the execution
of mathematical procedures at early
stages, when they find (minor)
difficulties of calculus.

Context
 Why happens?:
◦ Students usually perform a “visual”
study of mathematical subjects.
◦ Short time dedicated to solve “pen-and-
paper” exercises by themselves.

Objectives
 Avoid the (common) mistake of
studying mathematics by simply
reading exercises solved by the
teacher.
 Help students to face autonomously
the main mathematical procedures.

Objectives

Objectives
 Expected consequences:
◦ Improvement of students' abilities in
mathematics,
◦ Improvement of the results in
written examinations,
◦ Decrease of the high drop-out rate,
◦ Decrease of the number of blank
questions in written examinations.

Description of the project
 Students of Calculus at the first course
(2015-2016) of Mechanical Engineering at
the Polytechnic School of Zamora.
 Criterion for the selection of students: to
have faced the examinations of the
subject in three or more occasions.

 Students who have accumulated a
set of experiences of failure in
examinations:
◦ They are susceptible of abandon the
proposed mathematical tasks at early
stages.
◦ They can have doubts about their own
ability to have success at the written
tests.

 Both groups have access to the general
material of the subject via STUDIUM (the
virtual campus of the University of
Salamanca, based in Moodle).

 The project group have also access
to additional material specifically
developed, and they have followed
an extra classroom hour each week.
 During this extra classroom hour,
they work individually under the
supervision and monitoring of the
teacher.

 The extra hour includes: realization
of problems, consultation of doubts
about procedures or algorithms,
debate, etc., always in an active way
and encouraging the autonomous
work of the students (with the helping
of the teacher when needed).
 The material to solve is selected from
previous written examinations.

 The selection of these material is
important, because are exercises
that these students have not been
capable to solve in previous
occasions.
 They are selected to provide success
experiences and to change students’
opinions about their own capabilities.

Results
 Analysis of the main results:
◦ Drop-out rate during the course 2015-2016.
◦ Results obtained in the assessment test (mid-
term, final and second chance examinations).
◦ Blank questions.
 Other results of interest:
◦ Average scores.
◦ Average scores and standard deviation of the
failed exams.

Results
 Dropping rate:
CALCULUS (2015-2016) Control
Project
Group
any call for midterms or final
exams
10,9% 2,7%
the final exam 27,2% 16,2%
the second-chance examination 31,5% 26,9%

Results
 Dropping rate:
◦ The majority of the students of the project
group (97,3% vs. 89,1%) have faced any of
the examinations along the course. This
results show the increase of these students’
self-confidence. 21S. Nieto, H. Ramos, 2016
Project
Group
any call for midterms or final
exams
10,9% 2,7%

Results
 Dropping rate:
◦ The project group also has a better behavior
facing the final exam (83,8% vs. 72,8%),
which also indicates their intention of facing
the tests.
Project
Group

Results
 Dropping rate:
◦ Results about the second-chance
examination are better in the project group,
even taking into account exams from other
courses (73,1% vs. 68,5%).
Project
Group

Results
 Results in the assessment tests:
Project
Group
Students who passed
the mid-term exams 18,2% 10,8%
Students who passed
Students who passed

Results
 Results in the examinations:
◦ The results during the mid-term exams are
worse for the project group, probably
because they needed some time-lapse to
improve their mathematical skills and to
acquire self-confidence.
Project
Group
Students who passed
the mid-term exams 18,2% 10,8%

Results
◦ The results in the final exam are comparable
to those from the control group, which is a
great success for students who have failed
three or more times that kind of examination.
Project
Group
Students who passed

Results
◦ Results for the second-chance examination
are better for the experimental group,
probably due to the superposition of
examinations from other courses: these
students have tried to use all the opportunities
to pass the subject.
Project
Group
Students who passed

Results
10.8%
29.7%
7.6%
18.2%
30.9%
5.2%0%
10%
20%
30%
40%
mid-term exams final exam second-chance
exam
Project Group Control

Results
 Blank answers
◦ Much better performance in the experimental
group. Statistically significant (p<0.01).
Project
Group
on the final exam 3,68 1,47
on the second-chance exam 3,33 1,31

Results
 Blank answers
◦ The students of the project group tried to
solve a bigger amount of questions than the
control.
Project
Group
Maximum of blank answers
on the final exam (over 10) 7 4
Number of examinations reaching
the minimum 4 1

Results
 Other Results: average scores
◦ The project group shows a slight better
result in the final exam, and improves the
result of the control in the second-chance
exam.
Project
Group
Average scores in the final exam 3,06 3,61
Average scores in the second-
chance exam
2,61 3,25

Results
 Other Results: failed exams
◦ The students in the project group obtain better
scores even in failed exams.
◦ The standard deviation is much inferior, so their
behavior is more homogeneous.
Project
Group
Average scores of failed
examinations
2,14 2,78
Standard deviation of the scores
of failed examinations
1,35 0,58

Conclusions
 The students from the project group:
◦ They try to solve a bigger amount of
questions in the written test and they leave (in
a statistically significant way) a smaller
number of problems unanswered than the
control.
◦ They follow a consistently increasing line of
academic results, being worse than the
control at mid-term exams, comparable at the
final exam and better when facing the second-
chance exam.

Conclusions
◦ They show better average scores than the
control. This improvement in consistent (but
not statistically significant) and is shown in the
final exam and also in the second-chance
exam.
◦ They have better scores even in the failed
exams, and show less dispersion, and a more
homogeneous behavior.
◦ ¡Students with special difficulties in
mathematics!

Conclusions
◦ They show a very active and participative
attitude in the extra classroom hour.
◦ They attend tutorials more frequently, which
shows their interest and their greater
involvement.
◦ Have an inferior drop-out rate than the
control, probably because they faced the
mathematical exams with better success’
perspectives and higher confidence on their
mathematical skills.

A strategy to reduce the
blank answers on math
tests at first engineering
courses
Susana Nieto sni@usal.es
Higinio Ramos higra@usal.es
Thanks for your attention

A strategy to reduce the blank answers on math tests at first engineering courses

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