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) [email protected] Ramos (1) [email protected]

(1) Applied Mathematics Department(2) Institute of Educational Sciences

UNIVERSITY OF SALAMANCA

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ContextEngineering students at the

Polytechnic School of Zamora (University of Salamanca).

Math subjects at the first courses.

S. Nieto, H. Ramos, 2016

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ContextStudents 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]


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ContextPersistence along time of these

deficiencies.Poor mathematical skills + low level of

confidence about their capability of passing mathematical subjects = “vicious circle”.


Bad experiencesin examinations

Poor mathematicalperformance

Low level ofself-confidence

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ContextIt 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%Students who have not taken

the second-chance examination 31,5%

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ContextIt generates a increasing group of

repeating students (II)= bad results at examinations


CALCULUS (Mechanical Engineering)

2015-2016

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%

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ContextIn our experience, a big amount of

questions at the written examinations of mathematics remain unanswered

Maximum 7 over 10.


CALCULUS (Mechanical Engineering)

2015-2016

Average of blank answers on the final exam 3,68

Average of blank answers on the second-chance exam 3,33

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ContextDiagnosis:

◦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. S. Nieto, H. Ramos, 2016

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ContextWhy happens?:

◦Students usually perform a “visual” study of mathematical subjects.

◦Short time dedicated to solve “pen-and-paper” exercises by themselves.


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ObjectivesAvoid the (common) mistake of studying mathematics by simply reading exercises solved by the teacher.

Help students to face autonomously the main mathematical procedures.


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Objectives


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ObjectivesExpected 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.


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Description of the projectStudents 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.


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Description of the projectStudents 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.

Project group (37) vs. control group (55)


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Description of the projectBoth groups have access to the

general material of the subject via STUDIUM (the virtual campus of the University of Salamanca, based in Moodle).


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Description of the projectThe 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.


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Description of the projectThe 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.


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Description of the projectThe 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.


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ResultsAnalysis 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.


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ResultsDropping rate:


CALCULUS (2015-2016) Control Project Group

Students who have not taken any call for midterms

or final exams 10,9% 2,7%Students who have not

taken the final exam 27,2% 16,2%

Students who have not taken

the second-chance examination

31,5% 26,9%

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◦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.



Students who have not taken any call for midterms

or final exams 10,9% 2,7%

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◦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.




the final exam 27,2% 16,2%

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◦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%).




the second-chance examination

31,5% 26,9%

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Results Results in the assessment tests:



Students who passed the mid-term exams 18,2% 10,8%Students who passed

the final exam 30,9% 29,7%Students who passed the second-chance

examination 5,2% 7,6%

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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.



Students who passed the mid-term exams 18,2% 10,8%

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◦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.



Students who passedthe final exam 30,9% 29,7%

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◦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.



Students who passed the second-chance

examination 5,2% 7,6%

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0%15%30%

10.8%29.7% 7.6%

18.2% 30.9%

5.2%

Project Group Control

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ResultsBlank answers

◦Much better performance in the experimental group. Statistically significant (p<0.01).



Average of blank answers on the final exam 3,68 1,47

Average of blank answers on the second-chance

exam 3,33 1,31

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ResultsBlank answers

◦The students of the project group tried to solve a bigger amount of questions than the control.



Maximum of blank answers on the final exam (over 10) 7 4

Number of examinations reaching the minimum 4 1

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ResultsOther 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.



Average scores in the final exam 3,06 3,61

Average scores in the second-chance exam 2,61 3,25

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ResultsOther 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.



Average scores of failed examinations 2,14 2,78

Standard deviation of the scores of failed examinations 1,35 0,58

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ConclusionsThe 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.


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◦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!


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◦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 [email protected] Ramos

[email protected]

Thanks for your attention

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

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