A global approach to improve the mathematical level of engineering students

S U S A N A N I E T O I S I D R O sn i@usa l . e s

H I G I N I O R A M O S C A L L E h igra@usa l . e s

A GLOBAL APPROACH TO IMPROVE THE MATHEMATICAL LEVEL OF ENGINEERING STUDENTS

D E P A R T M E N T O F A P P L I E D M A T H E M A T I C SP O L Y T E C H N I C H I G H S C H O O L O F Z A M O R AU N I V E R S I T Y O F S A L A M A N C A

� In this work we have analyzed:

� The situation of the initial knowledge in mathematics at the engineering studies, (which is clearly unsatisfactory)

by means of an specifically designed test.

� The generation of groups of students with similar

Background:

� The generation of groups of students with similar mathematical deficiencies based on the way of entrance at the University.

� The possible solutions to the mathematical problems found for each group, using different initiatives due the previous diagnosis.

Background:

� Our aim is the development of a global approach to solve this situation, which includes:

�The use of an on-line tool to improve the mathematical level of some of the students.

�The measure of this improvement by means of �The measure of this improvement by means of qualifications and a self-confidence test.

�A strategy to prevent the most common mathematical errors found in written examination, using participative classroom sessions.

Model

We work taking into account the frame of the Spanish educational legislation about who can access at the University:

High School students

about who can access at the University:•Students from pre-graduate studies (High School).•Students from Vocational Training Modules.

Vocational Training Modules students

Model

The mathematical background of these groups is quite different:•Students from pre-graduate studies

(High School) have a specific andcompulsory mathematical background.But a group of them (usually the ones

High School students

Mathsexam ?

But a group of them (usually the ones having the poorest mathematical level)have avoided to take the final exam of mathematics in order to maximize their accessing score.

•Students from Vocational Training Modules have a bad mathematical background.

exam ?

YES NO

Vocational Training Modules students

VTM

Model

We have analyzed the mathematical levelof the students coming to the PolytechnicHigh School of Zamora, which belongs toHigh School of Zamora, which belongs tothe University of Salamanca.

We have six engineering degrees from different areas: Civil Engineering, Industrial Mechanics, Computing, Materials, Technical Architecture and Agriculture.

Model

The first step is to make a diagnosis of the situation of our students, as accurate as possible.

D

i

a

gas accurate as possible.

g

n

o

s

i

s

Model

This step is especially important becauseteachers usually are not conscious of thereal level of the mathematical knowledge

D

i

a

greal level of the mathematical knowledgeof their students.

The official information from the University does not include data aboutthe way of access of our students.

g

n

o

s

i

s

D

i

a

g

Model

To make this diagnosis we have designeda specific test which includes:•Some items to measure the knowledge of

g

n

o

s

i

s

•Some items to measure the knowledge of mathematical concepts.

•Some items to measure the knowledge of mathematical procedures.

•A header with anonymous information about the way of accessing at the University.

Model

The diagnosis shows the presence of three groups of students, which need to be treated separately, because they

D

i

a

g

YES

to be treated separately, because theyhave different kinds of problems (anddifferent kinds of solutions).

Some teachers make initial tests, but theresults are usually treated globally, as a proof of the “global” knowledge of that group of students.

g

n

o

s

i

s

VTM

NO

Model

Nevertheless, the results of the test are much better understood when we separate the students among

D

i

a

g

Calculate thederivative of

Correct answer

Incorrect answer

No answer

GLOBAL RESULTS

we separate the students among these three groups.g

n

o

s

i

s

derivative of answer answer answer

f(x)= 1/x 48.2% 23.8% 28.0%

g(x) =x ex 43.0% 22.8% 34.2%

h(x)=x/(x2+1) 38.9% 25.9% 35.2%

Model

D

i

a

g

Calculate the derivative of

Correct answer

Incorrect answer

No answer


Correct answer

Incorrect answer

No answer

f(x)= 1/x 59.3% 27.1% 13.6%

g(x) =x ex 55.1% 22.0% 22.9%

h(x)=x/(x2+1) 50.0% 26.3% 23.7%


Correct answer

Incorrect answer

No answer

GLOBAL RESULTSYES

g

n

o

s

i

s


f(x)= 1/x 48.2% 23.8% 28.0%

g(x) =x ex 43.0% 22.8% 34.2%

h(x)=x/(x2+1) 38.9% 25.9% 35.2%

f(x)= 1/x 42,9% 34,3% 22,9%

g(x) =x ex 37,1% 31,4% 34.3%

h(x)=x/(x2+1) 31,4% 34,3% 34,3%


Correct answer

Incorrect answer

No answer

f(x)= 1/x 18.9% 5.4% 75.7%

g(x) =x ex 10.8% 18.9% 70.3%

h(x)=x/(x2+1) 8.1% 16.2% 75.7%

VTM

NO

Model

D

i

a

g

YES

The worst results are found for VocationalTraining Modules (VTM) group.So, we focused on this group by means of a specifically designed on-line tool.

g

n

o

s

i

s


Correct answer

Incorrect answer

No answer

f(x)= 1/x 18.9% 5.4% 75.7%

g(x) =x ex 10.8% 18.9% 70.3%

h(x)=x/(x2+1) 8.1% 16.2% 75.7%

VTM

NO

on-line tool.

Model

D

i

a

g

YES


Correct answer

Incorrect answer

No answer

f(x)= 1/x 59.3% 27.1% 13.6%

g(x) =x ex 55.1% 22.0% 22.9%

h(x)=x/(x2+1) 50.0% 26.3% 23.7%


Correct answer

Incorrect answer

No answer

g

n

o

s

i

s

VTM

NO

Nevertheless, the results of the othergroups are not as good as desirable.


f(x)= 1/x 42,9% 34,3% 22,9%

g(x) =x ex 37,1% 31,4% 34.3%

h(x)=x/(x2+1) 31,4% 34,3% 34,3%

Model

D

i

a

g

YES For these students, we havefocused on the most common mathematical errors found in the

g

n

o

s

i

s

VTM

NO

mathematical errors found in thewritten examinations.

We have tried to correct this errors by means of some classroom sessions dedicated to fix the attention of the students on these common mistakes in order to minimize their presence.

Model

D

i

a

g

YESClassroom

sessions

A global approach

g

n

o

s

i

s

VTM

NO

sessions

On-line tool

Correction 1: VTM group

� This VTM group accessing Engineering studies is increasing nowadays due to two factors:

� The economic crisis, which is leading many workers to improve their training at the University.

� The current Spanish educational legislation (2010) � The current Spanish educational legislation (2010) includes no limitation in the number of VTM students who can access at the University.

� Other characteristic of this group is the big “drop-out” rate: 25% of them did not perform the final examination in the academic year 2011-2012.

� We have designed an on-line course using STUDIUM (based on Moodle) which is the official tool of

the “virtual campus” at the University of Salamanca.

� It is particularly useful for teachers, since it offers a wide range of tracking tools, including tools for


wide range of tracking tools, including tools for generating questionnaires, evaluation tools, etc.

� Detailed description in:

� Nieto and Ramos (2013) TEEM’13 Proceedings.

� Nieto and Ramos (2014) JCIT (in press).

� “Drop-out” rates:Groups 2011-2012 2012-2013

Performing examination 75% 85,7%Non-performing examination 25% 14,3%Students passing the exam. 25% 28,6%


� Performance at the final examination:

Students passing the exam. 25% 28,6%

Groups 2011-2012 2012-2013

Averaged qualification 2,6 3,4Passing the exam 5,5 5,7Non-passing the exam 1,1 2,4

� Test of satisfaction:

Questions Yes No

The course has been useful to understand themathematics at the classroom 100% -

The course has given you confidence to perform78,6% 21,4%


The course has given you confidence to performthe final examination 78,6% 21,4%

The course has been useful to improve yourmathematical knowledge 78,6% 21,4%

� An on-line course arises as a very useful tool to give students for Vocational Training Modules the mathematical contents they need to face their studies successfully.

The results show an increase of the academic

Correction 1: Conclusions

� The results show an increase of the academic qualifications and an increase in the percentage of students performing the final examination.

� A satisfaction test filled by the students shows an increase in their self- confidence in their mathematical knowledge and capabilities.

Correction 2: Common errors

� The second step is to avoid the repetition of the most common mistakes found in written examinations.

� This kind of ability is especially suitable to be trained in the classroom (and not by the use of on-trained in the classroom (and not by the use of on-line material) due to the immediate feedback given by the teacher to the students.

� We have analyzed the impact of this initiative over the performance of the students.


� The active-participative classroom session contains the following schema:

� We have compelled the students to complete the solution of a typical erroneous procedure in an anonymous sheet.

� We have mixed the anonymous sheets and we have � We have mixed the anonymous sheets and we have distributed them again so that each student corrects the results of one of his/her classmates

� The teacher has solved the whole process at the blackboard paying attention to possible bugs, asking the students to correct the work of their peers “as if they were the teacher”.


� The impact of this initiative has been measured comparing the errors committed by the students in the written examination for two consecutive academic years: 2012-2013 and 2013-2014.

We have used a classification of errors and failures � We have used a classification of errors and failures and have quantified them.

� In addition, we have quantified the absence of answers for the theoretical or practical questions related with the most “problematic” topic (diagonalization of a square matrix).

ERRORS/ FAILURES 2012-2013 2013-2014 Relative difference (%)

Matrix rank (not trained) 41,2%. 39,3% Similar (−4,6%)


� Some results: trained vs. not trained errors

Zeros of a function (not trained) 19,7%. 20,0% Similar (+1,5%)

Matrix determinant (trained) 34,4% 23,6% −−−−31,4%

Equation systems (trained) 61,9%. 37,0% −−−−40,0%

ERRORS/ FAILURES 2012-2013 2013-2014 Relative difference (%)

No answers fordiagonalization questions(theoretical)

44,7% 40% −10,5%


� Some results: questions unanswered

(theoretical)No answer for thediagonalization problem(algoritmic)

23,7% 10% −−−−57,8%

� Some active-participative classroom sessions are an effective tool to improve the mathematical performance of our students:

� The results detected in the written examinations show a decrease of the main errors or failures which were

Correction 2: Conclusions

decrease of the main errors or failures which were specifically trained, while the non-trained errors remain stable.

� The number of questions left unanswered have also decreased, particularly the ones related with algorithmic (not theoretical) procedures.

Conclusions:

� As mathematics teachers at first university levels, we must be aware of the shortcomings of our students and we need to find a way to help them to improve their mathematical performance.

The accurate diagnosis of the real knowledge of our � The accurate diagnosis of the real knowledge of our students is a fundamental tool to develop the best didactic approach for our students.

� A global approach witch take into account the presence of different groups of students can be seen as a effective strategy to improve students’ learning.

S U S A N A N I E T O I S I D R O sn i@usa l . e s

H I G I N I O R A M O S C A L L E h igra@usa l . e s

A GLOBAL APPROACH TO IMPROVE THE MATHEMATICAL LEVEL OF ENGINEERING STUDENTS

D E P A R T M E N T O F A P P L I E D M A T H E M A T I C SP O L Y T E C H N I C H I G H S C H O O L O F Z A M O R AU N I V E R S I T Y O F S A L A M A N C A

A global approach to improve the mathematical level of engineering students

Education

Transcript of A global approach to improve the mathematical level of engineering students