Creative Education
2013. Vol.4, No.7A2, 178-180
Published Online July 2013 in SciRes (
Copyright © 2013 SciRes.
Developing Mathematical Literacy,
Based on Elemental Software and
Academic Tools Development
Oscar H. Salinas1, Angel Estrada Arteaga2, Martha E. Luna1,
Marco A. Amado González1,2
1División Académica de Tecnologías de la Información y Comunicación
2Centro de Desarrollo de Software, Universidad Tecnológica Emiliano Zapata del Estado de Morelos,
Emiliano Zapata, Morelos, México
Received May 16th, 2013; revised June 16th, 2013; accepted June 23rd, 2013
Copyright © 2013 Oscar H. Salinas et al. This is an open access article distributed under the Creative Commons
Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the
original work is properly cited.
This report describes the procedure to develop mathematical literacy through learning basic mathematical
concepts, and applying the acquired knowledge for the development of elemental software to be used as
academic tool. Basic operations with matrix were performed using open and commercial sources software.
A simple and basic matrix calculator were developed integrating mathematical concepts and software de-
velopment skills, and the deliverable was a calculator developed on Java platform. The procedure started
from a traditional classroom explanation; worked on calculus worksheet, solving some academic prob-
lems about addition, subtracted product of two matrix, following by the use of some commercial software,
and finally the development of the own academic tool. These works were developed into the frame of
competency based education system.
Keywords: Mathematical Concepts; Didactic Tools; Software Development; Competency
Mathematics has been a tough topic to learn and even the
worst to teach traditionally. Most of the people think that is a
very difficult topic to overcome, because they think it is a topic
just for people with high intellectual coefficient. Therefore, the
professors face a big dare of teaching mathematics topics. Be-
sides in México, professors of higher education face up the
problem that most of the times young students coming from
basic education don’t have the basic mathematics concepts.
Sometimes the problem starts since the definition of Mathe-
matics is not well know of being described. This has been
changed trough the time (Devlin, 1998), but the current mean,
given from mathematicians, is “the science of patterns” (Devlin,
Mathematics: The Science of Patterns, 1996; The language of
Mmathematics, Making the Invisible Visible, Devlin, 1998;
Sawyer, 1995; Wittman, 2000) and this definition gives more
information about what mathematics is. Competency based
education system matches very well with the so called four
general objectives of teaching mathematics: “mathematising”,
exploring, reasoning and communication. It means students
learning mathematics, would have a deeper understanding on
them, when they face the dare of communicating what they
have learned. It has been established that the important things
are not the finished products but the short and long term ones
(Wittman, 2000), however academic products are not included
inside of this statement, according with the authors understand-
ing. Competency based education system was implemented at
Universidad Tecnológica Emiliano Zapata del Estado de More-
los (UTEZ), since 2009, following the Tuning Educational
Structures for Latin America (Latina, 2007). Inside the frame-
work of competency based education, professors have to iden-
tify the different learning mechanisms of students in the aim
that all of them get the same level of knowledge. It has been
demonstrated that there are six fundamental competencies
about Mathematics, to a person who gets the ability to apply the
mathematical knowledge to some specific and daily practical
situations, i.e. the development of mathematical literacy (Fig-
ure 1) (Turner, 2011).
Therefore, according to competency based education model,
students have to demonstrate they are able to apply acknowl-
edge they had been obtained. The integration of different com-
petencies is not an easy issue where the mathematics is in-
volved in the teaching-learning process. The proposal hypothe-
sis is: students that understand the basic mathematical concepts
are able to design and develop their own academic tools, like a
calculator, and they feel more comfortable learning or even
going far, teaching mathematics.
This job was developed following a simple four step process
of academic tools development (Figure 2). It starts with as here
is called a traditional classroom activity, it means professor
explains the topic and resolve some demonstrative problems at
the blackboard. At this step a preliminary survey was done
Figure 1.
Fundamental mathematical competencies.
Figure 2.
Process of academic tools development.
applying a simple questionnaire to know the students feeling
about mathematics.
Getting Theoretical Concepts: Mathematical
Basic Operations with Matrices
At the step two, students must have kept in mind the rules to
do basic operations with matrix (Sawyer, 1995):
Every term of the matrix is given by aij, where i is the row
number and j is the column number.
For addition or subtract, both matrix must have the same
For matrix multiplication, the number of columns of the
first matrix must be equal to the number of rows of the se-
cond one.
atrixAMatrix B
The order of the Resultant matrix is gotten from the numbers
of rows of the first matrix and the number of columns of the
second one (m x q). In this case the order of the factor affects
the product.
xB BxA (1)
The Mathematical representation of a Matrix is well de-
scribed at the literature (Sawyer, 1995), this kind of representa-
tion could be one reason why students of Engineering in Infor-
mation Technology, are dislike about mathematical in a general
way and matrix operations in a particular way.
Mathematical Basic Operations with Matrices,
Using a Calculus Worksheet
After the theoretical concepts were reviewed and used to
solve academic problems, students used a calculus worksheet to
develop a matrix calculator. Working on this kind of simple
tools could be looks like is very easy calculus exercise, but to
students must have understood all the concepts mentioned at
Getting theoretical concepts section. Students must develop the
exercise at their notebook, and compare with the results on the
worksheet to identify errors or if the calculator really works.
This is a very important step since students must to understand
the role of every cell, which can contains just a number, or a
data or a string or information in general. The importance of
matrix in mathematics and software development in general,
was deep understood, after the exercise, and they are able to
identify possible applications or as this case, design and de-
velop academic tools, for their own benefit or future genera-
At the first step of the step one of process shown in Figure 2,
a preliminary survey was done applying a simple questionnaire
to know the students feeling about mathematics. The results
show that just a few students think mathematics is related with
their engineering field (Figure 3).
Two from six groups were selected to work under the pro-
posal, what are represented by 60 out of 180 students, belongs
to All part of Figure 3. Just 8.33% of 180 students think
Mathematics are related to Engineering in Information Tech-
nology. Before the proposal test concept was done, just 8.33%
tough that Mathematics are related to Engineering in Informa-
tion Technology, after that 80% of students change their mind,
data from the two experimental groups. Students develop some
calculus on a basic matrix calculator, to corroborate they un-
derstand the procedure to do three basic mathematics operations
with matrix (Figure 4). And they are able to identify if there
are some calculus errors. A comparison for some preliminary
results about student’s notes in average was done (Table 1),
scale 0 to 10.
The results from software work are shown in Figures 4-6.
The mathematical knowledge application started with a calcu-
lus worksheet (Figure 4).
Figure 3.
Students feel about mathematics.
Copyright © 2013 SciRes. 179
Copyright © 2013 SciRes.
Table 1.
Preliminary comparis o n a b o ut n o t e s .
Grades from two experimental groups and the other ones
Two experimental groups Other groups
8.6 6.3
Figure 6.
Matrix calculator developed on LabVIEW software.
not an easy task, students that work under the proposal scenario,
face fewer problems compared with the other group, since the
operations procedure point of view.
Students working understood Mathematics concepts and
calculus procedure using available software got understood in a
deeply way, and therefore they changed their mind about Ma-
thematics and their career. Under this scenario, students could
get the fundamental competencies about Mathematics easier.
Some working academic tools were developed in LabVIEW
software and Java platform. The results showed that students
felt more comfortable to learn or even further, to teach mathe-
matics. Some other works related to this kind of proposal had
been done with similar successful results (Salinas, 2013).
Figure 4.
Matrix calculator developed on a calculus worksheet.
Authors want to thank students of UTEZ, for their commit-
ment about their work to support this proposal, and the dare to
put hands on about mathematics academic tools development
for future generations inside the UTEZ campus.
Devlin, K. (1996). Mathematics: The science of patterns. New York:
Devlin, K. (1998). The language of mathematics, making the invisible
visible. New York: Holt Paperback.
Figure 5.
Matrix calculator developed on a java application. Latina, T. A. (2007). Tuning América Latina.
Salinas, O. (2013). Physical concepts about telecommunications theory
focusing on the applicat i o n o f k n o w l edge. In press.
Students have built a simple matrix calculator integrating
their Mathematical literacy and basic software handling skills.
At this step students are able to detect themselves if there are
some doubts about mathematical concepts of matrix operations.
Next step consist of the designing and developing of own soft-
ware tools that can be used as academic help (Figure 5). Stu-
dents of Engineering in Information Technology study tele-
communications and signal processing as part of their career
sometimes they have to use a kind of specialized software, like
LabVIEW (Figure 6). Handling this kind of software could be
Sawyer, W. (1995). A prelude to mathematics. Harmondsworth, Med-
dlesex: Pinguin Books.
Turner, R. (2011).
Wittman, E. C. (2000). Institut de researche sur’l enseignement des