THE USE OF INTERACTIVE INSTRUCTORS OF RECREATIONAL
MATHEMATICS IN SECONDARY SCHOOLS
Gabriel L´opez-Morteo
Universidad Aut´onoma de Baja California, Calle de la Normal y Benito Ju´arez, 21280, Mexicali, B.C., M´exico
Marcos Galaviz-F´erman, Gilberto L´opez
CICESE, Km. 107 Carretera Tijuana-Ensenada, 22860, Ensenada, B.C., M´exico
M. Andrade-Ar´echiga
Universidad de Colima, Av. Universidad 333, 28040, Colima, Col, M´exico
Keywords:
Learning environments, learning objects, mathematics learning.
Abstract:
A methodology for secondary math teachers, designed to introduce information technology through Interactive
Instructors of Recreational Mathematics (IIRM) and an electronic ludic learning environment in its practice, is
studied. First, an instrument designed to findthe level of knowledge of the teachers in information technologies
was applied. We show the preliminary results of applying this device in 20 secondary schools of the region,
which allowed us to choose three different representative scenarios, to make the case of study. As a result of the
observations and interviews that were made, we show the form in which the teachers obtained a greater degree
of interaction and participation from the students in the particular subjects that were taught. It allowed them
to identify different levels of abilities and different learning progress among the students. Another important
result of the investigation is the stable and reliable answer of the learning environment in realistic scenarios.
1 INTRODUCTION
In recent years, the ludic approach for teaching math-
ematics supported by information technology, has ac-
quired relevance due to its capability of engage stu-
dents towards mathematics learning. Some of the dif-
ferent approaches used electronic learning environ-
ments (Sanch´ez, 1998) and computers games (Gorriz
and Medina, 2000; Gros, 2002). However, according
with (Wishart, 2000), the introduction of new technol-
ogy for learning requires the development of a learn-
ing environment founded on solid learning models.
In M´exico, most of the public secondary schools
have at least one computer laboratory, used mostly
for student’s training on the use of, the computer it-
self and office software. Thus, students and teachers,
including of course mathematics teachers, don’t use
these facilities in a regular basis for teaching. (Cabero
et al., 1997) says that some of the reasons teachers
don’t use the computer in the classroom, is the lack of
knowledge on its use for teaching as well as a negative
attitude towards them. We consider that the teacher
is, perhaps, one of the most significant factor for the
learning experience of the students in a classroom.
As an effort to improve mathematics learning us-
ing information technologies, we have developed an
electronic learning environment based on Interac-
tive Instructors of Recreational Mathematics (IIRM)
(L´opez-Morteo and L´opez-Mariscal, 2005), follow-
ing in part the recommendations of the USA National
Council of Teachers of Mathematics (NCTM, 2002)
for the use of information technology for teaching
mathematics. We have developed a test collection of
IIRM corresponding to a couple of topics of the cur-
ricula of mathematics courses of secondary Mexican
schools, as intent to incorporate it into regular learn-
ing activities in the classroom. The importance of the
search of new alternatives that improve mathematics
learning outcomes in our students is stressed by the
results of national (Backhoff et al., 2006) and inter-
national evaluations (OCDE, 2001), where Mexican
students show a very low performance for applying
its mathematical knowledge to solve problems.
Although remarkable studies have been made
about the impact on learning of electronic devices
(Cedillo, 2001), we believe there is a lack of stud-
554
López-Morteo G., Galaviz-Férman M., López G. and Andrade-Aréchiga M. (2007).
THE USE OF INTERACTIVE INSTRUCTORS OF RECREATIONAL MATHEMATICS IN SECONDARY SCHOOLS.
In Proceedings of the Third International Conference on Web Information Systems and Technologies - Society, e-Business and e-Government /
e-Learning, pages 554-558
DOI: 10.5220/0001290505540558
Copyright
c
SciTePress
ies about of the programs by which the teachers have
to be trained for a successful adoption of new technol-
ogy in the classroom. In this sense, is not clear to what
extend teachers’ attitudes towards the use of comput-
ers contributes to its adoption for teaching as an strat-
egy to improving learning. Also, we are certain that
we need to develop a program for teacher training on
pedagogical models that use technology as a learn-
ing strategy. According with this approach, in this
paper, we present the preliminary results of a study
of the computational literacy of Mexican teachers of
secondary schools as a critical factor for the adop-
tion of information technology in the classroom. Al-
though initially we include teachers of all the courses
of secondary schools, our main interest focus our
work on mathematics teachers in order to develop a
case study using our electronic learning environment
and the IIRM.
2 THE INTERACTIVE
INSTRUCTORS OF
RECREATIONAL
MATHEMATICS
Since 1999, we have been creating computer-based
instructional material to contribute to the process of
learning mathematics. The main objective has been
to enhance mathematical skills and to help develop
mathematical thought among users. For this pur-
pose, we have been developing educational software
components, specializing in mathematical concepts
presented through recreational mathematics, called
Interactive Instructors of Recreational Mathematics
(IIRM) (L´opez-Morteo and L´opez-Mariscal, 2005).
We build the IIRM from self-contained educa-
tional content, designed to provide a ludic problem-
solving approach for learning mathematical concepts
and promoting a positive attitude towards mathemat-
ics. Conceptually, an IIRM represents an educa-
tional unit, composed of several elements –digital and
rationale– with an instructional purpose on a well-
defined mathematical topic. The IIRM, therefore, can
be virtual laboratories, animated demonstrations, and
simulation tools that represent different metaphors of
computer-aided instruction such as the computer as a
tutor, a pupil, a simulation engine, and as a tool, as
described by (Crook, 1994). The IIRM conceptual ar-
chitecture (Figure 1), consists of several elements that
maintain a relation with the central element, in order
to add some of their features to the main mathematical
topic. These elements are: pedagogical support, ludic
context, interactivity support, the telematics support,
Telematic
support
Interactivity
support
Ludic
context
Metadata
Mathematical
topic
Pedagogical
support
Cognitive
Learning
Theory
Problem
Solving
Orientation
Figure 1: Conceptual model of the Interactive Instructor of
Recreational Mathematics.
and the metadata element. The rationale behind this
model can be consulted in detail in (L´opez-Morteo
and L´opez-Mariscal, 2005).
The learning environment has been tested in short
motivationally oriented math courses for high school
students. Based on different evaluations and a care-
ful appraisal of the general attitude of the students in
the course, the use of the electronic learning environ-
ment, as well as the approach imposed by the IIRM
model shows a positive effect on the students attitudes
towards mathematics. The use of this approach in
formal education could improvestudents’ mathematic
skills, mainly by enforcing the motivational aspect of
the learning process. The Learning Environment pro-
vides a close content-container relationship, resulting
in interesting didactic materials, with which students
using several services provided by the system in an
non-intrusive manner.
Nevertheless, despite the IIRM has been proved
its educational potential, we believe that it is nec-
essary more information about the mechanisms by
means of which teachers can incorporate it in the
classroom. In the very first place, we located teacher’s
computational literacy as a elementary element for
the adoption of these mechanisms, because of that
we conducted a surveybetween teachers of secondary
schools of the city of Ensenada, in Baja California,
M´exico. The survey was intended to classify teach-
ers by its knowledge and skills about the use of the
computer, office software, and Internet tools.
3 METHODOLOGY
The survey was called as Self-Evaluation of Com-
putational Knowledge for Secondary Teachers, was
applied to 20 of 40 secondary schools in Ensenada,
and was answered by 193 teachers representing the
27.3% of the total population of teachers of these
schools. The survey was based on the following pro-
grams, the Internet and Computing Core Certification
THE USE OF INTERACTIVE INSTRUCTORS OF RECREATIONAL MATHEMATICS IN SECONDARY SCHOOLS
555
from Certiport, and the Microsoft Office Specialist.
The items including questions about its perception
of them knowledge on, computer hardware, opera-
tive system, common utility functions to applications
(such as copy, paste, change fonts and layout, between
others), word processor, presentation software, work-
sheet, Internet web applications, and e-mail. On an
exclusive manner for mathematics teachers, we also
include a special section designed as assertions fol-
lowing the classic Likert scale structure with a 4 or-
dinal scale, for their attitudes towards the use of in-
formation technology and recreational mathematics in
education. The survey could be answered via the In-
ternet, as a MS Word file, and in a printed form. As
a complementary note, the last was almost the only
method that teachers used to answer the survey.
4 RESULTS
From the 193 surveys answered, we found that 90.7%
of the teachers have a home computer; from those the
91.4% already use it. The 64.8% has connection to
the Internet, but only the 67.4% use it. Considering
the gender, 61% were females and 39% males. The
age range oscillates between 20 to 65 years old, where
54.7% have less than 40 years. The distribution of age
ranges is presented in Figure 2.
Taking in account all the sections of the survey,
excepting that restricted only to mathematics teach-
ers, the results of the survey indicate that considering
knowledge and skills about the use of the computer,
33.7% of the teachers are located in the without basic
knowledge level, 31.1% are located in the basic level,
26.9% on the medium level, and only the 8.3% falls
in the advanced level. The distribution of the level of
knowledge and skills for the teachers, is presented in
Figure 3.
Its remarkable that despite 82.9% of the teach-
ers manifest that use the computer, almost the third
part of them doesn’t have the minimum knowledge
to use it, according with the requirements specified
in the two certification programs mentioned earlier.
This possibly could be explained if we considered that
most of the teachers only use the computer to perform
very basic activities, such as write a plain document
or simply browse the Internet, using a small number
of applications. Another singular point is that the per-
cent for the below minimum, basic and medium lev-
els have similar values, showing a regular distribution
among the group of teachers. Nevertheless, the to-
tal number of teachers with an advanced level corre-
sponds to the teachers of computer-related courses.
Considering the age variable, the results show that
of the 35.2% of the teachers with a medium and ad-
vanced levels, the 75% has less than 40 years. In the
other hand, we found that in the group of teachers
older than 40 years, are located the 69.2% of the total
teachers than fall in the without minimum knowledge
level.
About the technical knowledge related with the
use of software, results indicate that the 25% of the
teachers doesn’t have a basic knowledge level on the
use of the operative system, but 45% of the teach-
ers use without problem the word processor. About
the common utility functions to applications (such as
copy, paste, select, change fonts, undo, redo, etc.), the
56% feels that manage it very well. However, the sec-
tions of the survey that present the highest proportion
of teachers with the minimum knowledge level are
presentation software and worksheets, with the 46%
and 45% respectively; that is, almost the half of the
group of teachers!
From the sample, the 36% doesn’t have the min-
imum knowledge for Internet browsing, search con-
tent, print it and save it. In this section the rest of
the levels have percent values of 25%, 27% and 12%
for basic, medium and advanced levels respectively,
where only the last two levels (39%) can also use dis-
cussion forums, download files, and manage a book-
mark list. For the e-mail section, the percentages are
very similar to the previous section. Here, the 40%
of the teachers, including the 25% of medium level
an the 15% of the advanced level, doesn’t have prob-
lems reading, replying, resending, and managing their
e-mails, besides they can attach files and use the ad-
dress book. We want to stress that a relative small
number of the teachers sampled, are the only ones ca-
pable to realize some of the typical activities associ-
ated to the use of software for education, especially in
those models that use online applications and Internet
based activities.
4.1 The Attitudes of Teachers of
Mathematics Towards the Use of
Information Technology
29 teachers of mathematics representing the 40% of
the total answered this section. Remembering that
this section was designed as a Likert scale with four
scales, all the answers fall in the positive side of the
ordinal scale, indicating that teachers consider that the
use of recreational mathematics could be favorable to
the learning process, could foster mathematics adop-
tion, and could benefit mathematics learning if they
use the adequate information technology.
The preferred delivery technology for content that
help them to teach mathematics are, in descending or-
WEBIST 2007 - International Conference on Web Information Systems and Technologies
556
der, multimedia cd-rom (93%), web pages with multi-
media content (79%), web pages with links for down-
loadable software (72%), discussion forums (10%)
and chat rooms (8%). As a remarkable finding of
these teachers, is that 31% of them have used infor-
mation technology in their classes, where 66% has a
medium knowledge level. According with (Heuvelen,
2001), teachers with experience in the use of the com-
puter and technology innovations have proneness to
adopt technology in their regular teaching activities.
Considering that the average knowledge in the use
of information technology of the teachers sampled
falls in the basic level, it could be possible that this
lack of knowledge and skills limits the adoption of
teaching models that use interactive computer-based
content and electronic learning environments.
Figure 2: Distribution of ages.
Figure 3: Level of knowledge and skills by age ranges.
WMF=Without Minimum Knowledge, BN=Basic Knowl-
edge, MN=Minimum Knowledge, AN=Advanced Knowl-
edge.
4.2 Case of Study
In the first quarter of 2006, we conducted a field study
in three secondary schools in the city of Ensenada.
Two of them are public schools and one are a pri-
vate school, we selected this three schools to perform
a study following ethnographic techniques. We con-
sider their computational infrastructure, how teachers
used and the frequency students use it. In the study,
participated three mathematics teachers of third year
with groups of students between 14 to 15 years old
(third grade of secondary school). Only the teacher of
the private school reports that she has used informa-
tion technology in her pedagogical practice.
We developed three IIRM for the curricular units
according with the official Mexican program, follow-
ing the suggestions and requirements of the teach-
ers. The mathematical topics covered were factoriza-
tion, parabola and Tales theorem. All of them can
be consulted in Spanish at http://azul.cicese.mx/ ga-
lopez/marcos/semejanza/semejanza.html. The three
IIRM follows the conceptual model presented be-
fore, providing interaction, a ludic approach and a
problem-solving orientation.
Teachers were trained on the use of the electronic
learning environment and the IIRM, with a training
program developed exclusively for them in accor-
dance with their knowledge and skills profiles derived
from the preliminary survey. We emphasize the ser-
vices that the learning environment provides, the ped-
agogical model embedded in the IIRM, how they can
use it in the class, how the IIRM validate student’s re-
sponses, and how they can solve simple technological
problems with the learning environment. The training
was performed using their schools computer labora-
tory. Each teacher had the freedom of selecting the
way they can use the software with their students.
4.3 The IIRM in the Classrom
For this phase, we used qualitative observation tech-
niques, a questionnaire and interviews with the teach-
ers.
About the reliability of the learning environment.
The system performs very well along the study. The
three teachers believe the stability of the platform as
an important factor for its adoption during the teach-
ing process. They considering its use as transparent
for the user, and work in every case without any trou-
ble. As a remarkable point, we want to say that the
learning environment has been working since 2001
without interruptions.
About the use of the IIRM from teachers point
of view. Due to the learning environment worked
with no complications, teachers have agreed that nav-
igation through the platform were easy and the in-
terfaces were simple to use. During the interview,
teachers said while students worked with the IIRM,
they had a better degree of interaction and attended
more students during the class in the computer labo-
THE USE OF INTERACTIVE INSTRUCTORS OF RECREATIONAL MATHEMATICS IN SECONDARY SCHOOLS
557
ratory compared with a typical day in the classroom.
However we saw that the degree of interaction with
students depended on the personality of the teachers.
Two of the teachers considered useful to navigate the
IIRM structure from the beginning to the end in or-
der to accomplish the educative objective for that day,
nevertheless the remaining teacher used only the em-
bedded software to explore deeper the mathematical
topic and to reinforce the concepts. During the class,
we observed that the learning model associated with
the use of the learning environment and the IIRM
fostered collaborative work among students. In two
schools, due to the positive results with the students,
teachers decided to repeat the experience with another
two groups.
About the use of the IIRM from students point of
view. Students used the computer in groups of two to
three. Nevertheless, some of the students work alone
following the linear structure of the IIRM. Along the
study, we observedthat the interactiveembedded soft-
ware completely captures student’s attention.
From the observations performed during the
classes, we found that a critical factor that determines
a successful experience of the teachers with the use
of information technology was the technical support
provided during the first sessions with students. We
believe that the training for teachers in the use of new
technologiesin the classroom, should not be restricted
to a one-time workshop, but it should be extended
to the early phases of the adoption of this new way
of teaching mathematics. We strongly suggest that
teachers really need tutoring during this process.
5 CONCLUSIONS
(Braak, 2001) reports that experienced teachers on the
use of information technology tend to perform bet-
ter in the adoption of the technology in their practice.
However, this preliminary study shown teachers with
a basic level of knowledge and skills on the use of in-
formation technology and with a positive attitude to-
wards its use, can incorporate it for teaching if they
have an adequate training. Nevertheless, we believe
that is indispensable that teachers should been intro-
duced to the new educational models that incorporate
computer-based learning activities.
ACKNOWLEDGEMENTS
This work was sponsored, in part, by the Consejo Na-
cional de Ciencia y Tecnolog´ıa through a scholarship
for second author.
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