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

 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-

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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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