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TEM Journal. Volume 11, Issue 2, pages 876‐881, ISSN 2217‐8309, DOI: 10.18421/TEM112-48, May 2022.
Effective Methods for Teaching Mathematics
and Informatics in Higher Education
in the Digital World
1,2 3,1 1 1
Zlatinka Kovacheva , Kalinka Kaloyanova , Ina Naydenova , Emiliya Saranova
1Institute of Mathematics and Informatics, Bulgarian Academy of Sciences,
Acad. G. Bonchev Str., bl. 8, Sofia, Bulgaria
2University of Mining and Geology, Prof. Boyan Kamenov Str., 1700 Sofia, Bulgaria
3 Sofia University St. Kl. Ohridski, 15, Tsar Osvoboditel Blvd., Sofia, Bulgaria
Abstract – In the present paper we would like to The emphasis of the training is shifted from the
share our technology enhanced, interactive and student accumulation and memorization of knowledge to the
centric approach applied during our long-lived analysis and extraction of useful information needed
experience in teaching mathematics and informatics in to solve specific practical tasks.
higher education institutions. Our goal is to develop Teaching mathematics is a very challenging
active-engagement student-centered environment process because of the abstract nature of theoretical
instead of the traditional instructor-centered formulations. Many students find abstract thinking
environment. Our teaching is based on cooperative difficult. Therefore, teaching methods must provoke
learning, flipped learning, guided discovery, laboratory the interest of students in order to overcome their
approach, simulations and investigations. It is oriented feeling of anxiety. Mathematics helps humanity to
and involves
to the application of modern technologies
research elements. understand the world but many students have
Keywords – student-centered environment, flipped difficulty realizing the relation of mathematical
learning, guided discovery, simulations, research based statements to real life. Providing application
examples and including research experience
teaching, interdisciplinary approach. motivates the students.
1. Introduction Besides, it is important to understand that learning
is not only acquisition of knowledge and skills but
The training of students nowadays, in the also a social process [1]. Most of the methods require
conditions of the large volume of information from teachers not only to organize the material and
numerous digital sources, is a great challenge for educational goals for the learning process, but also to
teachers. model and moderate the interactions between
students and between students and teachers. These
extra efforts are worth it because the interactions
DOI: 10.18421/TEM112-48 have a positive influence on the learning outcomes as
https://doi.org/10.18421/TEM112-48 discussed in [2].
Corresponding author: Zlatinka Kovacheva,
2. Pros and Cons of the Main Training
Institute of Mathematics and Informatics, Bulgarian Methods
Academy of Sciences, Sofia, Bulgaria. Applied in our Practice
Email: zkovacheva@math.bas.bg
Received: 13 March 2022. The most traditional method is exposition – the
Revised: 25 April 2022. teacher explains the main concepts, gives examples
Accepted: 03 May 2022. and provokes a dialog with the students. This method
Published: 27 May 2022. is widely used. It requires less preparation, especially
for teachers with long experience. But it is not a
© 2022 Zlatinka Kovacheva et al; published student centric approach and the students find it
by UIKTEN. This work is licensed under the Creative boring because of their passive role.
Commons Attribution‐NonCommercial‐NoDerivs 4.0 Present students like to be involved more actively
License. in the learning process. One of the challenges
The article is published with Open Access at involves games. Learning by playing games activates
https://www.temjournal.com/ their attention and motivates them for better
876 TEM Journal – Volume 11 / Number 2 / 2022.
TEM Journal. Volume 11, Issue 2, pages 876‐881, ISSN 2217‐8309, DOI: 10.18421/TEM112‐48, May 2022.
understanding and retention. Games are effective an approach requires a high degree of teachers’
tools for simulation of real world problems. There efforts but makes the teaching process very effective
are many web resources such as Kahoot, Quizlet, and applicable to the real life. This method highly
Socrative, etc. which can be used for organizing motivates the students and leads to their satisfaction.
games. But compiling materials for organizing games They develop their own spirit of inquiry.
is a time consuming process and sometimes it is Investigation is oriented to the highest level of the
difficult to control the students and prevent the noise. Bloom’s taxonomy pyramid - “Create – produce new
Unfortunately, this approach is not suitable to all or original work”. It can be combined with the
topics of the syllabus and it should be applied method of co-operative learning.
precisely and with measure. The Laboratory approach or “learning by doing” is
Playing games combines well with the method of used to build readiness for the development of more
co-operative learning – students work in groups, abstract concepts. For example, teaching theoretical
discussing the solutions to the problems. This method concepts of mathematics, combined with laboratory
encourages the team work and social interaction. The experience of numerical methods and programming
role of the teacher is changing from leader to or physical experiments illustrates the material taught
facilitator and initiator. This method develops a sense and makes it more accessible to students. In the field
of responsibility to other members of the group and of informatics, the approach of “learning by doing” is
contributes to the concentration and realization of the very well accepted by the students, but there is a
full potential of students. It is successfully applied certain risk of applying ready-made templates in
for the tutorials. The main disadvantage of the solving specific tasks without fully understanding the
method is the difficult management of all groups concepts behind the solution applied.
simultaneously. The method of simulations provides a
From our experience, мany students prefer group reconstruction of a situation or series of events that
learning because of the opportunity to participate may happen. A simulation requires each student to
more actively in the learning process, to express their make decisions based on previous training and
opinions without worries and to compare their available information. It is a student-centered
assimilation of the material with the other approach to learning. Very often this method is
participants in the group. The competition between combined with the co-operative learning and relates
the groups motivates the students to develop their full mathematics to “real life situations”. Unfortunately,
potential and to feel satisfied with their efforts. like playing games, this method is not applicable to
During the online education, working in groups is all topics of the subject. It is time consuming for the
facilitated by the set of mobile applications, as Viber, teacher and may provoke more than permissible
WhatsApp, Kahoot, etc., that can be used for emotions and noise among the students but the
tutorials, homework or course projects. advantages are more than the limitations.
One of the most provocative teaching methods is We can summarize the application of the presented
guided discovery. It is opposite to the exposition methods from the revised Bloom’s taxonomy point
method and matches the category of synthesis of the of view in Table 1.
Bloom’s taxonomy [3]. The learners are not given
the rule or generalization. On the base of series of Table 1. Teaching methods/ Bloom’s taxonomy
examples or particular situations, the students have to
discover the generalized rule. For example, teaching Teaching method Bloom’s Taxonomy level
derivatives or integrals of polynomials, the teacher Exposition Remembering
can show the derivatives or integrals of some Understanding
polynomials and the students discover the rule Playing games Understanding
themselves. Self-discovery of the generalized rule Applying
leads to its more permanent memorization and Co-operative learning Understanding
application. Sometimes the students find difficulties Applying
which can lead to frustration. In such case, the Guided discovery Analysing
teacher has to assist and guide them, directing them Synthesis
to the right answer. Analysing
One form of discovery is investigation. Applying Investigation Evaluating
this method, the students define the problems, set the Creating
procedures and try to solve them. Investigation is Analysing
time consuming and it is very good for home works, Laboratory approach Evaluating
course works or group projects. Sometimes, more Creating
than one solution are correct. This provides an Analysing
opportunity to develop students' creative abilities and Simulations Evaluating
Creating
leads to improving their adaptive capabilities. Such
TEM Journal – Volume 11 / Number 2 / 2022. 877
TEM Journal. Volume 11, Issue 2, pages 876‐881, ISSN 2217‐8309, DOI: 10.18421/TEM112‐48, May 2022.
3. Some Innovative Approaches to the Teaching- start with the active participation of students in the
learning Process learning process. They should be given small tasks
which they can perform easily and willingly. The
3.1. Linking Research into Teaching independent participation of students in the learning
process can be carried out by the method of flipped
The knowledge of mathematics and informatics is learning - a student-centric pedagogy in which
useful and motivates students when it can be applied lecture is moved to the online environment and class
to particular situations in practice. Linking research time is spent engaging in active learning experiences
into teaching enhances the following important [7]. We provide students with materials - articles,
graduate attributes: critical understanding, awareness lectures, video tutorials, etc. on which they prepare to
of the provisional nature of knowledge; ability to understand the new topic of the syllabus and during
identify the problems/issues and evaluate and apply the class meeting the topic is discussed and specific
evidence based solutions. Students highly appreciate tasks are solved. In this way, the students are more
home works and course projects which involve actively engaged in the learning process and they
research elements. They feel themselves as co- take their learning responsibilities more seriously.
creators of knowledge and build their own worldview Flipped learning has many advantages: it creates
through experience. dynamic and interactive learning environment,
The research experience of the lecturer plays a key develops students’ creativity and engagement, gives
role in the successful implementation of this them more control over their education. But there are
approach. Our long research experience in the fields also disadvantages: self-preparation takes more time
of mathematics and informatics is a prerequisite for for students and creates difficulties for slow learners.
generating ideas in this direction. Also, it is possible to miss understanding some
For master, PhD students and young researchers, important topics of the educational content. The
real tasks are very useful because they usually need preparation of the learning materials is a time
methods on different levels, e.g., conceptual, consuming and difficult task. The teacher must
mathematical, informatical, numerical, and computer carefully choose the material and present it in a clear
modelling, data analyses and visualization. and understandable form. Its volume should not be
Sometimes the method for choosing a suitable too large to avoid overwhelming students.
conceptual method is an important part of the One of the main problems of teaching mathematics
education by investigation and may lead to research or informatics is the need to remind students of
papers [4]. definitions, concepts, rules and syntaxes they have
Integrating research and teaching prepares the studied before. For this reason, it is necessary to add
students to develop strategies, techniques and tools reference materials containing such information.
needed to solve complex and difficult reallife At a more advanced stage, when students have
problems [5], [6]. Students feel themselves engaged understood the usefulness and effectiveness of this
in the process of discovering new knowledge and approach, they are given more challenging tasks,
solutions and this motivates them to perceive such as finding and preparing the necessary materials
learning as an interesting, challenging and useful for the topic. In this case, the teacher and the students
activity. change their roles initially. Individually or in groups,
This approach encourages students not only to they can prepare a presentation of the lesson. The
solve the existing problems but also to create ideas teacher and the other students ask questions and
and other problems which need solutions. The role of provoke discussions. The role of the teacher is to
the teacher in this process is to guide, provoke, focus the students’ attention at the most important
encourage, and distinguish the right from the wrong points and to explain in details the most difficult
solution. topics in such a way that they can be understood even
Integrating research and teaching is a step to by slow learners.
convert the universities to the knowledge-building From our experience, some students like to prepare
communities where academics and students work in themselves videos where they explain the lesson. As
partnership to generate and disseminate knowledge. the students are familiar with the advanced
In these communities, communication is built on the technologies they accept and perform such tasks with
basis of dialogue and discussion, conducted and led pleasure. The learning process is optimized when
by the teachers. students take a leading role.
3.2. Flipped Learning 3.3. Blended Learning
To achieve the long-term goal of creating Blended learning is a pedagogical or educational
knowledge-building communities, it is necessary to approach that combines traditional teaching methods,
878 TEM Journal – Volume 11 / Number 2 / 2022.
TEM Journal. Volume 11, Issue 2, pages 876‐881, ISSN 2217‐8309, DOI: 10.18421/TEM112‐48, May 2022.
such as in a classroom setting, with e-learning The main goal of education nowadays is to create
technology, such as online courses, lectures, habits and skills in students to self-study throughout
presentations, quizzes, games, etc. [8]. It is a hybrid their lives. Familiarity with advanced technology
method which integrates technology and digital creates prerequisites for lifelong learning. Also,
media with traditional lecturer-led classroom online education is a good alternative in emerging
teaching. situations [12].
Blended learning has many advantages as: The application of a variety of ICT tools enhances
flexibility and personalization in creating course the students’ learning experience as well as their IT
modules, interactive simulations, students’ skills [13]. It has a positive influence even on
engagement, independence of geographical teachers. The modern textbooks should be digital
constraints, etc. But it requires high skills in e- books, containing many references to other electronic
learning of teachers and students and significant resources.
investment in technology resources. Teaching mathematics needs to use MATLAB,
From our experience, some students prefer to learn MAPLE, Scilab or other products, designed to
by reading, others prefer learning by doing. Blending connect the theoretical mathematical concepts with
learning provides different approaches: co-operative the solutions of specific applied problems. For
learning, playing games, online quizzes, etc. example, evaluating integrals or solving differential
Unfortunately, there is a lack of access to educational equations is easier using such packages.
technologies for many students but the increasing of Using Concept Maps [14] we present the
open educational resources leads to significant cost information visually – by charts, graphic organizers,
reduction. tables, flowcharts, Venn Diagrams, etc. Concept
Over the last decade, there have been at least five Maps help also to analyze and compare the
meta-analyses that have addressed the impact of information. For example, the similarity and
blended learning environments and its relationship to differences between two ideas can be visualized by
learning effectiveness. These studies have found two intersected circles. To create visual concept
small to moderate positive effect sizes in favor of maps we are using applications like Mindomo,
blended learning when compared to fully online or TheBrain and Miro.
traditional face-to-face environments [9]. Kialo Edu [15] is a very good tool for discussions
Both, flipped learning and blended learning and teaching critical thinking. This is a collaborative
provide an effective way to present the course platform, encouraging students to work together and
materials, engaging students, which is very effective exchange their ideas and opinion. In this way, they
in critical cases as pandemic situations, natural can demonstrate their knowledge and develop critical
disasters, etc. reasoning skills.
Go Animate is a software, available online, which
4. Application of Technology to the Teaching provides the opportunity to include animated objects
Process in the lesson presentation. Animation breaks the
monotony and boosts students’ enthusiasm to learn.
Technology is a key factor for the effective In mathematics and informatics regular revision is
teaching and learning process. The dynamic essential for deeper understanding but repeating the
development of modern knowledge places the main rules using the same methodology is
emphasis in the training on the development of monotonous and ineffective. The important learning
abilities for adaptation and continuous acquisition of outcomes of any topic of the syllabus can be
new knowledge and skills. In the presence of a huge recreated in an animation format at the end of the
amount of information from many sources, it is lesson. Animated characters increase students’
essential that students have the ability to find the interest. They can present a dialog between a teacher
most appropriate information to solve a specific and students. It is more effective when the students’
practical problem. The role of the teacher in this voices are involved in the record. Learners enjoy
process is changing from provider to facilitator. interactive learning through cartoon teaching since it
There are at least five hierarchical levels at which is efficient, effective and flexible. It facilitates the
technologies may be used: presentation, comprehension of abstract concepts and assures a
demonstration, drill and practice, interaction, and more meaningful and permanent learning [16].
collaboration. The potential for interactive and Today's students in higher education belong to the
collaborative learning can be best achieved by so-called Generation Z who was born into integrated
networked computers and connectivity to the World and globally connected world through the Internet.
Wide Web [10]. Online educational frameworks can This generation uses social media and mobile devices
be used even for performing exams and quizzes [11]. before going to school. They are kinaesthetic,
experiential, hands-on learners who prefer to learn by
TEM Journal – Volume 11 / Number 2 / 2022. 879
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