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tem journal volume 11 issue 2 pages 876881 issn 22178309 doi 10 18421 tem112 48 may 2022 effective methods for teaching mathematics and informatics in higher education in the digital ...

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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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...Tem journal volume issue pages issn doi may effective methods for teaching mathematics and informatics in higher education the digital world zlatinka kovacheva kalinka kaloyanova ina naydenova emiliya saranova institute of bulgarian academy sciences acad g bonchev str bl sofia bulgaria university mining geology prof boyan kamenov st kl ohridski tsar osvoboditel blvd abstract present paper we would like to emphasis training is shifted from share our technology enhanced interactive student accumulation memorization knowledge centric approach applied during long lived analysis extraction useful information needed experience solve specific practical tasks institutions goal develop a very challenging active engagement centered environment process because nature theoretical instead traditional instructor formulations many students find thinking based on cooperative difficult therefore must provoke learning flipped guided discovery laboratory interest order overcome their simulations investig...

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