Research Article, Res Rep Math Vol: 2 Issue: 3
Students Perception of the Mathematical Classroom while Integrating Digital Technologies
Irina Gurevich^{*} and Mercedes Barchilon BenAv
Department of Mathematics, Achva Academic College of Education, Israel
*Corresponding Author : Irina Gurevich
Department of Mathematics, Achva Academic College of Education, Israel, Arugot, 7980400, Israel
Tel: +97288588000
Email: [email protected]
Received: August 07, 2018 Accepted: August 13, 2018 Published: October 20, 2018
Citation: Gurevich I, BenAv MB (2018) Students Perception of the Mathematical Classroom while Integrating Digital Technologies. Res Rep Math 2:3.
Abstract
In the current research, we were interested in testing the impact of integrating technology on student’s perception of different mathematical courses regarding the constructivist versus traditional approach to teaching/learning. The study was performed in the mathematics department of our College of education. We analysed the students’ perception of our mode of teaching as well as of their own level of involvement in the learning process with respect to the usage of different digital tools according to the basic characteristics of the traditional versus the constructivist classroom. We compared the students’ assessment of the mathematical classroom in different courses that were taught with and without technological tools. The obtained results show that the students' perception of mathematical class while integrating technology corresponds to the basic characteristics of the constructivist class, whereas the class without the use of technology corresponds to the description of the traditional one. This result strengthens our suggestion that the appropriate usage of technology in teaching mathematics enables to transform the classroom from traditional to constructivist one.
Keywords: Mathematical classroom; Digital technologies; Teaching mathematics
Introduction
Over the few last decades the technology has become an integral part in mathematics classroom. Numerous recent studies indicated that integration of technology in teaching mathematics improves significantly mathematical learning [1,2]. Goos, claimed that technology integration offers many opportunities for creativity and a collaborative interactive and dynamic learning experience [3]. She states that embedding technology into mathematical classes can bring the teaching of mathematics to a completely different and much higher level.
Yerushalmy, exemplified how a technologysupported algebra curriculum can assist teachers in making powerful mathematical ideas accessible to learners [4].
Tabach et al. [5] presented a research on learning algebra in a technological environment, which supports students in becoming autonomous learners of algebra. Naftaliev and Yerushalmy [6], found that Narrating Interactive Diagrams can be a form of instruction toward the development of new mathematical knowledge for students.
Hall and Chamblee [7] discussed the benefits of GeoGebra usage in teaching graduatelevel geometry and algebra content courses in a teacher education program. The authors’ observations were that most mathematics teachers were excited when they first learn about GeoGebra and its various capabilities, and were eager to begin incorporating it in their own classrooms immediately. Budinski and Takaci [8] described their experience of GeoGebra usage in modellingbased teaching of mathematics. Gurevich is currently using GeoGebra to teach plan transformations in geometry course in a teacher education program [9,10]
The use of smartphones technology in classroom improves learning [11,12]. Moreover, Barchilon BenAv and Gurevich [13], showed that the use of the GeoGebra Mathematics App for smartphone enhances active students’ participation in the lessons and faster assimilation of the course material.
Abramovich presented a detailed review on various usage of modern digital technologies such as GeoGebra, Matematica, the Graphic Calculator, Matlab, Maple in teaching mathematics [14]. He stated that using digital technologies makes it possible to study traditionally difficult and conceptually rich topics in a new way. He noted that the appropriate use of computers in the schools can promote an experimental approach to mathematics that might improve the balance between informal and formal teaching and learning of mathematical ideas. Sachs, stated, that, as a result of integrating technology, even the teachers' way of “doing mathematics” may change  from the belief that in mathematics there are only correct or incorrect statements to the belief that mathematics may mean the process of solving a particular mathematical problem, while refining the understanding and clarifying the correct mathematical ideas [15]. Therefore, teacher educators could foster students’ skills of critical thinking by planning a lesson in line with the constructivist approach while integrating technological tools [16]. The constructivist approach to teaching and learning believes that development of pupils' understanding requires the learners' active construction of knowledge. Today, in the era of information explosion, we, as educators, should encourage pupils and students to foster independent learning and to use social communication. The constructivist approach intelligently utilizes a wide variety of computer capabilities to create a computerized learning environment which facilitates constructivist teaching methods [17].
Brooks and Brooks, defined constructivist mathematics classroom as a classroom where a concept development and construction of learner’s own solution is more important than memorizing procedures and formulas and using them to get the right answer [18].
According to constructivist approach, teacher behaves in an interactive manner. Brooks and Brooks described constructivist classroom versus traditional as follows:
Traditional Classroom characteristics: strict adherence to a fixed curriculum; curricular activities rely heavily on textbooks and workbooks; students are viewed as ‘blank slates’ onto which information is etched by the teacher; teachers generally behave didactically, disseminating information to students; teacher seeks the correct answer to validate student learning; assessment of student learning is viewed as separate from teaching and occurs almost entirely through testing.
Constructivist Classroom characteristics: pursuit of student questioning; curricular activities rely heavily on primary sources of data and manipulative materials; students are viewed as thinkers with emerging theories about the world; teachers generally behave interactively, mediating the environment for students; teachers seek the students’ point of view in order to understand their present conceptions for use in subsequent lessons; assessment of student learning is interwoven with teaching and occurs through teacher observations of students at work and through student exhibitions.
Ertmer, claims that the effectiveness of technology integration into teaching is strongly related to instructors’ pedagogical beliefs, which is in good agreement with the constructivist approaches to building knowledge [1921].
However, AbboudBlanchard and Lagrange [22] noted that although many technologybased innovations for improving the teaching and learning of mathematics have been developed and tested by research methodologies, still a common impression is that there is a wide gap between these innovations and the actual situation of classroom use of technology.
Educational researchers widely agree that one of the critical factors that can lead to the effective integration of technology into teaching is teachers’ belief that technology can improve learning [2326]. Unfortunately, a lot of mathematics teachers still worry that technology might harm the development of formal thinking in math students although they accept the advantages of computer visualization.
Motivation of the Study
Our research is based on a series of studies on the integration of technology into mathematics teaching conducted over the past approximately 15 years. The obtained results point to the improving both students’ usage of digital software and their overall achievement. In addition, we observed a significant improvement in students' attitudes towards integrating technology in mathematical courses [27]. We observed that the students while experimenting with the dynamic mathematical software created their own knowledge based on their findings. Moreover, the students’ questions led to additional elaborations of the studied topics, i.e. the learning activity became interactive. Thus, we as instructors realized that due to the integration of digital tools into our teaching, our classroom went through significant changes in both the mode of our teaching and the level of involvement of our students in the learning process [10].
Based on our own teaching experience, we believe that teaching mathematics in a computerized environment contributes to better understanding the formal subjects taught in mathematical courses. The students understand that although ultimately there must be a formal answer to a mathematical problem, there are various ways to reach the solution. Thus, we suggest that a computerized environment can improve both learning in class and working at home while preparing assignments.
In the current research, we were interested in testing whether our perception of the classroom as a constructivist one, coincides with the corresponding perception of our students.
Our research questions were:
What are the students’ attitudes towards integrating digital technologies into the teaching process?
How the students perceive the impact of digital tools on:
a. The mode of our teaching;
b. On the level of their involvement in the learning process?
Referring to these questions, we designed a research project in which we analysed several courses we taught embedding different digital tools if at all.
Methods
The research was conducted over the academic year 20172018. The participants were 47 studentteachers in the educational program for secondaryschool mathematics teachers in the Mathematics Teaching Department at a College of Education. The students participated in the following courses: Calculus, Analytic Geometry, and Function Theory. These courses were classified into two categories according to whether digital tools were used or not in the teaching process:
Control Group (18 participants in the Calculus course)  no digital tools were used.
Digital Tools Group (29 participants in Analytic Geometry and Function Theory courses) – two digital tools were used, namely, GeoGebra and Socrative Smartphone App. Socrative was used at the beginning of each lesson. This application enables creating a set of questions that can be deployed during the class. At the beginning of the class the students were instructed to answer a quiz composed of three to five review questions referring to the material of previous lectures. GeoGebra was used in most of the lessons. New topics were explained and presented both analytically and using GeoGebra.
To answer the research questions, we built a multiplechoice questioner. The questioner was formulated regarding basic characteristics of the constructivist versus traditional classroom defined by Brooks and Brooks [18]. All the students in the courses that took part in the study, were asked to answer the questioner (more than one answer could be marked). The questioner was:
Does any digital application is used in the course?
No.
Yes, Geogebra.
Yes, Socrative.
Do the computerized tools help you?
No.
Yes, helps to understand the material.
Yes, increases motivation to learn.
Yes, gives a didactic model to emulate.
Lesson plan:
Determined in advance by the lecturer.
Flexible and might be updated according to the students' questions.
Teaching material:
Relies on textbooks/work pages.
Includes active participation of the students in experiential/research activities.
Learning method.
Students are not involved in the process of imparting knowledge.
Students take an active part in the process of building the knowledge.
The lecturer teaches:
In a frontal manner without involving the students.
Interactively and contributes to the students' active participation.
Solving exercises in class:
The lecturer asks a question and waits for a correct answer.
The lecturer refers to student responses attempting to understand their way of thinking and thus accordingly adapt the course.
The above questions aimed to test both the mode of our teaching (questions 3,4,6) and the level of our students’ involvement into learning process (questions 5,7). In addition, in question 2 we asked about the students' perception of the contribution of digital technology to their learning.
Data collection and analysis
The data consisted of the students’ answers to the questioner. All the data were collected at the end of each academic semester. The data from the questioner were analysed and the frequencies of each answer were calculated for each question in each group. We grouped all the results according to three following categories:
Students’ attitudes towards digital technologies in teaching;
Students’ perception of mode of our teaching;
Students’ perception of their own involvement in learning process.
The results were compared between the two groups, χ^{2} tests were conducted for each category.
Results
Table 1 presents the frequencies of students’ answers to each question, separately for each group.
Group Question  Control Group (18)  Digital Tools Group (29) 
χ^{2} test by course 

Q1 Technology was used: No Yes, GeoGebra Yes, Socrative 
100%  3% 79% 52% 

Q2 Technology helps: No Yes, helps to understand the material Yes, increases motivation to learn Yes, gives a didactic model to emulate 
10% 79% 38% 55% 

Q3 Lesson plan: Is determined in advance by the lecturer Is flexible and might be updated according to the students' questions 
72% 28%  28% 72%  χ^{2} = 8.9525, p = 0.00277* χ^{2} = 8.9525, p = 0.00277* 
Q4 Teaching material: Relies on textbooks/work pages Includes active participation of the students in experiential/research activities 
72% 28%  21% 79%  χ^{2} = 12.2467, p = 0.000466* χ^{2} = 12.2467, p = 0.000466* 
Q5 Learning method: Students are not involved in the process of imparting knowledge Students make an active part in the process of building the knowledge 
67% 33%  7% 93%  χ^{2} = 18.9712, p = 000013* χ^{2} = 18.9712, p = 000013* 
Q6 The lecturer teaches: In a frontal manner without involving the students Interactively and contributes to the students' active participation 
67% 33%  0% 100%  χ^{2} >22.18, p <0.000002* χ^{2} >22.18, p <0.000002* 
Q7 Solving exercises in class: The lecturer asks a question and waits for a correct answer The lecturer refers to student responses attempting to understand their way of thinking and thus accordingly adapt the course 
33% 67%  10% 90%  χ^{2} = 3.7911, p =0.051526 χ^{2} = 3.7911, p =0.051526 
Table 1: The rate of the students’ answers to each question by two groups.
The results corresponding to the significant differences between the two courses (p0.05) are marked by *.
The results obtained with respect to the denoted categories are described as follows:
1) Students’ attitudes towards digital technologies in teaching
Most of the students of the Digital Tools Group found the digital tools being helpful in their learning, especially for understanding the material (79% of the students). In addition, 38% of the students noted that technology increases the motivation to learn, and 55% of them indicated that technology provides a didactic model to emulate.
2) Students’ perception of our mode of teaching
The students’ answers referring to this category, namely lesson plan, teaching material and the lecturer teaches revealed significant difference between the groups: most of the students’ answers of the Control Group (about 70% of the students) indicated that the lesson plan was determined in advance by the lecturer and the teaching material mostly relies on the textbooks, while most of the students of the Digital Tools Group (about 70% of the students) think that the lesson plan is flexible, depends on the students questions and implies their active participation in learning activity. Furthermore, most of the students of the Control Group (67% of the students) considered the mode of teaching being frontal, while all the students of Digital Tools Group indicated that the mode of teaching was interactive.
3). Students’ perception of their involvement in learning process
The results referring to this category, namely, learning method and solving exercises revealed significant difference only in the students’ perception of the learning methods. Most of the Control Group (67%) indicated that they are not involved in the process of imparting knowledge, while most of the Digital tools Group (93%) believed that they make an active part in the process of building the knowledge. Besides that, 90% of the Digital tools Group students believed that the lecturer attempted to understand their way of thinking and thus accordingly adapt the course.
Discussion
We, as instructors, understand how difficult is to change the method of teaching established for years. At the same time, it is obvious that in our day classroom, students become an active part in building knowledge process.
Based on our own teaching experience, we believe that teaching mathematics in a computerized environment contributes to understanding of the formal subjects taught in mathematical courses. The students understand that although ultimately there must be a formal answer to a mathematical problem, there are various ways to reach it. Thus, a computerized environment can improve both learning in classroom and working at home while preparing assignments.
The obtained results indicated that according to the students’ opinion, digital technologies help to understand the material and provide a didactic model to emulate, make teaching more flexible in matching the students’ needs and making it possible for students to become an active part in the process of building the knowledge. Moreover, it was observed that students believe that the use of technology affects the mode of teaching and the level of their involvement in the learning process. Thus, the obtained results strengthen our suggestion that integrating technology in teaching mathematics enables to transform the classroom from a traditional to a constructivist one.
Conclusion
We believe that integration of digital technology enables to combine the formal teaching of mathematics with the constructivist approach in teaching. Our findings concur with relevant studies, demonstrating the ability of the instructor to take advantage of the dynamic environment when the pedagogy of the course was entirely technologyoriented, claiming that the constructivist approach intelligently utilizes a wide variety of computer capabilities to create a computerized learning environment that facilitates constructivist teaching methods [1,17].
References
 Monaghan J (2001) Teachers’ classroom interactions in ICTbased mathematics lessons In: Heuvel MVD Proceedings of the 25th International Conference for the Psychology of Mathematics Education 3: 239257.
 Hollebrands KF (2007) The role of a dynamic software program for geometry in the strategies high school mathematics students employ. Journal for Research in Mathematics Education 38: 164192.
 Goos M (2012) Digital technologies in the Australian curriculum: Mathematics—a lost opportunity? In: Atweh B, Goos M, Jorgensen R, Siemon D (2012) Engaging the Australian National Curriculum: Mathematics—Perspectives from the Field, 135–152. Mathematics Education Research Group of Australasia.
 Yerushalmy M (2009) Technologybased algebra learning, epistemological discontinuities and curricular implications In: Schwarz BB, Dreyfus T, Hershkowitz R (2009) Transformation of knowledge through classroom interaction, Routledge, London, UK.
 Tabach M, Hershkowitz R, Dreyfus T (2013) Learning beginning algebra in a computerintensive environment. ZDM 45: 377391.
 Naftaliev E, Yerushalmy M (2013) Guiding explorations: Design principles and functions of interactive diagrams. Computers in the Schools 30: 6175.
 Hall J, Chamblee G (2013) Teaching algebra and geometry with GeoGebra: Preparing preservice teachers for middle grades/secondary mathematics classrooms. Computers in the Schools 30: 1229.
 Budinski N, Takaci D (2013) Using Computers and Context in the ModelingBased Teaching of Logarithms. Computers in the Schools 30: 3047.
 Gurevich I, Gorev D (2012) Examining the impact of an integrative method of using technology on students’ achievement and efficiency of computer usage and on pedagogical procedure in geometry. The International Journal for Technology in Mathematics Education 19: 95104.
 Gurevich I, Barchilon BenAv M (2017) The impact of technology use on the curriculum of the course “Plan Transformations in geometry”: a selfstudy. Submitted to Proceedings of the 13th International Conference on Technology in Mathematics Teaching ICTMT13, France, UK.
 BenAv R, Barchilon BenAv M (2013) Physics Laboratory in Your Pocket, 5th International Conference on Education and New Learning Technologies (EDULEARN13), July 13, 2013, Barcelona, Spain.
 Barchilon BenAv M, BenAv R (2016) Smartphones: From Distraction to Attraction. Journal of Educational Technology Systems 45: 93102.
 Barchilon BenAv M, Gurevich I (2017) Impact of GeoGebra Apps in Courses. (EDULEARN17), Barcelona, Spain.
 Abramovich S (2013) Computers in mathematics education: An introduction. Computers in the Schools 30: 411.
 Sachs JM (2014) Managing the challenges of technology to support learning: Some lessons from experience. In: Gosper M, fenthaler S: Curriculum models for 21st century: Using learning technologies in higher education, Springer, UK.
 Handal B, Campbell C, Cavanagh M, Petocz P, Kelly N (2012) Integrating technology, pedagogy and content in mathematics education. Journal of Computers in Mathematics and Science Teaching 31: 387413.
 Eshet Y, Hammer R (2006) Principles of design and analysis of computerbased learning environments. The Open University of Israel, ISrael.
 Brooks JG, Brooks MG (1993) The case for constructivist classrooms. Alexandria, Va.: Association for Supervision and Curriculum Development.
 Ertmer PA (2005) Teacher pedagogical beliefs: The final frontier in our quest for technology integration. Educational Technology Research and Development 53: 2539.
 Noss R, Hoyles C (1996) Windows on mathematical meanings: Learning cultures and computers. In: Bishop AJ, Mathematics Education Library 17: 1115.
 Zellermaye M, Mor N, Heilweil I (2009) The intersection of theory, tools and tasks in a postgraduate learning environment In: Payne CR, Information Technology and Constructivism in Higher Education: Progressive learning frameworks, PA: IGI Global, USA.
 AbboudBlanchard M, Lagrange JB (2007) Uses of ICT by preservice mathematics teachers: Towards a professional instrumentation? Int J Technol Math Educ.13: 183190.
 Drijvers P, Kieran C, Mariotti MA, Ainley J, Andresen M, et al. (2010) Integrating technology into mathematics education: Theoretical perspectives.
 So HJ, Kim B (2009) Learning about problem based learning: Student teachers integrating technology, pedagogy and content knowledge. Australasian Journal of Educational Technology 25: 101116.
 Chawla N, Mittal AK (2013) Pedagogy of mathematics: role of technology in teachinglearning mathematics. Journal of Indian Research 1: 105110.
 Torner G, Rolka K, Rosken B, Sriraman B (2010) Understanding a teacher's actions in the classroom by applying Schoenfeld's theory teachingincontext: Reflecting on goals and beliefs In: Sriraman B, English L, Theories of mathematics education: Seeking new frontiers. Advances in Mathematics Education 4: 401–420.
 Barabash M, Gurevich I, Yanovski L (2009) Usage of computerized environment in the course "Plane Transformations and Constructions in Geometry. The International Journal for Technology in Mathematics Education, 16: 4962.