TAXONOMY OF TECHNOLOGY-BASED SUPPORT FOR ACCELERATED LEARNING OF SCHOOL MATH

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TAXONOMY OF TECHNOLOGY-BASED SUPPORT FOR
ACCELERATED LEARNING OF SCHOOL MATH
A. Cunska
Vidzeme University of Applied Science (LATVIA)
Abstract
On the one hand, the Covid-19 pandemic period can be considered as one of the most successful in
the history of school education, as we have become technologically more advanced and digitally
smarter. The pandemic brought as many challenges as schools had not seen in the last century. And it
is clear that in the near future the education system will change significantly and especially in the
direction of acceleration.
On the other hand, distance learning has been a particular challenge for the subject of mathematics.
And schools will need to come up with new 'recovery' strategies in the future to help teachers and
students find and close knowledge gaps. Many students will need extra help in learning math content,
communicating and accepting the new cultural environment of schools.
In this context, the research was motivated by the basic question "What conditions help to learn school
mathematics faster and more efficiently?" As an answer to the question, a taxonomy of technology-
based support for accelerated learning of mathematics (ALOM) in general education schools is
proposed.
The results of a survey of 322 students from various Latvia general education schools and focus group
interviews with 53 Latvia teachers of mathematics showed that the proposed model achieves its goal by
allowing teachers of mathematics to understand the nature of ALOM, identify specific conditions and
select the most appropriate strategies in order to tailor the learning process to each class and each
student individually.
The research is carried out within the framework of the postdoctoral project “Support of Artificial
Intelligence for Accelerated Learning Approach of Mathematics (AI4Math) (1.1.1.2/VIAA/3/19/564)” at
Vidzeme University with the support of ERDF.
Keywords: Accelerated Math Learning, Support System, Technology-Based Learning, Taxonomy,
AI4Math.
1 INTRODUCTION
Every day, we face new challenges in the social, economic and environmental fields, which are also
significantly affected by the rapid pace of technological development. Challenges are our driving force,
creating new opportunities for the development of society. We cannot predict the future, but we must
always be open and ready for what happens next. Children who start school in 2021 will be in the active
workforce in 2040. And teachers must do their utmost to prepare students for professions that do not
yet exist, technologies that are still evolving, global challenges that are not yet foreseeable ([1]). It will
be a shared responsibility of teachers, students, parents and society to find the most effective solutions
that will help to overcome uncertainty, the unknown and failure in collaboration.
It is mathematics that is considered to be the basis of other sciences, which play an important role in
everyday and working life. Mathematics is taught at all levels of education. It has become an important
area in the development of technology, the circular economy and environmental modeling. However,
students still think that learning math is boring. Studies ([2], [3], [4], [5]) indicate a number of worrying
indications that are related to learning mathematics and are still relevant: 1) there are very few people
who are happy to remember their mathematics lessons; 2) many students do not have the pleasure, joy
and motivation to learn mathematics; 3) students' attitudes significantly affect achievements in
mathematics; 4) we lose a large part of our students in the learning process; 5) Reducing and facilitating
the content of mathematics teaching has not resulted in deeper knowledge and better results.
Based on the results of a student survey and teacher focus group interviews conducted by the
researcher in the spring of 2021, there is a belief that the mathematics teaching process is still teacher-
focused and that students are passive listeners. The topicality of the topic is also strengthened by the
Proceedings of ICERI2021 Conference
8th-9th November 2021
ISBN: 978-84-09-34549-6
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continuous discussions in the media of various countries about 1) low results of mathematics in TIMSS
(the Trends in International Mathematics and Science Study) research; 2) the impact of the Covid19
pandemic and the background created in relation to online training; 3) the huge amount of money that
is being spent on providing schools with state-of-the-art technology and the uncertainty of how to use
these technologies productively in the teaching process. In the future, there is great potential for more
effective integration of technology in school mathematics, so that mathematics can be learned not only
faster and more creatively, but also in a fundamentally different way. Schools need to be able to create
an environment and conditions that arouse students' curiosity and enthusiasm so that students' eyes
shine with joy when they go to math’s classes.
In this context, the motivation of the study was created by the problem of teachers' lack of understanding
of the factors that ensure and promote faster and more efficient learning of mathematics. The aim of the
research is to inform educators, content creators, researchers, industry specialists and technology
developers about the principles of accelerated learning of mathematics (ALOM) for a more efficient
learning process, offering technology-enriched taxonomy for faster learning of mathematics in general
education schools. The study includes innovation, as for the first time the definition and taxonomy of
ALOM is proposed, the usefulness of which was confirmed in focus group interviews by 53 Latvian
teachers of mathematics.
2 LITERATURE REVIEW
In order to create a qualitative classification of the support system, it is important to understand the
rationale for education, which is most closely related to the development of technology and the
possibilities of its application in the acquisition of mathematics.
2.1 Taxonomy in Education and Technology
In education, taxonomy or classification is commonly used as a way to describe the different types of
learning behaviors and characteristics that we want to develop in our students. They are often used to
identify stages in the development of training and to provide appropriate support measures ([6]). The
first and most common taxonomy of Benjamin Bloom's educational goals since 1956 is one that
distinguishes 3 psychological domains: Cognitive, Affective and Psychomotor ([7]). In the following
years, several other taxonomies were developed along with a deeper understanding of the meaning of
education. As an alternative to Bloom's taxonomy, in 1982 Biggs and Collis developed the SOLO
(Structure of Observed Learning Outcomes) taxonomy, a systematic way to describe learners' levels of
understanding from the simplest to the most complex: Prestructural, Unistructural, Multistructural,
Relational, Extended Abstract ([8]). In 2007, Churches published Bloom's Digital Taxonomy, which
complemented the existing learning outcome taxonomy with six levels of digital skills: Remembering,
Understanding, Applying, Analyzing, Evaluating, Creating ([9]).
Based on the technology classes of the International Patent Classification (IPC), an Information and
Communication Technology (ICT) taxonomy has also been developed, which defines 13 technology
areas, their corresponding technical features and functions to be performed: High speed network, Mobile
communication, Security, Sensor and device network, High speed computing, Large-capacity and high
speed storage, Large-capacity information analysis, Cognition and meaning understanding, Human-
interface, Imaging and sound technology, Information communication device, Electronic measurement,
Others – ICT related technologies not belonging to any of above categories ([10]).
Equally important to schools is software support that can be used to learn math. Researchers ([11])
have suggested the following taxonomy of mathematics learning software in their study:
1 Practice software, which is easy to use to quickly solve various tasks without the help of a teacher;
2 General software, sections of which teachers can use to teach students specific math topics;
3 Specialized software for learning new content on certain mathematical topics;
4 Virtual environment software;
5 Collaborative software.
2.2 Technology – Enhanced Learning
Since the 1980s, smart learning based on smart technologies has emerged as a new paradigm of
education ([12]). Smart technologies (Cloud Computing, Big Data and Analytics, IoT, Virtual Reality and
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Artificial Intelligence solutions) allow students to learn comfortably in both traditional and technology-
based ways. As a result, technology-enhanced learning (TEL) has gained increasing attention in
educational research. TEL is used to provide a flexible learning process. Technological progress has
affected the way we acquire knowledge and learn. It provides quick access to information, facilitates
collaboration, affects learning efficiency and saves our time. In the field of education, technology enables
access to digital content, creative expression and evaluation. With the development of mobile
technology, learning is possible anywhere and anytime. This is particularly important for the Z
generation, which was born in the age of technology, acquires knowledge mostly through technology
and focuses on finding information quickly. Researchers ([13]) have found that Generation Z students
1) use technology more often than traditional teaching methods, 2) prefer mobile applications to video
content available on the Internet, 3) prefer interactive online forms, 4) follow the example of teachers in
the use of technology, 5) observe others before they start doing the same.
There has been much discussion on how to maintain a balance between traditional learning models and
the use of technology, which has led to the notion of blended learning. “Blended Learning is an approach
that provides innovative educational solutions through an effective mix of traditional classroom teaching
with mobile learning and online activities for teachers, trainers and students. It is the TEL to extend
beyond the classroom walls and facilitates better access to learning resources” ([14]). The main idea of
this study is also based on smart schools, which use a combination of technology and teaching
strategies to provide each student with basic math skills, adapt individual learning trajectories and
improve the classroom atmosphere as a whole. Smart schools also use appropriate learning strategies
online to make the learning process more engaging, motivating and stimulating ([15]).
2.3 Accelerated Learning
To date, there is no clear and uniform definition of the concept of accelerated learning (AL). Researchers
and educational professionals in various fields are constantly discussing the concept of AL. And some
important components are also discussed in the literature. Initially, AL was defined as "faster acquisition
of skills and knowledge" ([16]). Other definitions also focus on the time factor, such as "any learning
system that seeks to optimize learning time in relation to the content acquired" ([17]). Researchers ([18],
[19]) have pointed out that AL is an approach that is used to improve students' learning abilities so that
students can learn faster and more efficiently, and that the learning atmosphere is designed as a fun
and active interaction between students and students. teachers. The involvement of "whole body, mind
and human experience" in the learning process was initiated by Meier ([20]). The Center for Accelerated
Learning (Alcenter) has pointed out that AL is today the most advanced of the methods that make up a
complete system for accelerating the learning process based on the latest brain research. AL is the way
we learn using all human talents: physical, creative, musical, artistic, etc. AL is an activity-based and
student-centered process with the following basic principles ([20], [21]): 1) learning encompasses the
whole human mind and body with all senses and emotions, 2) learning takes place on many levels
simultaneously, 3) learning is the creation of new knowledge and skills rather than consumption, 4)
learning is collaborative, 5) learning takes place through practice, 6) positive emotions greatly improve
learning, 7) visual images make it easier to perceive and store information.
According to Dave Meier, the AL approach helps students to develop a positive attitude towards
mathematics ([22]). The National Institute for Excellence in Teaching (NIET) emphasizes that
accelerated learning in mathematics is usually associated with children gifted with special programs or,
conversely, with students with special needs. It is often controversial, but understanding it in general
encourages greater involvement of teachers in the planning and regular evaluation of the learning
process. Pupils thrive in an environment where their needs are taken into account and their readiness
levels are determined ([4]).
3 METHODOLOGY
In order to find an answer to the research questions and achieve the set goal, the research design
(Figure 1) was created with the following research plan: 1) research of theoretical literature in the fields
of pedagogy, application of technology and acquisition of mathematics; 2) determination of the
ecosystem of accelerated mathematics acquisition by making observations in Latvian educational
institutions with applications of Phenomenology, Ethnography and Narrative approach; 3) analysis of
accelerated learning of mathematics experience data using qualitative methods (student surveys,
interviews with specialists in the field and structured interviews with teachers' focus groups); 4)
triangulation of research results and determination of correlations to increase the reliability of research
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data; 5) development of definitions and taxonomy for accelerated mathematics acquisition; 6) testing
and summarizing conclusions.
Figure 1. Research design scheme, Researcher’s concept
Given that the concept of ALOM is new and little research has been done on it, the Qualitative approach
was used. According to researcher Creswell ([23]), qualitative research is exploratory and useful in
cases where the most important and testable values are not known. And Patton ([24]) has argued that
research is qualitative if it aims to explore what people do, know, and think using a variety of data mining
techniques, such as observation, interviews, surveys, or document analysis. The strategy of the
qualitative approach allowed the study to be more creative and innovative in order to offer a new
taxonomy to school audiences that could affect a large part of the public in the future.
In order to fully explain the significance of the study results, their impact was studied from several
perspectives using a triangulation approach ([25]). By looking at different data sources (students,
teachers, industry professionals), methods (student surveys, industry interviews, teacher focus group
structured interviews) and types of analysis (ethnographic, phenomenological, narrative), the
triangulation approach increased the likelihood of drawing the right conclusions and making better
decisions. as well as increased the reliability and validity of the results.
As the main strategy of the qualitative approach to data analytics, phenomenology was singled out in
order to understand the processes taking place in the human consciousness and in the human world
during the acquisition of mathematics. “Phenomenology involves a change in the “sense of the world”:
everything acquires its sense and value only when it becomes the content of the lived experience of the
subject correlated to his intentional acts. This is the main thesis of the phenomenological method aiming
at overcoming the traditional opposition between rationalism and empiricism” ([26]). During three years
(2018, 2019, 2020), 183 students were observed and in-depth interviews were conducted with open-
ended questions within the mathematics study process for 1st year students of Vidzeme University of
Applied Sciences, as a result of which conditions were determined that motivate students to learn
mathematics better and better ([27]): good teacher explanation (32%), real use of mathematics (28%),
regular practice opportunities (25%), interesting learning approaches (19%), repetition of the subject
matter (14%), digital materials and technology opportunities ( 14%), understanding of the study content
(14%), humor and good attitude (13%), visible presentations (10%), individual consultations (6%),
feedback (5%), etc.
An ethnographic approach was used to study in depth the daily habits of students, teachers and
relationships in the natural school environment. “Educational ethnographic research is a research design
that involves observing teaching and learning methods and how these affect classroom behaviors. This
research model pays attention to pedagogy, its effects on learning outcomes and overall engagements
by stakeholders within the classroom environment” ([28]). As a result, observations were made and
documented over three years in several different schools in Latvia: one primary school, 5 primary
schools, 2 secondary schools and one technical school.
A narrative approach was used for data analysis to document, summarize and structure experiences in
social accounts and media spaces, especially during the Covid-19 pandemic, when there was no
opportunity to meet in person. “Like many research approaches, narrative research is taking new
directions in the digital age” ([29]).
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4 RESULTS
4.1 Results of the Student Survey and Structured teacher interview
Data were collected in several ways and over a longer period of time. First, electronically, by interviewing
students during distance learning in April 2021. The electronic questionnaire was created with Google
Forms and was filled in by 322 students from 1st to 12th grade from different levels of Latvian schools.
The questionnaire contained 26 questions, which were evaluated according to the Likert scale. The
complexity of the questions and the length of the questionnaire were adapted to the age of the students.
In order to verify the usefulness of the electronic questionnaire, discussions of industry experts were
organized, as a result of which two important permits were obtained for the research: 1) from The
Academic Ethics Commission of Vidzeme University of Applied Sciences, 2) from the Government of
Malta for Education Directorate for Research, Lifelong learning and Employability.
Second, a series of structured focus group interviews were conducted with 53 face-to-face, telephone
interviews, and five international online teacher ZOOM conferences.
Figure 2 clearly shows that during distance learning more than half of the students (60%) had stress in
learning mathematics, 68% of students lacked patience to read and understand the conditions of the
tasks correctly, 63% of students felt additional workload, 80% of students lacked teacher explanation,
84 % of students did not have the ability to plan time and learning process independently, 50% of
students needed to learn additional digital skills despite Generation Z abilities and existing skills.
Teachers also pointed out these as the most disturbing things in the focus group interviews, marking
them with sad emotion (L). The following students' answers were mentioned as positive emotional (J)
educators: “the mathematics teacher helps me enough” (69%), “I also have individual consultations
available” (68%), “the math teacher corrects the work fast enough and answers my questions” (63%),
“my workplace at home is comfortable and appropriate” (76%), “I have the right technology” (83%), “I
have a correspondingly fast data transfer” (61%), “I am happy with the technologies and programs we
use” (79%).
Figure 2. Survey of students on the acquisition of mathematics during distance learning in 2021
In focus group interviews, teachers indicated that, given the background created by the COVID
pandemic, they needed significant support from policy makers, academics and scientists to understand
the conditions and ways to learn mathematics in a more innovative, faster and efficient way in the future.
100% of all teachers indicated that the Framework of ALOM developed within the framework of the study
will be an important support in the development of school curricula and environment in the future.
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4.2 Accelerated learning of mathematics: definition and taxonomy
Based on the explanations of accelerated learning found in scientific research, the following definition
of ALOM is proposed: ALOM is a smart approach to the learning process to create a motivating
environment for student-teacher collaboration, resulting in high-quality mathematical competence.
The goal of ALOM is to provide quality learning opportunities for each student to promote the
development and realization of their potential throughout their lives. The tasks of ALOM are: 1) a positive
and creative atmosphere that promotes the well-being, competence and success of students; 2)
productive interaction of students and teachers, which supports positive emotions; 3) a flexible learning
process that responds to the needs of each student; 4) effective teaching strategies that are effective,
interdisciplinary and based on scientific research; 5) Analytics and evaluation to track change, adapt to
needs and promote growth.
At the suggestion of math teachers, the ALOM taxonomy (Table 1) is designed as a daily guide and
guide for math teachers, practitioners, school leaders and policy makers to help take all circumstances
into account and create a supportive environment for accelerated learning. It is just a recommendation
that any user can add to and develop according to their vision. The full description can be obtained by
scanning the QR code shown in Table 1.
Table 1. Taxonomy of accelerated learning of mathematics (ALOM), Researcher’s concept
Universal Design for Learning
Why?
Engagement
What?
Representation
How?
Action & Expression
1. UNDERSTANDING OF THE FRAMEWORK OF NORMATIVE AND
STRATEGIC DOCUMENTS
2. RESEARCH AND DATA ANALYTICS
3. CHOICE OF LEARNING STRATEGIES
4. IDENTIFICATION OF TECHNOLOGY SUPPORT
5. CREATING A SUPPORTIVE LEARNING ENVIRONMENT
6. PROMOTION OF COOPERATION
7. ENSURING BALANCE
8. BRIDGING SOCIAL GAPS
9. USE OF SCIENCE – BASED RESEARCH
10. PROFESSIONAL DEVELOPMENT
11. IDENTIFYING AND ANTICIPATING FUTURE TRENDS
Solo Taxonomy: Prestructural, Unistructural, Multistructural, Relational,
Extended abstract ([8]).
Bloom’s Digital Taxonomy: Remembering, Understanding, Applying,
Analyzing, Evaluating, Creating ([9]).
ICT Taxonomy: High speed network, Mobile communication, Security, Sensor
and device network, High speed computing, Large-capacity and high-speed
storage, Large-capacity information analysis, Cognition and meaning
understanding, Human-interface, Imaging and sound technology, Information
communication device, electronic measurement, Others – ICT related
technologies ([10]).
A Taxonomy of Software for Mathematics Instruction: Practice Software,
General Software, Specific Software, Environment Software, Communication
Software ([11]).
The ALOM taxonomy is designed as a classification system based on the basic principles of
Developmental Teaching and Learning (DTL), that the main goal of teachers is to help students develop
thinking in specific areas so that students can develop independently in areas of interest ([30]). The
basic concept of DTL is focused on the professional support and development of teachers in order to
further provide quality support to students in the learning process and personal development. Teachers
need to develop their own personal learning theory to get rid of dogmas and doubts, to broaden their
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horizons with useful theories and knowledge that help learn students' needs, feelings, interests,
emotions and help create a quality learning environment for productive classroom work. Teachers need
to continually improve in order to learn the most effective teaching strategies, how to analyze and
address the challenges of education and how to understand students' needs ([30]). The essence of DTL
lies in the close cooperation of students and teachers to ensure the efficiency of the learning process.
A conscious learning strategy has been chosen as the horizontal scale of the ALOM taxonomy systemic
matrix, meaning that I take responsibility for purposeful learning myself: What do I learn? Why do I learn?
How do I learn? with matching keywords: Engagement (Why?), Representation (What?), Action &
Expression (How?) ([31]). The following are recommended for the basic elements of the vertical scale
of the ALOM taxonomy systemic matrix: Understanding of the framework of normative and strategic
documents; Research and data analytics; Choice of learning strategies; Identification of technology
support; Creating a supportive learning environment; Promotion of cooperation; Ensuring Balance;
Bridging social gaps; Use of science-based research; Professional development; Identifying and
anticipating future trends. The ALOM taxonomy framework is complemented by other science-based
taxonomies (Solo, Bloom’s Digital, ICT, Software for Mathematics Instruction), which most directly help
to create a technology-rich and balanced learning environment.
Understanding of the Framework of Normative and Strategic Documents – It is important to support
teachers by educating and raising awareness of national normative and strategic documents that
contribute to the achievement of educational goals not only at the classroom but at the national level.
Research and Data Analytics – Big data can show big solutions. It is especially important for teachers
to learn Data Analytics to understand how data can work for us. How and why we access information,
and what we do with it, is more important than the information itself to ensure personalization, knowledge
persistence and transfer ([4]).
Choice of Learning Strategies – Properly chosen learning strategies usually provoke students to actively
think and engage in the learning process. Researchers ([32]) indicate that deep involvement or
immersion in activities and tasks creates positive emotions, enjoyment and well-being.
Identification of Technology Support – If today's children are to enter the labor market freely in the future,
they need to acquire digital skills from the start of school. It is no longer a matter of showing the use of
digital devices at school, students learning to create and program smart tools and robots. This requires
a digital transformation of education and the use of appropriate technologies.
Creating a Supportive Learning Environment – Creating an appropriate learning environment at school
and in the math classroom encourages immersion and engagement in the learning process. As a result,
the learning process becomes more meaningful, cognitive, creative, safer, more equal for all and more
relevant to intellectual, mental and physical development. In this way, the learning environment is
oriented towards mutual trust, cooperation and support, as well as promotes students' motivation and
independence.
Promotion of Cooperation – Collaborative learning usually affects all partners. According to researchers
([33]), when students work together on a task, they develop a coordinated approach to meaning making
and a goal-oriented approach.
Ensuring Balance – Fear of math is for most people, and the problem of math anxiety has been one of
the most studied for many years. A team of researchers ([34]) has shown that emotional well-being is
inextricably linked to motivation. Therefore, in the process of learning mathematics, it is very important
to create a balance between motivation and achievement, so that students work with pleasure and joy
([34]). It is equally important to take into account the pace of development in technology and education.
Where education was once a driver of technological progress, technology now dominates educational
capacity, which reduces prosperity and creates social inequalities ([35]). This is clearly shown in the
author's innovative Figure 3 – if motivation has a higher priority than results in mathematics lessons,
then joy and well-being arise, otherwise students develop fear and stress. If technology is used in a
balanced and thoughtful way in mathematics lessons, students become motivated, otherwise there is
discomfort and social tension. In those periods when a balance is achieved between motivation and
results, as well as between technology and the content of education, a "feeling of happiness" emerges,
which is also our greatest goal.
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Figure 3. A happy period is created by balance, Researcher’s concept
Bridging Social Gaps – As one of the most innovative pedagogical strategies of 2020, The Open University
named Social Justice Pedagogy in its annual publication Innovating Pedagogy, which aims to educate and
enable students to become active participants who understand social discomfort and can help build
equality. classrooms. Researchers ([36]) point out that teachers need to identify students' interests, unique
experiences and needs in order to apply an appropriate and equitable distribution of learning resources
and technologies that allow everyone to integrate productively into the learning process.
Use of Science-based Research – A successful research process requires a research-based and
interdisciplinary approach. Recent research in the fields of education, psychology and neuroscience can
enrich teachers' understanding of more effective teaching approaches. Understanding the
neurocognitive processes that underpin the development of mathematical competence can provide
important insights into the optimization of mathematical education ([37]).
Professional Development – Professional development must become an integral part of every school's
culture, as the education sector is evolving rapidly and teachers cannot afford not to learn the latest and
most relevant things.
Identifying and Anticipating Future Trends – According to OECD research, foresight mobilizes cognitive
skills (analytical and critical thinking) to predict what may be needed in the future in a particular field or
how actions taken today may affect the future. Both reflection and anticipation are harbingers of
responsible action ([1]).
5 CONCLUSIONS
Based on the motivation of the study to offer educators a technology-enriched taxonomy for faster
learning of mathematics in general education schools, the impact of the results was studied from several
perspectives using a triangulation approach to target groups. Confirming the need for taxonomy, 322
students of general education schools and 53 mathematics teachers expressed their opinion.
The study has suggested that educators need to raise awareness of the benefits of the ALOM principles.
The most important contribution of the study is the collection and systematization of existing but
fragmented knowledge in a transparent taxonomy, which provides a valuable basis for planning and
promoting learning in the future. ALOM is a new and evolving field, so the proposed taxonomy is
innovative, but of a recommendatory nature. It is a freely accessible system that can be opened with the
help of a QR code (or https://qrco.de/bcOH6y) in Table 1 and supplemented with new current and future-
oriented cases.
ACKNOWLEDGEMENTS
The research is carried out within the framework of the postdoctoral project “Artificial Intelligence (AI)
Support for Approach of Accelerated Learning of Mathematics (AI4Math) (1.1.1.2/VIAA/3/19/564)” at
Vidzeme University of Applied Sciences with the support of ERAF.
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