Technology-based Interdisciplinary Approaches to Accelerated

Learning of Mathematics

Aija Cunska

Socio-Technical Systems Engineering Institute, Vidzeme University of Applied Sciences, Cesu 4, Valmiera, Latvia

Keywords: Mathematics Learning, Interdisciplinary Approaches, Technology-based Learning.

Abstract: As technology enters everyday life more quickly and purposefully, the education system is also becoming

more accessible and efficient. In 2020, during distance learning in Latvia general education schools, based on

a survey of the Latvian Ministry of Education and Science, 18 main problems were identified that most

directly relate to learning mathematics and require a change in teaching strategies and approaches. These

problems raised much debate and led to think about the need for a more efficient education system in the

future, where close cross-sectoral cooperation with an interdisciplinary approach can make a new

contribution. The research question is: What interdisciplinary digital technology-based approaches stimulate

students' interest in learning maths, motivate them and improve attitudes in the long term? The aim of the

study is to point out to educators, policy makers, industry entrepreneurs and researchers the necessity for

collaborative and interdisciplinary approaches for accelerated learning in mathematics in general schools. In

the future this will contribute to the development of AI solutions and a quality support system for mathematics

teachers. The study identifies and describes eight technology-based interdisciplinary approaches to

accelerated learning of mathematics that can make mathematics a more accessible and meaningful subject.

1 INTRODUCTION

We live in a rapidly changing world and face

increasingly global and complex challenges on a daily

basis, such as income disparities, environmental

problems, migration issues, organized crime and

more. These complex problems cannot be solved in

isolation from the perspective of individual sectors.

Complex problems require an interdisciplinary

approach. We are living in an unprecedented period

of history, when the Covid19 pandemic is demanding

rapid changes in many aspects of our lives, and this is

especially true in the education sector. In March

2020, schools were closed almost overnight and till

now were available mostly online. And it became

clear that in the age of Artificial Intelligence (AI),

with the faster and more targeted entry of technology,

the education system will change radically in the

future and will never be the same again. These

changes have raised much debate and led

policymakers, researchers and educators to think

together about the necessity for a more efficient

education system in the future that meets the

requirements of the Fourth Industry, providing

students with tomorrow's jobs and eliminating any

inequalities.

One of the most sensitive and important subjects

in schools is mathematics, which is the basis of many

professions. If students are well acquainted with

mathematics, then in the future they will have better

access to many fields, such as finance, economics,

engineering, IT, medicine and others. Mathematics

must keep pace with technological advances such as

AI, robotics, virtual reality, big data analytics, 5G

data transmission, 3D modeling, genetic engineering,

and more. Today, technology is developing much

faster than general education, leading to uncertainty

and social tensions, also known today as the digital

gap. Only when the curve of the general education

system intersects the curve of technological

development, social tensions will decrease and the

well-being of society increase (OECD, 2019).

2 PROBLEM STATEMENT

It is written in the research of Professor Zanda

Rubene of the University of Latvia that the current

114

Cunska, A.

Technology-based Interdisciplinary Approaches to Accelerated Learning of Mathematics.

DOI: 10.5220/0010473901140121

In Proceedings of the 13th International Conference on Computer Supported Education (CSEDU 2021) - Volume 2, pages 114-121

ISBN: 978-989-758-502-9

target audience of schools is “Generation Z” or digital

age children born between 2001 and 2015, whose

everyday life is fully merged with modern

technologies that read little printed text, have visual

world perception, accept AI solutions, have

insufficient social skills, are sensitive to criticism, are

over-cared for and grow up in a child-centered society

(Rubene, 2020).

Our challenge is to create a digitally based

education system and support so that social tensions

do not increase. Therefore, outdated books,

uninteresting environment and inert teachers will not

seem attractive to the younger generation. Researcher

A. Persico has pointed out that the strategies and

methods of teaching mathematics that were popular

several years ago are now being replaced by more

effective research and Big Data-based methods aimed

at making mathematics a more accessible and

meaningful subject (Persico, 2019).

During distance learning in Latvia general

education schools in 2020, based on information in

interviews and media, focus group discussions and a

survey of the Latvian Ministry of Education and

Science (IZM, 2020), the author identified 18 main

problems most directly related to mathematics and

changing strategies and approaches, and supporting

technology, in particular AI:

→ Lack of computer equipment and data

transmission for both schools and households,

→ Lack of digital skills for both teachers and

students,

→ Disproportionate involvement of parents in

ensuring the learning process,

→ Different effects on urban and rural schools, on

talented and less able pupils,

→ Lack of a unified methodology for the use of

technology in the teaching process of

mathematics,

→ Lack of a unified system and digital platform for

communication and solving various tasks,

→ In the effort to ensure quality, part of the topics

of mathematics remained untaught,

→ Inability to plan time, anxiety and stress for both

students and teachers,

→ Lack of motivation, encouragement and support

for both students and teachers,

→ Lack of patience for students to read and

understand math problems independently,

→ Teachers’ suspicions about students' honesty in

solving math problems independently,

→ Lack of explanation by teachers for especially

more complex mathematical tasks,

→ Lack of socialization for both students and

teachers,

→ Too much time for teachers to provide feedback

and correct work,

→ Overloading of teachers in preparing for digital

online lessons, looking for more creative tasks,

creating more options and correcting students'

work,

→ Lack of interdisciplinary approaches and

activities in nature,

→ Passive lifestyle at home and lack of sports

activities,

→ Lack of cooperation between education and IT

professionals to create innovative solutions and

reduce the tensions created by digital

technologies.

Teaching higher mathematics to students of the

Faculty of Engineering of Vidzeme University of

Applied Sciences in a 3-year period (2018, 2019 and

2020), the author surveyed 253 students to find what

their main interests are, which occupy a large part of

their lives and make their daily lives happier and more

creative. Students were able to provide answers in a

free-form form, and the summary provided a daily

student profile (Figure 1) that accurately

demonstrated the necessity of interdisciplinary

approaches to learn math with interest and pleasure as

a creative and multidimensional subject.

Figure 1: IT specialty freshman students interest profile.

As shown in Figure 1, 62% of students are

interested in sports, 42% of students are interested in

Information Technology, 30% of students are

interested in music, 21% of students are interested in

literature and poetry, 17% of students are interested

in traveling and outdoor recreation, 15% of students

are interested in video games, 11% of students are

interested in cars. Students are also interested in art

and drawing (11%), dance (8%), garden and field

work (8%), dogs and cats (8%), photography (8%),

social sciences and history (8%). Other student`s

interests include: handicrafts (6%), logic puzzles

(4%), films (4%), cooking (2%), languages (2%),

theaters (2%), self-improvement (2%).

Technology-based Interdisciplinary Approaches to Accelerated Learning of Mathematics

115

The research question is what interdisciplinary

digital technology-based approaches stimulate

students' interest in learning math, motivate them and

improve attitudes in the long term?

The aim of the study is to point out to educators,

policy makers, industry entrepreneurs and researchers

the necessity of collaborative and interdisciplinary

approaches to accelerated learning in mathematics in

general schools. This will in the future contribute to

the development of AI solutions and a quality support

system for mathematics teachers to stimulate the

emergence of innovative learning approaches and

enable mathematics to be taught as a creative and

multidimensional subject.

3 METHODOLOGY

The study is a compilation of current information and

many years of experience with an interdisciplinary

approach, and the methodology includes:

→ 3-year student survey (2018, 2019 and 2020) of

253 first-year students of Vidzeme University of

Applied Sciences, who come from the whole

Latvia;

→ Compilation, analysis, comparison of the survey

results and creation of a student's daily interest

profile, which shows the necessity of

interdisciplinary approaches;

→ A selection and brief description of eight

technology-based interdisciplinary approaches

based on experience, 30 years of mathematics

lessons, teacher success stories from around the

world and expert advice;

→ Qualitative research methods (observations, semi-

structured interviews, focus groups, secondary

research) to explore the views and experiences of

pupils, teachers, students, parents and industry

professionals during distance learning through

daily conversations, information in the media,

success stories, social media profiles;

→ Primary data, so as to reveal the problems of

distance learning, the Ministry of Education and

Science of Latvia (IZM) in cooperation with the

company Edurio surveyed 4662 teachers, 8352

parents, 10177 students in May and June, 2020

(IZM, 2020).

4 THEORETICAL FRAMEWORK

4.1 Interdisciplinary Approach

In the field of education, the word "interdisciplinary"

has been around for years. Several studies (Kim,

2020; AldertKampAdvies, 2017; RSE, 2020) indicate

that interdisciplinary learning is innovative, attractive

and exciting, as well as driving 21st century education

reforms. Interdisciplinary learning is a way of

learning and thinking that is based on several

disciplines in order to acquire new knowledge and

skills. For interdisciplinary training to be effective,

researchers (McPhee et al., 2018; RSE, 2020)

emphasize the following framework conditions: 1)

interactivity of different fields, 2) teamwork and

cooperation between people, 3) internship in relevant

fields in the workplace, 4) breadth of knowledge and

skills, 5) creativity and curiosity, 6) constant access

to knowledge and lifelong learning, 7) changes in

school curricula , 8) support for teacher education and

development, 9) digital and social skills.

4.2 Accelerated Learning of

Mathematics

Our brains are adaptable, and when students learn or

change their approach to learning, incredible

developmental results can be created. In recent years,

a new science has developed, neuroplasticity, which

specifically studies improvements in brain function

and emphasizes that brain function can and should be

improved at any age (Boaler, 2019). Based on

research (Accenture, 2018; Area9, 2020; Boaler,

2019; Duval, 2019), seven basic principles can be

identified that significantly improve and accelerate

the learning of mathematics:

→ For growth to take place, the learning process

must be regular and continuous;

→ Mistakes and error correction improve the long-

term sustainability of mathematical skills;

→ Positive communication from parents and

teachers, which inspires faith in the student's

strengths, is especially important for promoting

growth;

→ Applying an interdisciplinary approach activates

neural pathways and learning in general;

→ Open and creative math problems are important,

which promote deeper learning and retain

attention;

→ Meaningful collaboration and exchange of ideas

accelerates neuronal flow and improves learning.

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That's why group and project work is so

important in math lessons.

→ There is a strong correlation between memory and

time, and by repeating the subject, students are

able to learn mathematics much faster.

Neuroscientists (Boaler, 2019; Duval, 2019) point

out that the knowledge we currently have about brain

function is so important that it should change the way

we teach students and run schools. Our brains have a

tremendous ability to grow and change at any stage of

life. This is demonstrated by a study of black cab

drivers in London, which showed that extensive and

complex spatial training has led to a significant

increase in the amount of brain hippocampus in

humans, which is important for all spatial and

mathematical perceptions (Maguire et al., 2000). Taxi

drivers in London must undergo extensive training,

learning how to navigate between thousands of places

in the city. This training is colloquially known as

“being on The Knowledge” and takes about 2 years

to acquire on average. To be licensed to operate, it is

necessary to pass a very stringent set of police

examinations (Maguire et al., 2000). Similarly,

neuroscience researchers (Coyle, 2009; Duval, 2019;

Moser et al., 2011) confirm that the best time for brain

growth is when people work on challenges, make

mistakes, correct them, fight, and move on. But

teachers usually do their best to make students' work

easier by breaking down problems into smaller tasks,

or by giving answers in front of them, or by

facilitating the content of teaching. As another

important piece of evidence for neuroscience,

researchers (Boaler, 2016; Boaler et al., 2016;

Menon, 2015) point out that five impulses act on the

brain when working on math problems, two of which

are related to visual perception (Figure 2). This leads

to the conclusion that brain connections will be much

more productive if mathematical tasks if they are

designed as visible interdisciplinary combinations of

numerical expressions and images.

Figure 2: Brain networks for mental arithmetic (Duval,

2019).

4.3 Artificial Intelligence

A study (Guo & Han, 2020) indicates that AI is a

cross-disciplinary discipline that encompasses

several disciplines, such as neuroscience,

psychology, mathematics (including statistics),

information science, and computer science. Today,

AI, represented by deep data-based learning, is

developing rapidly and is widely used in many fields.

It is believed (Southgate et al., 2019) that AI

algorithms have existed since the late 1970s, but their

widespread use with the available computing power

in the world and modern AI chips began only 5-7

years ago. AI is a term used to describe a set of

computer systems and computer programs that use

human-like thinking features to perform tasks. AI

systems are able to analyze images and videos, listen

to sounds, understand and synthesize language,

predict exchange rate fluctuations, predict electricity

consumption and perform many other tasks that only

humans have been able to do so far. If more and more

new AI solutions appear in production (for example,

in Latvia company Balticovo the quality of eggs is

analyzed with the support of AI, before the eggs reach

the final tests), then in school education AI is still at

an early stage of development.

5 FINDINGS

Based on the identified problems during distance

learning, neuroscience research and pedagogical

success stories, the following technology-based

interdisciplinary approaches to accelerated learning

in mathematics can be suggested:

5.1 Contextualizing: Mathematics

through the Prism of History

Research (Nikitina & Mansilla, 2003) indicates that

contextualization is a review of mathematics and

science in history. It shows the connections between

the theories of science and mathematics and their

historical and cultural roots. The historical

foundations of a particular mathematics topic can

serve as a core for a better understanding and more

effective acquisition of the topic. In the lessons, it is

valuable to create a link between the natural sciences

and the humanities by creating an interdisciplinary

link. For several years now, in the course of studying

applied mathematics with students, studying specific

topics, we look at the history of the origin of this

topic.

Technology-based Interdisciplinary Approaches to Accelerated Learning of Mathematics

117

A good example of this approach can be seen by

studying the topic of solving systems of linear

equations with the Gaussian method, when students

find the answers to many mathematically mediated

questions: Why is the ingenious German scientist

Karl Gauss called the King of Mathematicians and the

Innovator of Science? How can I count the numbers

from 1 to 100 the fastest? How to divide a circle into

equal parts using a circle and a ruler? How did

number theory become science? How can astronomy

solve complex mathematical problems? What are

trigonometric or Gaussian sums? How did the surface

theory for the development of geodesy come about?

How did the unit of measurement “gauss” in physics

come about? The example shows that in one lesson,

mathematics can successfully meet history, science,

art, astronomy, astrology, geography and physics to

stimulate students' interest in real applications of

mathematics. The strength of this approach is the

creation of a cultural-historical reference, which

forms a strong basis and support for the development

of students' personal knowledge of mathematics.

5.2 Problem-Centering Approach:

Applying Math and Science to

Solving Real-World Problems

Research (Biccard & Wessels, 2011) indicates that

problem-focused approaches give students the

opportunity to explore mathematics for themselves

and offer sensible solutions. All attention in the

classroom is focused on the problem to be solved, as

a result of which there is an active discussion both

among the students and between the teacher and the

students. In addition, these types of classes can take

place in nature, outside classrooms, using digital

technologies and other aids (maps, tape measures,

rulers, compasses, measuring instruments,

thermometers, etc.).

The strength of this approach is personal

involvement, which increases motivation and

interest. Leading a math group for 3rd to 7th grade

students during the Covid19 pandemic, when distance

learning was identified and students mostly learned

from home, we developed 10 sets of tasks that

encouraged students to go to nature to find the

information they needed and make calculations

independently.

For example, one of the tasks was as follows: A

number is called symmetric if it can be read equally

from the right and the left. There has been one

important symmetrical year in the development of the

Kalnamuiža park territory. Find this year on the

information board of the park territory. Name the next

symmetric year. Calculate the difference between the

two symmetric years. Is the difference a symmetric

number? If not, can the digits make a symmetric

number and which one?

5.3 Visualization: Combinations of

Mathematical Numbers and Images

It is said that a picture is worth a thousand words. This

is especially true in mathematics, where an image or

some other type of visual model can be useful in

describing a mathematical idea (Tenannt, 2006). Over

the last twenty years, with the development of

computer visual imaging capabilities, a new field of

mathematics called visual mathematics has emerged.

Especially for younger students, it is important to

work with constructions and colors. In this way,

students can better see how planes and three-

dimensional shapes are formed and how formulas

work. Today, many students have a visual perception.

They learn the substance best when they can see what

is happening, and a non-visual approach can even

hinder their efforts to solve the problem.

A good example of a visualization strategy for

learning mathematics is the famous Königsberg

“bridge walking” problem, which can be easily

explained by creating a graph diagram as a visual

representation of the situation.

5.4 Active Approach: Mathematics in

Step with Sports

Parents, educators and health professionals have

pointed out that today's children do too little exercise,

which is further exacerbated by distance learning at

home. It is well known that without movement a child

cannot grow up healthy. The more and different

movements a child has, the more active the brain is

and the more intense intellectual development takes

place. The movement creates emotional well-being

and improves perception. Pre-school and primary

school teachers in particular have given a lot of

thought to developing an interdisciplinary approach

between sports and maths lessons.

But the most innovative solution has been created

by the Canadian technology company LÜ

(https://play-lu.com/). It has developed an interactive

area that uses light, sound and video effects to

transform any gym into an engaging and

comprehensive learning environment. LÜ is a smart

space that understands the behavior and interaction of

the people in it in real time. Using information from

ceiling-mounted 3D cameras, students can learn math

from wall-mounted tasks in sports.

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5.5 Parallel Approach: Mathematics in

Combination with a Foreign

Language

In Latvian schools, English is mostly studied as the

first foreign language and German or Russian is

chosen as the second foreign language. Taking into

account that teachers often lack digital mathematics

tasks and worksheets in Latvian, they search for them

on the Internet in foreign languages. In this way, an

interdisciplinary approach is promoted while learning

mathematics and a foreign language. Open tasks can

be mastered in this way especially productively. A

study (Pehkonen, 1999) indicates that tasks are

considered open if their starting or target situation is

not specified. Open problems usually have more than

one solution and can be accomplished in more than

one way. This leaves students free to tackle the task

and allows them to use different ways of thinking.

The approach works very well in mixed classrooms,

where the level of knowledge of the students is from

the lowest to the highest, because everyone can

provide answers according to their knowledge and

skills. The teacher has the opportunity to find tasks,

the simplest of which are possible for all students in

the class, but higher levels of difficulty challenge the

abilities of the most talented students.

A good example of an open problem strategy in

mathematics lessons is the task: 10 participants come

to the seminar, and each shakes hands with each other

exactly once. How many handshakes have occurred?

There is only one answer - and it is 45, but there are

at least seven methods of solving: looking at all

possibilities, with the help of graphs, with the help of

visualization, with the help of a table, with the method

of mathematical induction, with combinatorial

formulas. Finally, students can be asked to find a

general case for the task.

5.6 Modeling: Math Applications

Not all students love math at first glance. To some it

may seem tedious and complicated, especially if only

theory, formulas and methods are taught. Math

lessons can be made more interesting and digitally

engaging with apps that can be found on the Internet

for free and for different ages.

The following applications, for example, will

provide an interdisciplinary and visually appealing

approach between mathematics and technology

lessons: Mathspace (https://mathspace.co/us),

Buzzmath (www.buzzmath.com/en-us/), CK 12

(www.ck12.org), Shapes 3D (www.mathsisfun.com),

Khan Academy (www.khanacademy.org), Photo

Math (photomath.app), GeoGebra (www.geogebra.

org), etc. In turn, the application of mathematics and

modeling will be helped by more professional

programs, such as MATLAB (www.mathworks.com)

or Wolfram | Alpha (www.wolframalpha.com).

5.7 Coding and Programming: Math

through Logic and Algorithms

Coding and programming are great helpers and

powerful methods for students to better understand

mathematics. For example, first-year students of the

Faculty of Engineering learn applied mathematics

much more quickly and train algorithmic thinking if,

in parallel with theoretical lessons, the functions of

the mathematics math module of the Python

programming language are mastered. Primary school

students, on the other hand, become much more

interested in mathematics and develop logical

thinking more deeply if they attend robotics lessons

and are able to write working codes for robot

movements without errors.

5.8 Artificial Intelligence: Synergy of

Mathematics and Neuroscience

The highest point of the interdisciplinary approach is

AI solutions that promote socialization, quick

feedback, interactivity, involvement, multiple

repetition, generation of different tasks according to

each student's individual abilities. Research in the

new field of neuro-education (Bidshahri, 2017;

Wilson & Conyers, 2013) emphasizes that, in

collaboration with AI, individual brain activity data

can be used in the future to understand each student's

strengths and weaknesses and make math learning

much faster, deeper and more personalized. AI and

mathematics have the strongest synergies, as AI is

based on mathematics (linear algebra, statistics,

probabilities, logic, etc.) and AI-based solutions can

be successfully used to learn math faster.

Researchers (Perera & Aboal, 2019) describe an

example where an online adaptive learning solution

called “Mathematical Adaptive Platform” (PAM) has

been developed in Uruguay, the content of which is

adapted to the national mathematics curriculum.

PAM provides personalized feedback according to

each student's skill level, based on an analysis of the

student's experience. PAM provides assistance to

students through more than 25,000 differentiated

tasks and 2,800 feedbacks to explain the solution to

each task.

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6 CONCLUSIONS

As technology enters everyday life more quickly and

purposefully, the education system is also becoming

more accessible and efficient. And teaching of

mathematics in general schools must keep pace with

technological advances, with the result that our task

is to create a digital technology-based education

system that does not increase social tensions and

inequalities.

In order to make school mathematics a more

accessible and meaningful subject, technology-based

interdisciplinary approaches are needed, which are

clearly indicated by the following trends:

→ the current target audience of schools is

“Generation Z” or children of the digital age,

born from 2001 to 2015, whose everyday life is

fully merged with modern technologies and AI

solutions (Rubene, 2020);

→ former teaching methods are being replaced by

more effective research and Big Data-based

methods (Persico, 2019);

→ currently (especially during distance learning in

2020) technologies have different effects on

urban and rural school students, talented and less

able students;

→ distance learning points to the necessity for

interdisciplinary approaches that promote sports

and outdoor activities;

→ distance learning points to the lack of

cooperation between education and IT

professionals in order to create innovative

solutions and reduce the tensions created by

digital technologies;

→ the student's daily interest profile modeled in the

research (Figure 1) indicates the desire to learn

mathematics in a modern way, with interest and

joy as a creative and multidimensional subject;

→ neuroscience researchers (Boaler, 2019; Duval,

2019) point out that the knowledge we currently

have about brain function is so important that it

should change the way we teach students and run

schools. Brain connections will be much more

productive if mathematical tasks are designed as

visible interdisciplinary combinations of

numerical expressions and images;

→ one of the most beautiful aspects of mathematics

is its many facets, when ideas, problems and

solutions can be represented in several visible

ways, for example, with numbers, algorithms,

codes, visual images, tables, models, graphs, etc.

A study (Guo & Han, 2020) indicates that AI itself

is an interdisciplinary discipline that combines

several disciplines, such as neuroscience,

psychology, mathematics, big data analytics, and

computer science. If more and more new AI solutions

emerge in production, AI in school education is still

at an early stage of development. Mathematics is one

of the most rewarding subjects where AI solutions

can be successfully used to foster collaboration and

individual approach, to speed up task correction and

feedback, to generate more and different tasks, to

relieve teacher time and respond to student emotions.

AI education is a feature of intelligence, and schools

need to keep pace with the times, make changes,

innovate and change the roles of teachers / students to

adapt future populations to the “age of artificial

intelligence” (Shen, 2020).

The most important questions in the near future

will be the following: Are today's teachers ready to

develop the leaders necessary for tomorrow? Will

educators be able to be active and collaborate with

industry professionals to improve mathematics

teaching in general? It is extremely important to look

for interdisciplinary collaborative solutions, because:

→ An important task is to reduce the technological

tension caused by the discrepancies between the

pace of technological development and people's

ability to apply it. And the education sector alone

will not be able to cope with it;

→ The task of the state is to create support and

preconditions so that every student and teacher is

not excluded from the development of digital

technologies;

→

As digital technologies take over everyday life,

the most important task is to create an

appropriate and flexible education system with

the opportunity to acquire more new skills;

→ During the Covid19 pandemic in 2020,

significant paradigm shifts have taken place,

such as no direct contacts, no traditional services,

information needs to be prepared in advance to

be passed on, etc.;

→ We must not lose value and the quality of

teaching, nor unduly reduce the content of

teaching.

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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