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Frontiers in Education 01 frontiersin.org

Advantages and challenges of

using digital technologies in

mathematical modelling

education – a descriptive

systematic literature review

MustafaCevikbas

1

*, GilbertGreefrath

2 and Hans-StefanSiller

3

1 Mathematics Education, Faculty of Education, University of Hamburg, Hamburg, Germany, 2 Institute

for Mathematics Education and Computer Science Education, University of Münster, Münster, Germany,

3 Institute of Mathematics, University of Würzburg, Würzburg, Germany

Mathematical modelling is essential for teaching and learning of mathematics

aimed at improving students’ competence in solving real-world problems with

mathematical means. Innovative technology-rich approaches can provide

new paradigms for mathematical modelling education, which may produce

new opportunities for the learning and teaching of mathematical modelling.

On the other hand, there may be a few challenges to the successful use of

technology in modelling. Although several studies have focused on the use of

digital technologies in modelling education, there is a lack of research on the

educational potential of digital technologies in mathematical modelling. To close

this research gap, wedecided to conduct a descriptive systematic literature review

on the advantages and challenges of using digital technologies for learners and

instructors in mathematical modelling. The literature on mathematical modelling

education was searched via three recognized databases. Literature search

revealed 38 papers that were eligible for analysis. Based on empirical evidence,

this paper describes the educational opportunities oered by digital technologies

(e.g., academic, emotional/psychological, cognitive, social, and instructional/

pedagogical enhancements) and challenges to their eectiveness (e.g., learners’

and instructors’ lack of competence or experience in using technology and

“black-box” threats). The results of the study reveal that the advantages of the

use of digital technologies in the modelling process outweigh the emerging

challenges, which is a promising result discussed in detail.

KEYWORDS

advantages, challenges, descriptive systematic review, digital technologies,

mathematical modelling, mathematics education

1. Introduction

Mathematical modelling is a well-structured research area and its importance has been

strongly emphasized in many curricula (Niss and Blum, 2020). e mathematical modelling

education (learning and teaching mathematical modelling) focuses, how the relationship

between mathematics and the “rest of the world” is established (Pollak, 1968). According to

Kaiser (2020, p.556), “the idealized process of mathematical modelling is described as a cyclic

process to solve real problems by using mathematics, illustrated as a cycle comprising dierent

OPEN ACCESS

EDITED BY

Kotaro Komatsu,

University of Tsukuba,

Japan

REVIEWED BY

Allen Leung,

Hong Kong Baptist University,

Hong Kong, SAR China

Rina Durandt,

University of Johannesburg,

SouthAfrica

*CORRESPONDENCE

Mustafa Cevikbas

mustafa.cevikbas@uni-hamburg.de

SPECIALTY SECTION

This article was submitted to

STEM Education,

a section of the journal

Frontiers in Education

RECEIVED 11 January 2023

ACCEPTED 06 March 2023

PUBLISHED 11 April 2023

CITATION

Cevikbas M, Greefrath G and Siller H-S (2023)

Advantages and challenges of using digital

technologies in mathematical modelling

education – a descriptive systematic literature

review.

Front. Educ. 8:1142556.

doi: 10.3389/feduc.2023.1142556

COPYRIGHT

© 2023 Cevikbas, Greefrath and Siller. This is

an open-access article distributed under the

terms of the Creative Commons Attribution

License (CC BY). The use, distribution or

reproduction in other forums is permitted,

provided the original author(s) and the

copyright owner(s) are credited and that the

original publication in this journal is cited, in

accordance with accepted academic practice.

No use, distribution or reproduction is

permitted which does not comply with these

terms.

TYPE Review

PUBLISHED 11 April 2023

DOI 10.3389/feduc.2023.1142556

Cevikbas et al. 10.3389/feduc.2023.1142556

Frontiers in Education 02 frontiersin.org

steps or phases.” In order to create a real model of the real-world

situation, the real-world problem should be simplied. To do this,

multiple assumptions can bemade, and key inuencing elements must

be identied. e real-world model must be transferred into a

mathematical model based on mathematical language. Calculations

are made to arrive at mathematical results within the mathematical

model. e mathematical results have to beinterpreted into the real-

world context followed by the validation of the real-world outcomes

and the entire modelling process. Learners should have the necessary

skills to engage in this described modelling processes, learn about

existing models, and evaluate instances of modelling processes that

are provided (Niss and Blum, 2020). e development of mathematical

modelling competencies to solve real-world problems using

mathematics is in demand as one major goal of mathematics education

worldwide is the inclusion of the promotion of responsible citizenship

(Kaiser, 2020).

In the last two decades, the use of digital technologies to improve

mathematical modelling education has attracted increased interest

among researchers (Siller and Greefrath, 2010; Greefrath etal., 2018).

Recent developments (e.g., the COVID-19 pandemic and recent

technological innovations) may accelerate the integration of digital

technologies into modelling education, as well as in other elds of

mathematics education (Mulenga and Marbán, 2020; Soto-Acosta, 2020;

Borba, 2021). New technologies can play a signicant role in learning

and teaching mathematical modelling as they can open new horizons to

explore dierent mathematical situations (Drijvers, 2003; Niss etal.,

2007) and foster new ways of understanding, evaluating, and interpreting

real-world situations (Molina-Toro etal., 2022). Some researchers have

argued that it is possible to integrate digital tools (e.g., dynamic geometry

soware [DGS], computer algebra systems [CASs]) into dierent stages

of the modelling cycle (Siller and Greefrath, 2010; Geiger, 2011; Daher

and Shahbari, 2015). From this perspective, technology can promote

learners’ modelling processes. For example, in some cases, technology

supports individuals in calculating complicated numerical and algebraic

results and validating them, which may not befeasible without the use

of digital technologies (Lingeärd, 2000; Greefrath etal., 2018).

e opportunities presented by information and communications

technologies (ICTs) may change the way weunderstand mathematical

concepts and processes in modelling (Borba and Villarreal, 2005; Calder

and Murphy, 2018). Technology can play a central role in inquiry,

reasoning, and systematization to handle modelling situations (Geiger,

2011; Molina-Toro etal., 2019). It may also help to simplify mathematical

problems by visualizing, organizing, and evaluating big data and may

allow for multiple representations to enhance learning (Confrey and

Maloney, 2007; Greefrath etal., 2018). Technology-enriched learning

environments may also increase students’ self-condence, improve their

modelling skills (Lingeärd, 2000), and foster student engagement

(Hoyles and Noss, 2003; Cevikbas and Kaiser, 2022). It means that digital

technologies can beconsidered essential infrastructure for mathematical

modelling in current and future societies (Geiger, 2017).

According to previous discussions in the eld, digital technologies

play a signicant role in conceptualizing the understanding of the

modelling activities (Geiger et al., 2010). However, the use of

technology may introduce challenges to the modelling process; for

instance, technical glitches may generate some problems such as

outdated web links and errors in a technological system (Merck etal.,

2021). Ramirez-Montes etal. (2021) reported that technology may not

always support students’ skills to complete all stages of the modelling

cycle as technology may restrict the extensive route of modelling with

the acquisition of computational results. For example, technology can

support students in measurement and calculation processes, but not

in interpretation of the results. In addition, learners might

beunfamiliar with digital technologies or inexperienced in the use of

new technologies for modelling. is may negatively aect the

instructional quality and students’ understanding (Merck etal., 2021).

As mentioned earlier, new technologies may generate new

opportunities for learners as well as various challenges. Considering

the rapid developments in technology, it is important to develop a

scientic evidence-based perspective on the opportunities and

challenges associated with the use of dierent technologies in

modelling. As Blum (2011) emphasized years ago, it is unclear how

technology should beused in modelling education. ere is still no

clear answer to this question, although the body of knowledge about

the use of digital technologies in modelling has increased within the

last two decades (Geiger, 2017). A few review studies have examined

the literature on mathematical modelling (Frejd, 2013; Schukajlow

etal., 2018; Molina-Toro etal., 2019; Cevikbas, 2022; Cevikbas etal.,

2022; Hidayat et al., 2022). However, these studies do not fully

concentrate on the overall potential of digital technologies in

mathematical modelling processes; rather, they focus on the

conceptualization, measurement, or fostering of modelling

competencies or on the integration of technologies solely in the

modelling cycle. ese studies conrmed that there was a need for

research on the advantages and challenges associated with the use of

digital technologies in mathematical modelling education and the

ways in which such technologies can beeectively used have not been

comprehensively investigated. e present descriptive systematic

review study aims to close this gap by exploring research trends in the

eld and holistically describing state-of-the-art research, providing

scientic evidence and empirical results regarding the potential of

digital technologies in mathematical modelling education.

2. Background of the study

2.1. Theoretical framework on the use of

digital technologies in mathematical

modelling

Digital technologies can beused to support the learning process

in some specic way, to answer problems, for investigating on the

Internet, for communicating, or to prepare teaching materials (Borba

et al., 2013). Digital technology is dened in the “European

Framework for the Digital Competence of Educators (DigCompEdu)”

(Redecker, 2017, p.90) as follows:

Any product or service that can beused to create, view, distribute,

modify, store, retrieve, transmit and receive information electronically

in a digital form. In this framework, the term “digital technologies” is

used as the most general concept, comprising.

• computer networks (e.g., the Internet) and any online service

supported by these (e.g., websites, social networks, online

libraries, etc.,);

• any kind of soware (e.g., programmes, apps, virtual

environments, and games), whether networked or

installed locally;

Cevikbas et al. 10.3389/feduc.2023.1142556

Frontiers in Education 03 frontiersin.org

• any kind of hardware or “device” (e.g., personal computers,

mobile devices, digital whiteboards); and

• any kind of digital content, e.g., les, information, data.

According to DigCompEdu framework digital technologies are

divided into the three main categories (1) digital devices, (2) digital

resources, namely digital les + soware + online services, and (3)

data (see Figure1). By digital technology in mathematics education,

we mean technical aids such as content-specic soware, digital

materials, and digital devices (e.g., computers, tablet PCs, and

handhelds) with mathematical facilities.

In particular, the concept of mathematical modelling involves

developing a simplied description of the extra-mathematical world

within the mathematical world, working within the mathematical

model, and then interpreting and validating the mathematical results

thus obtained into the extra-mathematical world (Niss etal., 2007;

Niss and Blum, 2020). With regard to the discovery of mathematical

relationships in modelling, digital technologies are of particular

importance for experimental work and conducting investigations on

the Internet (Borba et al., 2013; Villarreal et al., 2018). Digital

technology makes it possible to construct several dierent

representations that are interactively connected (Arzarello et al.,

2012). Especially with CASs, operations can bereduced to schematic

sequences (Berry, 2002). Checking and validating solutions obtained

is another important mathematical activity that can besupported by

digital technology. ese considerations clearly show that digital

technology can prove useful in dierent phases of the modelling

process (Greefrath, 2011; Ramirez-Montes etal., 2021; Frenken etal.,

2022). Figure2 shows dierent ways of applying digital technology (in

italics) within a modelling process in Blum and Leiß’s (2007) seven-

step modelling cycle. Geiger (2011) shares the view that digital

technology is applicable at several points in the modelling cycle.

ere are other modelling cycles that take digital technology into

account. Confrey and Maloney (2007) also consider digital technology

holistically as appropriate for learning and place the multiple forms of

representation made possible by digital technology at the centre of

their model. In a study of students’ diculties in modelling, the role

of digital technology was found to beparticularly pronounced when

the technology is used to move from the real model to the

mathematical results, using the terminology of the modelling cycle

shown in Figure2 (Galbraith and Stillman, 2006). Schaap etal. (2011)

also see potential for digital technology in the rst steps of the

modelling cycle. In addition to the potential benets for understanding

the problem, the authors place particular emphasis on simplifying the

situation through drawing and mathematisation using digital

technology, but they also mention the potential benets for validation.

A more individualized view allows for the labelling of the use of digital

technologies at dierent points in the modelling cycle, depending on

the use (Daher and Shahbari, 2015).

If welook more closely at the step of working mathematically

with digital technology, wend that the digital technology can only

beused once the mathematical expressions have been translated

into the language that the technology understands. e results

produced by the technology must then betranslated back into the

language of mathematics. Some authors put a special focus on these

translations (Adan etal., 2005; Pierce, 2005; Savelsbergh etal.,

2008). Even more generally, mathematical modelling can

beconsidered in a technology-based environment where students’

knowledge production is in focus (Soares and Borba, 2014).

However, the use of digital technologies also requires novel

examples that can beworked on with dierent technology in the

classroom and that can lead to dierent models.

In the meantime, many well-founded ndings on modelling with

digital technology exist (Greefrath etal., 2018; Villarreal etal., 2018).

e view expands from the use of individual tools to learning

environments: “While the use of digital tools in mediating the

modelling process is receiving increasing attention …, research has

again tended to focus on how students learn to model within

technology-rich environments. “(Geiger etal., 2018, p.220). However,

many concrete questions still remain open. “In future analysis of

contributions in modelling authors should also take into account how

technologies can be used for modelling or more generally what

interaction between humans and media are meaningful” (Schukajlow

etal., 2018, p.11).

2.2. Mathematical modelling and

technology in previous literature reviews

As mentioned in the previous section, a limited number of review

studies focusing on dierent aspects of mathematical modelling

education have been conducted in recent years. For instance, review

studies have focused on modes of modelling assessment (Frejd, 2013);

cognitive aspects of the promotion of modelling (Schukajlow etal.,

2018); research trends in modelling (Molina-Toro etal., 2019); and the

conceptualization, measurement, and fostering of modelling

competencies (Cevikbas, 2022; Cevikbas etal., 2022; Hidayat etal.,

2022). ese review studies approach mathematical modelling from

dierent perspectives, but do not comprehensively investigate the

potential advantages and especially challenges of technology use in

mathematical modelling education.

Frejd (2013) conducted a review of approaches to assessment of

mathematical modelling education and identied several categories of

assessment modes, including projects, test instruments, portfolios,

and contests. Hidayat et al. (2022) reviewed the literature on

assessment on mathematical modelling education published between

2017 and 2021 and found that test instruments were frequently used

to measure modelling competencies. Although these review studies

oer detailed perspectives on the quality of models to assess students’

modelling work, they did not oer comprehensive results regarding

the assessment of modelling with technology.

FIGURE1

Concept of digital technology.

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Frontiers in Education 04 frontiersin.org

Schukajlow etal. (2018) carried out a review on the promotion

of mathematical modelling competencies, focusing on papers

published between 2012 and 2017. They found a lack of

quantitative research in modelling education; the majority of

empirical studies focused on cognitive variables (e.g., analysis of

learners’ solution processes, investigation of the effect of

instructional methods on learning performance). In their review,

Schukajlow etal. (2018) did not focus on the use of technology in

modelling education. Rather, they suggested that future studies

consider how technology could beused in modelling education

and which kinds of interactions between individuals and

technology are beneficial.

Molina-Toro etal. (2019) performed a narrative review in

which they analyzed the articulation of modelling and technology

in education. They recommended expanding both theoretical and

empirical research to clarify the effect of digital technologies in

mathematical modelling education. The results of their review

showed that studies mostly used CAS, DGS, and spreadsheets in

the modelling process to visualize representations of data, make

calculations, validate models, and simulate the phenomena.

According to the results, technology supports learners at different

stages of modelling cycle. Technology not only served as a

resource for learners and instructors but also provided support for

reorganization of the dynamics of modelling, allowing for

extension of thought processes during the developmental process

of modelling. Molina-Toro etal. (2019) strongly emphasized the

lack of studies investigating the key features of digital technologies

used in modelling and how their potential should beexploited to

promote modelling education. The authors proposed that future

studies explore how modelling cycles are structured using various

technologies. However, this study has some limitations. For

example, it does not capture the latest developments in the field

(like most of the previously reported review studies), as the

literature search was conducted in 2016 and was limited to a single

database (Scopus).

Cevikbas etal. (2022) conducted a comprehensive systematic

review study of mathematical modelling focused on the

conceptualization, measurement, and fostering of strategies for

developing modelling competencies. eir results, which were

based on 75 peer-reviewed studies, revealed the dominance of

analytical/atomistic approaches for conceptualizing mathematical

modelling competencies. ey identied several approaches for

measuring and fostering modelling competencies. e results show

that only a few studies (4 of 75) considered using technology (e.g.,

programmable calculators, mobile devices, GeoGebra, and

MATLAB) to measure or foster learners’ modelling competencies.

Based on this result, the authors recommended focusing especially

on new technologies in order to extend current approaches to

measure or foster modelling competencies. Cevikbas (2022)

analyzed in more detail the strategies for fostering modelling

competencies, including (1) training strategies and exposing

learners to modelling tasks, (2) enhancing learners’ metacognitive,

emotional, and psychological development, (3) using dierent

conceptual and theoretical approaches, and (4) using digital

technologies. Conrming the results of other studies, this systematic

literature review showed that only a few studies (4 of 44)

concentrated on the use of technology and its potential for

promoting modelling competencies. Considering the lack of

research on the potentials of technology in mathematical modelling,

Cevikbas (2022) strongly suggested that future studies consider the

opportunities and challenges associated with the use of the digital

technologies in mathematical modelling education and explore

when and how these technologies should be used to support

learners’ modelling competencies.

Although the aforementioned review studies do not have a

common focus on how technology can be integrated into

mathematical modelling education, they agree on the need for studies

to explore the potential of digital technologies in teaching and learning

modelling. It is worth noting that these review studies do not

suciently address the challenges that may beencountered when

using technology in modelling process; instead, they mostly focus on

the advantages of various technologies. In other words, the potential

advantages and challenges of digital technology in mathematical

modelling education have not yet been fully explored. erefore, our

descriptive systematic review study aiming to close this research gap

is timely.

2.3. Research questions

e main purpose of the current study is to address the following

research questions:

(1) What kinds of digital technologies are used in mathematical

modelling education, and what are the purposes of using

these technologies?

(2) What are the advantages of using digital technologies in

mathematical modelling education?

(3) What are the technology-related challenges facing

mathematical modelling education?

To answer these questions, weconducted a descriptive systematic

review on the use of digital technologies in mathematical modelling

education. In the following section, wepresent our methodological

approach to the current review. en, weprovide the key results of our

review on the possibilities of using digital technologies in

mathematical modelling education. Ultimately, weconclude with a

comprehensive discussion of the use of digital technologies to enhance

mathematical modelling education.

FIGURE2

Usage of digital technology in mathematical modelling (Blum and

Leiß, 2007, p.22; Greefrath, 2011, p.303).

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Frontiers in Education 05 frontiersin.org

3. Methodology of the descriptive

systematic literature review

To structure our study and to improve the transparency, accuracy,

and quality of the review, wefollowed the most recent guidelines of

Preferred Reporting Items for Systematic reviews and Meta-Analysis

(PRISMA) (Page etal., 2021). Weconducted a descriptive systematic

review attempting to scope out a body of empirical studies on the use

of digital technologies in mathematical modelling education.

Descriptive review studies assemble, codify, and analyze numeric data

that reect the frequency analysis of the body of research and

concentrate on the overall study characteristics and methodologies

such as authors, publication years, research methods, samples, topics,

domains, direction of study outcomes (e.g., positive, negative, or

non-signicant) (King and He, 2005; Pare etal., 2015). Descriptive

systematic reviews are useful for drawing overall conclusions

concerning the merit of existing conceptualizations, approaches, and

applications in the eld through identifying research trends and

presenting interpretable patterns (Pare etal., 2015).

3.1. Strategy for the literature search

e literature search was performed on 8 December 2021 using

three well-known databases: Web of Science, ERIC, and EBSCO

Teacher Reference Center. To reach as many potentially relevant

studies as possible, a search request was performed with Boolean

operators and asterisks to identify words in the articles’ titles, abstracts,

and keywords (see Table1).

3.2. Manuscript selection criteria and

procedure

e present review focuses on empirical mathematics education

studies that are strongly related to the use of digital technologies in

mathematical modelling education, including advantages and/or

challenges for learners and educators, and that were published in peer-

reviewed journals or books. e included studies had to bewritten in

English. Our literature search was intended to explore relatively

current research. erefore, werestricted the publication years to

between 2000 and 2021. To identify included manuscripts for the

review, weutilized six inclusion criteria, which are presented in

Table2.

Our manuscript selection process has three major stages: (1)

identication, (2) screening, and (3) inclusion (Figure3 shows the

ow diagram of the entire manuscript selection process in accordance

with the PRISMA 2020 framework). In the identication process,

weaccessed 29,496 records from the selected electronic databases

using our keywords. en, weeliminated 28,531 records based on our

eligibility criteria (language, document type, research categories,

publication year). In the screening phase, weexamined the titles,

abstracts, and keywords of the 965 records and found 94 potentially

eligible papers. In the last stage, weassessed the full texts of 94 papers

and identied 21 papers eligible for our review. Aer the electronic

database search, wecarried out a manual search of proceedings of the

International Conference on the Teaching of Mathematical Modelling

and Applications (ICTMA) that were not indexed in selected

databases, as they play an inuential role in research on mathematical

modelling education (Cevikbas etal., 2022). We did not focus on

ICTMA papers published between 2007 and 2015, as these papers

were already indexed in one of the selected databases. Our manual

search yielded 335 records. Aer screening the titles and abstracts of

these records, weidentied 41 potentially eligible studies. Based on

full text analysis, werecruited 17 studies for this review. With the

consensus of all authors, 38 papers were included in the current

descriptive systematic review study. A list of the included studies can

be found in the appendix, which is presented in the electronic

supplementary materials.

Our literature search may have excluded some interesting studies,

such as those not published in English or in journals or books not

indexed in the included databases. erefore, our sample and the

TABLE1 Search strings.

Database Search terms

Web of Science (mathematical model*) (Topic) AND

(technolog* OR digital) (Topic)

(Rened by: Document types: Articles

or Review Articles or Book Chapters or

Early Access/Web of Science

Categories: Education Educational

Research or Education Scientic

Disciplines/Language: English/

Publication Year: 2000–2021)

ERIC AB (mathematical model*) AND AB

(technolog* OR digital) (Rened by:

Language: English/Document Type:

Peer-reviewed Journal Articles or Peer-

reviewed Book Chapters/Publication

Year: 2000–2021)

Teacher Reference Center AB (mathematical model*) AND AB

(technolog* OR digital) (Rened by:

Language: English/Document Type:

Peer-reviewed Journal Articles or Peer-

reviewed Book Chapters/Publication

Year: 2000–2021)

TABLE2 Study selection criteria.

Category Criterion

Domain Studies at all levels of mathematics

education

Research focus

Studies use digital technology(ies) in

mathematical modelling and report

advantages or challenges associated

with using digital technologies in

mathematical modelling

Document type Empirical peer-reviewed journal articles

and book chapters

Language English

Publication Year 2000–2021

Database Web of Science, ERIC, or EBSCO

Teacher Reference Center

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Frontiers in Education 06 frontiersin.org

results may be biased towards trends important in the English-

speaking research discourse. is can beviewed as a limitation of

our study.

3.3. Data analysis

We screened the full texts of 38 included studies, encoded the data

based on qualitative content analysis (Miles and Huberman, 1994),

and classied the codes into three main categories: (1) types of

technologies and the purposes of using these technologies in

mathematical modelling education, (2) advantages oered by digital

technologies in mathematical modelling education, and (3) challenges

associated with the use of technology in mathematical modelling

education. e coding manual and sample coding are displayed in the

electronic supplementary materials. Aer the initial coding procedure,

to calculate coding reliability rate, weused Miles and Huberman’s

method (coding reliability = number of agreements/number of

agreements and disagreements). First, the rst author conducted a

code–recode technique that included re-coding of all reviewed studies

aer a period (in our case, an eight-week break). e coherence ratio

between the two dierent codes was 0.92. e initial codes were

revised based on the results of the re-coding strategy. Second, an

expert experienced in qualitative data analysis cross-checked 21% of

reviewed papers to determine the coherence of coding. ere was

relatively high agreement (0.90), which was accepted as a satisfactory

rate of intercoder reliability (Creswell, 2013). Ultimately, a consensus

was established by discussing the discrepancies between the

dierent codes.

4. Results of the study

For this review, weorganized our synthesis of the results into four

sections. First, wepresent a general overview of the reviewed studies.

Second, wefocus on the types of technologies used in studies and the

intended use of them in modelling processes. ird, wereport

advantages aorded by digital technologies in mathematical

modelling education, followed by potential challenges. Weconclude

with a discussion of the potential of digital technologies in

mathematical modelling education based on the reported

empirical results.

4.1. General overview of the included

studies

Our analysis revealed that 38 eligible papers (15 journal articles

and 23 chapters) were published between 2001 and 2021. Figure4

visualizes the publication trends in the eld, which does not indicates

a steady progress over time. e increase of publications in recent

years is promising but not satisfactory.

We also analyzed all authors’ affiliations (n = 88) and found

that the majority of the researchers came from Europe (33%, n

= 29), followed by North America (25%, n = 22), Australia (16%,

n = 14), South America (11%, n = 10), Asia (11%, n = 10), and

Africa (3%, n = 3) (see Table3). In detail, the researchers came

from 19 different countries, with UnitedStates, Australia, and

Germany being the most prominent. Concerning the research

methodologies, qualitatively oriented studies were predominant

FIGURE3

Flow diagram of the manuscript selection process.

Cevikbas et al. 10.3389/feduc.2023.1142556

Frontiers in Education 07 frontiersin.org

in the field (84%, n= 32), and other methodologies—quantitative

methods (11%, n = 4) and mixed method (5%, n = 2)—were

rarely used (see Figure5). Almost half of the studies focused on

undergraduates, including pre-service teachers (47%, n= 18),

followed by secondary school students (34%, n = 13) and

in-service teachers (ISTs) (16%, n= 6). Only one study (3%,

n= 1) recruited primary school students as participants. Most

of the studies (79%, n = 30) have small sample sizes (less

than 100 participants), which confirms the lack of large-

scale studies.

4.2. Types of technologies and purposes of

using them in mathematical modelling

education (research question 1)

Considering that dierent technologies have dierent potentials

for teaching and learning mathematical modelling, weanalyzed the

types of technologies used in studies and the purposes for which they

were recruited in order to reveal trends in the use of technologies in

research on mathematical modelling education. Weclassied digital

technologies used in studies according to framework of DigCompEdu

namely, (1) digital resources, (2) digital devices, and (3) data

(Redecker, 2017). Our results indicated that numerous technologies

were used in the reviewed studies (see Table4).

e analysis showed that the most popular technologies in

mathematical modelling education under the category of digital

resources were DGSs (34%, n= 13), Internet and Internet-based tools

(32%, n= 12), spreadsheets (26%, n= 10), some specialized soware

(26%, n= 10), graphing calculators (21%, n= 8), and CASs (21%,

n= 8). Other types of technologies were also used, albeit rarely, such

as simulations (13%, n= 5), videos and video games (11%, n = 4),

sensors (8%, n= 3), apps (3%, n= 1), animations (3%, n= 1), applets

(3%, n= 1), and programming languages (3%, n= 1). Concerning the

digital devices used in the included studies, the most oen reported

category was computers (29%, n= 11), followed by mobile devices

(21%, n= 8), detectors (5%, n= 2), electric/electronic circuits (3%,

n= 1), and smartboards (3%, n= 1). Our analysis conrmed that the

use of emerging technologies (e.g., augmented and virtual reality,

eye-tracking, and articial intelligence) and innovative pedagogies

(e.g., ipped classroom) are still not discernible in mathematical

modelling education, at least according to the reviewed studies.

Concerning data as a sort of digital technology, a few studies (8%,

n = 3) reported that data were used with digital sources in

modelling process.

More than half of the studies used one (24%, n= 9) or two (34%,

n= 13) types of technologies for modelling, followed by three (18%,

n= 7), ve (11%, n= 4), six (8%, n= 3) and four kinds of technologies

(5%, n= 2). ese results indicate that most researchers were hesitant

to combine dierent types of technologies in mathematical

modelling education.

FIGURE4

Publication trends regarding the use of technology in modelling.

TABLE3 All authors’ countries of aliations.

Continent Country n%

Europe

Germany 9 10

Sweden 6 7

Serbia 4 5

Portugal 3 3

Spain 2 2

Tur k e y 2 2

Denmark 2 2

Netherland 1 1

North America USA 15 17

Mexico 7 8

Australia Australia 14 16

South America

Argentina 3 3

Brazil 3 3

Colombia 3 3

Chile 1 1

Asia

Japan 7 8

Israel 2 2

Indonesia 1 1

Africa South Africa 3 3

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TABLE4 Type of technologies.

Category Sub-category n*%** Sample research

Digital resources

DGS 13 34 Greefrath and Siller (2018)

Internet and web-based tools (e.g., online databases, interactive online map, Google

Map, StreamStats, Wolfram Alpha, online forums, webinars) 12 32 Orey and Rosa (2018)

Spreadsheets 10 26 Daher and Shahbari (2015)

Specialized soware such as engineering and design soware (e.g., HEC-HM hydrologic

engineering soware; Game Maker Studio; Video Physics; Curve Expert; 3D printing

design soware packages such as Tinkercad, Google SketchUp, and OnShape; Screen

Hunter; Modellus; Function Probe)

10 26 Soares (2015)

Graphing calculators (e.g., Desmos, MathCad, TI-Nspire, and Free GraCalc) or

programmable calculators 8 21 Andresen and Petersen (2011)

CAS (e.g., Mathematica) 8 21 Geiger (2017)

Simulations and simulators 5 13 Frejd and Ärlebäck (2017)

Videos or video games 4 11 Sacristan and Pretelin-Ricardez (2017)

Apps (e.g., game apps, apps for automatic feedback, and MathCityMap) 3 8 Buchholtz (2021)

Sensors (e.g., sensory-motor systems for a mobile robot, temperature, voltage and

movement) 2 5 Gallegos and Rivera (2015)

Animations 2 5 Simon and Cox (2019)

Applets (e.g., Algebra Arrows) 1 3 Jupri and Drijvers (2016)

Programming languages (e.g., Python, IPython, C++, and Octave) 1 3 Villarreal etal. (2018)

Digital devices

Computers 11 29 Geiger (2017)

Mobile devices (e.g., iPads, smartphones, and laptops) 8 21 Molina-Toro etal. (2022)

Motion detectors 3 8 Confrey and Maloney (2007)

Smartboards 1 3 Geiger (2017)

Electric/electronic circuits (e.g., connectors, capacitor, resistance and batteries) 1 3 Gallegos and Rivera (2015)

Data Data 3 8 Hidiroglu and Guzel (2017)

*n represents the number of studies and due to multiple assignments, the sum of the percentages is more than 100. **Percentages were calculated over 38 studies.

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Another important issue was the purpose of the use of digital

technologies in mathematical modelling education. e results give

insight into the implementations of these technologies in research (see

Table5). ese results indicated that dierent types of technologies

were used in dierent stages of the mathematical modelling process

with dierent purposes, which supports the claim that it has been

possible to apply digital technologies at all stages of the modelling cycle.

In the following two sections, wepresent the reported advantages

and challenges to technology use in mathematical modelling

education. In doing so, weaim to provide important insights into the

potential of technologies for modelling.

4.3. Advantages of using digital

technologies in mathematical modelling

education (research question 2)

Our analysis revealed that the use of digital technologies in

mathematical modelling education provides tremendous advantages

(see Table 6 and subsequent explanations). e vast majority of

reviewed studies (89%, n= 34) reported at least one outcome in this

category. e benets of technology were observed not only in the

context of academic issues but also in the context of emotional/

psychological, pedagogical, cognitive, and social issues. e majority

of the studies reported advantages of technologies for students, rarely

for teachers explained below in detail.

e most cited advantages of digital technologies refer to the

academic enhancement of technology for learners, more than one

third of the studies (39%, n= 15) reported that learners’ content

knowledge and development of understanding in mathematical

modelling were supported by the use of digital technologies such as

explanatory videos, games, CASs, DGSs, graphic calculators, the

Internet, handheld digital devices with mathematical facilities (data

TABLE5 Purposes of using digital technologies in modelling.

Sub-category n*%** Sample

research

Problem solving 15 39 Greefrath and Siller

(2018)

Visualization of data,

results, and models 10 26 Sekulic etal. (2020)

Calculations (manual or

automatic) 10 26 Villarreal etal. (2018)

Drawing geometrical

objects or producing

graphs

8 21 Komeda etal. (2020)

Seeking information and

gathering data 7 18 Villarreal etal. (2018)

Validation of solutions

and models 7 18 Merck etal. (2021)

Making predictions,

estimations, and

assumptions,

5 13 Ekici and Alagoz

(2021)

Analyzing, testing, and

assessing a solution or a

mathematical model

5 13 Andresen and

Petersen (2011)

Designing or

manipulating modelling

concepts

4 11 Ekici and Alagoz

(2021)

Enhancing the

understanding of

modelling concepts

3 8 Simon and Cox

(2019)

Interpretation of

calculations, analyses,

and solutions

3 8 Orey and Rosa

(2018)

Mathematization 3 8 Greefrath and Siller

(2018)

Measurement 3 8 Greefrath and Siller

(2017)

Comparing results,

representations, and

models

3 8 Hidiroglu and Guzel

(2017)

Formulation/

reformulation of

problems and models

2 5 Orey and Rosa

(2018)

Selecting variables 1 3 Villarreal etal. (2018)

Dening the

characteristics of

modelling concepts

1 3

Sacristan and

Pretelin-Ricardez

(2017)

Enhancing creativity in

modelling 1 3 Watson and

Enderson (2018)

*n represents the number of studies and due to multiple assignments, the sum of the

percentages is more than 100. **Percent ages were calculated over 38 studies.

FIGURE5

Research design and sample.

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and function plotters), computers with mathematically enabled apps,

animations, modelling soware, 3D printing, websites, and online

databases. Almost one-third of the studies (29%, n= 11) showed that

technology (e.g., apps, mobile devices, spreadsheets, CASs, DGSs,

programming languages, and simulations) may help both students

and instructors to explore possible solution pathways for modelling

problems, giving ideas, and providing experience with solving

dierent types of problems. Another reported benet of technology

TABLE6 Advantages aorded by technology in modelling.

Category Sub-category n*%** Sample research

Academic enhancement Understanding and knowledge 15 39 Geiger (2017)

Exploration of solutions 11 29 Sekulic etal. (2020)

Making connections 9 24 Kawakami etal. (2020)

Validation 8 21 Ramirez-Montes etal. (2021)

Visualization 7 18 Villarreal etal. (2018)

Formulation/development of a problem/

model 6 16 Geiger (2011)

Representation 6 16 Lingeärd and Holmquist (2001)

Competence development 5 13 Greefrath etal. (2018)

Simplication and calculation 5 13 Sekulic etal. (2020)

Evaluation and analysis 5 13 Soares (2015)

Interpretation 5 13 Hidiroglu and Guzel (2017)

Data and information 3 8 Orey and Rosa (2018)

Prediction 3 8 Daher and Shahbari (2015)

Drawing 1 3 Greefrath and Siller (2017)

Measurement 1 3 Greefrath and Siller (2017)

Emotional/Psychological enhancement Motivation 5 13 Gallegos and Rivera (2015)

Enjoyment and feelings of appreciation 4 12 Merck etal. (2021)

Interest 3 8 Frejd and Ärlebäck (2017)

Attitude 3 8 Frejd and Ärlebäck (2017)

Feelings of condence 1 3 Orey and Rosa (2018)

Feelings of being supported 1 3 Merck etal. (2021)

Feelings of being comfortable 1 3 Flores etal. (2015)

Perception 1 3 Merck etal. (2021)

Satisfaction 1 3 Sacristan and Pretelin-Ricardez

(2017)

Social enhancement Discussion 4 11 Greefrath etal. (2018)

Interaction 3 8 Soares (2015)

Collaboration 3 8 Geiger etal. (2010)

Cognitive enhancement Investigation/inquiry 3 8 Orey and Rosa (2018)

Cognitive load 3 8 Hidiroglu and Guzel (2017)

Correction 3 8 Geiger etal. (2010)

Reasoning 2 5 Confrey and Maloney (2007)

Mathematical thinking 2 5 Flores etal. (2015)

Creativity 1 3 Watson and Enderson (2018)

Autonomy 1 3 Orey and Rosa (2018)

Instructional/Pedagogical enhancement Feedback/scaolding 7 18 Confrey and Maloney (2007)

Engagement 5 13 Geiger etal. (2010)

Instructional support 2 5 Buchholtz (2021)

Reective practice 2 5 Sacristan and Pretelin-Ricardez

(2017)

*n represents the number of studies and due to multiple assignments, the sum of the percentages is more than 100. **Percentages were calculated over 38 studies.

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(e.g., CASs, data, mobile devices, map/GPS, scripts, digital circuits,

simulations, and videogames) was about its ability to connect dierent

types of knowledge, variables, and representations, which strengthens

the connections between various aspects of mathematics (24%, n= 9).

A few studies found that dierent technologies could mediate the

modelling process at almost all stages of the modelling cycle and could

foster transition between these stages. In detail, digital technologies

(e.g., CASs, DGSs, and graphing calculators) can promote

simplication of dicult problems and calculations and save time to

allow for concentration on the meaning of problems and solutions

(13%, n = 5). Technology (e.g., spreadsheets, CASs, video, and the

Internet) may support individuals in making predictions regarding

mathematical relations or technological constructions (8%, n= 3).

Dierent technologies (e.g., graphing calculators, computer specic

soware Curve Expert, DGSs, CASs, and spreadsheets) can provide

opportunities for formulating/reformulating problems and creating/

improving models (16%, n= 6). In addition, digital technologies (e.g.,

DGSs) can support measurement in the modelling process (3%, n= 1)

and they (e.g., spreadsheet, graphing calculators and soware, DGSs,

and CASs) can help with analysis of problems or results and evaluation

of assumptions, problems, or models (13%, n= 5). It is also possible to

enrich the interpretation of the results and models with technology

such as simulators, DGSs, CASs, and online resources (13%, n= 5).

Finally, technology (e.g., animations, videos, DGSs, graphing

calculators, engineering soware, and CASs,) can support individuals

in validating solutions or models and verifying conjectures (21%,

n= 8). Studies have also reported other advantages that technology

aords in regard to the modelling process, such as approaches for

collecting data and accessing and sharing information (8%, n= 3),

drawing (3%, n= 1), visualization (18%, n= 7), and the ability to use

multiple representations (16%, n = 6). In addition, studies have

reported that visualization and multiple representations of variables,

solutions, and models can facilitate students’ understanding of

modelling and that these reported advantages of technology may

support individuals’ modelling competencies (13%, n = 5). es e

results support that the use of digital technologies might behelpful at

dierent stages of the modelling process.

As mentioned earlier, the use of technology in mathematical

modelling education can assist the emotional and psychological

development of individuals. In this category, the most commonly

reported result is that digital technologies (e.g., modelling soware,

3D printing, online databases, simulations, CASs, spreadsheets, and

gaming apps, and mobile devices) can foster students’ and teachers’

motivation in the modelling process (13%, n = 5), followed by

enjoyment and free participation in modelling activities (11%, n= 4),

interest in modelling tasks (8%, n= 3), and positive attitudes towards

modelling (8%, n= 3). Technology (e.g., online forums, the Internet,

CASs, and mobile devices) may also make students and teachers feel

condent (3%, n= 1), comfortable (3%, n= 1), and supported (3%,

n= 1) in the context of mathematical modelling. Appropriate use of

technologies (e.g., modelling soware, game soware, and

simulations) may satisfy learners in the modelling process (3%, n= 1),

and students may have positive perceptions of learning modelling in

a technologically rich environment (3%, n= 1).

In addition, the analysis revealed that the use of technology (e.g.,

the Internet, online discussion forums, mobile devices, CASs, and

modelling soware Modellus) can enhance individuals’ social skills.

Active participation in discussion sessions (11%, n = 4),

teacher–student and student–student interactions in modelling (8%,

n= 3), and collaboration in modelling activities (8%, n= 3) were

encouraged by digital technologies.

Another important result is related to the cognitive enhancement

of technology for students in mathematical modelling process. A few

studies emphasized that digital technologies (e.g., CASs, the Internet,

and online forums) assisted students with inquiry and investigation of

authentic and complex modelling problems (8%, n= 3). On one hand,

the use of technology (e.g., computer and DGSs) may decrease

students’ cognitive load and mediate the cognitive demand of

modelling tasks (8%, n= 3). On the other hand, it (e.g., using apps,

spreadsheets, computers, motion detectors, modelling soware, and

CAS calculators, and online resources) can support mathematical

thinking in modelling (5%, n= 2), coordination of the reasoning

process (5%, n= 2), autonomy in the exploration of dierent models

(3%, n= 1), and creativity in applying mathematical concepts (3%,

n= 1). Technology (e.g., DGSs, CASs, and mobile devices) can also

assist the error correction process in mathematical modelling

education (8%, n= 3).

In general, the use of digital technologies (e.g., apps, CASs, the

Internet, modelling soware Modellus, mobile devices, and

computers) in mathematical modelling education provides

pedagogical/instructional advantages, such as providing scaolding

and immediate feedback regarding solutions/models (18%, n = 7),

enhancement of student engagement in modelling activities (13%,

n= 5), application of theoretical knowledge in practice (5%, n= 2), and

customized instructional support as a result of enhanced teaching of

modelling concepts and support of task presentation (5%, n = 2).

Overall, the review generated a wealth of results about how digital

technologies could improve mathematical modelling education. It also

revealed trends regarding the use of technology in research on

mathematical modelling education.

4.4. Challenges to the use of digital

technologies in mathematical Modelling

education (research question 3)

In addition to the many benets of digital technologies, there are

a few challenges to their use in mathematical modelling education (see

Table7). It is noteworthy that 15 (39%) of 38 studies did not report

any technology-related challenges, and that the reported challenges in

23 studies were not as diverse as the reported advantages of the

technologies in mathematical modelling education. e majority of

the studies reported disadvantages of technologies for both students

and teachers, but many technical problems directly concern teachers,

which is explained below in detail.

In detail, reported challenges are centered around two main

categories, the most commonly cited challenge was students’ and

teachers’ lack of competence and experience in the use of digital

technologies (32%, n= 12), followed by black-box threats (21%, n= 8).

It was evident from the review that lack of competence/experience

in using digital technologies (e.g., GeoGebra, spreadsheets,

programming languages, and applets) restricted students from

creating dierent mathematical models and nding multiple solution

pathways. In addition, lack of experience in the subject matter limited

teachers’ capacity to use digital technologies and create modelling

problems. Accordingly, the lack of connection between content

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knowledge and competence in using technology restricted the exible

and creative use of technology in learning/teaching modelling (3%,

n= 1). Lack of experience in using digital technologies for modelling

can also negatively aect individuals’ emotions. For example, a few

studies reported that some students felt more condent if they solved

the modelling problem without digital tools because of their

deciencies in the use of technology (3%, n= 1). For these students,

modelling with technology may befrustrating (5%, n= 2). Individuals

with the least experience with technology may fail to beproductive in

modelling activities when using technology (3%, n= 1). In addition,

individuals unfamiliar with the use of technology for modelling faced

problems with adapting to more open and collaborative modelling

activities using dierent technologies (3%, n= 1). Further, some

students may nd it dicult to eectively manage their time (5%,

n = 2), and using new technologies for modelling may increase

students’ cognitive load (3%, n= 1) and make them exhausted because

of the time-consuming processes required to use technology for

modelling (5%, n= 2). Additionally, even if students and instructors

are willing to use technologies for modelling, the implementation of

these technologies in schools may bedicult because of their cost

(3%, n= 1).

As already mentioned, one of the most oen reported potential

challenges to the use of technology in modelling is the black-box

problem (21%, n = 8). From a side perspective, a variety of

investigations concentrated on the “black box” term to using digital

technologies. According to O’Byrne (2018), this term refers to any

complicated system whose inputs and outputs weknow but whose

inner workings wedo not. e black box issue frequently arises when

the creator and user are not the same person (Greubel and Siller,

2022). Concerning this challenge, research has shown that the

diculties frequently encountered in solving modelling problems in

digital group work appear to be a direct result of the automatic

calculation provided by technological tools (Siller etal., 2022). Studies

highlighted that for students who avoided necessary validity checks,

it might beeasy to blindly trust digital technologies, get lost in the

modelling process, and disengage from the solution to the modelling

problem. Studies also reported that challenges regarding the black-box

issue could directly be related to the consequences of automatic

calculations performed by technology (e.g., calculators, applets,

specialized soware, and spreadsheets) or use of the data and graphs

provided by digital tools, which might obscure the meaning behind

calculations and mathematization in modelling approaches. According

to a few studies, learners may focus solely on a certain approach to the

modelling process and may not be aware of dierent ways to

solve tasks.

Furthermore, our analysis revealed that instructors’ beliefs may

prevent the use of technology in modelling education due to black-box

concerns. According to a few studies, some teachers believed that

learners must rst learn the fundamentals of mathematics and then

begin to use digital technologies in modelling education. Otherwise,

the teachers believed, learners could not fully understand the

mathematical procedures used in the modelling process. is result

conrmed that instructors’ beliefs may strongly restrict the integration

of technology in mathematical modelling education.

5. Discussion

is descriptive systematic review study focused on current

research on the potential advantages and challenges of digital

technologies in mathematical modelling education. Weanalyzed 38

peer-reviewed studies. Our results conrmed that the opportunities

oered by technology in mathematical modelling education outweigh

its challenges, which is a promising result. e positive role of

technology in modelling aligns with the results of previous studies

(Molina-Toro etal., 2019; Cevikbas, 2022), although the challenges

generated by digital technologies in modelling have not been explored

suciently to date. In the following sections, wediscuss the results

within three main categories: (1) research trends, (2) the main

advantages of technologies, and (3) important challenges to the use of

technologies in mathematical modelling education.

5.1. Research trends in the use of

technology in mathematical modelling

education

It is promising that researchers from all continents contributed to

the eld, but there was heterogeneity in the distribution of the

reviewed studies by country (researchers from the United States,

Australia, and Germany dominated), which may point to the

pre-existing educational inequalities of countries in terms of accessing

the necessary digital technologies and using them for the purpose of

learning and teaching modelling. is result should trigger researchers

from dierent parts of the world, to engage in the most recent

discourse on the use of technology in modelling education. Given that

the activities of a domain are framed by its culture (Brown etal., 1989),

researchers from dierent cultures may generate interesting strategies

TABLE7 Technology-related challenges in modelling.

Category n*%** Sample

research

Lack of competence/

experience in using

technology

12 32 Merck etal. (2021)

Black-box 8 21 Geiger (2011)

Time consumption,

exhaustion 2 5 Simon and Cox

(2019)

Frustration/annoyance 2 5 Frejd and Ärlebäck

(2017)

Time management 2 5 Orey and Rosa (2018)

High cognitive load 1 3 Jupri and Drijvers

(2016)

Technical problems 1 3 Merck etal. (2021)

Beliefs 1 3 Geiger (2011)

Adaptation problems 1 3 Orey and Rosa (2018)

Cost 1 3 Flores etal. (2015)

Lack of condence 1 3 Flores etal. (2015)

Lack of creativity 1 3 Watson and Enderson

(2018)

Lack of engagement 1 3 Geiger etal. (2010)

*n represents the number of studies. **Percentages were calculated over 38 studies.

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for integrating technology into modelling. Successful implementations

across the world may contribute to existing knowledge and experience

in the eld. In this vein, researchers should consider dierent cultural

contexts of research that investigate the power of technology in

modelling education. ere are many opportunities for future

intercultural and cross-cultural research on mathematical modelling

education (Cevikbas etal., 2022). Another reason of the heterogeneity

in the geographical distribution of the studies might berelated to the

manuscript selection criteria used in this review. For instance, the

exclusion of publications written in languages other than English may

have resulted in the exclusion of potentially interesting studies from

non-English speaking countries.

Our review showed that qualitative research techniques were

frequently used by researchers. is result is supported by Hidayat

etal. (2022) and Schukajlow etal. (2018). Conducting large-scale

quantitative studies may provide more insight into the development

of modelling education across the world, attaining greater knowledge

and understanding of modelling with technology.

Another gap in the eld is the lack of research on the eects of

technology on modelling in early school years (i.e., primary

education). Although it is possible for younger generations, as digital

natives, to show interest in learning with technology (Prensky, 2001),

some technical glitches may arise in the use of educational

technologies in modelling (Merck etal., 2021) and these glitches may

negatively aect younger students’ learning interest. Additionally,

extensive use of technology among younger age groups may lead to

concentration problems in learning activities (Landhuis etal., 2007).

In this regard, it is necessary to investigate the appropriateness of

technology use in early school years and examine possible strategies

for integrating technology into modelling. Research on the

consequences of technology use and how this impacts junior learners’

academic, cognitive, and socio-emotional development is in its

infancy. More high-quality research is needed to better understand the

potential of digital technologies for children (Gottschalk, 2019).

Another important result of the current review study is the trend

regarding mainstream technologies and their intended uses in

modelling. Our analysis revealed that researchers and educators have

implemented diverse technologies in mathematical modelling

education; 18 dierent technologies were used in the reviewed

studies. e most popular technologies were DGSs, Internet and

web-based tools, CASs, mathematically enabled design and

engineering soware, spreadsheets, graphing calculators, simulations,

videos (digital resources), computers and mobile devices (digital

devices). Molina-Toro et al. (2019) also reported that studies

frequently used CASs, DGS, and spreadsheets, which is partially

compatible with our results, but we have found more diverse

technologies used in studies.

Our results also reveal the lack of application of emerging

technologies (e.g., augmented and virtual reality and articial

intelligence) and technologically rich innovative pedagogies (e.g.,

ipped classroom and blended learning) in mathematical modelling

education. Although new technologies and innovative instructional

approaches have not yet attracted much attention in the eld of

mathematical modelling, this decit may have arisen due to challenges

encountered during the integration of these innovations into

modelling education. To overcome this problem, collaboration with

experts in the eld of educational technology may beadvisable, or

professional development programs may help to improve educators’

and learners’ skills regarding technology use in

mathematical modelling.

Dierent technologies may serve dierent purposes in

mathematical modelling education. Our results conrmed that digital

technologies were frequently used for

• solving problems;

• visualizing data, models, results, or representations;

• accessing desired data and information;

• validating solutions or models;

• supporting predictions and calculations; and

• evaluating and interpreting models and solutions.

ese purposes support engagement in dierent stages of the

modelling cycle. is issue is discussed in detail in the

following section.

5.2. Advantages of using digital

technologies in mathematical modelling

education

As mentioned earlier, our analysis revealed that digital

technologies can support learners and instructors in the modelling

process in various ways. It is noteworthy that the vast majority of

studies reported positive results regarding the academic development

of learners. Many researchers focused on the positive role of

technology in learners’ knowledge, competence, and understanding

of the modelling process (e.g., Sacristan and Pretelin-Ricardez, 2017;

Asempapa and Love, 2021; Merck etal., 2021) as well as their skills in

developing or modifying a model or solving modelling problems with

the help of various technologies (e.g., Lingeärd and Holmquist, 2001;

Galbraith etal., 2003; Daher and Shahbari, 2015; Geiger, 2017). Our

results revealed that technology has played a great role in increasing

students’ understanding of modelling concepts by providing

visualizations and multiple representations (e.g., Brown, 2015;

Greefrath et al., 2018). It also assists individuals in creating new

solution pathways for modelling problems (e.g., Galbraith etal., 2003;

Geiger, 2017; Molina-Toro etal., 2022). In this way, technology can

enhance connections between various types of mathematical

knowledge (Geiger, 2011). Overall, studies reported that technology

oered plenty of opportunities for students and conrmed that

technology can be successfully applied at dierent stages of the

modelling cycle, including simplication, mathematization, making

connections, evaluation, interpretation, and validation (Siller and

Greefrath, 2010; Geiger, 2011; Daher and Shahbari, 2015). In line with

our results, Molina-Toro etal. (2019) found that studies on modelling

used digital tools to visualize the representation of data, make

complicated calculations, develop or validate mathematical models

and simulate phenomena. Furthermore, technology might accelerate

the transition between these stages. Considering the complexity of the

modelling process, the reported outputs of technology usage in

mathematical modelling are promising. However, Ramirez-Montes

etal. (2021) oer a dierent perspective than most other researchers,

stating that technology may not applicable to all stages of the

modelling cycle. For example, they argue that technology provides

great opportunities for calculation and measurement, but not for

interpretation of the results. ese mixed results suggest that future

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studies should explore the application of dierent technologies

separately for each phase of the modelling cycle. In addition, more

studies should compare the potential of technologically rich

approaches and conventional approaches for learners’ academic

development in the context of modelling.

Apart from the academic potential of digital technologies, our

review showed that technology may have psychological and emotional

benets for learners and instructors. Some studies reported that

students became motivated to work on modelling tasks with the help

of technology and that they were satised with being active in the

modelling process (e.g., Sacristan and Pretelin-Ricardez, 2017). ey

also enjoyed using technology to solve modelling problems (e.g., Frejd

and Ärlebäck, 2017). Some studies highlighted that technology may

positively aect learners’ and instructors’ perceptions, attitudes,

interests, and self-condence during the entire modelling process

(e.g., Flores etal., 2015; Orey and Rosa, 2018; Watson and Enderson,

2018; Merck etal., 2021). ese empirical results implied that the use

of technology has positive impacts on students’ and instructors’

emotional development and contributes to their well-being. is is

crucial, as improvement of learners’ cognitive and emotional outcomes

are important goals of mathematics education (Schukajlow et al.,

2018). Students and instructors’ well-being is particularly important

amid the current challenges facing educational systems due to the

COVID-19 pandemic (Goldberg, 2021). Moreover, our results

indicated that the use of technology stimulated learners to besocially

active in modelling activities, including participating in discussion

groups, interacting with peers and teachers, and collaborating to

complete activities (e.g., Geiger etal., 2010; Gallegos and Rivera, 2015;

Orey and Rosa, 2018). ese results illustrate that technology can

support social learning and help teachers to guide their students,

which in turn presents signicant opportunities for students to move

through the zone of proximal development (Cevikbas and Kaiser,

2020). is means that students can construct knowledge and

meaning socially with the help of technology.

Another salient advantage of technology is related to the cognitive

development of learners. According to the results of our review,

technology supported students in creativity, reasoning, mathematical

thinking, and error correction and decreased their cognitive load (e.g.,

Flores et al., 2015; Soares, 2015; Watson and Enderson, 2018;

Buchholtz, 2021). In addition, our results illustrated that technology

has the potential to encourage students to inquire about existing

modelling applications and explore new complex applications (e.g.,

Confrey and Maloney, 2007). Furthermore, technology can enrich

authentic applications of modelling as a bridge between theoretical

and real-world situations (e.g., Sacristan and Pretelin-Ricardez, 2017).

Lastly, wefound that digital technologies have great potential to

provide immediate feedback and scaolding when students need

support (e.g., Confrey and Maloney, 2007; Geiger, 2017; Buchholtz,

2021). In this way, technology can individualize learning, allowing

students to progress through the modelling process interactively and

at their own pace.

Overall, the results show that students need to beexposed to the

use of technology (especially domain-specic technologies) in

modelling activities (Cevikbas, 2022). Technology can help individuals

eectively deal with real-world problems, and as a result, learn about

content-related topics (Brown etal., 1989). Our review shows that the

majority of the empirical studies focus on the benets of digital

technology on students’ academic development in modelling, followed

by its advantages for students’ and educators’ emotional/psychological,

instructional/pedagogical, cognitive, and social development. ese

results conrm that digital technologies have the potential to change

mathematical modelling education positively by enhancing students

and educators in various ways.

5.3. Challenges of digital technologies in

mathematical modelling education

No instructional mechanism, including a technology-supported

strategy, oers only advantages or disadvantages. Although technology

aords many important opportunities for modelling, it may generate

several challenges for both learners and instructors. As was frequently

reported in the reviewed studies, technologically inexperienced

students and teachers might nd it challenging to successfully engage

in modelling activities using technology (e.g., Geiger, 2011; Villarreal

etal., 2018). Lack of knowledge and experience in technology use or

in content-related areas may limit individuals’ creativity in modelling,

especially for those with the least experience (e.g., Watson and

Enderson, 2018). Concerning the role of technology in students’

modelling competence, in their experimental study, Greefrath etal.

(2018) found no signicant dierence between the mathematization

competence of students in the experimental group, who worked with

GeoGebra in modelling, and students in control group, who worked

without digital technologies. In addition, they found that directly aer

the teaching unit, learners who involved in the DGS group tended to

perform slightly worse on the mathematizing test than the control

group. However, this result can only beinterpreted in relation to its

context, as there were three main limitations of the study. First, the test

used in the study was a paper-and-pencil test and did not contain any

dynamic tasks. Second, students in the experimental group were not

competent in the use of GeoGebra. ird, the four-lesson intervention

may change the structure of modelling instruction, but not students’

modelling competencies, given that it was such a short period of time.

erefore, Greefrath et al. (2018) highlighted that future studies

should focus on this issue when exploring the role of DGS in students’

modelling competencies.

From the emotional perspective, a few studies reported that

individuals may benegatively aected by the use of technology. For

example, they may feel disengaged in modelling activities, and they

may experience low self-condence throughout the process (e.g.,

Geiger etal., 2010; Flores et al., 2015). Another challenge may

beadapting to the new modes of learning and teaching created by

the use of technology. In other words, for some students, it can

bedicult to adapt to the less autocratic and more open forms of

communication between students and teachers in technologically

rich environments (e.g., Orey and Rosa, 2018). Furthermore,

technical glitches and time-consuming processes of using

technology may frustrate students and teachers (e.g., Frejd and

Ärlebäck, 2017; Merck etal., 2021) and may increase their cognitive

load (e.g., Greefrath etal., 2018). Moreover, the use of technology

in modelling may result in extra costs for learners and instructors,

as it requires energy, time, and nancial resources to access useful

technologies and learn how to use them in mathematical modelling

education (e.g., Flores etal., 2015; Simon and Cox, 2019). In some

cases, these challenges may hinder the eective use of technology

in mathematical modelling education.

Cevikbas et al. 10.3389/feduc.2023.1142556

Frontiers in Education 15 frontiersin.org

Another signicant challenge to the usage of digital technologies

in modelling education is that some individuals tend to simply use

technology in modelling without questioning what the technology is

doing mathematically. Many researchers have pointed to this so-called

black-box issue (e.g., Lingeärd and Holmquist, 2001; Geiger, 2011).

Although technology can foster the modelling process, it may also

lead individuals to avoid inquiry and validation of technological

outputs. Geiger (2011) found that the black-box risk could produce

negative teacher beliefs about the use of technology in modelling and

that some teachers might consider that students should learn basic

mathematics before using technology for modelling. However, in this

scenario, some low-prole students may never have a chance to work

with technology for modelling (Geiger, 2011). Concerning the

black-box issue as a potential challenge of technology, Lingeärd and

Holmquist (2001) emphasized that concentrating on validation of the

modelling may be more important than ever in the presence

of technology.

Remaining aware of all the potential challenges generated by

technology in modelling may encourage the use of well-designed

instructions to perform modelling applications successfully in the

future. In this vein, our review contributes to the eld by going beyond

previous review studies on this subject, among others, by disclosing

the potential challenges of digital technologies in mathematical

modelling education for learners and educators.

6. Conclusion

To sum up, various digital technologies are highly relevant for

mathematical modelling, and they provide increased computational

power and broaden pre-existing opportunities for approaches to

learning, teaching, and assessment (Niss et al., 2007). Our study

extends the debate on the potential of digital technologies to improve

mathematical modelling education by systematically reviewing

manifold advantages of digital technology and its challenges for

learners and educators. In addition, our review explores the

technologies most commonly used in the modelling process and for

what purposes they are used at which stages of modelling. In other

words, this descriptive systematic review study sheds light on trends

in the current research on the use of technology in mathematical

modelling education and contributes to the contemporary academic

debate on the potential of digital technologies and their applications

in mathematical modelling education. e results provide insight into

the successful integration of technology into mathematical modelling

process and support that various sort of digital technologies can

beused at all stages of modelling cycle. e existence concerns about

the integration of technology into entire modelling process (e.g.,

Monaghan etal., 2016; Doerr etal., 2017) makes this result remarkable.

e identied research gaps can guide future research in the eld, and

new technologies and innovative pedagogies (e.g., augmented reality,

virtual reality, articial intelligence, and ipped classroom) may

become more visible in mathematical modelling education. Overall,

researchers and educators can take advantage of our results to improve

mathematical modelling education with the successful integration of

digital technologies.

Author contributions

MC, GG, and H-SS contributed to the study conception, design,

and commented on previous versions of the manuscript. Material

preparation, data collection and analysis, and the rst dra of the

manuscript was written by MC. All authors contributed to the article

and approved the submitted version.

Conﬂict of interest

e authors declare that the research was conducted in the

absence of any commercial or nancial relationships that could

beconstrued as a potential conict of interest.

Publisher’s note

All claims expressed in this article are solely those of the

authors and do not necessarily represent those of their affiliated

organizations, or those of the publisher, the editors and the

reviewers. Any product that may be evaluated in this article, or

claim that may be made by its manufacturer, is not guaranteed or

endorsed by the publisher.

Supplementary material

e Supplementary material for this article can befound online

at: https://www.frontiersin.org/articles/10.3389/feduc.2023.1142556/

full#supplementary-material

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