Upgrading MatematiX: A Modern Approach to Learning Geometry for

Middle School Students

Daniela Popit

and Adriana Mihaela Coroiu

Department of Computer Science, Babes

-Bolyai University, Cluj-Napoca, Romania

Keywords:

Geometry Software App, middle-school Students, Gamiﬁcation, Serious Games.

Abstract:

The paper presents an upgrade version of our previous application MatematiX. The software has been upgraded

with additional features designed for middle school students (grades 5–7), emphasizing the development of

geometric reasoning skills necessary to address mathematical problems related to geometric ﬁgures. The

upgrades contain an instructional module on angles and their characteristics, presenting a visual explanation

of angle deﬁnitions, sequential guidance for angle measurement, and an interactive game that involves students

in angle measurement using a virtual protractor. The application was validated by a group of 70 middle school

students. Their feedback was overall positive, mentioning that the app helped them understand angles and

their measurement, even before formal classroom instruction, underlining its efﬁcacy as a resource for early

geometry teaching.

1 INTRODUCTION

In a continuously digitalized environment, the educa-

tional process must adapt to fulﬁll the requirements

and anticipations of today’s learners. In this sense,

technology can signiﬁcantly enhance learning, espe-

cially in areas that are frequently seen as difﬁcult,

such as geometry (Cahya and Indriana, 2023). Mid-

dle school students in Romania in their ﬁfth, sixth

and seventh years sometimes have difﬁculties com-

prehending geometric concepts, potentially resulting

in diminished interest and performance in the subject

(Moral-S

anchez et al., 2022).

Geometry, an essential discipline of mathematics,

cultivates logical reasoning, problem solving abilities,

and spatial cognition. Traditional pedagogical ap-

proaches, predominantly dependent on textbooks and

lectures, often lack the engagement and interactivity

necessary to captivate the attention of current digitally

native middle school students. Consequently, interac-

tive educational applications that facilitate geometry

learning through visual, tactile, and stimulating ap-

proaches have to be incorporated (Abdan Syakuran

et al., 2022).

The material, which is intended for ﬁfth, sixth, and

seventh grade middle school students, can effectively

https://orcid.org/0009-0005-6518-1505

https://orcid.org/0000-0001-5275-3432

reinforce knowledge and promote a natural compre-

hension of geometric ideas. It can enable the tran-

sition from repetition to active learning, providing a

tailored experience that enhances middle school stu-

dents’ curiosity and inventiveness. In this context,

the development and implementation of novel digital

solutions is important in order to upgrade the educa-

tional process in Romania.

The incorporation of gamiﬁcation and narrative

techniques in the development of a geometry appli-

cation for Romanian middle schools is relevant, as it

fulﬁlls essential educational requirements by improv-

ing engagement, motivation, and conceptual com-

prehension. Gamiﬁcation components, like prizes

and interactive challenges, enhance student engage-

ment and ongoing participation, whilst storytelling

offers context and relatability, aiding students in

comprehending intricate geometric concepts through

narrative-based learning experiences. Collectively,

these methods foster a dynamic, learner-centered en-

vironment that corresponds to contemporary instruc-

tional approaches and enhances the cultivation of crit-

ical thinking and creativity (Butean et al., 2015).

The paper presents an improved iteration of

MatematiX (Popita and Coroiu, 2024) incorporating

interactive angle measurement tools and instructional

modules, which have been validated by middle school

students for efﬁcacy in early geometry education.

800

Popita, D. and Coroiu, A. M.

Upgrading MatematiX: A Modern Approach to Learning Geometry for Middle School Students.

DOI: 10.5220/0013357000003932

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 17th International Conference on Computer Supported Education (CSEDU 2025) - Volume 2, pages 800-807

ISBN: 978-989-758-746-7; ISSN: 2184-5026

2 STATE OF THE ART

Current advancements in educational apps for geome-

try exhibit considerable promise for changing conven-

tional teaching methodologies. By incorporating ad-

vanced features such as interaction, personalization,

and gamiﬁcation, these solutions respond to the var-

ied learning requirements of students (Pambudi et al.,

2022).

Educational technology has produced multiple

projects aimed at enhancing geometry education.

Globally, platforms like GeoGebra, Khan Academy,

and Brilliant have been recognized for their impact

on mathematics education.

GeoGebra 1 is an open-source software exten-

sively utilized for the exploration of mathematical

ideas via dynamic visuals. It enables students to han-

dle geometric forms, execute transformations, and re-

solve issues interactively, so rendering abstract top-

ics more comprehensible (Hohenwarter and Hohen-

warter, 2002).

Figure 1: Geogebra APP.

Khan Academy 2 provides a systematic program

in mathematics, featuring interactive lectures, videos,

and practice tasks designed for different grade levels.

It underscores sequential elucidations to facilitate un-

derstanding (Prensky, 2011).

Figure 2: Khan Academy APP.

Brilliant 3 emphasizes problem solving and con-

ceptual comprehension by offering challenges and

circumstances that demand critical thinking and the

use of geometric principles (Liljedahl et al., 2016).

Figure 3: Brilliant App.

These platforms exemplify the efﬁcacy of inte-

grating visual learning, interactive activities, and per-

sonalized feedback that enhance mathematical think-

ing. Nonetheless, their content and structure are fre-

quently generalized and may not correspond to partic-

ular country curricula, such as Romania’s educational

framework for middle school geometry.

The present state of research offers substantial ev-

idence for the importance of software applications in

enhancing geometry education. These tools augment

learning via interactivity, motivation, and personaliza-

tion, while assisting educators in providing successful

instruction. For these applications to realize their full

potential, they must conform to the curriculum, tackle

accessibility concerns, and offer extensive assistance

for educators (Yan, 2023).

The paper (Moral-S

anchez et al., 2022) presents

Recent societal transformations necessitate that edu-

cation adapts to the digital natives of the 21st cen-

tury. These modiﬁcations demand a shift in the ex-

isting educational paradigm, wherein active method-

ologies and ICT serve as instruments for attaining

this objective by formulating comprehensive teach-

ing sequences that incorporate STEM techniques to

facilitate student learning. This article presents a

didactic idea in geometry centered on STEM ﬁelds

through a gamiﬁed approach. This idea integrates

resources such as AR, VR, tactile materials, and so-

cial networks with methodologies such as m-learning,

cooperative learning, and ﬂipped learning, facilitat-

ing methodological transformation. The study was

conducted over two academic years within an ac-

tion research framework. It diverged from a conven-

tional approach, and through two cycles, the tech-

nique was enhanced by the advantages that gamiﬁca-

tion offers to STEM initiatives in Secondary Educa-

tion. Data collected throughout the experiment were

analyzed using a mixed-method approach. The out-

comes of learning, implemented techniques, achieve-

ments, and mistakes, along with the ﬁndings of a

Upgrading MatematiX: A Modern Approach to Learning Geometry for Middle School Students

801

questionnaire, are delineated. Evidence indicates a

transition from a 50% failure rate to a 100% pass

rate in academic performance. The majority of stu-

dents exhibited increased motivation, with full group

engagement. Over 80% demonstrated pleasant emo-

tions, and cooperative learning enhanced group cohe-

sion (Moral-S

anchez et al., 2022).

Research by Jones (Jones, 2013) demonstrates

that interactive geometry software enhances spatial

reasoning and conceptual understanding. By visualiz-

ing and manipulating geometric shapes, students de-

velop a deeper comprehension of abstract concepts.

The dynamic nature of such tools fosters engage-

ment, particularly in middle school learners who ben-

eﬁt from visual and experiential learning.

Research conducted by Hamari and Koivisto

(Koivisto and Hamari, 2019) demonstrates that gam-

iﬁcation components, including points and prizes,

markedly enhance student motivation and engage-

ment in educational activities. This method is es-

pecially efﬁcacious for geometry, where interest fre-

quently diminishes due to the subject’s apparent com-

plexity.

According to Kovanovi

c (Brooks et al., 2023),

adaptive learning systems enhance learning results by

customizing content to align with students’ capabil-

ities. Geometry programs that monitor progress and

modify difﬁculty levels offer tailored feedback, allow-

ing students to learn at their own speed and pinpoint

speciﬁc areas for enhancement.

Singh and Misra (Mishra and Singh, 2021) as-

sert that educational software incorporating teacher

resources, such as automated grading and lesson plan-

ning, improves instructional efﬁciency. Educators can

utilize these traits to discern student challenges and

formulate targeted solutions, thereby enhancing the

efﬁcacy of geometry instruction.

Guti

errez et al. (Guti

errez and Penuel, 2014) em-

phasize the necessity of connecting educational soft-

ware with the school curriculum. Applications devel-

oped with national standards are more likely to be em-

braced by educators and effectively incorporated into

classroom instruction.

Valverde and Garrido’s (Valverde-Berrocoso

et al., 2020) study identiﬁes challenges including

restricted access to technology, inadequate digital

literacy among educators and learners, and opposi-

tion to transformation within conventional teaching

settings. Confronting these obstacles is essential for

the effective deployment of geometry software.

Serious games are games designed for more than

just pure entertainment. Used in all kind of ﬁelds

nowadays, serious games are created for mastering

certain skills. while playing a serious game, the user

can develop or reinforce knowledge while having an

entertaining and interactive experience. These kinds

of games have proven their efﬁciency for preschool

and primary education, not only in learning Mathe-

matics, but other subjects too. For example reading,

writing, strategic abilities, problem solving, creativ-

ity, science, geography and so on as described in the

paper (Papanastasiou et al., 2017).

Playing games is seen as a recreational activity

by most students who struggle to learn the traditional

way and consider it a burden. That means that serious

games could spark their interest in learning by creat-

ing fun games that help them assimilate and exercise

the learned notions through play. This aspect is cru-

cial, as the more students engage in a learning activity,

the better their academic achievements may be. That

is the main reason why even if developing games for

all the academic curricula might seem as an unneces-

sary long struggle, it is a worthwhile endeavor.

A game in itself, increases the level of involve-

ment of the user, allowing them to be spontaneous,

test different outcomes without a physical punish-

like consequence. They have the possibility to play

a game multiple times, which increases their knowl-

edge in the subject that the serious game is trying to

teach. This way the calm and mental cognition with

which a real life situation will be faced is developed;

the user is conscientious that a real life situation can

have multiple outcomes and that they have to discover

the best solution to solve the problem faced.

A study conducted in Greece, Portugal and Italy

(Barbieri et al., 2021) discovered that serious games

can increase students motivation, and deepen their un-

derstanding of math concepts. The researchers de-

veloped a serious game, CLASH OF WIZARDRY,

which was tested in all three countries, with around

400 students. The process showed that a carefully

developed serious games, properly aligned with the

curricula, would be valuable tools for supporting the

educational process. The study did not only inﬂuence

the STUDENTS, but also the teachers, some of them

retaught their way of teaching mathematical subject

after taking part in the experiment.

The experiment also proved that this kind of appli-

cation would need efforts from the teachers, it would

be necessary for them to ﬁnd a way of integrating

these types of materials in the teaching process.

3 TECHNICAL

IMPLEMENTATION

The application architecture has not changed since the

ﬁrst implementation of the app. The application fol-

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802

lows the classic Server-side web application architec-

ture using c# for the API with Microsoft SQL Server

and Html, JavaScript and CSS for the interface.

We mention here one of the main HTML5

elements used by our application, the

<canvas> ... </canvas> tag. This element

represents the base for drawing all the elements for

the games and explanations using JavaScript code.

Elements are being redrawn on the canvas, at a

certain speed or are scheduled to be drawn at a certain

time during the animation in order to create a smooth

look for the animation using different functions spe-

ciﬁc for the canvas element.

We have redesigned the colors in the application

interface to ensure that the resources can be used

by people with various visual impairments. For this

we used the feature Accessibility tools provided by

Adobe Color website.

4 THE NEW SET OF FEATURES

INTRODUCED IN THE

APPLICATION: MatematiX

We decided to add some new features to our Matem-

atix application for the older pupils, mostly for middle

school students (5th, 6th, 7th grade). We approached

the subject of geometry, given the fact that for learn-

ing geometry, children have to develop a geometric

way of thinking in order to be able to solve mathe-

matic exercises with geometric ﬁgures.

We created a new set of features for the educa-

tional unit that deﬁnes angles and their properties: a

visual explanation of the deﬁnition of an angle, offer-

ing instructions for how to correctly measure an angle

and a game that tests the process of measuring angles

using a protractor.

4.1 First Feature: The Angle. Deﬁnition

and Properties

This webpage consists of a visual explanation of an

angle following the deﬁnition: An angle is formed

from two half-lines that extend from the same point

of origin.

When users ﬁrst arrive on the webpage, an anima-

tion is triggered that shows two lines moving to the

center of the canvas. After the lines have both reached

the center, their commune origin, the point O, appears

on the screen, and the now half-lines grow for a brief

moment in the opposite directions of O in order to

demonstrate that because they are half-lines, they can

each grow inﬁnitely from the ﬁxed point.

Figure 4: Explanation - ﬁrst part.

At the end of his grow animation, point A appears

on the ﬁrst half-line and point B appears on the second

half-line. Following the end of the animation, a text

is written on the canvas that presents possible names

and notations for the drawn angle, and a button with

the text ”Measure the angle” appears under the written

text.

If the user clicks on the mentioned button, the

previously written text is erased and another text ap-

pears above the drawn angle that instructs the user

how to correctly measure the angle. The angle that

was present in the previous animation remains on the

screen, and the mouse is transformed into a protractor

(see Figure 5) that can be used to measure angles with

values from 0 to 360 degrees. The user can now use

the protractor to measure the angle.

Figure 5: Explanation - measure shown.

There are two other buttons present on the screen;

one with the text ”See the angle’s measure” and an-

other one with the text ”Measure another angle”. If

the user clicks on the ﬁrst button, the measure of the

drawn angle is shown on the screen. If the user clicks

on the second button, a new angle is drawn having

Upgrading MatematiX: A Modern Approach to Learning Geometry for Middle School Students

803

another measure, and the user can use any of the two

buttons (see Figure 5).

4.2 Second Feature: ”Find the

Enemies”

On this webpage, the users have access to a game

called ”Find the enemies”. The purpose of this game

is to test the user’s knowledge on how to correctly ﬁnd

and read the measure of an angle using a protractor.

To start the game, the user needs to click on the

”Start” button (see Figure 6). The interface of the

game looks like a radar, the screen is darken, and the

user can move an aim, like a ray of light, using the

mouse. The aim moves in a circular manner. There

are a number of monsters that move to the center of

the screen ( the number of monsters and their speed

varies depending on the level). To win the level, the

player has to hit all the monsters before they reach a

certain distance from the center of the circle.

Figure 6: Game’s ﬁrst screen.

There is also a protractor drawn as shown (see Fig-

ure 7) that can help the user measure the angles cor-

rectly. The player can see the number of targets that

are left, the level, and the score in the top left cor-

ner. There are two types of level for this game that

alternate while the user has not lost the game. One

level gives for each monster angle measurements in

degrees (see Figure 7). The user has to correctly posi-

Figure 7: Given angle measure.

tion the center of the aim at that angle in order to see

the monster. If the aim is centered correctly, the user

can press the spacebar and the monster disappears.

For the other kind of level, the player must ﬁnd the

monster using the aim, read the angle from which the

monster is coming from, write the measure in the sig-

naled input box and press Enter (see Figure 8). If the

provided measure is correct, the monster disappears.

The game goes on with these two kinds of levels until

Figure 8: Angle measure has to be written.

one of the monsters is at a certain signaled distance

from the center of the circle and the game is lost.

As for the previously designed games, there is a

score table where the players can see the top 5 scores

obtained in the game with the username of those who

got them. The children are motivated to play the game

to get higher on the leader board.

5 VALIDATION OF THE NEW

FEATURES

5.1 Describing the Process

To validate the application, we tested it with 70 chil-

dren from the school Ion Ag

arbiceanu from Alba Iu-

lia. We had two ﬁfth-grade classes, two sixth-grade

classes, and one seventh-grade class. In total, we had

70 children test the application.

We used the Smart board to project the applica-

tion in order for the whole class to see it. We chose a

volunteer from each class to come and play with the

explanation (measure angles with the protractor, look

at other types of angles, check if they have measured

it correctly etc.) while the other children watched and

answered questions about the presented geometry no-

tions.

Then the children came one at a time to the laptop

in front of the class and played the game. Some of the

children came in pairs, one of them would look for

the right angle measure on the Smart board while the

CSEDU 2025 - 17th International Conference on Computer Supported Education

804

other one would write the correct angle in the input

box.

After using the application, each child had to an-

swer the following questions:

• How would you rate the application from 1 to 5?

• How would you rate the navigation process on the

application from 1 to 5?

• Did the application help you understand an an-

gle’s properties and measure angles using a pro-

tractor?

• What would you change/add to the application?

• What other mathematical subjects would you like

us to approach in the future?

5.2 Results

An Excel document with the children’s answers was

generated at the end of the testing process.

For the ﬁrst question, ”How would you rate the

application from 1 to 5?” (see Figure 9) 90% of the

children rated it 5 out of 5, 9% 4 out of 5 and 1% 3

out of 5. Most of the children considered the appli-

cation very exciting and enjoyed interacting with it.

The answers to the second question ”How would you

Figure 9: Application rating.

rate the navigation process on the application from 1

to 5 ?”(see Figure 10) were similar to those of the ﬁrst

question, 89% of the children said that it was easy to

navigate the app.

All children said that the game and explanation

helped them understand what an angle is and how to

correctly measure it. This result is especially impor-

tant because the angle is a mathematical unit that is

learned only at the end of the ﬁfth grade and the ﬁfth

graders said that they now know how to measure an

angle, even if they have not learned that before inter-

acting with our application.

When asked ”What would you change to the ap-

plication?” 60% of the children said that they like

the application as it is. The remaining percentage

Figure 10: Navigating the app.

wanted different enemies for the game, or wished for

the game to be harder, or for the game to include more

geometrical subjects.

Figure 11: Suggestion’s chart.

6 SWOT ANALYSIS: THE

SIGNIFICANCE OF A

GEOMETRY INSTRUCTION

APPLICATION IN ROMANIA

For the question ”What other mathematical subjects

would you like us to approach in the future?”, we rep-

resented the answers in a chart (see Figure 11). The

answers were: The Gauss Summation, Fractions, Di-

visibility, Calculations with Ratios, Computation with

Parenthesis, Pythagoras’s Theorem, the Circle, par-

allel lines, Quadrilaterals, Calculations with Degrees

etc. The children noted that they would see the use

of this kind of software in helping them learn those

notions.

The children managed to play the game very well,

after a few tries they even reached higher levels. The

teachers also considered the game and the explanation

interesting.

The use of a geometry teaching application for

Romanian middle school students presents several ad-

Upgrading MatematiX: A Modern Approach to Learning Geometry for Middle School Students

805

vantages that could substantially improve the educa-

tional experience. A key advantage is the interactive

nature of these applications (Zaharin et al., 2021), en-

abling dynamic visuals and real-time exercises that

enhance comprehension of geometric ideas. The in-

corporation of gamiﬁcation aspects within the appli-

cation may enhance student engagement and motiva-

tion. Moreover, the software’s personalization and

ﬂexibility features provide the adjustment of infor-

mation to individual learning levels while monitor-

ing progress, enabling teachers to efﬁciently identify

and solve students’ weaknesses. Such tools provide

signiﬁcant assistance to educators by supplying pre-

constructed resources and automated assessment ca-

pabilities, thereby conserving time and improving in-

structional efﬁcacy. Furthermore, the program guar-

antees access to current, curriculum-compliant in-

formation, incorporating contemporary pedagogical

methods that promote innovation in educational set-

tings. A notable asset is its capacity to enhance

students’ digital competencies, preparing them for a

technology-oriented future.

Considering these positives, speciﬁc drawbacks

must be recognized. Economic and infrastructural

obstacles provide considerable difﬁculties, as not all

educational institutions or households have access to

the necessary technology or dependable internet con-

nectivity. Moreover, numerous schools in Romania

have deﬁciencies in the technological infrastructure

required for the effective integration of such technolo-

gies (Durach et al., 2021). Digital literacy consti-

tutes a constraint, as certain educators and learners

may encounter difﬁculties in utilizing the program,

necessitating investments in training and adaptation.

Excessive reliance on technology may lead students

to depend excessively on the application, thus limit-

ing their capacity to solve impediments manually or

comprehend concepts profoundly. Moreover, if the

application’s content does not entirely conform to the

national curriculum, it may be considered irrelevant

or inadequately utilized by instructors.

The external environment offers numerous op-

tions for the effective execution of a geometry teach-

ing application. The growing utilization of digital

tools in education in Romania creates a conducive en-

vironment for the integration of such software. This

transformation is helped by governmental and Eu-

ropean Union programs designed to enhance digi-

tal infrastructure in educational institutions, including

funding prospects for execution. The increasing sig-

niﬁcance of STEM education underscores the neces-

sity of a geometry-centric tool, as geometry cultivates

essential abilities like spatial reasoning and problem-

solving (Moral-S

anchez et al., 2022). Parental sup-

port for interactive and contemporary teaching tools

is growing, highlighting the potential acceptability

of such an application. Partnerships with local edu-

cational authorities, non-governmental organizations,

and educational technology ﬁrms offer additional av-

enues for promoting extensive adoption and integra-

tion.

Nevertheless, speciﬁc outside threats can affect

the execution and efﬁcacy of any project. Economic

discrepancies among various locations may intensify

the digital divide, marginalizing some student de-

mographics and fostering inequity in educational ac-

cess. Resistance to change from educators and par-

ents favoring conventional education techniques con-

stitutes a notable impediment. Moreover, programs

that gather and analyze student data may encounter

examination under GDPR and other privacy stan-

dards, requiring stringent compliance requirements.

Technological complications, such application fail-

ures or device incompatibility, may lead to customer

displeasure. Ultimately, the existence of other educa-

tional applications, including established foreign al-

ternatives, may restrict the market adoption of a newly

launched application.

7 CONCLUSIONS

After improving and testing our application, we con-

cluded that a geometry teaching application for mid-

dle school students in Romania has signiﬁcant poten-

tial to update and enhance the educational process.

The children and teachers who participated in the test-

ing exercise found the application useful and engag-

ing, which is an encouraging result.

However, the success of this type of software

hinges on overcoming both internal and external con-

straints. A concentrated strategy will be necessary to

address infrastructure and training obstacles, synchro-

nize content with curriculum, and ensure compliance

with data protection requirements.

Additionally, the teacher’s involvement and will-

ingness to try this kind of software are essential for

its successful implementation and integration in the

educational system.

Furthermore, capitalizing on opportunities such

as digital education trends and collaborative partner-

ships can promote the extensive adoption and efﬁ-

cient use of the program, ultimately revolutionizing

the teaching and learning of geometry in Romania.

CSEDU 2025 - 17th International Conference on Computer Supported Education

806

8 FUTURE WORK

Following the results of this experiment, we found

how we can better our application. First, because we

saw an interest for this kind of software from older

children (5th, 6th, 7th grade) we wish to create more

resources for them, centered on the needs that they

brought up while testing the application (see Figure

11).

Secondly, we would like to make the application

adaptive to any kind of screen so the children are be

able to use it on their phones too.

We also wish to further research how we can best

integrate artiﬁcial intelligence into our application

and what other features we would be able to introduce

with the help of AI.

Moreover, we want to improve our current re-

sources based on the feedback received so far. One

of the improvements would be to add sounds in the

games and more visual animations.

Last but not least, we want to test both existing

features and future developments in various educa-

tional contexts that involve more Romanian schools.

A solution for this would be to deploy the application

and link it with a complex feedback form that teachers

and students would ﬁll out after using the application.

Enough support from different schools and teachers

would be much needed.

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