This study explores how online mathematics games contribute to Grade 8 learners’ understanding of basic principles and more sophisticated aspects of algebra. This project documents the trajectory of a purposive sample of 30 Grade 8 learners doing mathematics and one mathematics educator. The study is premised on the argument that learners with the guidance of the teacher can grasp algebraic concepts better and learn to manipulate these imaginatively and independently, by integrating new online mathematics games into standard classroom teaching of mathematics. The study was located within the interpretive qualitative research paradigm and used a case study approach. Data were collected by means of (1) lesson observations, (2) questionnaires and (3) semi-structured interviews. The data collected were analysed through the lens of the sociocultural theory, social constructivism and the activity theory. This study supports the view, set out in the literature reviewed, that the way in which resources are utilised can substantially improve the teaching and learning of algebraic concepts. Teachers should encourage learners to venture into the world of online mathematics games to learn algebra because they help learners to be creative, look for patterns, make conjectures, collect data, express their own thoughts, accept the ideas of others and establish structured forms of cooperation. The teacher’s role is to show and guide the learners how to use online mathematics games to solve mathematics problems. This study’s main recommendation, among others, is a revision of the curriculum to integrate online mathematics games into all subjects in classrooms at all levels.

As the result of complex historical, socio-economic and political factors, post-liberation South Africa presently is embroiled in a predicament in mathematics education, especially in algebra, which has resulted in the country positioned last in the Third International Mathematics and Science Study (Smith & Hardman,

Although algebra provides access to forthcoming studies and mathematically significant ideas, it often acts as a wall that blocks the path of many learners. As Drijvers (

Online mathematics games introduce learners to fundamental steps of learning where they easily attain knowledge without consciously sensing that they are being taught through gameplay guided by the teacher. An online mathematics game enables learners who would otherwise have given up to flourish in mathematics. The aim, therefore, is to assess how and why online mathematics games attract, educate, engage and stimulate learners to find out more about algebra. There is limited literature on how online mathematics games advance learners’ understanding of algebra. Becker (

This study, therefore, aims to investigate how online mathematics games help Grade 8 mathematics learners understand algebra. Many authors argue that algebra teaching in South Africa could be improved by providing suitable and well-designed online mathematics games that address learners’ weaknesses in algebraic concepts (Jupri & Drijvers,

There is substantial evidence in the literature on the advantages of online mathematics games for teaching mathematics (Barkatsas, Kasimatis, & Gialamas,

Wiersum (

The use of online mathematics games is effective only when the games are used to encourage learners to think and make connections between objects and an abstract mathematics idea (Murray,

Zoltan Dienes’s work (1969 cited in Moyer,

On the other hand, other scholars such as Mahmoudi, Koushafar, Saribagloo and Pashavi (

This study used two online games, namely Dragon Box Algebra and Algebra Meltdown. With Dragon Box, algebra concepts are simplified into a simple game and it is an innovative educational game that through gameplay teaches learners concepts relating to solving algebraic equations. Dragon Box covers the following algebra concepts: addition, multiplication and division. By controlling cards and attempting to confine the Dragon Box on the other of the online game, the learner progressively learns the tasks required to confine

These online mathematics games were designed to reinforce algebraic concepts. They are both intuitive and engaging and contain fun elements. Learners develop skills to solve equations in a playful and colourful game environment, where they are encouraged to experiment and be creative (Pearce,

In order to have in-depth information on whether online mathematics games contribute to learners’ understanding of algebra, the study used the following theories: activity theory, socio-constructivism theory and sociocultural theory. These theories are relevant and help us comprehend the development of learners’ understanding in the process of learning mathematics. In addition, the chosen theories agree on the notion that knowledge is inseparable from practice. Learners understand better by doing and mediating through tools and signs.

The activity theory views the human mind as the product of our interaction with other people, objects and artefacts in the context of everyday activity (Kaptelinin & Nardi,

Engestrom (

Activity theory diagram.

Engestrom and Sannino (

Subject: This is the focal point of the examination; for our motivations the subject is the learner.

Mediating artefacts: These are apparatus that the subject utilises to follow up on the item space. Altogether, the apparatus intervenes thought during the cooperation between the subject and the setting within an activity. Crucially, apparatus are not non-partisan. They have built-up history of utilisation and convey inside them social implications (Kaptelinin,

Rules: These are standards, conventions and social collaborations of the schoolroom, which drive the subject’s activities (Hardman,

Community: The subject is an individual from a network who takes up interest in following up on the mutual item. There is division of work inside the network, with obligations, assignments and control unceasingly being negotiated (Hardman,

Division of labour alludes to the arrangement of duties, errands and force relations inside a mathematics classroom just as all through the school. The introduction of the online mathematics games can possibly compel a move in the job of the instructor and learners, with learners working more as instructors of other learners in the mathematics classroom.

The sociocultural theory is rooted in the concept that learning takes place in cultural contexts and is mediated by language and other symbol systems (John-Steiner & Mahn,

The study follows a qualitative approach using an interpretive paradigm, with a case study design. Qualitative research encompasses the study of groups of people so the researcher can guide and support the creation of a hypothesis (Frederick,

According to Adendorff (

The study was undertaken at a high school in the Metro North Education District in Cape Town, Western Cape. The school accommodates all learners from different social backgrounds. The school employs English as the language of teaching and learning. The researcher chose a Grade 8 class because that was the foundational class for high school mathematics. The school climate was conducive to learning which made it easy to engage learners. The school has limited technological resources: mathematics learners are not readily exposed to technological aids during lessons. The site was chosen because it was easily accessible and logistically convenient. In line with Wegner’s (2007, p. 214) argument, convenience sampling was chosen as it allowed the researcher to select convenient sampling units. The choice of a single school allowed for an in-depth case study and addressed time constraints and accessibility problems.

The participants for this study comprised 30 Grade 8 learners and the Mathematics teacher. The class was large enough to facilitate in-depth comprehension of the contribution of online mathematics games on algebra understanding in Grade 8. Thus, the sample consisted of 31. The composition of the sample is described below:

Grade 8 Mathematics learners

Grade 8 Mathematics teachers

Total sample size:

Data collection lasted four weeks in the month of August 2018. The principal and the teacher were informed about the study, and permission was granted. All participant learners provided informed consent with their parents signing the parent consent forms. The online mathematics games were used as supplement to the class instructions. No additional time was provided for playing the online mathematics games. The games were played during the regular class time for 15 minutes per period to reinforce the concept taught during that lesson and to make abstract concepts clear to the learners.

Learners were directly observed as they played online mathematics games during the lesson. As noted by Creswell (

A questionnaire was also used to gather data from the participants. Through the questionnaire, participants’ perspectives and perceptions on the use of online mathematics games when doing algebra were recorded. According to Van Vuuren and Maree (2002, p. 281), the use of questionnaires is economical, ensures anonymity, gives participants enough time to think about the answers they want to give and provides room for uniform procedures. The questionnaires were completed by all 30 participants in the research. They became the lens through which to measure and understand how the participants viewed their own development after using online mathematics games (Schmidt et al.,

Moreover, interviews were conducted to generate feedback on the contribution of online mathematics games to learners’ understanding of algebra. Participant learners were interviewed individually, with the researcher audio recording the conversations. The interviews focused on their views on online mathematics games. The interview questions for the learners were developed based on their experiences during the lessons. Random sampling was used to choose six participant learners from a sample of 30 learners to take part in the interviews (Creswell,

The study utilises the inductive data analysis approach by employing data triangulation as it combined field observation and interviews. Themes were identified and analysed to capture the essence of online game-based learning through the voices of those who have participated directly in its implementation.

The study attained ethical clearance from the Cape Peninsula University of Technology’s Ethical Committee for the Faculty of Education and the Western Cape Education Department. All ethical measures were complied with. The study granted anonymity to research participants to ensure confidentiality. This contributed to the researcher gaining the trust of the participants thereby ensuring that the data are trustworthy.

Participants’ perceptions on the contribution of online mathematics games.

Statement | Number of respondents and percentage (%) response |
|||
---|---|---|---|---|

Yes |
No |
|||

Number | % | Number | % | |

Do you think learning without online mathematics games is boring? | 29 | 97 | 1 | 3 |

Do you feel comfortable playing online mathematics games? | 25 | 83 | 5 | 17 |

Do online mathematics games contribute to understanding abstract concepts? | 20 | 67 | 10 | 33 |

Do you feel the use of online mathematics games helped you in understanding algebra better? | 20 | 67 | 10 | 33 |

Do online mathematics games increase concentration levels of learners during lessons? | 24 | 80 | 6 | 20 |

Do online mathematics games arouse your interest in class? | 24 | 80 | 6 | 20 |

Is algebra difficult when taught without online mathematics games? | 24 | 80 | 6 | 20 |

The results in

The results in statement 1 revealed that the majority (97%) of participants agreed that learning without online mathematics games was boring while only (3%) disagreed with the statement.

In statement 2 the results revealed that most of the participants (83%) agreed that they felt comfortable playing online mathematics games while (17%) disagreed with the statement.

Statement 3 uncovered that most of the members (67%) agreed that online mathematics games contributed in understanding abstract concepts while (17%) disagreed with the statement.

In addition, the results in statement 4 revealed that most of the participants (67%) felt that the utilisation of online mathematics games helped them understand algebra better while (17%) disagreed with the statement.

Statement 5 revealed that most of the members (80%) agreed that online mathematics games increased concentration levels of learners during lessons while (20%) disagreed with the statement.

In statement 6 the majority of participants (80%) agreed that online mathematics games aroused their interest during lessons while (20%) disagreed with the statement.

Statement 7 showed that most of the participants (80%) agreed that algebra was difficult when taught without online mathematics games while (20%) disagreed with the statement.

Looking closely at the learners’ questionnaire responses, the following game effects were observed:

The online mathematics games had an experiential nature. That allowed learners to interact with familiar environments in the games and construct their mathematics concepts through completing game missions.

The online mathematics games changed learners’ perceptions on mathematics.

The learners understood the relationship between mathematics and real life. As a result, their mathematics phobia was diminished (Paraskeva et al.,

Six learners were interviewed after they had used online mathematics games to solve algebra. Each interview took 20 minutes and was audio-recorded followed by transcription. Various themes emerged that indicated the fluidity of the teacher’s and learners’ perspectives and understanding of online mathematics games. In-depth probing was employed to obtain additional relevant information. The main themes identified from the analysis of interviews related to learners’ beliefs on online mathematics games and learner motivation.

The following are some of the participants’ comments during interviews.

Learner 2 said that:

‘I didn’t really understand what equivalence was. The Dragon Box really helped me a lot because it simplified the algebraic concepts into a game. I now understand that both sides of the equal sign have the same value.’

The gameplay simplified the difficult algebra concepts as echoed by Learner 2. As argued by Star and Seifert (

Learner 3 said that:

‘For an expression like 2(

This narrative confirms Van de Walle’s (2013, p. 257) view that the variables used in algebra take on different meanings depending on context. For instance, in the equation 4 +

The questions asked during the interviews were important as they allowed the researchers to understand whether learners were familiar with the online gameplay as well as understanding the reasons for using online mathematics games. Interviewing the learners helped to cross-validate data from observations made during the lessons. The learners were of the view that the online mathematics games positively affected their algebraic understanding, focus skills and motivation. The narratives below support the views noted above.

Learner 2 stated that:

‘When our teacher introduced gameplay in our algebra lesson, I started looking forward to the next lesson. The lessons were now vibrant, accommodating and inspiring. I now understand mathematics concepts more than I did when we depended on textbooks only. Gameplay during lessons is the right way to learn mathematics.’

The interviews confirm that the learners’ achievements and motivation were positively impacted by the online mathematics games. Further, the comments express feelings of increased enthusiasm and eagerness towards learning through computerised games.

Learner 5 commented that:

‘The first week the gameplay made me feel embarrassed. Most of the learners were advancing to the next levels whilst I remained at the first. Though the teacher kept on guiding and explaining on how to play, as I kept on playing, I ended up being angry with myself.’

This isolated incident revealed by Learner 5’s comment shows that although learners can face challenges, they may continue to play until they win or advance to the next levels of the game. This determination by the learners, coupled with the frustration, can cause low self-esteem or aggressive behaviour, especially if the child keeps losing the game (Annetta, Minogue, Holmes, & Cheng,

Although a few learners expressed negative responses regarding the online mathematics games, the interviews showed that to a greater extent the online games positively influenced the learners because online mathematics games help learners to ‘be creative, look for patterns, make conjectures, collect data, express their own thoughts, accept the ideas of others and establish forms of cooperation’ (Siemon et al.,

This research provides a starting point for looking into the integration of online mathematics games into the teaching and learning environment for mathematics. This research provides a platform for integrating online mathematics games into the teaching and learning environment for all conventional mathematics topics. Based upon the findings and caveats of this research, teachers may safely encourage learners to use online mathematics games in the learning of algebra because online mathematics games help learners to be creative, to look for patterns, make conjectures, collect data, express their own thoughts, accept the ideas of others and establish forms of cooperation (Siemon et al.,

These findings indicate that learners spend a considerable amount of time playing digital games and tend to identify with the characters they adopt or take on in the course of playing the game. Thus, we need to further examine what boys and girls prefer in games in order to develop educational online games that suit different personality types and, more importantly, exploit multiple skills and intelligences, in true reflection of real-life collaborative environments, in the context of learning algebra specifically and mathematics in general.

According to Paraskeva et al. (

The relation between online mathematics games and self-esteem cannot be clearly defined yet, since research so far has yielded conflicting or ambiguous results (Paraskeva et al.,

From the first author: My sincere gratitude is conveyed to the following people who made it possible for my research to be successful:

My supervisor, Dr Stanley A. Adendorff for the support and guidance you provided me since I started this journey. You have given me so much of your time and expertise. Thank you for your ideas, suggestions and valuable insights and inspiration.

My editor, Dr Rusenga, thank you for your meticulous proofreading and editing, constructive suggestions, inspiration and technical expertise in formatting and the layout of this thesis.

My wife Evelyn for the love, care, support and motivation which directly contributed to my achievement. Thank you for not feeling ignored when I dedicated much of the time to my studies. My two children, Moreblessings and Asher, I thank them for their patience when I could not attend to their needs immediately.

The principal Mr Young for giving me permission to conduct research at the schools as well as guidance and advice.

The authors have declared that no competing interests exist.

T.M. was responsible for initiating and formulating the research, identifying the sample and collecting data, and writing up the research. SA.A. advised and guided the conduct of the research, proofread, edited and gave recommendations on the write-up, supplied resource materials and finalised the article.

Education Faculty Ethics Committee (EFEC), CPUT (certificate number EFEC 1-6/2018).

The researchers made it clear that participating in the research was voluntary and that if for some reason participants wanted to withdraw from it, they had the right to do so at any time. Participants were informed that they would be protected from physical or psychological harm, discomfort or danger that might arise due to any research procedures. Participating learners were told that the information gathered would be confidential and no one would know their identities except for the researchers. The names of the subjects were removed from all data collection forms as pseudonyms were used. The researchers obtained permission to conduct the research from Western Cape Education Department, Cape Peninsula University of Technology, and the principal of the participating school.

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Data lists and summaries, figures and tables can be obtained from T.M.’s MEd thesis.

The views and opinions in this article are those of the authors and do not necessarily reflect the official policy or position of any affiliated agency of the authors.