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Math in Minecraft: Changes in Students’ Mathematical Identities When Overcoming In-game Challenges

Erik Ottar Jensen, Thorkild Hanghøj

Aalborg University, Copenhagen, Denmark.

erikoj@hum.aau.dk

thorkild@hum.aau.dk

Abstract: This paper presents empirical findings from a qualitative study that uses Minecraft as a mathematical

tool and learning environment. Even though Minecraft has been used for several years in classrooms all over

the world, there is a lack of detailed empirical studies of what subject-related content students can learn by

working with the game. The study is based on a teaching unit for 5th grade, which focused on using the

coordinate system already embedded in Minecraft as a means of navigating and exploring the game in order to

solve mathematical problems. Based on a design experiment with the teaching unit, we explore the following

research question: How do 5th grade students experience a change in their mathematical identities when they

participate in an inquiry-based teaching unit with Minecraft? A thematic analysis explore data from six group

interviews. The theoretical perspectives used in the coding of data were based on domain theory and an

interpretive framework for understanding students’ mathematical identity. The key analytical findings regard

the students’ experience of the coordinate system as part of both the academic domain of mathematics and as

a part of their everyday domain playing Minecraft, how students actively use the coordinate system to

improve play in Minecraft, and how students experience new ways of participating in mathematics.

Keywords: Minecraft, mathematics education, student identity, domain theory, coordinate system

1. Introduction

Games have existed as a part of mathematical education for a long time and have been investigated for several

years (Bright, 1983; Oldfield, 1991). According to one review, games are used more frequently for teaching

mathematics than for other subjects (Hainey, Connolly, Boyle, Wilson, & Razak, 2016). Thus, there is a

widespread belief that games have a great potential in mathematics education.

Some scholars point to video games as an ideal medium for teaching mathematics in middle school (Devlin,

2011). Yet, recent meta-analysis show only small and marginally significant positive learning effects of using

games in mathematics education (Byun & Joung, 2018; Tokac, Novak, & Thompson, 2019). The proposed

potential for games are yet to be fulfilled. One issue raised in the reviews was that the researchers trying to

understand learning of mathematics with games are often specialized in other fields than mathematics

education. Most being from educational technology, computer science and engineering with only 5 of 71

researchers having a mathematics education profile (Byun & Joung, 2018). In this way, there is need for more

research on using games for mathematical purposes, which relate closer to the research field of mathematics

education.

One of the main reasons for teaching with games is to increase motivation. Student interest in mathematics is

reported to be one of the most significant predictors when determining mathematical performance and

perseverance (Hannula et al, 2016). Moreover, a prevailing problem for mathematics education is that many

students do not come to see mathematics as a constructive endeavour (Boaler, 2015). Cobb (2007) argues that

classroom activities being worthy of student engagement in its own right, from a student perspective, is an

important part of the cultivation of students interest in mathematics and should be considered an important

goal for mathematics educators. Thus, we want to address the use of games in math class by using the

theoretical construct of sociomathematical norms (Cobb, Gresalfi & Hodge, 2008) to understand how students’

mathematical identities are affected. This leads us to the research question: How do 5th grade students

experience a change in their mathematical identities when they participate in an inquiry-based teaching unit

with Minecraft?

2. Learning mathematics in Minecraft

Minecraft is an educational tool used in classrooms worldwide. Similarly, there has been conducted research

on the use of Minecraft to promote learning for several years, spanning a wide variety of subjects (Nebel,

Schneider & Rey, 2016). A number of studies have explored teaching activities with Minecraft in mathematics

educational settings. Some highlight envisioned potentials for the use of Minecraft for learning mathematics

and relate the use of the game to desirable mathematics education standards (Bos et al, 2014; Floyd, 2016;

Tromba, 2013). However, the explored potentials in these studies are based on rather limited empirical

examples. Other studies on Minecraft originate from the fields of computer science and educational

technology and report on class experiments (Al Washmi et al, 2014; Foerster, 2017; Freina et al, 2017) or

propose a study (Nguyen, & Rank, 2016) with Minecraft in a mathematics education setting. However, none of

the above articles use mathematical educational theories to understand student learning or analyze data. One

exception is the study by Kørhsen & Misfeldt (2015), which takes an ethnomathematical approach to

understanding mathematical activity in Minecraft in an after-school programme through Bishops six

fundamental categories (Bishop, 1991). Kørhsen & Misfeldt (2015) present evidence of player activity related

to each of the categories (Counting, Measuring, Locating, Designing, Explaining and Playing). They find that the

activities are influenced by the design of Minecraft, which challenges the students to visualize and systematise

constructions following the social and cultural conditions in the after-school programme. The children

collaborate and learn from each other and develop game narratives that requires demanding constructions. In

summary, the studies indicate potentials and promising teaching designs and approaches for using Minecraft

in mathematics education. However, there are few articles, which focus empirically on the players’

mathematical activities. In this way, there is a need for more detailed studies of how Minecraft can help

students learn mathematics.

3. Case: Teaching unit with Minecraft

The current study is based on a teaching unit with Minecraft in a 5th grade class (22 students), which involved

15 lessons distributed over five days in one week. One of the researchers conducted prior meetings with the

teacher, who contributed with input to the design of the unit. The initial idea for the intervention, originated

from the fact that a the mathematical concept of Cartesian coordinates from the mathematics educational

curriculum was accessible in Minecraft and that 3D navigation is a key challenge in the game. The accessibility

of such an underlying mathematical dynamic is not commonplace in commercial games, where the

mathematical rules are often hidden from the players (Lowrie & Jorgensen, 2015). Our initial hypothesis or

humble theory (Prediger, 2019) was that the mathematical concept of Cartesian coordinates could be

introduced as a means to solve the real player problem of locating objects in the Minecraft in order to help the

students master the game and also affect their understanding of the game. Minecraft worlds are randomly

generated so a key element in the game is the exploration of the specific virtual world you are playing in. But it

can be difficult to navigate Minecraft successfully and locate specific objects or other players can experience

problems such as having built a structure and not being able to return to that structure because you got lost.

3.1 Navigation with Cartesian coordinates

In Minecraft the player can access the avatars x, y and z coordinates in the game. The x-axis indicate position

on an east-west axis, the z-axis on a south-north axis, while the y-axis indicate elevation. See figure 1. One

whole number on the axis is equal to the length/height of one block in the game, which in turn is equals one

meter in the real world.

Figure 1: The x, y and z coordinates in Minecraft

When the players move their avatar in the virtual world, the values of the axis’ chance according to the

position. So moving directly up or down will affect the y-axis and moving directly towards the east will increase

the value of the x-axis. Looking at figure 2, we see a player avatar standing on the first, second and third step

of a staircase in Minecraft. For each picture the avatars coordinates is in the upper right corner.

Figure 2: Change in coordinates

Following the avatar through going up the stairs the y-axis changes from 68 to 69 to 70. The x-axis also changes

because the avatar is also moving west when going up the stairs. The change in the numbers after the decimal

point indicates that the avatar can be placed on different locations within one square-block.

4. Theoretical perspectives

Our research question is explored through two complementary theoretical perspectives: a domain theory of

educational gaming and an interpretive framework for analysing students’ mathematical identities.

4.1 Domain theory

Using commercial games in mathematics education involve an interplay of different in- and out-of-school

domains and knowledge practices, which raises a number of questions that must be addressed and negotiated

- i.e. what counts as valid knowledge and valid ways of doing math when playing games in the mathematics

classroom? Following the domain theory of educational gaming developed by Hanghøj et al (2018), the use of

Minecraft in the classroom is understood as an interplay of three domains illustrated in fig 3.:

1. The school-based domain of mathematics education. This involve particular forms of teacher-student

authority as well as validity criteria for determining mathematical knowledge.

2. The game domain of Minecraft. This both refers to the existing (if any) knowledge of Minecraft and

their experience of playing the game in the classroom, and

3. The everyday domain of the students. This relates to their lifeworld and everyday experiences beyond

having mathematics and playing Minecraft.

Fig 3

4.2 Mathematical identities

To understand how the use of Minecraft may affect students’ participation in mathematics education, we use

the notion of mathematical identity. According to Cobb, Gresalfi and Hodge (2008), normative identity

describes the obligations that define and constitutes the role of a good mathematical student in a specific

classroom. There are three different aspects of the classrooms obligations. Authority refers to whom the

students are accountable to, and how authority is distributed in varying degrees between students and

teacher. Agency address how the students are able to act legitimately in the classroom. There are two basic

forms: Disciplinary agency concerns students’ use of established solution methods, whereas conceptual agency

is about choosing methods, develop meaning and relations between concepts. The third aspect is

mathematical competence, which refers to what the student is responsible for in terms of mathematical

reasoning and argumentation. Finally, Cobb, Gresalfi & Hodge (2008) also introduce the notion of students’

personal identity, which refers to how the students relate to these obligations and see value in mathematics as

it is realised in the classroom. There are three typical ways of doing this: the students identify with the

obligations, they simply cooperate with the teacher, or they resist engaging in classroom activities. These

concepts allow us to explore how students experience their relation to mathematics and whether they see

value in mathematics as it is realized through the intervention.

5. Methodological approach

This pilot study is part of an on-going design-based investigation (Barab & Squire, 2004) of how commercial

games can be linked to curricular aims. The collected data is based on six semi-structured group interviews

(Kvale & Brinkmann, 2009) with two 5th grade students in each group. The interviews were conducted after

the enacting of the teaching unit. There were a majority of boys and of bilingual students in the class. The

teachers described the class as being disruptive and difficult to manage with a generally low performance in

mathematics with a few mathematically skilled students. The student groups were selected prior to the

intervention to represent a broad spectrum of mathematical achievement in class as defined by the teacher.

6. Analysis

The analysis is based on a thematic analysis (Braun & Clarke, 2006) of the data and is structured around four

overall themes relating to the students’ mathematical identities and their experience of the different domains.

The analysis will show a number of new connections between the different domains and how the normative

identity as a doer of mathematics in the intervention was different from their regular math class. The analysis

describes these existing and new possible ways of identifying with math class as available students positions.

6.1 Being a math student

This section explores the students’ experience of the obligations in everyday math teaching as they experience

it through regular math class. One theme is that doing calculations quickly is important to be considered

mathematically competent. Here Melanie is asked when she experience, that she is a good math student.

Melanie: When I know something. Or if I have listened and understood it. Then I can be fast and answer quickly.

For Melanie being a good math students is connected to how fast answers are produced, knowing something

or being able to understand the teachers explanation. Henrik also uses speed to describe what it means to be a

good student:

Henrik: … You have to be good at calculating, fast.

The examples shows that the quality of an answer and the experience of being a mathematically competent

student, is dependant on how fast answers can be produced. Henrik further explains that sometimes it is

simply best to know new concepts and answers before they are introduced by the teacher, because this gives

you an advantage in terms of answering quickly and correctly.

Another aspect is that the students rarely experience that activities and concepts from the mathematical

subject domain has connections with activities and concepts from their everyday domain. This can be seen

through Henrik reflections on the intervention:

Henrik: It was the first, almost.

Interviewer: It was the first?

Henrik: mm. approximately.

Interviewer: uhm. I’m just trying have to understand. The first what?

Henrik: I could use in all subjects, from mathematics.

Interviewer: Ahh. It was the first you have experienced in mathematics…

Henrik: That you can use in all subjects. Yes.

Henriks experience of the concept of the coordinate system in the intervention becomes a first in terms of

concepts that can be used outside of math class. The realisation of mathematics being connected to the

everyday domain is something he has very seldom experienced. But it also indicate that he might have

experienced it, or that he is aware that what he learns in math class can have connections to the world. The

use of the word “first” also seem to indicate that he expects more connections made. However, the subject

domain of mathematics as it is experienced through normal math class is characterized by being disconnected

from other domains.

The above examples and the other themes regarding regular math class, shows that the normative identity are

about listening and paying attention, especially when the teacher presents on the whiteboard. Disciplinary

agency is the primary way students legitimately can express agency. Talking with other students about a task is

often regarded as cheating and students are mainly accountable to the teacher with little distribution of

authority to the class. In the following sections, we will describe how new positions emerged in the class, when

the students were given opportunity to connect mathematical concepts to specific situations outside of math.

6.2 Being a mathematical Minecraft player

The position of being a mathematical Minecraft player refers to the students’ experiences of using the

coordinate system to remember and find places in Minecraft. When the students experience that they can use

the coordinate system in the game to solve the mathematical task given by their teacher in math class, they

establish new connections between the two already established, but initially separated domains; mathematics

and the everyday domain, which in turn transform both domains:

Interviewer: … have you learned anything new about the coordinate system that you didn’t know before.

(Hasan: yes) Or can you do something now that you couldn’t do before?

Hasan: Yes. Well. I didn’t know, even though I have been playing Minecraft a lot I didn’t know where the

coordinate system was. Even though i pressed F3 and it, then it appeared, but I didn’t know, I didn’t know what

it was. When I moved it just changed a lot and I turned it off again and I didn’t know what it was. But now, now

I know what it is. Now I use it often in Minecraft.

Interviewer: Okay, so you have used it afterwards (Hasan: Yes) after the course.

Hasan: Yes, because if I have to find something that I have forgotten but I have the coordinates to, then I can

just, then I can just go over to them.

Hasan knew that he could press F3 and prompt a series of information but could not translate the information

into something meaningful. After learning what the numbers mean, he uses them often to locate objects. In

terms of knowledge domains, Hasan uses activities in Minecraft (the game domain) to explain why the

coordinate system from the mathematical domain is useful. In this way, he creates a strong connection

between the different domains. His use of the coordinate system in Minecraft becomes a new way of

interacting with the game. If we expand the notion of agency in math class to understand the changes in how

Hasan play the game. Then his statements validates the use of the coordinate system as a legitimate way of

expressing what we could call player agency in Minecraft because it can be used to address actual challenges

in the game.

6.3 Being repositioned as math students

The previous example showed how the intervention created student positions in terms of being a

mathematical Minecraft player. However, the intervention also affected the students’ personal identity

towards mathematics. As an example, we will focus on two students Mads and Adam, who the teacher

deemed the best math students in the class. Here Mads explains how always being the first to finish tasks,

would put them in an awkward position.

Mads: And then they always get angry and say, you shouldn’t always say “we are finished, we are finished”...

But we understand why they say it.

Interviewer: Okay.

Mads: Because it is only. Most of the time we are the only ones who finish first. It may never, they can’t look

forward to finishing faster than us.

When mathematical competence is dependent on the speed of solutions and the same students often finish

the tasks first, the other students find themselves in a situation where it is difficult for them to be regarded as

mathematical competent. It seems that the other students feel they do not have a chance to be the first to

finish. Because of this they direct frustration and anger towards Mads and Adam. They had little knowledge of

Minecraft, but as we will see, they clearly identified with the mathematical content of the teaching unit. This

could be connected to the fact that the everyday classroom obligations presented a problem for Mads and

Adam, because the other students would get upset when they were not able to complete a task that Mads and

Adam would complete quickly:

Adam: But when we are working in pairs and we are together then (Mads: Then they all get mad) sometimes.

Because we are very fast and they have to keep up, but are slower, but in this, it was just fantastic

Interviewer: Yes, and how can it be that this was fantastic?

Adam: Because. it. We usually don’t play Minecraft, but the others they can? do? The others that need some

time to understand mathematics, they have played Minecraft, so they can react faster and know everything

you have to do and everything you can build. We had to learn that form them

Interviewer: You had to learn from them?

Adam: Yes, and then we could see how it is when we do math quickly and they have to keep up with us

Mads: But with this, with this Minecraft then we were all equal (Adam: yes) nobody was better or worse

Interviewer: to play Minecraft?

Mads: To everything

As the intervention uses Minecraft, it draws on knowledge from both mathematics and the game domain

concerning Minecraft. Mads and Adam’s description of having to learn from the other students, can be seen as

a renegotiation of the authority in the classroom towards more distributed model of teaching and learning

than they normally experience. As the teacher is not the Minecraft expert, the game opens up a space for

agency to be expressed in more conceptual ways in a crosslinks between the domains. Valuable knowledge is

not just tied to who is the first to finish a mathematical task, but who can integrate knowledge between the

domains. This challenges Mads and Adam to understand knowledge about Minecraft, which becomes a valid

and valuable part of being competent in the intervention. The students who are skilled at mathematics are not

necessarily the students, who are skilled Minecraft players, which means that the students’ competences are

redistributed across different domains. Mads and Adam experience being more on the same level as the other

students, which releases Mads and Adam from the normal classroom obligations of finishing quickly. What

they address with this change is not however that they are losing an opportunity to display mathematical

competence towards the teacher. Rather, the release from this obligation is “fantastic” and is a shift toward

positive identification. It underlines the fact that the focus on being the first to finish creates very narrow

opportunities for the students to identify with the classroom obligations.

7. Discussion

The study shows how the intervention created an identity shift towards understanding mathematics as part of

the students’ lifeworld and being useful as a resource in Minecraft. This clearly marked a change from the

students’ everyday experience of “doing mathematics”. We suggest that the reason for this successful transfer

of knowledge between game and school domains is that the students can actually use the coordinate system

in Minecraft to overcome meaningful challenges, which are relevant for them.

As we have showed, using a game like Minecraft for translating experiences across domains offers a number of

affordances. We suggest that one of the key elements for this to succeed is that the game must offer a

possibility to access an underlying mathematical aspect of the game, e.g. the coordinate system, enabling the

students to work with it. Another key element is that the activities in the intervention was aimed at qualifying

the way the students played Minecraft giving them new opportunities to navigate in the game world enabling

them to engage in what the students deem a significant practise from the everyday domain but in a

mathematically substantial way. This points to a need for more detailed analysis of how particular

mathematical concepts are parts of specific games and how students can use these concepts to improve their

interaction with the games.

In terms of the students’ experience of obligations in math class, the intervention motivates shifts in both

authority, agency and perception of competence. These shifts are partly due to the learning goals of the

interventions are in the intersection between domains and not exclusive to the subject domain. This creates a

more diverse way of being competent when participating in the intervention because knowledge of Minecraft

becomes essential. This is in opposition to the normal way of complying with the classroom norms, by

providing answers quickly. Which for one students is interpreted to an extent, where already knowing the new

concepts being introduced, and therefore being able to answer quickly and correctly, is a way of explaining

what it means to be a good student. It highlights the problematic nature of a focus on speed. It depends of

course on the teacher’s intent with the introduction of new concepts. If it is to help the students understand

these concepts, it seems counterintuitive that some students feel that their best possibility of engaging in the

activity in a mathematically competent way, is to already know the new concepts being introduced.

The intervention also shifts the authority from being primarily teacher-centered to more student-centered,

because some students have knowledge about Minecraft, which not even the teacher has. This means there

are both several different ways of being competent and also several ways of getting help from both the

teacher and other students. There is also a shift in what counts as legitimate agency, because there are more

ways of participating conceptually, assessing if mathematical concepts can be used in Minecraft. Different

ways of being recognized and expressing agency affects possible student positions in the classroom. For some

students this evens the playing field giving rise to new ways of participating positively.

For Cobb (2007), an important consideration when formulating curriculum goals for student learning in

mathematics education, should be to describe central mathematical ideas in particular mathematical domains

and that a justification of these goals should be in the terms of activities that students will gain future access

to. Our data shows that Cobb’s (2007) two statements regarding future access and activities worthy of

engagement can be connected in such a way that the access is moved to the present. In summary: instead of

students gaining a perceived future access to a domain through mathematics, they experience the access

themselves in the present.

The idea that students should gain access to significant practices in the future seems a very justifiable end-goal

for mathematics education. However, several examples in our data suggest that the way mathematics is being

taught does not help the students sufficiently to make connections between the subject domain and their

everyday domain experiences. One implication of this could be that students lose interest in mathematics long

before they realise that mathematics can be useful outside of math class, making Cobb’s (2007) proposed end

goal seem unattainable. The analysis shows that students can experience that mathematical concepts enable

them to participate in significant practices in substantial ways. Not significant in terms of democratic or critical

end-goal for mathematics education, but significant practices and substantial ways in a more humble sense,

viewed from the students’ perspective and everyday domain. And that this experience seems a catalyst for the

perspective that math actually have something to do with the students everyday domain.

8. Conclusion

The study shows that Minecraft used in an inquiry-based approach in math class can change students’

identification with mathematics, create new ways of participation and “doing mathematics”. The intervention

thus enables the students to participate in what the students experience as significant practices outside of

mathematics education (Cobb, 2007). The point here is not that playing Minecraft is a significant practice for

mathematics educations in itself, but when the game is used to create significant mathematical practices, the

intervention gives access to new ways of participating in that practice. This can open up to new ways of

identifying with mathematics bridging a gap between the students’ everyday life experiences and the subject

domain.

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