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Mathematics Game Design: Users as Co-designers. Developing an Ideal Design Process for an Educational Virtual Environment for supporting the Teaching and learning of mathematics

  • Formerly University of Leeds
Mathematics Game Design: Users as Co-designers.
Developing an Ideal Design Process for an
Educational Virtual Environment for supporting
the Teaching and learning of mathematics
(University of Bristol, 2012, Unpublished Essay)
Ideal Design and Development Process.
This reflects the procedural paths.
This present essay presents a game design and development processes, that is
specifically geared towards a Mathematical game software to support the learning of
Rationale of the Design process
The Initial Idea
The Concept workshop 1
Clarification and Validation of Concept
Concept Development and Prototyping
The concept Workshop 2
The Concept workshop 3
Designing Content align with Curriculum
Testing the Designed Content
Figure 1
Over the past few decade electronic games have become so entrenched in the family life,
individuals and the fabric of the society (Walsh et al. 2005, Oblinger, 2006). Educators,
Parents and Policy makers felt troubled over children’s fixation with these games but
researchers in the fields of education, Psychologist, HCI communities and
Neuroscientist have rather proposed taping in and harnessing the motivational and
immersive potential of such games for educational purposes.
Using a User Centred Design (UCD) approach the learners is seen as Co-designer and a
partner in the creative adventure. This will enable me build in from the onset the needs,
interest and preferences and to free- up my ideas for a more constructive and informed
design (Facer & Williamson, 2004).
Initial Idea
Mathematics is frequently perceived as boring and irrelevant by students. An idea of a
Game-based learning in Mathematics will aim at making the learning of Mathematics
fun and engaging through the use of games and also to spark up interest that goes
beyond the curriculum and grades. This idea will be targeted towards pupils within the
age bracket of 9-13years. And with emphasise on the learning of mathematics,
developing self-confidence and transferable skills for other situations.
When I was much younger one of my greatest difficulties in mathematics was on how to
open up, add, subtract, multiply maths sum with several brackets. For instance 3a(5b
+4a){(6ab-3c+2a)}+(7ab-10ac) or equations like {30+23(35-25+17)÷10} this two
equations usually drove me mad at school and it has not changed for many students as
well. The game avatar will in team work help to unravel the order of the operation.
Skills form here will eventually be transferable to higher level of mathematics problems.
My purpose therefore is to design a game that will make the mental confusion in
equations such as this clearer.
This idea will be school/home based and modelled from real life.
This envisages a multi player Simulation game.
Two pertinent questions that will guide this development are:
How should mathematics game be designed and used so that users are engaged
in the exploration of mathematical concepts and problem solving skills?
How should such a mathematics game be designed and used that will create
“pleasurable learning, learning through doing and learning through
collaboration”? (Kiriemuir & McFarlane, 2004)
Literature Review
The entire game will be built on the theoretical framework of social Constructivism
Piaget (1954), Vygotsky (1962) and Papert (1993) and other principles in game theory.
These argued that students learn through an active, social process of meaning
construction and sense making, understanding is built through an ongoing
conversational contact with others, constructing artefacts and reflecting on those
conversations and artefacts.(Yishay et al. 2006) Rooted as well in the history and
practice of games in learning environment. ( Van Eck, 2006). Researched evidence and
informed opinions of HCI, Neuroscientists, software designers and other experts will be
Multi player
Van Eck (2006) lay out principles of how and why games work as tool of deeper learning
since game employ play theory, cycles of learning and engagement, situated cognition
and learning, encourages question asking and problem solving through a cognitive
disequilibrium and scaffolding, making student responsible for what they learn.
Educational games are fast becoming part of everyday life. Not every game tagged
educational may actually enhance learning. Gee (2004) asserts that unless games are
researched informed and have good learning principle built into them it may detract
instead of fast tracking learning. Prensky (2001) provides a mantra of discernable
characteristics that makes digital game a motivating and engaging learning experience
among those spelt out were;
Games are a form of fun: that gives us enjoyment and pleasure.
Games are a form of play: gives us passionate involvement.
Games have goals: that gives us motivation.
Games have outcomes and feedback: that gives us learning.
Games are adaptive: that gives flow
Games have conflict/competition/challenge/opposition: that gives us
Games have interaction: that gives us social groups…. (p.106).
Gee (2004) along this same line provides several learning principles that must be built
into good video games if they are to be relevant and have great potentials for learning.
Among his 36 learning principles good video games need to be infused with are:
Empowered learners by
Co-design- where learners are active and co-creating the world they
are immersed in.
Customize-good games should be able to give the player the space to
decide how, when, what to do creatively.
Manipulation-human feel a surge of empowerment when they can
manipulate at a virtual distance, objects, tools and events.
Pleasantly frustrating
Cycles of expertise: “expertise is formed in an area by repeated cycles
of learners practicing skills until they are nearly automatic”. (p.4)
From professional and researched informed evidence, for any game to earn a place in
the classroom and to be tagged educational it must score high on these attributes and
learning principles. ( Cf. Umameh, 2011). Csikszentmihalyi (1990) adds Flow as the
optimal state of learning in a game.
Concept Workshops: Learners as Co-designer
Herbert Simon (2000) proposed this guide in the UCD. “A first step toward improved
instruction is to examine the understanding we hope students will acquire, the things
they should be able to do with their knowledge... next, we must design a series of
experiences that will enable students to learn the relevant cues in the situations they
encounter and to evoke from memory the actions that are effective and appropriate in a
specific situations” (pp.117-118)
It has become a dictum in the HCI community that users should not adapt to a system
but rather the system should be built in such a way as to creatively suit and
accommodate the peculiarity of the needs of the users and therefore be usable by the
users (McGrenere, 1996). Usability then becomes a central concept in the HCI, making
the system easy to use and learn by users. Affordance a term popularised by Norman
(1988) refers to the design of something that afford, suggest or provides it functional
properties that dictates its use.
Druin (2002) outlined four main roles that children can play in technology design
process: Users, testers, informants and design partners. But Facer & Williamson (2004)
argued these as approaches for involving users in the design process: 1. Ethnography 2.
User testing 3. Informant designer 4. Participant designers and cooperative inquiry.
For the present design and developmental process, the users as design partners (Druin,
2002) and informant designer (Facer & Williamson, 2004) will be the framework and
provide the guiding principles for all the concept workshops.
As design partners, here Children will have equal opportunity and space to add their
voices in a way that will creatively improve the design and give them the sense of
ownership of the means of learning. (Gee, 2007). For Druin (2002) ‘they too have
special experiences and viewpoints that can support the technology design process that
other partners may not be capable of contributing’. (p.19) using a low tech prototyping
tools (paper, crayons,clay and string) provide materials to sketch ideas. In this context
co-operative inquiry will be the modus operandi. Druin (1999) put this forth;
1. Contextual inquiry: To observe what Children do with what technology they
currently have
2. Participatory design: to hear what Children have to say directly by collaborating
on the development of low tech prototype of paper mock-up
3. Technology immersion
The informant designer, in the approach the children are actively involved in the ideal
design process via interviews, probing by researchers about their understanding and
exploration of specific concepts, comparative view of abstract and real life events,
supporting them collaboratively to develop an idea on a future system and bring out
mock-ups and low fidelity prototypes (Scaife et al. 1997, Facer & Williamson, 2004).
This approach further offers great opportunity to draw upon the activity, creativity,
imagination and expertise of intended end users to improve the quality, relevance,
usability and effectiveness of the digital resources for education (Marti & Bannon,
2009). The unique challenges of this approach are that partners must begin to negotiate
team decisions. Methods of shared communication, effective collaboration and
productive partnership must be evolved to accommodate adult and Children.
(Druin,2002). Another challenge is to find researchers, professionals and designers who
see Children as stakeholders and are ready to work with them as partners and informant
in their own right.
Therefore team members need to be selected wisely choosing those who can endure the
“messiness, noise and accept the unconventional research activities this kind of
collaboration can bring and expect that Children will always be Children” (p.27)
Concept Workshop—I
The central aim of the concept workshop-I is to enable one have a clear, systematic,
research-based and tested game design methodologies and theoretical rooting that takes
into account the needs, preferences, experiences and context specific requirement of
different users into a better consideration (Ermi et al, 2005) the aim of this design is to
arrive at a final product that would support teachers and learners in developing,
reinforcing and building a mathematics thinking skill and other transferable abilities
learning and social interaction thereby teaching mathematics better and learning a
better mathematics (Roschelle et al, 2000).it is aimed at giving the abstract ideas in
mathematics a more tangible form (CTL Report, 2007) do arithmetic fluently, reduce
cognitive load, sense making with multiple representations, developing flexible
strategies (Ellington, 2003) and favours a better performance in algebra and
comprehension (McFarlane et al. 2002) since instructional games can only be effective
when designed to meet specific instructional objectives and used as intended( Hays,
Workshop—I will then have the users as central design partners and informants,
teachers, parents and experts in VWs and 3D animations in the team. During this
workshop the goal and objectives are clearly set, instructional objectives, game strategy,
role of users, rules, events and criteria for wining, manuals and relevant activities that
rewards players. The elements of challenging goal, embedded in a competitive and
collaborative atmosphere, fantasy that is emotionally appealing with flow experience,
curiosity and solid instructional quality with feedback that support the instructional
objectives (Malone, 1981, Hays, 2005 & Ermi et al. 2005).
The participation of the teacher is aimed at integrating the pedagogical aspects and
learns from teachers’ experiences in teaching areas of difficulties and where the need for
scaffolding is greatest. The Children use of mathematical games like Mighty maths,
Aquamoose, Thinklets, Zoombinis and Millie Math this will aid one in building on what
enabled focused attention, gives sense of control, playability, frame story, gamefulness
and usability of the game in making (Kiili, 2005).
Screen shot of the AquaMOOE maths game. This will act as a sample we intend to
improve on.
The experts in VW and 3D will help to identify and place how the simulation will help
create an authentic micro world that attempts to capture an aspect of mathematical skill
phenomena so that learners can be immerse in it, interact with it and observe the effects
of their interactions. Using Likert type multiple points questionnaire, observations, field
notes, interviews and recorded events will be the source of the needed feedback.
An authentic atmosphere of friendliness will be created to enhance discussion and
sharing of ideas, interest and suggestions. Using video recording and a critical analysis
of the transcription, one would make the ideal design more users centred, pedagogically
sound and situated within the users boundary of experiences.
Clarification and Validation of Concept.
Workshop-I over, with feedback from the sessions the design team we will concentrate
on fine tuning. (Kiili, 2005). Saljo (2011) further this argument thus “We cannot look at
human competencies solely in our minds and bodies. Instead our knowledge is
expressed in our abilities to merge and collaborate with external tools and integrate
them into the flow of our doings, whether there are intellectual, physical or mixed
(p.62) Interfaces, features and scenarios and menu configurations that are adaptable to
the age bracket will be inculcated. Personal user preferences and creation of avatar that
meets the needs, interest and facilitates the achievement of the learning objectives and
game as instrument of fun and immersion will be specified and defined.
Chat rooms, discussion boards and facebook design team group and friendly informal
meetings will be created for team shared experiences. The game will be accessible by
means of any digital devices as long as there is internet connectivity, such that the
imaginary boundary of formal and informal learning fades out and parents and teachers
can be part of the learning of their Children in School and out of school.
Concept development and Prototyping
With ample feedback from workshop-I, the clarification and validation of concept, the
team will rely majorly on these data on which we will base all the logic of design. Sources
from various fields of research, player research, market strategies, comparative studies
of other games and designers own experience and vision (Ermi et al. 2005).
The response-and-feedback conversational dialectics in the team work is rooted in the
games design, which describes game design principles in terms of its rules, its play
quality and its social qualities (Saleh & Zimmerman, 2004) coupled with the theory of
intentional learning (Bereiter & Scardamalia, 1993) and situated learning (Lave and
Wenger, 1991) which argues that tasks learners are immerse or engaged in during an
instructional space should be as concrete and familiar as much as possible so that the
task will resemble the everyday settings, steep in the theory of optimal experience and
flow (Csikszentmihalyi, 1975)
In the mould of social constructivism Dede (2004) sees these as learner’s interest and
preferences in any learning situation;
Fluency in multiple media and in simulation based virtual settings
Communal learning involving diverse, tacit, situated experience, with knowledge
distributed across community and a context as well as within an individual
Co-design of learning, experiences personalised to individual needs and
One as a potential designer may fall in love with one’s idea that one loses the ability to
be critical and thorough. I will take advantage of all previous researches that has been
conducted on the place of games in mathematics teaching and learning. For instance E-
Gem (2002) (Electronic Games for Education in mathematics and Science) and
FutureLab series Report 8: Literature Review in games and learning, 2004).
Involving teachers and getting feedback is to enable one get insight and awareness into
areas where my game will be the needed scaffold. There will be an effective collaboration
between these teams of novices (users) and experts, parents, teachers, technology
experts, technical and software designers. This will open up all the possibilities,
potential and opportunities of diverse perspective unified in the team work for a better
game design.
A Graphic design of this nature will make the game fun to play.
Drawing on the feedback and outcome of the workshops and inputs from experts, user
personas will be created to fit into the needs, interest and preferences of users.
The selection of genres, interface, settings, environment, navigational paths,
construction of computational features, coping strategies, simulations, tools, tasks,
representation and animation will be accessed and synchronised. This will be done by
the collaborative networking of the teams of content specialists, professional designers
and software engineers. This will offer a concrete and visual mechanism for making the
principles and the idea of the game visible and shareable, supporting reflection and
evaluations. Dede (2004) argues that we need users as co-designers in developing
personalised learning pathway and as key source of both content and pedagogy. There is
a move towards self scaffolding and tool scaffolding since adults may not effectively
understand the young people’s world.
I will also use a scenario based player design. A fictional narrative that would describe a
person in situation and the cycles of interaction between user and the game content and
proposed system flow, this will be used to discuss, picture, visualise what it will be when
the actual game is in use, this will equally show what shape, size and layout would look
The reason for chosen the scenario-based design is to show the concrete nature of the
scenario and give a deeper feel of the functionality of the game. Ermi et al. (2005)
argues that, the scenarios may help the users recognise and discuss their previous
experiences from traditional games, digital games and mobile devices, assisting
researchers in gaining information regarding what kind of games and game elements
users are interested in and what elements give them pleasure and displeasure. The
design approach is always iterative allowing one to use informed feedback and advice to
input better features, content and improve the mechanics.
Key to the prototyping, is to use the game play scenario, formulate specific questions for
each prototype and create an iterative cycles with reflective review involving users,
teachers and experts. (Flanagan et al. 2005)
Iterative prototyping guided by these principles;
Be consistent
Give feedback
Make everything as easy as possible
Limit the number of steps for an action
Do not strain the players short term memory
Provide short cuts for experienced players
Tell the players what they need to know
Offer actions the players can perform (Adams et al. 2006)
Besides these other things that one will look at deeply
The educational and design aspects of the prototype
Ensure early identification of problems and potentials for improvement
Check resonance of the prototype with the expectations of the users
Verify if the mechanics proposed will have a smooth flow (Facer & Williamson,
Doing this early at this stage is to give room for a better redesigning. The central
emphasis is the testing of the paper-based prototype model of the game design.
Workshop-III Play testing
This workshop is so designed to play test the prototype’s usability with great attention to
the users. This workshop elicits from the Children, parents, teachers and all the other
members of the team a test, retest feedback and revise the game structural design and
architecture. Users offers suggestions, critiques, comparative comments, write out other
elements they want seen in the game, with the insightful outcome and how users have
connected emotionally and the idea is finally taking a more tangible form.
Questions were asked to help get feedbacks that are needful: what essentially do you
want the game to do in supporting your maths learning, is this platform meeting that?
The chosen interface, font colour and size and outlook are they satisfactory? The
designed pattern of interaction, navigation and flow do they meet the interest and
preferences you asked for?
This workshop sets the stage for the development of the next high fidelity prototype.
Design Content aligned with curriculum Content
The research team comes together with an iterative cycle of testing the high fidelity
prototype. The designer, developers, software specialist, graphic designers and other
professionals will have evaluative cycles of testing every aspects of the game design.
They will perform usability test on the various elements, its functionality, game
instructions, orientation, navigation and immersive depth, pedagogical faithfulness and
the collaborative interface and make sure the needs, interest, preferences of the target
users has priority of place and confirm the market value and strategy for promotion.
The will be a pilot testing by a volunteers, testing for playability and informative and
formative ability of the game, refined the aesthetics and 3D visualisation, testing the
customizable features and how well these work together as a unit. (Evensen et al. 2009)
A form of 3D features
expected in the game
The core activity at this stage is to make sure this high fidelity functional model is what
all the team members desired it to be and the technical aspect are in good working and
synchronised working order. Here we must make sure that we have put effectively ‘the
game in the maths, rather than putting the maths in the game’ (Hancock & Ostreweil,
1996). The Curriculum content for this stage of schooling is laced in as well in fulfilling
the set broader aim of developing a game that is educational and relevant to the user
and the formative stage they are in.
With the evaluative cycles of iteration the research team concludes with multiple stages
of evaluations, analyses, revisions, fine tunings, until there is a confirmed satisfaction
that this game is set to push off all other mathematical game off the markets, schools
and homes, since it will be taking its rightful place as best to none in meeting the
educational and entertainment needs of the users. Then we have the final product.
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Note: This article was UPDATED and revised in 2015 in a new article entitled "DGBL: Still Restless After All These Years" which can be found in Research Gate and at Educause Review. What follows are BOTH abstracts: 2006 Abstract: After years of research and proselytizing, the proponents of digital game-based learning (DGBL) have been caught unaware. Like the person who is still yelling after the sudden cessation of loud music at a party, DGBL proponents have been shouting to be heard above the prejudice against games. But now, unexpectedly, we have everyone’s attention. The combined weight of three factors has resulted in widespread public interest in games as learning tools. 2015 Abstract: Nearly a decade ago, I wrote an article for EDUCAUSE Review about digital game-based learning (DGBL) and the challenges it faced.1 I suggested that once proponents of DGBL were successful in convincing people that games could play a role in education, they would be unprepared to provide practical guidance for implementing DGBL. Just as when the person shouting to be heard at a party is suddenly the center of attention at the moment there is a lull in the conversation, we DGBL proponents had everyone's attention—but not much to say. In the article I also suggested that our sometimes overzealous defense of videogames (hereafter often referred to as "digital games") ran the risk of overselling the benefits (and underreporting the challenges) of using digital games in formal education. Digital games, I said then and still believe today, are effective as embodiments of effective learning theories that can promote higher-order outcomes. Our inability to provide guidance in doing so a decade ago was ceding the DGBL front to digital games as tools for making didactic, instructivist learning (i.e., lectures) more "engaging." DGBL, I suggested, was effective not as a means for making learning "fun" or for "tricking" students into learning; DGBL was effective because it supported powerful learning strategies such as situated learning, authentic environments, and optimized challenge and support (scaffolding). What was needed was a renewed focus on (1) research about why DGBL is effective and (2) guidance on how, when, for whom, and under what conditions to integrate digital games into formal education. I was not the only one with these ideas, but my timing and the venue combined to reach many people. That 2006 article has been cited more than 1,000 times since then.2 Yet though these ideas continue to resonate with many people, much has changed in terms of research, practice, and to some extent, my own beliefs about the future of DGBL.
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Exciting research in cognition today combines computer modeling with neuropsychological studies of the functioning of the brain and with the experimental study of human learning and problem solving. The computer models are compared with findings about brain processes and their organization and findings about the moment-by-moment progress of humans as they learn and solve problems. This research is helping to test and improve detailed theories of the human symbolic processes used in learning and thinking and to build theories of how skills and knowledge can be taught effectively and efficiently.
Conference Paper
The value of involving people as ‘users’ or ‘participants’ in the design process is increasingly becoming a point of debate. In this paper we describe a new framework, called ‘informant design’, which advocates efficiency of input from different people: maximizing the value of contributions tlom various informants and design team members at different stages of the design process. To illustrate how this can be achieved we describe a project that uses children and teachers as informants at difTerent stages to help us design an interactive learning environment for teaching ecology.