1. Παιχνίδια Μαρία Κορδάκη Dept of Computer Engineering and Informatics
Patras University, 26500, Rion Patras, Greece

2. 1. Introduction
Games:
most enjoyable activities for the young (McFarlane and Sakellariou, 2002)
players can attain a state of ‘flow’ (Csikszentmihalyi, 1990)

3. 1. Introduction
In the course of playing appropriately designed computer games, children have the opportunity to be naturally introduced to new concepts, topics and skills that they can continue to explore through offline reading, discussions or activities
formal (i.e., classroom) and informal (i.e., outside the classroom) education (Fisch, 2005)

4. 1. Introduction
Games can support student learning in terms of (Oblinger, 2004):
(a) multi-sensory, active, experimental, problem-based learning,
(b) activation and use of prior-knowledge in order to advance,
(b) self-correction by providing immediate feedback on student actions,
(c) self assessment by exploiting the scoring mechanisms,
(d) intrinsic motivation and computer-based interaction (Loftus and Loftus, 1983),
(e) acquire essential learning ‘competencies’ such as logical and critical thinking as well as problem-solving skills (McFarlane Sparrowhawk and Heald, 2002),
(g) learn in different ways from those often in evidence, or explicitly valued, in the school setting (Kirriemuir and McFarlane, 2004). In fact, young people seem to expect different approaches to learning which are shaped by their frequent interaction with computer games outside schools

5. 1. Introduction
empirical results seemed to be in contradiction (Kafai, 2001; Kirriemuir, 2002; Facer, 2003; Kirriemuir and McFarlane, 2004)
motivation and the acquisition of skills gained by the learners through game-play at the same time ignoring specific learning outcomes (Kirriemuir, 2002; Facer, 2003)
the playing of games can support valuable skill development such as strategic thinking, planning and communication, application of numbers, negotiating skills, group decision-making and data-handling

6. 1. Introduction
Computer games have been particularly effective in raising achievement levels of both children and adults in various areas of knowledge such as:
science and math (Kirriemuir, 2002; Klawe, 1999),
language (Kirriemuir, 2002; Rosas, Nussbaum, Cumsille, Marianov, Correa, Flores, et al., 2003),
geography (Virvou, Katsionis and Manos, 2005) as well as
physical education and computer science (Papastergiou, 2009a; 2009c)
where specific learning objectives can easily be stated

7. Design principles
learning is considered to be an active subjective and constructive activity placed within a rich and meaningful context for learners
games should first and foremost be fun and then encourage learning

8. Design principles
Designers of learning games should initially ask themselves the following questions:
(a) is the game fun enough that someone would want to play it (and would learn from it)?
(b) would people using it think of themselves as ‘players’ rather than ‘students’ or ‘trainees’?,
(c) would the experience be addictive? Would users want to play repeatedly until they won and possibly after?,
(d) would players’ skills in the subject matter and learning content of the game significantly improve at a rapid rate and get better the longer they played?,
(e) could the game encourage reflection about what has been learned?

9. Design principles
active participation (Fabricatore, 2000) within contexts that are attractive to learners
the game structure itself encourages learning
incidental learning or gaming strategies to intentional learning tasks (Kirriemuir, 2002).

10. Design principles
interactivity within an attractive context, with clear learning aims, proves effective
Learners’ previous knowledge
scaffolding and appropriate help on learners’ actions is also of great importance
feedback and hint structures, in ways that assist and scaffold children to cope with difficult content

11. Design principles the degree of difficulty is important here
the educational content of a game, it must be sound, age-appropriate, and well integrated into the game (Fisch, 2005)
fundamental and timeless concepts
the educational content must be at the heart of game play
emphasis on structure rather than content
neither too complicated neither too simple

12. Design principles
Key structural characteristics of computer games (Prensky, 2001, pp. 118–119) which, when combined, can strongly engage the players have been reported:
(a) fun,
(b) play,
(c) rules,
(d) goals and objectives,
(e) interaction,
(f) outcomes and feedback,
(h) winning,
(i) competition / challenge/ opposition.

13. Design principles
These characteristics can correspondingly contribute to the players’ engagement in terms of:
enjoyment and pleasure,
intense and passionate involvement,
structure,
motivation,
doing,
learning,
ego gratification,
adrenaline.

14. Description of the game
to play against the computer using cards featuring binary numbers
interactive and structured
learning aims:
(a) the base used for the construction of the binary system,
(b) the value of each digit included in a binary number in relation to its position,
(c) the conversion procedure of a decimal number into a binary one with equal value, and vice versa, and
(d) basic rules that govern both decimal and binary numerical systems

15. Description of the game
review and reflect on their previous knowledge of the decimal system
construct their knowledge by thinking about these numbers analogically
a help pattern
attractive, novel and meaningful context for the pupils,
fun /rules/ goal to win the ‘mama’

16. Description of the game
In the heart of this game is the content
clear learning objectives
incidentally learn about binary numbers in order to play the game
act as players during the game play and not act as students

17. Description of the game
fully interactive
put the learner in an active role
immediate feedback on each pupil actions
visual hints : scaffold pupils easily progress
meaningful help for each of its functions
neither too complicated nor too simple with respect to pupils’ age

18. Pilot evaluation Twenty 6th Grade pupils (ten males and ten females),
typical primary school,
Patras,
the role of the researcher,
type of data,
2 hours per pupil

19. Pilot evaluation
Learning experiment based on a ‘didactical scenario’ consisting of three phases:
i) reviewing and reflecting on their previous knowledge of the decimal system in the context of the ‘Decimal System’ function,
ii) experimenting with the binary system by interacting with the ‘Binary to Decimal with help’, the ‘Binary to Decimal without help’ the “Decimal to Binary’ functions’ and then consolidating the knowledge they acquired by getting involved in playing the aforementioned card game, and
iii) extending their knowledge of the binary system by reflecting on their experience during this experiment and also trying to form appropriate generalizations and connections between this system and the decimal one.

20. Results
Phase 1: Reviewing and reflecting on previous knowledge of the decimal system: Questions
Q1.1) How many different digits can we use to write a decimal number?
Q1.2) ‘Click on a new card: Can you analyze the number illustrated in this specific card and fill the gaps with the numerical value of each of its digits?’
Q1.3) What is the value of each digit constituting this number?
Q1.4) What do you think the relationship between the value of these digits is?.

21. Results Phase 2: Experimenting with the binary system
Teacher: ‘All of us realized during the previous task that we can use 10 different numerical digits in order to form any number in the decimal system. However, despite the fact that we can understand the meaning of each number constructed in this way, computers understand numbers written only by using combinations of 1s and 0s. How is it possible to represent any number with such combinations?’

22. Results
Questions:
Q2.1) What is the meaning of the dots inside each of the rectangular frames illustrated in this card?,
Q2.2) What is the number represented in each of the rectangular frames?,
Q2.3) What do you think the relationship between these numbers is?,
Q2.4) What is the number of dots that would be included if we were to add another rectangular frame to the left of the frame with 16 dots?,
Q2.5) What is the value of each digit of the binary numbers represented in this card?,
Q2.6) What is the meaning of “0” and of “1” in different positions?,
Q2.7) What is the value of the binary number represented on this card?.

23. Results The use of the ‘Decimal to Binary’ function by the pupils
Explanation1: ‘think about this decimal number as a sum of certain of the numbers 32, 16, 8, 4, 2, and 1, which corresponds to the value of each position in a 6-digit binary number. Select the appropriate numbers and in order to form the binary number fill the positions that corresponds to each of the selected numbers with ‘1s’ and the remaining positions with ‘0s’.

24. Results The use of the ‘Decimal to Binary’ function by the pupils
Explanation2:‘starting from the left, check if the value of this position is less than or equal to the decimal number you have to converse into its binary form. If yes, then put ‘1’ in this position and subtract this value from the decimal number. If no, then put ‘0’ in this position. Repeat the procedure until the initial decimal decreases to zero after the entire procedure of subtractions’.

25. Results
The Card Game:
no-one had difficulties in calculating the binary numbers which were illustrated on their cards, nor the sum of the points illustrated on the values’ cards they picked up during the game
flow
addiction

26. Results
‘what you interested/disinterested most during this experiment?
they learned a lot about binary numbers: ‘In so little time I learnt a lot about binary numbers’, “During these two hours I have learned as much I have learnt in the whole my school life’,
this way of learning is informal and rarely found in school practices: ‘I like this game because it is not something trivial while our every day lessons are usually boring’. It is worth noting that, all pupils expressed that they liked this informal way of learning.
they have strong motivation to be actively involved, as players and not as typical learners: “we liked to play in order to win the computer’,
the learning aims were at the heart of the game play: “ we did not understand how easily we learnt about binary numbers; we played and learned together’,

27. Results
‘what you interested/disinterested most during this experiment?
(e) they had fun: “it was so fun to play with cards!’,
(f) it was a playful activity: ‘I liked so much to play”,
(g) the game has rules: “ the rules of the game helped me to learn in order to win”,
(h) the game has goals, winning, competition and challenge: “It was a challenge for me to achieve the goal of winning the mama!,
(i) the game emphasize interaction, adrenaline, outcomes and feedback: ‘I was anxious to pick the next cart as well as to check the outcomes of my attempts by receiving the feedback given by the computer’,

28. Results
‘what you interested/disinterested most during this experiment?
(j) the game is easy, provides scaffolding and representation: ‘It was a very easy game and I was helped very much to understand about binary numbers by the dotted-cards as well as by the help provided’,
(k) emphasis on basic aspects of the subject matter and not its details: “I learnt a lot in a little time; little but significant things; not boring details’,
(l) Clear learning aims: “It was clear what we learned’.
As a disinterest, some pupils expressed that they would prefer to play this game online with their friends.

29. Results
Phase 3: Encouraging pupils to extend their knowledge of binary numbers
construct the binary form of specific numbers greater than 63: ‘please, explain how you realized this construction’
‘Based on your experience could you please make some generalizations and find some rules about the conversion of a decimal number to its binary form?’

30. Results
Phase 3: Encouraging pupils to extend their knowledge of binary numbers
analyze the following binary numbers in such a way as to convert them into decimal numbers.
1001=1*__ + 0*__+ 0*__ + 1*__=___
0111=0*__ + 1*__+ 1*__ + 1*__=___
0101=__*__ + __*__+ __*__ + __*__=___
1111=__*__ + __*__+ __*__ + __*__=___

31. Disscussion and conclusions
basic aspects of the binary system can be successfully introduced in education starting from the primary level
the context of this card-game was pleasant, meaningful and attractive for the pupils where they had fun and felt as players and not as school-students

32. Disscussion and conclusions
Pupils were also active during the whole experiment .The factors that contributed in this active participation were:
(a) interactivity of all functions included
(b) attractiveness in playing using these cards
(c) novelty in both; the didactical approach used (game ply) and the learning concepts in question

33. Disscussion and conclusions
Essential factors that contributed in pupils’ motivation were estimated, namely:
(a) fun in playing using cards against the computer
(b) pupil in the role of player
(c) specific rules to participate in the game,
(d) establishment of goals,
(e) interaction, immediate feedback on pupils’ actions for self-correction and specific outcomes,
(f) challenge/competition/risk/feelings of winning,
g) challenge of competition against the computer
(h) novelty in terms of learning approaches used and the learning subject in question,
(i) learning aims at the heart of the game-play.

34. Disscussion and conclusions
Factors that encouraged pupils’ learning in the context of game play:
(a) clear and appropriate didactical scenario
(b) specific learning aims
(c) activation/doing
(d) reflection on previous knowledge
(d) introduction and consolidation on the new knowledge
(e) acquisition of essential learning competencies such as: reflection, analogical reasoning, reverse thinking, consolidation, self correction, extension and generalization
(f) asking appropriate questions to enhance learning
(g) intrinsic motivation
(h) content hidden
(i) content in the form of examples included within ‘Help’
(j) emphasis on the basic points of the learning in question,
(k) learning of the subject matter as necessary to play the game
(l) incidentally learning
(m) neither too complicated neither too simple
(n) structure
(o) structure: constrain-support-motivational
(p) support: visual hints/help/feedback
(q) double-aimed functions: educational and engagement.

35. Useful URLs http://plaincards.com/Education.html

36. Thank you very much for your attention!!!!
Maria Kordaki, PhD., MEdu