Track 11. Gamification Ecosystems Authors: Elvira G Rincón Flores, María Soledad Ramírez Montoya and Juanjo Mena

1. CHALLENGE-BASED GAMIFICATION
AND ITS IMPACT INTEACHING
MATHEMATICAL MODELLING
Elvira G. Rincón Flores
Tecnológico de
Monterrey
Mexico
María Soledad Ramírez
Montoya
Tecnológico de
Monterrey
Mexico
Juanjo Mena
Universidad de
Salamanca
Spain

2. Educational Innovation
• Brousseau (1990) argues that innovation is a teaching mechanism
that proposes strategies that work and that are easily communicated
to others. However, innovation not only involves improving teaching
techniques or introducing new teaching technologies or strategies
(Sánchez, Mena & Pinto, 2013) but also developing real changes that
stimulate learning (Ramírez-Montoya,2015; Fidalgo & Sein-Echaluce,
2014; García-Peñalvo, García de Figuerola & Merlo, 2010; Gros-Salvat
& Lara-Navarra, 2009).

3. Why students don´t undertand the
meaning of dx?

b
a
dxxf )(
How can I do that the things improve?

4. Innovative strategy
Gamification
Active Learning
Improve learning

5. Gamification
In recent years the teaching strategy of Gamification has been gaining
more strength thanks to the ludic element that characterizes it. The
game is a universal activity and has been present in various areas such
as art, sport and science (Chamoso, Durán,García, Martín, and
Rodríguez, 2004; Minović, García-Peñalvo, & Kearney, 2016; Sánchez
& Peris, 2015). It has become a teaching strategy that can potentiate
the engagement of the learners.

6. Gamification
• In education it is used with the purpose to place the student in
scenarios involving challenges and exciting missions to increase
their level of commitment and competitiveness (Hanus and Fox,
2014; Mas-Sansó & Manresa-Yee, 2016).
• Challenge based learning can be an element that complements the
gamification and vice-versa. A challenge is a hard problem or
situation in which a student finds his/herself into. The student must
solve this challenge through the application of what they have
learned, encouraging a greater creativity in problem solving
determining the level of learning achieved (Martin, Rivale & Diller,
2007; Minovic , García-Peñalvo & Kearney, 2016)

7. Table 1. Examples of different designs of gamified environments based on
the model of Werbach y Hunter (2015) and Bunchball (2012)
DYNAMICS MECHANICS COMPONENTS
Emotions
Competition
Feedback
Trophies
Chances
Badges
Levels
Leaderboards
Narrative
Challenges
Chances
Transaction
Turns
Competition
Avatars
Badges)
Combats
Leaderboards
Levels
Relationships Competitions
Cooperation
Feedback
Challenges
Avatars
Badges
Team-Leaderboards
Levels
Progressions
Challenges
Competitions
Rewards
Avatars
Badges
Progress bar
Points

8. Gamification
Gamification have valuable elements for the students’ well-rounded
education. Domínguez, Saenz-De-Navarrete, De-Marcos,
Fernández-Sanz, Pagés & Martínez-Harraíz, 2013,
Nisbet & Willians 200) agree that playing is a unique opportunity to
integrate cognitive, emotional and social aspects.These angles
are to be considered when designing gamified activities.

9. • The purpose of this paper is to show the advantages of challenge
based gamification in the learning of integral calculus for
mathematics and engineering students in a higher education
institution. We specifically focused on the subject content of solids of
revolution calculus with the strategy of the differential take ( Alanís &
Salinas, 2010). It also shows whether the short-term learning stayed
valid long-term taking as reference the phases of the modeling
routes from (Blum & Niss, 1991; Borromeo & Blum, 2009).
Objective of the research

10. Sample
The research was carried out during the semester from
January to May 2016 where 48 students from Engineering
and Integral Calculus Courses in Tecnológico de Monterrey
(Mexico) participated. The students were divided into two
groups, each consisting of 24 students and grouped in
teams of four people.

11. Methodology
Phases of the modeling cycle (Blum & Leib, 2007)
0 1 2:H  
1 1 2:H  
Students’ performance in the partial and the final
exams is the same.
Students’ performance in the partial exam is different
from the performance in the final exam (being higher
in the final)
Cognitive, afective and social dimensions.

12. Gamified Activities
Name of the activity Educational content
1. Clay model of a diferential
volume
Cutting a differential volume to relate the
elements that are present in a cylinder (radius
and height) with the mathematical function that
describes the shape of a cup (construction
stages and simplification).
2. Integral Implementation Implementation of the integral built in level 1 to a
particular context (calculation of the volume of a
flask).
3. Volume Application Calculate the volume of a knob that was formed
by three functions.
Table 2. Gamified activities

13. Gamified Activity Level 1

14. Gamified Activity Level_1

15. Gamified Activity levels 2 and 3

16. Partial Examination

17. Final examination

18. Results
Mathematization phase has less
mean and variance in the final
exam.
It is worth noting that the
opposite happens with the
validation phase for which mean
and variance are higher in the
final exam.
Table 3. Descriptive statistics results (mean and
variance) per each phase of the partial (1) and
final exam (2).

19. Phase P value
P1. Construction 0.4005
P2. Simplification 0.5255
P3. Mathematization 0.5776
P4. Mathematical Work 0.1214
P5. Interpretation 0.0001**
P6.Validation 0.0002**
P7. Presentation 0.0510
Figure 1. Normality test results for phase 3:
Mathematization in the partial exam.
Table 4. Inferential Statistics using the
non-parametric Mann-Whitney U test
(figures below the 5% significance level
are in bolt font). ** Statistical significance
at the 0.01 level

20. Results of dimensions: cognitive, afective and social

21. Conclusions
• There is no significant difference
between partial and final tests in the
mathematical modeling routes phases
(Blum & Leib, 2007): simplification,
mathematization, mathematical work and
presentation.
• Gamification is a didactic strategy that
attracts students to learning, however it
has to be supported by a good didactic
design and a reflexive process to allow
continuous improvement (Marín, 2015;
Rodríguez & Santiago, 2015; Villalustre &
Del Moral, 2015).
• This study demonstrates that cognitive,
affective and social elements are
essential aspects for the creation of
gamified environments (Domínguez et al,
2013; Nisbet & Williams, 2009; Pulos &
Sneider, 1994)

22. Future Investigations
• It would be interesting to apply and
study the challenge based gamification
in a wider range of topics within the
same subject.
• Using a quasi-experimental research
design (i.e., control - experimental
groups) in future studies could yield to
more explicative results that help us to
understand to what extent this strategy
works better (or not) than traditional
instruction.

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27. “ In my perspective, the worst thing for a student is
teaching them through means of terror, force and artificial
authority. This procedure destroys itself the good
feelings, sincerity and security of a student..”
Albert Einstein
¡Thank you!
elvira.rincon@itesm.mx
solramirez@itesm.mx
juanjo_mena@usal.es

28. Gamified Activity 2_Levels 1, 2 and 3

29. Gamified Activity 3_Levels 1, 2 and 3