CHALLENGE-BASED GAMIFICATION AND ITS IMPACT IN TEACHING MATHEMATICAL MODELLING

Elvira G. Rincón FloresTecnológico de

MonterreyMexico

María Soledad Ramírez Montoya

Tecnológico de Monterrey

Mexico

Juanjo MenaUniversidad de

SalamancaSpain

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).

Why students don´t undertand the

meaning of dx?

b

a

dxxf )(

How can I do that the things improve?

Innovative strategy

Gamification

Active LearningImprove learning

GamificationIn 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.

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)

Table 1. Examples of different designs of gamified environments based on the model of Werbach y Hunter (2015) and Bunchball (2012)

DYNAMICS MECHANICS COMPONENTS

EmotionsCompetitionFeedbackTrophiesChances 

 BadgesLevelsLeaderboards

NarrativeChallengesChancesTransactionTurnsCompetition 

AvatarsBadges)CombatsLeaderboardsLevels 

Relationships CompetitionsCooperationFeedbackChallenges 

AvatarsBadgesTeam-LeaderboardsLevels

ProgressionsChallengesCompetitionsRewards

 

AvatarsBadgesProgress bar

Points

GamificationGamification 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.

• 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

SampleThe 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.

Methodology

Phases of the modeling cycle (Blum & Leib, 2007)

Partial ExaminationFinal Examination

Gamified Activity

3

Gamified Activity

2

Gamified Activity

1 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.

Gamified Activities

Name of the activity Educational content1. 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

Gamified Activity Level 1

Gamified Activity Level_1

Gamified Activity levels 2 and 3

Partial Examination

Final examination

ResultsMathematization 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).

Phase P valueP1. Construction 0.4005P2. Simplification 0.5255P3. 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

Results of dimensions: cognitive, afective and social

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)

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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“ 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.mxsolramirez@itesm.mx juanjo_mena@usal.es

Gamified Activity 2_Levels 1, 2 and 3

Gamified Activity 3_Levels 1, 2 and 3