### Game Based Learning and Gamification in Maths teaching

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# Pedagogical and didactic motivations

Anyone at any age loves to play and we have known for many years that play is a crucial component of cognitive development from birth to adulthood. The child’s desire to play is an innate biological response to survive in the world. Play is widely practiced by many animals too.

Learning through games has several advantages:

encourages the acquisition and development of different skills;

stimulates problem solving;

encourages experiential learning;

increases motivation.

Gamers learn through repetition, failure, goal achievement in a risk-free environment and it is important that teachers use play to shape the learning experiences they create for their students.

Solving a problem or an equation with mathematical tools is often complex and boring for teenagers, but we have all tried to solve puzzles, placed in graphic form or contextualized in such a way as to hide the mathematical background necessary to obtain the required solution: a lot of Maths appears in puzzle magazines, which people browse as a pastime.

On social networks we often find puzzles like this , completely analogous to the one expressed alongside (Fig. 2), written in mathematical language:

*Fig.1 (CC-BY)*

*Fig. 2 (CC-BY)*

Most people try to solve the more captivating graphical problem, even if those who arrive at the correct solution faster use the appropriately reworked mathematical model (Fig. 3) .

*Fig. 3 (CC-BY)*

Students grew up in the civilization of the image and prefer a graphical approach but they must understand that they can arrive at the correct solution through mathematical reasoning.

Game Based Learning (GBL) is, therefore, a lock pick to interest the class, capture students’ attention and allow them to understand the concepts of Maths and its procedures in an intuitive way: at a later time it will be possible to define the theoretical and abstract procedures that allow us to create models and solve problems. This approach can be used in any discipline and for any school age even if Maths is particularly suitable for this type of teaching.

**Difference between GBL and Gamification**

GBL is a teaching technique which allows the cognitive sequence to be reversed by introducing game elements in problem solving: in this way each student finds a personal solution method, which the teacher can then integrate, correct or summarize in a theoretical context, discussing which solution strategies adopted by the various pupils are more efficient and lead to the solution in a safer and faster way. Games are used to introduce, apply or enrich learning concepts in an active way: after the activity the teacher must discuss to contextualize and develop the learning that occurred during the game.

Gamification, on the other hand, does not act in general on the way in which a problem is solved, but it is a way of assessing (often, informally) the skills acquired by students: often a prize is raffled off which is given to those who solve a proposed problem in the shortest time or in the most efficient way. In gamification we use engaging elements typical of the game (challenge, randomness, competition, cooperation, rewards, desire to win) adapted to the teaching process: students learn the rules, take risks, understand that you can make mistakes and try again later, thus developing resilience skills.

The two strategies, therefore, are different, although it is possible to combine them in the same educational path.

# Examples of GBL in Maths education

It is important for the students to “touch Maths”, making it concrete and manipulable for them.

Over the years I have developed some effective teaching strategies such as the participation in international projects, as in “Escape from Maths”, carried out with two colleagues from France and Germany: this was my first experience of GBL in teaching and from there I developed some ideas, reworked and adapted later in other eTwinning projects and in daily practice with my classes.

## Tarsia and the factorization of polynomials

This activity requires the use of ICT skills by the teacher, but the students work in an unplugged way, with paper and scissors.

The teacher must download Tarsia (by Hermitech Laboratory) for free on his computer: this software can be useful for STEM subjects, foreign languages or in CLIL teaching to consolidate vocabulary on concrete objects.

In this video-tutorial I show some of the possibilities of Tarsia, which allows you to create puzzles or dominoes, for students to play with.

The activity that I find most interesting to carry out with Tarsia is related to the factorization of polynomials with a bottom-up approach.

*Fig. 4 (CC-BY)*

*Fig. 5 (CC-BY)*

After having introduced the main factorizations to the class and having verified that most of the students acquired the minimum concepts, I ask the groups of students to solve a puzzle by matching the factorizations to their expansions, distributing to the teams some sheets obtained with the Tarsia Output visualization (Fig. 4): the triangles are the pieces of the puzzle. The students know most of the factorizations, but not all of them: this is an opportunity to introduce the others. The aim of the activity is to complete the puzzle (Fig. 5) and write a table in which each product is associated with its polynomial expansion (Fig. 6). At the end of the allotted time (usually in less than 60 minutes all the groups have finished their work) I verify that all the puzzles have been solved correctly (Fig. 7) and the results shown in the table summarizing the matches are right. Having done this activity several times, I have noticed that the students are always very interested in this task, even those who usually have a passive attitude during the lessons. The discussion involves the whole class and the time needed to assimilate this normally difficult topic is significantly shortened.

*Fig. 6 (CC-BY)*

*Fig.7 (CC-BY)*

Here you can download both the Tarsia file and the outputs produced, i.e. the pieces of the puzzle, the table with the breakdowns and the image of the solution.

## The virtual escape rooms

In my opinion the simplest, the most versatile and immediate tool for this purpose is Genially, particularly suitable for eTwinning projects because international groups of students can collaborate at distance.

I usually prepare an example of an escape room that my pupils can play with, then I organize them into groups and ask them to create a new one on the topic that I want to consolidate or deepen. The activity can be done in the classroom during a lesson module or online.

These are the steps I follow:

create a screenplay, deciding in advance the theme, the setting, the backgrounds, the characters and the objects to be placed on the scene (which can be moved with Genially allowing you to hide the clues and the key to access the next room), the texts or audios through which to give directions and the games used.

deactivate the sequential advancement mode between the pages, building a graph for navigation

use the games to obtain the access code set to reach the following step: one or more questions related to the topic you want to deep must be placed on each page . You can use crossword puzzles or word searches created for instance with LearningApps to obtain a keyword at the end of the game to use as a password to access the following scene.

remove the backgrounds of characters and objects to insert in the escape room with Remove Background,.

once the groups have finished their job, I ask each team to solve the escape room created by another one.

end the activity with a discussion on the choices made (the most frequent remarks are those on questions that are too easy or too difficult, have inadequate logic, are not pertinent to the theme, the screenplay is poor ).

Creating an escape room will allow students to acquire logic and script skills; working in groups they will learn to organize tasks according to their skills, enhancing the role of each; reworking the contents will take place in a soft way and at everyone’s pace, so this activity is inclusive and allows you to recover concepts that may have been underestimated in more traditional lessons. Computer skills are also enhanced, as are language skills if the activity is carried out remotely, for example in an eTwinning project where students have to work with foreign partners.

*Fig. 8 (CC-BY)*

**Sitography**

Aaron Baum – Legends of Learning

Bartosz Mierzejewski – Gamification vs Game-based Learning: what’s the difference?

Enrica Maragliano – Gamification in High School Math classes

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*Enrica Maragliano teaches Mathematics and Physics in the classical and linguistic lyceum “G.Mazzini” in Genova. She is ICT coordinator and Erasmus+ contact person in her school and also a teachers’ trainer, Scientix ambassador and eTwinning/Erasmus+ ambassador in Italy, her country. Curious and enthusiastic about learning, she loves collaborating with colleagues from all over Europe and experimenting with new teaching methodologies with her students.*

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