The construction of number in concrete and electronic games: the Kalah game case

Gonçalves, Érica de Cássia; Saravali, Eliane Giachetto; Sousa, Lilian Pacchioni Pereira de; Bessa, Sônia

doi:10.1590/1980-4415v38a240093

Brasil

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ARTICLE • Bolema 38 • 2024 • https://doi.org/10.1590/1980-4415v38a240093 linkcopy

The construction of number in concrete and electronic games: the Kalah game case

A construção do número em jogos concretos e eletrônicos: o caso do jogo Kalah

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Games have sparked interest as an object of study in multiple areas of knowledge. In this research, we will discuss the impacts of the new formats and configurations of games in current times, based on the Piagetian interactionist theory’s contributions. The main objective of the study was to analyze the effects of an intervention with the Kalah game, in its concrete version and in its electronic version, for the construction of the notion of number. Thirty-eight children took part in the investigation, their ages ranged from seven to ten years old, from both genders, enrolled at two county Elementary Schools, located in a small town in the state of Minas Gerais, Brazil, subdivided into 3 groups: EG¹ - Experimental Group, subjected to the intervention with Kalah in its electronic version; EG² – Experimental Group, subjected to the intervention with Kalah in its concrete version and CG-Control Group. As instruments of pretest and posttest, the operatory tests/proofs of conservation, classification, and serialization were utilized, to verify if there were qualitative and/or quantitative changes to the thought’s structures. The results indicated the most expressive differences in the assessed structures amongst the subjects from the Experimental Groups when compared to the Control Group, just as there was a distinction in the performances of the subjects from the experimental groups, after the intervention. During the sessions with the Kalah electronic game, it was found that the fundamental principles of the Piagetian theory could not be assured, possibly being one of the pedagogic interventions’ limitations.

Keywords
Electronic Games; Concrete Games; Genetic Epistemology; Number notion

Experimental Group 1 Participants – Electronic Games
2^nd GRADE	3^th GRADE	4^th GRADE	5^th GRADE
ALY (7)	LUI (7)	JOL (9)	VIT (10)
JUL (7)	GUH (8)	JON (9)	ELO (10)
MIC (7)	REN (8)	MAR (9)	JOE (10)
VIN (7)

Experimental Group 2 Participants – Concrete Games
2^nd GRADE	3^th GRADE	4^th GRADE	5^th GRADE
BRU (7)	ING (7)	CAR (9)	MAI (9)
KEL (7)	GUO (7)	CAU (10)	RAI (10)
JOS (7)	ADR (7)	PED (9)
TIA (7)
DAV (7)

Control Group Participants - No Intervention
2^nd GRADE	3^th GRADE	4^th GRADE	5^th GRADE
ROD (7)	GER (7)	RAF (9)	ISA (9)
NIC (7)	MAT (7)	JOP (9)	LOR (9)
JOV (7)	LUA (8)
ART (7)	VIO (8)

Discreet Quantities’ Conservation
Level	Experimental Group 1	Experimental Group 2	Control Group
NC	31%	38%	50%
TR – A	31%	16%	17%
TR – B	15%	23%	17%
TR - C	23%	23%	17%
OC	---	----	----
Class Inclusion
NI	54%	46%	75%
TR	46%	54%	25%
OI	---	----	----
Rod Serialization
NS	77%	62%	75%
TR	33%	38%	25%
OS	---	----	----
Subtitles

Section	Concrete	Electronic
1^st	1) Free exploration of the board and game pieces. 2) Introduce the game’s rules, but first, ask whether they have any idea how to play. 3) Raise questions that make it possible for them to understand the game’s rules, such as: a) How many seeds can be put in each hole? b) How many seeds are there in total? c) In which direction must the seeds be distributed? d) Which holes can the player utilize during their round? e) During a game, when a player lands on their opponent’s kalah, what should they do? f) When does the game end? g) Who wins the game? 4) Play a few rounds, noticing whether they understand the game’s rules.	1) Free exploration of the board and game pieces on the tablet. 2) Introduce the game’s rules, but first, ask whether they have any idea how to play. 3) Raise questions that make it possible for them to understand the game’s rules. Such as: a) What happens when you click on this hole? How many seeds are placed in each hole? b) How many seeds are there in total? c) In which direction are the seed being distributed? How do you know this? d) Which holes can the player utilize during their turn? e) Why is it that you got the chance to play again? f) How did you manage to capture the seeds? g) When does the game end? h) Who wins the game? 4) Play a few rounds, noticing whether they understand the game’s rules.
2^nd	1) Remind them of the game’s rules and play a few rounds, noticing the players’ behavior. 2) Problem situations based on the matches: a) Each player begins the game with the same number of seeds? How do you know this? b) If you choose this hole, where do you think you’ll put your last seed? c) What can you do to add more seeds to your Kalah? d) Insert a special rule for those that have already grasped how to play. e) Is it possible for a player to play more than once? f) How many seeds are needed for you to be able to play again?	1) Remind them of the game’s rules and play a few rounds, noticing the players’ behavior; 2) Problem situations based on the matches: a) Each player begins the game with the same number of seeds? How do you know this? b) If you choose this hole, where do you think you’ll put your last seed? c) What can you do to add more seeds to your Kalah? d) Is it possible for a player to play more than once? e) How many seeds are needed for you to be able to play again?
3^rd	1) Play a few rounds, noticing the strategies the players use. 2) Problem situations based on the matches: a) Insert the second special rule: seed capture. b) When is it possible to capture seeds? c) During this round is there a possibility of one of the players capturing the other’s seed? d) Is it possible for a player to win during this round? e) Does it matter which hole you choose for your first move? Why? f) Now it’s your peer’s turn to play, if you were them, which move would you make? 3) Problem situations that should be recorded: a) Imagine that you’re player number 1 and you’ll move first. Which hole would you choose to start with? b) Look at the following game setup, if you were player number 2, which house would you move the seeds to? Why?	1) Play a few rounds, noticing the strategies the players use. 2) Problem situations based on the matches: a) When is it possible to capture seeds? b) During this round is there a possibility of one of the players capturing the other’s seeds? c) Is it possible for a player to win during this round? d) Does it matter which pit you choose for your first move? Why? f) Now it’s your peer’s turn to play, if you were them, which move would you make? 3) Problem situations that should be recorded: a) Imagine that you’re player number 1 and you’ll move first. Which hole would you choose to start with? b) Look at the following game setup, if you were player number 2, which house would you move the seeds to? Why?
4^th	1) Write down the score of each round, noticing the following situations: a) Do you have more, less or the same number of seeds in your Kalah, when compared to your opponent? b) What do you need to do in order to have more seeds in your Kalah than your opponent? c) And less? And the same amount? d) During which round did you capture the most seeds for your Kalah? e) Observe round “X.” What would need to happen for the game to end in a tie? f) How many seeds, the player that had less by the end of the round would’ve needed to win the game? g) How was your experience playing this game? Register it in words, drawings.	1) Write down the score of each round, noticing the following situations: a) Do you have more, less or the same number of seeds in your Kalah, when compared to your opponent? b) What do you need to do in order to have more seeds in your Kalah than your opponent? c) And less? And the same amount? d) During which round did you capture the most seeds for your Kalah? e) Observe round “X.” What would need to happen for the game to end in a tie? f) How many seeds, the player that had less by the end of the round would’ve needed to win the game? g) How was your experience playing this game? Register it in words, drawings.

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[TFN1] Participants are identified with initials of fictitious names, followed by their age at the beginning of the investigation, in years

[TFN2] Source: Research Data