We conducted this project with the goal of supporting students' mathematics learning (mainly topics of area and multiplication) through creating a 2-dimensional version of Inversé.
This post provide provides a short summary of the project process and examples of students' redesigned games. You can read more about this project here: Kim, Bastani & Takeuchi, 2021;Kim & Bastani, 2020; Bastani, 2022; Jaques et al., 2019
Participants: Grade 3/4 students
Principal Researcher: Dr. Beaumie Kim
Inversé Board Game
Inversé board game pieces
Game components and rules: - A two-player game, each player has a set of five different wooden blocks (3D blocks) with the same volume but different dimensions (and colors) - How the game works: Players take turns to place their pieces until one of them can no longer fit a piece. Its rules include not touching same-color pieces, not placing same-color pieces in the same orientation, and not touching same-height pieces (next figure). In each turn, the player should consider possible positions of their 3D pieces to fit them on the board while making the next move more difficult for the opponent - Winning condition: The person who could fit the last piece on the board would win
A possible play situation based on the rules
Inversé redesign project process:
Students playing Inversé in their groups and mastering the rule
Groups brainstorming on how to change the components and rules of Inversé to create a game with 2-dimensional pieces (aiming to change the game mechanics)
Testing their ideas and making their game components using simple materials such as grid papers, scissors and markers
Group "Extreme Versé" (one of the groups):
making three sets of pieces as they decided to have a 3-player game
Group "Markit"(another group): trying their game with different size dice
Iteratively discussing their design ideas, such as the number of players, game components, and game rules, with their teacher
The teacher made sure about their use of math through their designs and discussed the topics of area and multiplication with them based on their game design decisions
Group Extreme Versé: discussing the concept of area with the teacher
Playtesting their games in their own groups and with other groups, modifying their game components, rules, and the winning condition based on the feedback they received through playtesting
Group "Extreme Versé":
playtesting their game to decide about the size of their game board
Creating a rulebook for their designed game
Asking students from another class to play their games and give them feedback, revising their games based on the feedback
Making their games' components using more enduring materials such as cardboard
Inviting their parents and other classes to play their games in a game night event
Examples of redesigned games:
1. Extreme Versé A three-player game, each having the same set of pieces (with the same color) consisting of prepared rectangles in different sizes Game rules and goal: Players take turns to place their pieces on empty spaces on the board in a way that same colors (i.e., a players’ own pieces) and same shapes (played by different players) wouldn’t touch. The last person to fit a piece would win.
Examples of main changes from the original game (Inversé) Mechanics: - The redesigned game is a 3-player game (vs. 2) - The redesigned game has two-dimensional pieces (vs. 3D blocks), - The redesigned game has same color pieces for each player Aesthetics: - The redesigned game is a 2D game (2D pieces vs. 3D blocks), - The color of the pieces represents the player Dynamics: - Players' decisions are based on the condition of the 2D board (e.g., pieces' area vs. pieces base area and their height), - players' position of their own pieces impact their next moves, so it could be considered in strategizing 2. Markit A two-player game with each player having a marker with a specific color and using two dice to determine the rectangles they need to draw on a 20x20 grid board each turn Game rules and goal: players take turns to roll the dice to determine the sides' length of their rectangular piece, draw the piece where they could find estimated spaces. the drawn pieces have to touch other pieces’ corners (and only their corners and not their sides. the last person who could fit a piece would win.
3. Blockade
A two-player game with each player having a marker with a specific color and using two dice to determine the rectangles they need to draw on a 30x30 grid board each turn
Game rules and goal: Players take turns to roll dice, which determine the sides' length of their rectangular pieces, and draw their piece. They need to calculate and write down the area of their rectangle with the same color (to mark which rectangles belong to which player in the game). The rectangles cannot overlap with one another on the board. The goal for players is to draw their pieces on the board in a way that they surround the other players' rectangles (one or more). The first player who could do so would win the game.
Using a cultural game in the design of Blockade:
This group of students used the condition of surrounding in the Chinese game Weiqi (围棋), known as the board game Go in Canada, in redesigning Inversé and making their own game. This idea came from a newly-arrived immigrant student from China. In the students' designed game, players' fitting their pieces in estimated spaces on the board resembles an aspect of gameplay (game dynamics) in Inversé, but their winning condition, i.e, surrounding the opponent is similar to a condition of getting points in the game Go.
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