A newly published article highlights the impact of Agrinautica, one of the Math Snacks games developed by the Learning Games Lab, in collaboration with other NMSU departments. Researchers in Extension, math, education and computer science conducted a study with more than 400 learners to identify the impacts of the game. The open access article offers insights to the value of the game to learners, and the ways it transforms math learning and teaching.

Cezarotto, M. A., Martinez, P. N., Torres Castillo, R. C., Stanford, T., Engledowl, C., Degardin, G., & Chamberlin, B. (2024). Open-Ended Mathematics Learning: Implications From the Design of a Sandbox Game. International Journal of Game-Based Learning (IJGBL), 14(1), 1-19.

## Why Expressions Matter

One essential aspect of pre-algebra is a basic understanding of how math expressions work. Anyone on social media has seen the various “math challenges” that arise on your timeline and cause great debate. They usually present some kind of numeric expression, often including multiple operators (addition, subtraction, division, multiplication) and at least one set of parentheses. You will often find in the comments a range of answers, as well as strongly held opinions regarding the right way to solve the expression.

The truth is: math offers a specific set of rules, and those rules help us know the right way to solve these expressions. Our ability to do algebra is only as good as our ability to craft mathematical expressions that match our intent. If we want to write an expression using parentheses and multiple operators, and we want the answer to be “9”, we should be able to write that expression with confidence.

## How to Play with Expressions

Often, expression instruction begins with sheets of expressions, and students are given a mnemonic device for remembering the order of operations, such as PEMDAS (parentheses, exponents, multiply, divide, add, subtract). Students then work the expressions, which often gradually increase in difficulty, and are graded on how many they get correct. Unquestionably, as a student works more and more expressions, that student will build their understanding and skill, but proper feedback on those expressions is critical. In order to progress, students must grasp where their understanding was correct, and where it was incorrect.

The Math Snacks game Agrinautica was designed to help users build their own understanding of how math operators, parentheses and expressions work, and to prompt learners to voluntarily write lots of expressions. Inspired by the popular classroom activity Bowling for Numbers, the game gives players a considerable amount of independent autonomy in experimenting with how expressions evaluate, that is, how expressions get to the correct answer. Agrinautica gives users a random set of four numbers (such as 3, 2, 4, and 1), unlimited operators, and parentheses, then encourages players to create lots of expressions. As the player creates an expression, they can see how it evaluates on screen, learning the order and the answer. The player is then given a fantastic plant based on their expression. For example, an expression that uses two different operators and one set of parentheses yields an imaginary flower: if the answer to the expression is “2”, it is the flower Duobloomia faetheria. If the answer to the expression is “5”, it yields the flower Quinbloomia faetheria. Learners see visually how different expressions yield different flowers.

As players spend more time in the game, each student starts developing their own plans for their garden. Some are collectors, and try to get one of every plant. Some serve as designers, and try to create duplicate plants with different numbers. Others try to line their plants up perfectly, getting all of the cards for expressions with the answer “9”, for example. Because the player has the autonomy to decide what kind of plants they want, they are highly motivated to experiment with different expressions to try and get those plants. Classroom observations have noted that giving learners an opportunity to see what plants their peers have created is also highly motivational. Because each student is given a different set of numbers (one might have 1, 2, 3 and 4 where another may be given 6, 5, 3 and 3), students then start coaching each other on how to craft an expression with each set of numbers, to yield the desired plant.

Sandbox games such as Agrinautica are defined by an open-ended environment, in which players can set their own goals for development. Compared to a leveled game, in which players must pass a certain point of success to move to the next level, sandbox games allow users to play on their own, usually through creating items, environments or completing tasks in different orders. Sandbox games are, of course, not the only kind of educational games. The Math Snacks series includes six other games that use other game mechanics. However, sandbox games offer students the environment for freeform learning that works especially well within the social dynamics of the classroom or other collaborative environments. For Agrinautica, a sandbox game enabled the shift from repeatedly asking students to solve expressions as the learning mechanic, to giving the students the ability to build expressions to learn.

## Research Demonstrates Success

Agrinautica has been successful in encouraging pre-algebra students to “play” their way to a better understanding of algebra. A recently published article in the International Journal of Game Based Learning offers details on the impact of the game on players in a study with 410 players, and recommendations on creating other educational games in open-ended, sandbox environments.

In terms of writing many expressions, the students in the study averaged 180 individual expressions during gameplay, meaning that most students wrote lots of expressions, receiving feedback on how each evaluated (Cezarotto et al., 2024). This is likely a higher number of practice expressions than a student would voluntarily write in a given math class. Moreover, more than half of the learners improved to a higher level of sophistication in their expression building, in response to game play.

## Other Important Findings

In addition to the impact on math learners’ ability to write expressions, the article also shares research on the impact of Agrinautica gameplay on math teachers’ perceptions: including a willingness to give students more independence and exploration in understanding math concepts. The study analyzed personal journal reflections of teachers using the games, as well as interviews with teachers to discover how their perceptions of games in the classroom and their approach to teaching was changed.

The article also offers design recommendations on crafting other sandbox games for learning; such as allowing for discovery by players (rather than giving them specific instruction), supporting games with out-of-game application experiences, and considering what types of learning goals work in sandbox environments.

Written by Barbara Chamberlin, Department Head, Innovative Media, Research and Extension

## Reference

Cezarotto, M. A., Martinez, P. N., Castillo, R. C. T., Stanford, T., Engledowl, C., Degardin, G., & Chamberlin, B. (2024). Open-Ended Mathematics Learning: Implications From the Design of a Sandbox Game. International Journal of Game-Based Learning (IJGBL), 14(1), 1-19.

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