Eric Butler

A mixed-initiative tool for designing level progressions in games

Creating game content requires balancing design considerations at multiple scales: each level requires effort and iteration to produce, and broad-scale constraints such as the order in which game concepts are introduced must be respected. Game designers currently create informal plans for how the games levels will fit together, but they rarely keep these plans up-to-date when levels change during iteration and testing. This leads to violations of constraints and makes changing the high-level plans expensive. To address these problems, we explore the creation of mixed-initiative game progression authoring tools which explicitly model broad-scale design considerations. These tools let the designer specify constraints on progressions, and keep the plan synchronized when levels are edited. This enables the designer to move between broad and narrow-scale editing and allows for automatic detection of problems caused by edits to levels. We further leverage advances in procedural content generation to help the designer rapidly explore and test game progressions. We present a prototype implementation of such a tool for our actively-developed educational game, Refraction. We also describe how this system could be extended for use in other games and domains, specifically for the domains of math problem sets and interactive programming tutorials.

Automatic Game Progression Design through Analysis of Solution Features

A long-term goal of game design research is to achieve end-to-end automation of much of the design process, one aspect of which is creating effective level progressions. A key difficulty is getting the player to practice with interesting combinations of learned skills while maintaining their engagement. Although recent work in task generation and sequencing has reduced this effort, we still lack end-to-end automation of the entire content design process. We approach this goal by incorporating ideas from intelligent tutoring systems and proposing progression strategies that seek to achieve mastery of not only base concepts but arbitrary combinations of these concepts. The input to our system is a model of what the player needs to do to complete each level, expressed as either an imperative procedure for producing solutions or a representation of features common to all solutions. The output is a progression of levels that can be adjusted by changing high-level parameters. We apply our framework to a popular math puzzle game and present results from 2,377 players showing that our automatic level progression is comparable to expert-crafted progression after a few design iterations based on a key engagement metric.

Large-Scale Educational Campaigns

Educational technology requires a delivery mechanism to scale. One method that has not yet seen widespread use is the educational campaign: large-scale, short-term events focused on a specific educational topic, such as the Hour of Code campaign. These are designed to generate media coverage and lend themselves nicely to collaborative or competitive goals, thus potentially leveraging social effects and community excitement to increase engagement and reach students who otherwise would not participate. In this article, we present a case study of three such campaigns that we ran to encourage students to play an algebra game—DragonBox Adaptive: the Washington, Norway, and Minnesota Algebra Challenges. We provide several design recommendations for future campaigns based on our experience, including the effects of different incentive schemes, the insertion of “tests” to fast-forward students to levels of appropriate difficulty, and the strengths and weaknesses of campaigns as a method of collecting experimental data.

A Framework for Parameterized Design of Rule Systems Applied to Algebra

Creating a domain model expert behavior is a key component of every tutoring system. Whether the process is manual or semi-automatic, the construction of the rules of expert behavior requires substantial effort. Once finished, the domain model is treated as a fixed entity that does not change based on scope, sequence modifications, or student learning parameters. In this paper, we propose a framework for automatic learning and optimization of the domain model expressed as condition-action rules based on designer-provided learning criteria that include aspects of scope, progression sequence, efficiency of learned solutions, and working memory capacity. We present a proof-of-concept implementation based on program synthesis for the domain of linear algebra, and we evaluate this framework through preliminary illustrative scenarios of objective learning criteria.

Approaches for teaching computational thinking strategies in an educational game: A position paper

Computer science is expanding into K12 education and numerous educational games and systems have been created to teach programming skills, including many block-based programming environments. Teaching computational thinking has received particular attention, and more research is needed on using educational games to directly teach computational thinking skills. We propose to investigate this using Dragon Architect, an educational block-based programming game we are developing. Specifically, we wish to study ways of directly teaching computational thinking strategies such as divide and conquer in an educational game, as well as ways to evaluate our approaches.

Synthesizing interpretable strategies for solving puzzle games

Understanding how players interact with games is an important challenge for designers. When playing games centered around problem solving, such as logic puzzles like Sudoku or Nonograms, people employ a rich structure of domain-specific knowledge and strategies that are not obvious from the description of a games rules. This paper explores automatic discovery of player-oriented knowledge and strategies, with the goal of enabling applications ranging from difficulty estimation to puzzle generation to game progression analysis. Using the popular puzzle game Nonograms as our target domain, we present a new system for learning human-interpretable rules for solving these puzzles. The system uses program synthesis, powered by an SMT solver, as the primary learning mechanism. The learned rules are represented as programs in a domain-specific language for condition-action rules. Given game mechanics and a training set of small Nonograms puzzles, our system is able to learn sound, concise rules that generalize to a test set of large real-world puzzles. We show that the learned rules outperform documented strategies for Nonograms drawn from tutorials and guides, both in terms of coverage and quality.

Dragon architect: open design problems for guided learning in a creative computational thinking sandbox game

Educational games have a potentially significant role to play in the increasing efforts to expand access to computer science education. Computational thinking is an area of particular interest, including the development of problem-solving strategies like divide and conquer. Existing games designed to teach computational thinking generally consist of either open-ended exploration with little direct guidance or a linear series of puzzles with lots of direct guidance, but little exploration. Educational research indicates that the most effective approach may be a hybrid of these two structures. We present Dragon Architect, an educational computational thinking game, and use it as context for a discussion of key open problems in the design of games to teach computational thinking. These problems include how to directly teach computational thinking strategies, how to achieve a balance between exploration and direct guidance, and how to incorporate engaging social features. We also discuss several important design challenges we have encountered during the design of Dragon Architect. We contend the problems we describe are relevant to anyone making educational games or systems that need to teach complex concepts and skills.

A Framework for Computer-Aided Design of Educational Domain Models

Many educational applications, from tutoring to problem generation, are built on a formal model of the operational knowledge for a given domain. These domain models consist of rewrite rules that experts apply to solve problems in the domain; e.g., factoring, \(ax + bx \rightarrow (a+b)x\), is one such rule for K-12 algebra. Domain models currently take hundreds of hours to create, and they differ widely in how well they meet educational objectives such as maximizing problem-solving efficiency. Rapid, objective-driven creation of domain models is a key challenge in the development of personalized educational tools.

Program synthesis as a generative method

Generative methods (also known as procedural content generation) have been used to generate a variety of static artifacts such as game levels. One key property of a generative method for a particular domain is how effectively the approach allows a designer to express the properties and constraints they care about. Generative methods have been applied much less frequently to dynamic artifacts such as boss behaviors, in part because the complex representation required to describe boss morphology and behavior is not amenable to existing generative techniques. It is challenging to describe a generative space of varied yet valid behaviors. Expanding on previous work that introduced a programming language for representing boss behaviors, we illustrate how such a language can be used by a designer to describe desirable design properties and constraints for bosses. That is, we define a generative space of bosses as a space of well-formed programs. We present a constructive algorithm that extends generative grammars to efficiently generate well-formed programs, and we show a complete example of generating Mega-Man-like bosses with complex attack patterns. We conclude that designing a generative space of dynamic behaviors can be fruitfully framed as a programming-language design problem.