This chapter describes the design, development, and testing of a successful mathematics game-based intervention, Math Snacks, for students in grades 3–7. This program shows the impact of an integrative approach of developing Technological Pedagogical Content Knowledge (TPACK), where interactive digital media are combined with inquiry-based activities in classrooms facilitated by teacher involvement. Teachers played a key role in development and testing of Math Snacks, both by using them in their classrooms and by teaching core mathematics concepts connected to each module during annual summer camps. Via this multi-faceted participation, teachers experienced a change in their understanding of how digital tools can connect with inquiry-based pedagogy, mathematical content and pedagogical knowledge to facilitate successful learning for students. Teachers began to approach multimedia and games as part of an inquiry-based pedagogical approach for mathematics learning, rather than seeing games as tools for student practice after learning a concept.
The design of Math Snacks began with an investigation of common gaps in students’ understanding of math concepts in grades 3–7. The mathematics education research team in the Institute for Excellence/Equity in Mathematics and Science Education (IEMSE) at New Mexico State University analyzed the results of 24,000 student scores on the New Mexico Standards-Based Assessment (NMSBA). On this test, half of the items were open-ended or short answer questions, so it was possible to see student misconceptions in mathematical thinking in ways not possible on multiple-choice-only tests. Researchers looked at the analysis of test results in several different districts and puzzled over almost identical patterns of strengths and weaknesses in student performance across districts, regardless of economic status, number of English Language learners, or size of the district. For example, students across all districts had particular trouble with number concepts and operations, as demonstrated by low average score points on test items focused on operations with decimals and fractions. Similar patterns of common mistakes were found across the districts in all of the mathematics strands, including geometry, data, and algebra. This research provided a road map for developers interested in designing materials to address common student misconceptions. These findings became the basis of an NSF-awarded grant for the development of innovative media, resulting in modules called Math Snacks.
Key Terms in this Chapter
Inquiry-Based Teaching: Inquiry-based instruction, in which teachers engage students in investigations and problem-solving, is part of foundational education reform. The type of learning requires teachers to shift emphasis from textbooks to exploring questions that are student-centered and can be answered empirically. The inquiry-based strategy uses authentic questions that are generated from student experiences ( Crawford, 1999 ).
Math Snacks: A series of educational games and animations focusing on key concepts in math learning. Produced in collaboration among mathematics educators, mathematicians, learning specialists and game developers, Math Snacks supplements instruction by making math more accessible and conveying topics in a creative, visual, and applied ways. Each of the modules aligns with Common Core Standards and is accompanied by teacher and learner guides, a teaching protocol, and an instructional video.
TPACK: An integrative approach of developing technology, pedagogy, and content knowledge in teachers.
OLE (Observation of Learning Environment): Tool for observation of classroom learning environment that sets high standards for student-centered and inquiry-based teaching strategies.
Serious Games: Also frequently called educational games or our preferred term, transformational games , games designed to change learner’s knowledge, understanding or behavior.
Game-Based Learning: Often used to contrast a type of game-play that is different from gamification , game-based learning reflects learning that occurs when immersed in gameplay, usually specific to a content area or type of behavioral change. Gamification is the application of game-like mechanics to provide incentives for doing a certain type of behavior (such as awarding points in a frequent flier program or having different friends compete to complete the most steps on their motion tracker). Game-based learning reflects deeper learning and transformation, and generally includes an immersive environment in which learners solve problems, explore and reflect. It can include both the game, and companion activities that build on what the game introduces.
The Mathematics Reform Curriculum: A mathematics curriculum that focuses on conceptual learning of content for students by focusing on fewer concepts that are taught and learned at a deep level. This curriculum is in response to research studies of mathematics education in high-performing countries that suggest mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. The resulting Standards (Introduction to Common Core Standards for Mathematics) aim for clarity and specificity. There are many ways to organize curricula. The challenge, now rarely met, is to avoid those that distort mathematics and turn off students ( Steen, 2007 ).