We develop immersive online virtual worlds to help students conceptually understand mathematics and achieve computational fluency. The games within our world have a deep integration of neuroscientific learning principles, effective pedagogy, and engaging game-play design.
Our virtual world, Fog Stone Isle, is initially focused on the rational number system (5th - 8th grade): fractions, ratios, proportions, and unit rate. These are important topics that need to be mastered in order to be successful in algebra and beyond.
Each student is assigned a unique virtual world that allows them to use their own ideas and creativity while crafting their environment. For example, students are immersed in creating buildings, farm plots and corrals while adding, subtracting, multiplying and dividing fractions. The math is meaningful to the tasks they are doing. Work is done independently and/or collaboratively as students make sense of their ideas. They enthusiastically share their virtual worlds in class while explaining their thinking.
The math problems to be solved in a student’s virtual world are adaptive to their level. Cignition automatically creates problems that keep students working at a pace that is appropriate for them. Their design tasks challenge and extend their thinking at their level. Every math topic (e.g., fraction addition) is broken into the full sequence of conceptual leaps required to master the topic. Students will automatically move to the next conceptual leap when they are ready. Within a conceptual level, the game will adapt as students improve their procedural fluency. Once at a new concept level, students will continue to work on problems in the previous levels as they master the new level.
The games within the virtual world optimize specific learning goals by careful control of working memory load. Working memory provides a mental workspace to process information. Cignition’s approach is to modulate working memory requirements during critical moments of conceptual learning to allow for better focus on concepts.
Learning is reinforced and recall improved by absorbing information via different systems in the brain. Careful consideration has been taken to stimulate different brain systems during information acquisition to build stronger neural networks of integrated information that center around a concept. As students create farm plots in their virtual world, learning is improved by engaging multiple brain systems in every move.
The games within our virtual world use a variety of interactive visual illustrations and virtual manipulatives to demonstrate abstract math concepts that would otherwise be difficult to describe or imagine. While students create buildings in their virtual world, a sketchpad tool is used to help students understand how common denominators can be used to make fraction addition easier. The tool also reminds students how to use multiplicative identities to find equivalent fractions.
Our comprehensive teacher workstation provides actionable feedback for the class and each student. Every subject (e.g., fraction addition) is broken into the full sequence of conceptual leaps required to master the topic. At a glance, educators can immediately view how their classes are progressing on each concept and accurately diagnose students’ difficulties.
A snapshot of fraction addition performance for one class shows a red dot in Patrick’s row, which tells us that he started having difficulty when a change in both denominators was needed. The green dots show that students understand that particular concept, and the yellow dots indicate the students that are developing their abilities in a particular area.
For each concept within a topic, a teacher can view an individual student’s conceptual understanding and procedural fluency.
Additional analysis of general student skills are included such as mastery of multiplication tables, gleaned from performance on a variety of tasks. When the teacher looks at Patrick’s multiplication table performance, light green and orange squares on the chart shows that Patrick is not fluent in those multiplication facts.