**Overview**

In Concept Builder workspaces, students engage with a variety of instructional strategies—explore tools, animations, classification tools, and worked examples—to develop their understanding of math concepts. These workspaces provide students with essential learning opportunities to prepare them for the Mastery workspaces that follow. Concept Builder workspaces that occur at the end of a Unit make important connections and/or summarize the learning from the previous workspaces.

Just as with Mastery workspaces, MATHia supports students as they learn in Concept Builder workspaces. There are on-demand hints if they ask for support and just-in-time hints if they make multiple errors.

While students are working, MATHia collects the number of errors students make, the number of hints they ask for, and the amount of time spent in the workspace.

In MATHia, a concept builder workspace provides a fixed number of problems for students to practice that concept. All problems must be completed to finish the workspace.

**How do we communicate progress in Concept Builder Workspaces?**

The progress rings in Concept Builder workspaces communicate to the student which problem they are on and how many problems they have left in the workspace. It also displays which step they are on in their current problem and how many steps they have left in that problem. Students move on when they complete all learning activities within the workspace. In short, this gives the student the view of their progress to completion for the workspace.

**Overview**

Mastery workspaces have long been the heart of the research-based approach behind Carnegie Learning’s software. Mastery workspaces provide students with highly individualized and self-paced instruction that adapts to their exact needs to deepen their conceptual understanding of the mathematics. Through adaptive learning technologies, they engage in reasoning and sense-making. As students work through Mastery workspaces, they are both developing and demonstrating their knowledge.

In MATHia, a mastery workspace gives students problems that let them demonstrate the mathematical skills they are learning. To complete a mastery workspace students must work through an indefinite number of problems until they have shown mastery of all the skills in the workspace.

**How do we communicate progress in Mastery Workspaces?**

The progress rings in Mastery workspaces represent MATHia's estimate of the student's knowledge of each skill. When students first start out learning something new, the skill starts at zero, but as they work and get things right, the skill increases. This happens because MATHia has evidence they are learning the skill. The skill can go down, however, when students make a mistake or ask for the answer. These actions provide MATHia with new evidence, which informs a revised estimate of how well they know that particular skill. When this happens, students will see their current estimate of mastery as well as their ‘personal best.’ If MATHia estimates that the student has mastered the skill, it will turn green. Students move on when they master all skills in a workspace (workspace is Mastered) or when they reach the maximum number of problems in a workspace without demonstrating mastery (workspace is Not Mastered). In short, this gives the student a view of their progress to skill mastery.