1. Mathematical Reasoning and Tutors Amruth N. Kumar amruth@ramapo.edu

2. Benefits Of Tutors Active learning, Self-paced learning Increased time-on-task Helps build appropriate “mental models” Helps improve self-confidence of female students Medium of choice for millennials

3. Design - Model-Based Design As opposed to: – Rule-based design – Class per problem design Reusability Composability Serialized problem specification

4. Loop Invariant Analysis: Given a loop and a loop invariant, verify whether the invariant applies to the loop Synthesis: Given a loop, identify the loop invariant – Identify the variables – Identify the relationships among the variables – Verify the applicability of the loop invariant Back-stepping post- to pre- through the loop statements

5. Features - Error-Flagging Error-detection, but not error-correction support when answering Improves student scores – Prevents inadvertent mistakes – Significant for non-multiple-choice problems Less time per problem – Speeds up problem-solving process? Do not necessarily revise more often

6. Evaluation Built-in pre-practice-post protocol? Adaptation – From pre-test to practice – From practice to post-test – Maximizes learning, Minimizes time spent