Mathematical Reasoning and Tutors

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