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Enhancing Mathematical Reasoning Through Effective Tutoring Approaches

This document discusses the benefits of tutoring in mathematical reasoning, emphasizing active and self-paced learning that leads to increased engagement and improved self-confidence, especially among female students. It explores model-based design as a superior method compared to rule-based design, focusing on reusability and composability. Key features like error-flagging enhance student performance by helping identify mistakes without direct correction, allowing for efficient problem-solving. Additionally, it outlines evaluation protocols that maximize learning outcomes while minimizing time spent.

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Enhancing Mathematical Reasoning Through Effective Tutoring Approaches

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  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

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