MA4100 Mathematical Scholarship and Diagnostic Tutoring Pedagogy

This course introduces the scholarship of teaching and learning in mathematics, providing students with hands on experiences to practice diagnostic and prescriptive instructional strategies to teach collegiate calculus at the Academies. Students learn to identify gaps in student understanding, analyze error patterns, design targeted interventions to support conceptual learning, and analyze and reflect on the interactions with calculus learners. This reflection helps deepen the students’ proficiencies and anchor their personal knowledge as they learn how to teach others. The course integrates mathematical communication, differentiated instruction, and tutoring practice in a student-centered learning environment. In addition, students examine the historical development of mathematics and its evolving role in military applications, connecting foundational concepts to modern defense-relevant problems.

Prerequisite

MA3607 or consent of instructor.

Lecture Hours

3

Lab Hours

0

Course Learning Outcomes

1. Explain misconceptions, procedural errors, and conceptual gaps in student calculus work by analyzing the student’s written work and identifying the specific source of each error.
2. Demonstrate effective questioning, scaffolding, and feedback techniques during tutoring sessions — including Socratic questioning, hint sequences, decomposition scaffolds, and error-specific feedback — to guide student thinking in calculus.
3. Assess the effectiveness of diagnostic and tutoring strategies by using structured session reflections, peer feedback rubrics, and evidence-based analysis of student learning to identify and implement specific adjustments necessary to address diverse learner needs, including the use of digital tools and worked example libraries, to support student understanding and improve the effectiveness of subsequent tutoring sessions.