How should instructors evaluate a student's understanding of a new math concept?

Evaluating a student's understanding of a new math concept is most effectively achieved through questioning and observing their work process. This approach allows instructors to see not only the final answers but also the methodologies and thought processes that students employ while tackling problems. By actively engaging with students through targeted questions, instructors can gauge their level of comprehension, clarify any misunderstandings, and provide immediate feedback. Observing how students approach and solve problems offers valuable insight into their critical thinking skills and can highlight areas where additional support may be needed.

Relying solely on a multiple-choice test might not fully capture a student’s grasp of the material since it often tests recognition rather than understanding. Watching instructional videos can provide information but does not assess whether the student has absorbed the material. Assigning more homework could lead to practice but does not necessarily reflect how well a student has internalized the concept or their ability to apply it in different contexts. Thus, a more interactive and observational approach is preferable for gauging true understanding.