A good diagram is valuable despite the choice of a mathematical approach to problem solving
Alexandru Maries, Chandralekha Singh

TL;DR
Drawing diagrams significantly aids physics problem solving, but providing partial diagrams can hinder students' ability to create their own effective diagrams, impacting their performance.
Contribution
This study reveals that explicitly asking students to draw diagrams improves problem solving, while providing partial diagrams may have unintended negative effects.
Findings
Students who drew productive diagrams performed better.
Providing partial diagrams reduced students' likelihood to draw their own diagrams.
Diagram drawing correlates with improved problem-solving performance.
Abstract
Drawing appropriate diagrams is a useful problem solving heuristic that can transform a problem into a representation that is easier to exploit for solving the problem. A major focus while helping introductory physics students learn problem solving is to help them appreciate that drawing diagrams facilitates problem solution. We conducted an investigation in which 118 students in an algebra-based introductory physics course were subjected to two different interventions during the problem solving in recitation quizzes throughout the semester. Here, we discuss the problem solving performance of students in different intervention groups for two problems involving standing waves in tubes, one which was given in a quiz and the other in a midterm exam. These problems can be solved using two different methods, one involving a diagrammatic representation and the other involving mostly…
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