Data from written tests and videotaped problem-solving interviews show that many physics students have a stable, alternative view of the relationship between force and acceleration. This ''conceptual primitive'' is misunderstood at the qualitative level in addition to any difficulties that might occur with mathematical formulation. The misconception is highly resistant to change and is remarkably similar to one discussed by Galileo, as shown by comparison of his writings with transcripts from student interviews. The source of this qualitative misunderstanding can be traced to a deep-seated preconception that makes a full understanding of Newton's first and second laws very difficult. In such cases learning becomes a process in which new concepts must displace or be remolded from stable concepts that the student has constructed over many years.