Do Our Students Really Know the Purpose of Assessments in School?

Here are two students, Nick and Sarah, trying to explain why they took a formative reading and math assessment today. Unfortunately neither one can really answer the question.

Here is Dale giving a pretty good explanation of why we assess.

If we spend so much time assessing students, shouldn't they understand the purpose of the assessment? When I think about the years I spend assessing students without giving them a good reason for the assessment (either by explaining what I hoped to learn or by using that information to help make decisions in class) I feel bad. What is a teacher's responsibility in regards to the students and their assessments?