Nowadays, students are assessed on a regular basics in school to find out areas of deficiency and achievement. Students are tested in all areas of the curriculum. They are given pre-test to assess abilities and placement. Then, the teacher drives her instructions towards the data to build on areas that need improvement. Next the students are given post test to find out the results of the data driven instruction and strategies used.
According to the website at http://vudat.msu.edu/assess examples of objective/assessments alignments is to demonstrate critical thinking skills and the assessment is a problem analysis.
The objective is to test vocabulary knowledge and the assessment is multiple choice test.
The objective is to assess writing skills and the assessment is to write a composition.
Assessments gives the teacher a clear picture of where the students' achievement gap exist.

There are many kinds of assessments that can be used, such as open ended questions and short answer questions that are measured in math extended response questioning. They are also scored by rubrics. Other kind of test includes, oral report, which can be summative or formative. Exhibition assessments are great to use because it engages students in active learning. Scoring for these types of assessments are done using a scoring rubric as well. When I first started using rubrics to measure achievement, I had a difficult time getting use to them. Now, I would recommend using a rubric to any educator.
The video below has many interesting facts about assessment that I found to be helpful in determining that we need to assess children primarily to give feedback because assessing is just another teaching strategy and it must be included in our planning.