There are two general categories of assessments: formal and informal.
Formal assessments have data which support the conclusions made from the test. We usually refer to these types of tests as standardized measures. These tests have been tried before on students and have statistics which support the conclusion such as the student is reading below average for his age. The data is mathematically computed and summarized. Scores such as percentiles, stanines, or standard scores are mostly commonly given from this type of assessment.
Informal assessments are not data driven but rather content and performance driven. For example, running records are informal assessments because they indicate how well a student is reading a specific book. Scores such as 10 correct out of 15, percent of words read correctly, and most rubric scores are given from this type of assessment.
The assessment used needs to match the purpose of assessing. Formal or standardized measures should be used to assess overall achievement, to compare a student's performance with others at their age or grade, or to identify comparable strengths and weaknesses with peers. Informal assessments sometimes referred to as criterion referenced measures or performance based measures, should be used to inform instruction.
The most effective teaching is based on identifying performance objectives, instructing according to these objectives, and then assessing these performance objectives. Moreover, for any objectives not attained, intervention activities to re-teach these objectives are necessary.