Math instructors give formal tests after completing a set of concepts they are teaching. Formal assessments can be used to see overall achievement in a math class in the form of a chapter or section test. Often, a type of formal assessment called “standardized” or “norm referenced” is given yearly district-wide or statewide, because educators want to know how students’ knowledge base ranks when compared to students across the district, state or nation. Norm-referenced tests help determine what the average student understands at a particular age and grade level. Teachers and districts compile data derived from these tests and use it to predict future achievement of groups or individuals. Teachers are often able to get the results and assist students by looking at what concepts students are struggling with.
Teachers are constantly conducting informal assessments such as asking students to complete brief problems at the beginning of the class -- right after the bell rings -- or having individual conferences with students to assess their levels of understanding. Some teachers favor written journals in which students explain how they would complete problems or jot down questions to ask the teacher later. Other types of informal assessments are daily homework assignments and group projects. Math teachers also design checklists known as rubrics to note which problem steps are most confusing to students.
Both types of assessments provide information about struggling students. Formal assessments can help teachers do long-range planning. According to an article published in the "Nonpartisan Education Review" in April, 2011, 93 percent of researchers said that standardized tests had a positive effect on student achievement. However, formal assessments must be planned and are often time-consuming. Researchers who published a study in the June, 2012, issue of "Frontiers in Psychology" discovered that some second- and third-grade students experienced math anxiety and did not perform well on formal assessments even when they knew concepts. Informal assessments are great for quickly assessing specific student needs at a particular moment in time. However, informal assessments are often subjective and do not provide extensive relevant data for improvement.
Formal assessments are important to understanding where students are performing in relation to their peers. Formal classroom assessments like chapter tests can show if students are ready to move on to a new concept. Formal assessments can help ensure that the same topics are taught in the same grades throughout a state or even nationwide. Informal assessments are often a quick, casual way for teachers to identify students who are struggling with concepts they are teaching in one lesson. For example, teachers may do informal observations to see if students have learned how to set up word problems on their own or write equations. By using both forms of assessment, teachers can efficiently and effectively gain a complete picture of student performance.