Formative assessments help teachers gauge students’ understanding as the lesson is going on while summative assessments help teachers evaluate students’ understanding at the end of a lesson. For example, a seventh-grade math teacher might have students complete a small quiz on adding and subtracting decimals to gauge how students are progressing through a lesson on decimals. The results of this quiz will indicate to the teacher what elements of adding and subtracting decimals she might need to cover again, as well as which elements the students have mastered. She might then require students to take a test on decimals, the results of which will indicate how much of the material on decimals students have retained following her instruction.
Self and peer assessments help students examine their own progress or development in a class, and develop strategies for improvement. For example, an eighth-grade math teacher might have students write a brief reflection on how they understand rational and irrational numbers and develop a plan of action for comparing rational and irrational numbers. Similarly, a sixth-grade math teacher might have students “grade” each other’s work after they’ve solved an algebraic equations with variables.
An assessment is objective if its value or grade is attached to a right and wrong answer independent of anybody’s judgment. An assessment is subjective if its value or grade comes from an individual’s -- usually a teacher’s -- personal judgment. For example, a middle school math assessment that asks students to solve algebraic equations would be objective because the equations would have a right or wrong answer that the students must discover. However, a middle school math assessment that asks students write a description of where they might use their knowledge of decimals in a “real world” experience would be subjective because the teacher would have to evaluate how accurately a student described such a situation.
In addition to the different kinds of assessments that middle school math teachers might use in their classrooms, many middle school students are also required to take formal or standardized assessments that are developed by agencies outside of the school. For example, middle school students in states that have adopted the Common Core Standards will take a standardized exam built off of those standards. Though middle school math teachers don’t design these exams, they can still use them to guide their curriculum development. Additionally, middle school math teachers might consider the results of such standardized exams to determine what material they might need to revisit with their students in future lessons.