Types of Assessment in Mathematics

The following is a brief description of various types of assessment which can be used within the mathematics classroom:

1. Formative and Summative Assessment - Simply stated, formative assessment is assessment for the purpose of "forming" or guiding instruction. Types of formative assessment include conversation, observation, journal writing, and daily work. Summative assessment is assessment for the purpose of judging a student's mastery of concepts. Types of summative assessment include quizzes, tests, and standardized tests.
2. Objective and Subjective Assessment - Objective assessments have a correct answer. Examples of objective assessment are multiple choice or true-false questions. In subjective assessments, the teacher's judgment determines the grade. In mathematics, this equates to multi-step problems which have a clear correct answer, but where the teacher grades and gives partial credit based on the knowledge the student displays through the problem solving process.
3. Self-Assessment, Peer Assessment - Self-Assessment or Peer Assessment types of assignments are provided for quick student feedback. Examples include practice quizzes, practice written assignments, and other interactive exercises.
4. Selected Response and Constructed Response - Selected Response is the same as Objective Assessment and includes the same examples as stated in (2) above. Constructed Response assessments are more conducive to the higher order thinking skills in Bloom's Taxonomy. Examples include a broad range of things, including essays and art projects. In the grading system at my school, one of the grading categories is "alternative assessment", and Constructed Response projects would fall into this category.
5. Authentic and Standardized Assessment - Authentic Assessment includes a task for students to perform and a rubric by which their performance on the task will be evaluated. A great online example is included in this Authentic Assessment Toolbox created by Jon Mueller. Standardized Assessment are tests administered to large groups of students for the purpose of measuring academic achievement. The most common example used throughout the state of Pennsylvania are the PSSA exams.

So which types of assessment are best used within the mathematics classroom? The answer, in brief, is all of them! Different types of assessment are appropriate at different times within the math classroom. Most of the quizzes and tests that I give my students include both objective and subjective pieces. It is important for students to recall math facts - ie, What is the difference between Standard Form, Intercept Form, and Vertex Form of a Quadratic Equation? But, it is also important to apply these facts in a subjective manner - ie, applying the Quadratic Equation in solving a word problem.

For today's students, it is very important to use different types of assessments at different times. During classroom instruction, it is important to do intermittent formative assessments within a lesson to make sure that students are progressing toward the end goal of completely solving a mathematics problem. If they are stuck on step 2 of a 6 step process, they are done! So, teachers need to know if they understand step 2 before getting to the end of the 6 step process.

Constructed response assessments are helpful to allow students to "think outside the box" and apply a mathematics concept to the real world. Often times, these types of assignments are the ones that students remember for years to come. They may not remember how to construct a geometric proof, but they may remember the project they did to see how geometric concepts were used by the ancient Egyptians in constructing the Pyramids.