Written by Nicole F. Ice and Wendy B. Sanchez, Kennesaw State University
(News Bulletin, December 2005)
If you are an educator, you have certainly heard students ask, “Will this be on the test?” The implications of this statement are far-reaching, since we know that students will focus their attention only on concepts and skills that they know will be evaluated. Assessment, according to NCTM’s Assessment Standards for School Mathematics, is a process of gathering information about students’ understanding for a variety of purposes, only one of which is evaluation. Evaluation is a process of assigning value to students’ understanding. Although assessment is a valuable tool for teachers, students are most concerned about evaluation and their grades. In a very real sense, what teachers choose to put on tests helps students determine what mathematics is important, and in fact, helps shape their view of the nature of mathematics. For instance, if students see nothing but test items that evaluate their ability to do rote mathematical procedures, then it is very likely that they will come to view mathematics as a set of rote procedures.
To illustrate how our selection of test items can affect our students’ attitude toward mathematics and their learning, consider the following example from the Open-Ended Assessment in Math Web site, at www.heinemann.com/math.:
Below is one student’s response.
Clearly, this student is proficient at generating equivalent fractions to compare two fractions. However, the student has not demonstrated an understanding of the concept that to compare fractional parts you must also consider the sizes of the original wholes. This student would be able to correctly answer the question, “Which is greater, 1/2 or 1/4?” But a teacher who asks questions that are phrased like the example above will be able to assess the student’s conceptual understanding in addition to his or her ability to perform mathematical procedures. From this assessment, the teacher will be able to determine whether more instruction is needed or not.
The NCTM Standards documents advocate learning mathematics with understanding, as opposed to merely learning rote mathematical procedures. The processes of problem solving, reasoning and proof, communication, making connections, and representing mathematics in a variety of ways play a fundamental role in developing students’ conceptual understanding of mathematics. If teachers truly value these processes, then not only do students need to have opportunities to engage in such processes, but the processes also need to be evaluated in ways that have a significant impact on students’ grades.
For example, if teachers value problem solving, students should be given opportunities to solve problems. There is a difference between working exercises and solving problems. An exercise involves following procedures that are the same as or very similar to examples shown in class. Problem solving, however, involves “engaging in a task for which the solution method is not known in advance” (Principles and Standards for School Mathematics, NCTM 2000, p. 52). If teachers want to send the message that problem-solving is an important part of mathematics, then not only should the opportunity to solve problems occur during homework, classwork, and extra-credit assignments, but it should also occur during evaluation. That is, the process of problem solving needs to be evaluated in a way that has a significant impact on students’ grades.
When students ask the question, “Is this going to be on the test?” they are really asking you what you value about mathematics. We encourage you to take a look at some of your recent tests and consider what message you have been sending to your students about mathematics through the test content. Do your tests really reflect what you believe and value about mathematics?