How will you know when students have learned the basic facts?

Edward C. Rathmell
University of Northern Iowa

Traditionally, students "knew" their basic facts if they could successfully complete all the basic facts for an operation in some predetermined time period. For example, some schools require 100 addition facts to be completed in 2 or 3 minutes. In other words, speed, with a reasonably high level of accuracy, is the primary criteria.

However, assessment on the basic facts needs to include a variety of tasks. For example, drill (timed tests) can provide information about the speed and accuracy of students for basic facts. But Brownell's second goal would be ignored. Teachers should also identify the thinking strategies that students are using. They should be able to use some efficient thinking strategy for any basic fact that is presented. One way to determine how the students are thinking is to provide a few word problems in an interview. Ask the student to think aloud as they solve each of the problems. Probing, as necessary, can provide the teacher considerable information about the thinking of the student. If there is a question about the use of a strategy, the teacher can suggest that the student use that strategy while solving a different problem.

Another aspect of understanding addition and subtraction facts is to determine if the students understand the part-part-whole concept. Give the parts and whole, using larger numbers. Choose numbers where the students will not know the answer to the problem. For example, the parts are 19 and 16 and the whole is 35. Then ask some related questions. What is 35 - 19?

Over fifty years ago, William Brownell indicated that his goals for teaching basic facts were to have students be able to provide (1) an immediate response and (2) an explanation or verification that the fact is correct. Those two goals are still appropriate today. The second goal may not be as commonly accepted today as the first one is, but it is important. Research has shown that students, who can explain or verify basic facts, learn the facts sooner, are able to use them in mental computation with larger numbers, and remember them longer. Also, without these student explanations, it is more difficult for teachers to know if students understand, just know rotely, or were guessing.

Students who know the basic facts will be able to respond to facts quickly (about 3 seconds per response). They will be highly accurate. If drill is postponed until after the students can use an efficient thinking strategy, then the practice that drill provides enables students to be more than 95% accurate. Furthermore, they will be able to explain many of the efficient thinking strategies as ways in which they solve basic fact problems. The students need to be flexible enough with the use of these strategies so they decide which strategy will work best in a given situation.

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