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In recent years, numerous reports have called for reform in American education in general and mathematics education in particular (e.g., Leitzel[1991]; NCTM [1991]; National Research Council [1989, 1990, 1991]). One suggested reform is revamping the curriculum to include mathematics more relevant to society and student current needs. In addition to changing the curriculum. these report have recommended changes in the method used to teach the curriculum. Among the suggested changes in methodology are an increased use of technology and opponunities for students to connect mathematical ideas.

Las Vegas, Nevada 89154 Scene'. The Repp, 1935) concluded that drill makes efficient that which is actually being drilled. Thus, if students are using a counting procedure to solve basic facts and teachers introduce drill activities, the students will become more proficient with the counting strategy. To complain that students do not have immediate recall while providing them with opportunities to drill theircountingprocedures is deplorable. Drill does not guarantee automatization of the fact(s), only automatization of the technique(s) being employed to solve the fact(s).Many of the techniques used to help students master the facts (such as counting-on, tapping reference points on the numerals, or thinking strategies) are procedures introduced during initial instruction or remediation in order to develop accuracy and occasionally meaningful understanding, notspeed.We then begin drilling the facts, typically by requiring students solve a number of facts within a given time limit, in the hopes of developing speedy responses. This is also done in the erroneous belief that if we provide enough drill, students will abandon the crutches they have been taught or developed themselves, and their responses will become automatic. Experience shows that for many students, this does not happen. This may be because of our misunderstanding, and subsequent misuse, of drill and practice activities.Although a thesaurus and the historical use ofthe words drill and practice suggestthe words are synonyms, a subtledifference exists between them. To understand the difference, look at them in the light of learning to play the piano. Why is a child told to "practice thepiano?" Ifpracticeanddrillare synonymous, why isn't the child told to "drill the piano?" In actuality, a child would drill the scales while practicing the piano. Drill is the repetitious activity used to make certain responses (e.g., finger placement) automatic. Practice involves more thanjust drill. It means getting to know a new piece of music, determining how phrases should be played, working on the passages until they feel comfortable. In other words, practice means developing an understanding of the music and becoming accurate with finger placement. Then the music is drilled in order to automatize the playing.If a distinction between drill and practice exists when considering the playing of a musical instrument, then it might also exist when considering the learning of basic facts. In this instance, practice wouldinvolve the developmentofmeaningful understanding and accuracy of responses while drill would be the repetitious activities needed to develop speed and automaticity of those responses. Furthermore, there should be discernible differences between activities designed for drill and those designed for practice.In order to pinpoint any differences between drill and practice activities, consider a typical form of drill-the timed test. In this activity, students are required to solve a certain number of basic facts within a given time limit. This is generally ...