From the FileAuthor(s): Judy CrawfordSource: The Arithmetic Teacher, Vol. 31, No. 5 (January 1984), p. 35Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41190893 .

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Policy makers. The minimal-com- petency activities in various countries are frequently being initiated by par- ents, school administrators, politi- cians, the business community, or a combination of these groups. In some cases, they are reacting to the appar- ent lack of success experienced under the programs of the 1960s. In other cases, they are challenging the schools and teachers to demonstrate that their current programs are effec- tively meeting the needs of the stu- dents and the community and that their mathematical education is worth the money being spent on it. Against this background, the formulation of minimal-competency policy has sometimes been kept out of the hands of the educators who must implement the competency-based programs and

administer the minimal-competency tests.

Conclusion The members of the Study Group on Minimal Competencies in Mathemat- ics view the task before them as three- fold. First, details of competency- based programs in mathematics, including content, assessment instru- ments, and standards, will be accumu- lated and distributed. Second, the re- sults of any large-scale remediation programs will be analyzed. Third, components of competency programs that help achieve a balance between bringing a large number of students up to minimal levels while successfully educating most students at much high-

er levels will be sought. The study group participants wel-

come the contributions of mathemati- cal educators throughout the world. Anyone interested in participating in future discussions or in sharing with the group their own national experi- ences should feel free to contact me.

For additional information on the activities of the study group or on minimal-competency programs world- wide, the reader might wish to refer to An International Review of Minimal Competency Programs in Mathemat- ics (Columbus, Ohio: SMEAC Infor- mation Reference Center, March 1981). This publication, edited by Robert J. Riehs, includes specific re- ports on basic mathematics programs in twenty-five countries on six contin- ents, w

From the File

J Fraction^ /^ SUBTRACTION OF FRACTIONS WITH BORROWING

My students seemed to have trouble with the concept of "borrowing" with mixed numbers when I was teaching subtraction of fractions. Then I discovered a method that helped my students feel successful with this concept.

After the fractions that are being subtracted have common denominators and students realize that "borrowing" is necessary, the student "borrows" one whole number, strikes through the given whole number, and writes the number that is one less. The student rewrites the borrowed "1" as a fraction, adds the fraction to the given fraction, and then subtracts. Figure 1 illustrates this method with common denominators, and figure 2 illustrates this method with unlike denominators. Fig. 1 6 19 Fig. 2 8 52

/ 12 y 10 " * 40

12 * 8 ~ ¿ 40

412 =A 3 64Õ"

Change "1" to 12/12 and add to 7/12. Change "1" to 40/40 and add to 12/40.

From the file oř Judy Crawford, Lilburn, GA 30247 AT-1-84

January 1984 35

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