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Even when calculators make obvious errors, some people continue to trust them.

In a study on estimating, sponsored by the National Institute of Education, University of Missouri mathematics Professor Robert E. Reys interviewed a group of subjects who had demonstrated a flair for estimating the answers to arithmetic problems. Using a series of seven exercises, Professor Reys asked the 55 secondary-school students and adults to verify their answers on a calculator.

But the calculator was programmed to provide answers that were 10 to 50 percent off the correct answer--and the errors got larger with each set of problems.

In spite of the subjects' proven skill in estimating, many were reluctant to reject the calculator's answers. Twenty percent of the subjects told the interviewers that the calculator was wrong after working out the first exercise, but more than one-third went through all seven exercises without voicing any doubt about the calculator's answers.

"Any conclusions drawn from this would be tentative," the researchers write, because the sample was small and other factors might have affected the subjects' responses. But the researchers found, in general, that males were more likely than females to challenge the calculator, and that "even subjects making good estimates were reluctant to challenge the calculator's result."

"The results," they write,"indicate an aura of infallibility exists surrounding the calculator."

Enormous "plate-waste" was one factor cited in the Reagan Administration's decision to make budget cuts in the federal school-lunch program.

Heretofore, the most accurate method of verifying such claims has been weighing the food left on children's plates.

A new study, however, suggests that school-lunch officials may be able to monitor "plate-waste" without going through the time-consuming and unry process of weighing the scraps left behind by children.

The study, sponsored by the U.S. Department of Agriculture and conducted by researchers at Abt Associates Inc., of Cambridge, Mass., suggests that trained observers can accurately estimate the amount of plate-waste. Their estimates correlated highly with measures obtained by weighing leftovers.

The researchers, Elizabeth M. Comk, Robert G. St. Pierre, and Yevgenia D. Mackiernan, also found that children judged with fairly high accuracy the amounts of leftover food, but students' estimates were not as reliable as those of adult observers.

"These results support the use of indirect measures of individual plate-waste," according to the researchers. The study was published in the September 1981 Journal of the American Dietetic Association.

Bearded teachers and other professionals whose jobs require gaining childrens' trust may instead be frightening them with their hairy faces, according to two researchers at Brigham Young University.

Psychologists Darwin F. Gale and Parley W. Newman based their conclusion on the reactions of approximately 250 Utah and California children to four drawings depicting men with varying amounts of facial hair.

The men in the pictures were identical except that one was clean shaven, one had short sideburns and a small mustache, one had longer sideburns and a larger mustache, and the last had a full mustache and beard. The children were shown the drawings and asked to identify "the nice man" and "the scary man."

A large majority of the subjects said the bearded face was scary and the clean-shaven face was nice, according to the researchers.

Children rarely picked the faces with mustaches as either scary or nice, they said, and responses did not differ significantly between boys and girls nor between children from Utah and California.

Copies of the report can be obtained from Professors Gale and Newman at the Department of Educational Psychology, Brigham Young University, Provo, Utah 84602.

American teen-agers are ambivalent--and in many ways very traditional--about working mothers, according to a survey conducted by Louis Harris and Associates for General Mills, Inc.

Fifty-four percent of the 235 teen-agers surveyed said children under 13 years of age are harmed when both parents work, while only 12 percent thought both parents' working was good for young children.

A majority of the teen-agers also said one parent--in most cases specifying the mother--should stay at home with pre-school children. Children "are more likely to get into trouble" when both parents work, the teen-agers agreed.

The respondents also said, however, that the effects of working parents are generally good for teen-agers. One big advantage, they said, is that children become more self-reliant and independent when both parents work--as is the case in more than half of American families today.

That pattern is likely to continue when the current generation of teen-agers reaches adulthood. Most (58 percent) of the teen-aged girls surveyed plan to work outside the home even if it is not economically necessary. But nearly three-quarters of the girls also expect to have primary responsibility for the home and children, although they agree overwhelmingly that parents should share such duties.

Among the survey's other findings:

Teen-agers overwhelmingly disagreed with the statement that working parents "spoil their children to make up for not spending time with them," while adults over age 40 tended to agree with that statement.

A large majority of teen-agers believe homemaking has more advantages than other kinds of jobs, while adults tended to say homemaking has more disadvantages.

Boys and girls felt equally pressured to get an education but believed boys are under more pressure to get a good job after graduation.

Four-fifths of the teen-agers said they are consulted at least part of the time about family financial decisions.

Copies of the report, the fourth in an annual series on family issues, may be obtained by writing to The American Family Report, General Mills, Inc., Box 6, Department 760, Minneapolis, MN, 55460.

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