The energy crisis, expected by at least some segments of our society for several years, has arrived. Its precise causes are unclear and perhaps always will remain so, but it is likely to have profound effects on many aspects of our economy as well as on our environment. Some of these effects may be positive in nature. For example, expanded use of smaller, more economical automobiles; renewed efforts to locate and develop additional sources of energy; and the evolvement of a more energy-conscious citizenry are likely to result.

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- Author or Editor: Thomas R. Post x

### Thomas R. Post

Despite the recent introduction of the calculator and emphasis on the metric system, fractions continue to occupy an important place in school mathematics programs. Persuasive arguments for continued emphasis can be made not only because of their social utility but also because of their place in the development and structuring of mathematical ideas to follow. Accordingly, the National Assessment of Educational Processes (NAEP) allocated a substantial portion of the second mathematics assessment to fractions.

### Thomas R. Post

The results of national and international assessments indicate that students have significant difficulties in learning about rational numbers, in 1979 only 24 percent of the nation's thirteen-year-olds could estimate the sum of 12/13 and 7/8 given the following possibilities: 1, 2, 19, 21, and I don't know. Fifty-five percent selected either 19 or 21 as the estimated sum!

### Thomas R. Post

The mathematics program in too many of today's schools is textbook dominated, con. cemed primarily with the manipulation of symbols, and, all too often, largely removed from the real world of the child. Mathematics enjoys (or suffers from, depending upon one's perspective) a reputation which is clearly less than inspiring. Why are there such large-scale negative attitudes towards mathematics? Endless repetition, meaningless memorization, a never-ending series of worksheets or practice exercises, and a gen. eral lack of interest and understanding are but a few of the reasons that might be listed. One problem with a textbook-dominated approach to teaching and learning is that young people do not exist in a twodimensional world. Children exist in a world that they are very eager to learn about until that eagerness and enthusiasm is dulled by the establishment of numerous artificial situations to which they are required to respond. What is needed is a mathematics program that is very much alive and vibrant, and relevant and meaningful; a program that parallels the way in which young learners are alive and vibrant and continually searching for relevance and meaning as they seek to understand the world around them.

### Carol Carrier, Thomas R. Post and William Heck

Microcomputers in elementary school classrooms will soon be as common as handheld calculators and reading stations. Luehrmann (1981) states that within 3 years the average school will have 16 microcomputers. The acceptance and availability of reasonably priced computer technology for the classroom and the home suggests that elementary teachers will be encouraged to incorporate computer-based activities into many areas of the curriculum. Although some of the most intriguing applications of computers in instruction at the elementary level can be seen in tutorials, si mulations, or interactive systems such as Logo, many teachers will continue to use the computer primarily to give children skill-building experiences in ma thematics and other school subjects.

### Kathleen A. Cramer, Thomas R. Post and Merlyn J. Behr

The aptitude-treatment interaction (ATI) study reported here explored the relationship between cognitive restructuring ability, as measured by the Group Embedded Figures Test (GEFT), and treatments varying in amounts of teacher guidance. It specifically investigated how these two variables affected performance on rational number tasks involving perceptual distracters.

### Thomas R. Post and Michael L. Brennan

It was the purpose of this study to investigate the effects of various modes of presentation of general heuristic processes on students' problem-solving ability. It was felt that if students are to become effective problem solvers they must be formally instructed in the established techniques of, and approaches to, problem solving. It was hypothesized that these techniques would both faci litate students' efficiency in solving problems and improve their ability to solve various kinds of problems. This study, then, was an attempt to formally instruct students in a particular heuristic problemsolving process so that awareness and ability could be developed, and subsequently to evaluate the effects of this instruction on their ability to solve problems.

### Michael L. Brennan and Thomas R. Post

The improvement of problem-solving ability continues to be an elusive, yet important, goal of mathematics education. A variety of individual attempts have been made to improve student performance in this area. The Journal for Research in Mathematics Education (JRME) has performed a valuable service to the profession by facilitating interaction between individuals who have made or are contemplating such attempts. Only through such professional interaction will old ideas be reshaped and new ones generated. In this manner perhaps we shall someday provide definitive answers to questions we know to be of mutual concern. The following comments constitute our response to Kulm's critique of our previous JRME article (Post % Brennan, 1976).

### Thomas R. Post, Debra S. Monson, Edwin Andersen and Michael R. Harwell

in the early 1990s, after a long series of disappointing results on national and international mathematics achievement tests—for example, TIMSS (1998) and NAEP (Campbell, Hombo, and Mazzeo 2000)—the National Science Foundation (NSF) funded the development of thirteen complete mathematics programs at the elementary school, middle school, and secondary school levels.

### Patricia M. Heller, Thomas R. Post, Merlyn Behr and Richard Lesh

This study examined the relationship between junior high school students' directional reasoning about rates and numerical reasoning on proportion-related word problems. Also explored was the extent to which the ability to solve context-free fraction exercises is related to the ability to solve mathematically similar word problems. Four hundred twenty-one seventh-grade and 492 eighth-grade students were given a test consisting of eight directional and eight proportion-related word problems and a fraction test that included 11 items that precisely paralleled the mathematical structure of the word problems. The correlation between the directional and numerical scales was .38 for seventh grade and .45 for eighth grade. Regression analysis indicated that a high directional score is related to greater numerical success on proportion-related problems. The low correlations between the mathematically similar problems on the fraction and word-problem tests indicate that students are not capitalizing on the structural similarities inherent in the problems, even when the numerical quantities are identical.