The groundwork for explorations in heuristics was established by Polya in "How to Solve It (1945)" and given a much more extended treatment in his "Mathematical Discovery" (1962, 1965). He described a variety of useful strategies but did not describe research in mathematical problem-solving. In the 1970s, many experimental studies of mathematical problem-solving had been made in America. Most of these studies had adopted Polya's definition (heuristics model) of mathematical problem-solving and focused on the problem-solving processes of students as they solve problems. Several researchers (Kilpatrick, 1968; Lucas, 1974; Webb, 1979; Days, 1979) have identified and studied mathematical problem-solving processes, heuristics in particular. The purposes of this paper are to make a survey of their studies and are as follows; I. to consider the experimental method used to clarify and elucidate the mechanisms of mathematical problem-solving behaviors, II. to consider the procedure of data analysis. The results obtained are as follows; (1) The Thinking Aloud Technique was used successfully to study problem-solving strategies in school-age children. (2) The protocol coding and scoring system was used to analyze the tape-recorded protocols. (3) The small-sample experiments, as opposed to the large-sample experiments, were designed to clarify and elucidate problem-solving processes. (4) Analysis of Variance was chiefly used to analyze problem-solving processes as the procedure of data analysis.
Which school year should be more appropriate for developing "Conception of function" at an elementary school? It has been moved to third grade or fourth grade every time the course of study was revised. It seems, however, that there have not done sufficient examinations by having an experimental class to control some conditions in class for comparison. Judging from this point of view, we conducted lessons, through common direction and instructor, to three groups of pupils of 2nd, 3rd, and 4th grade where these three groups were set homogeneous in arithmetic, to survey the possibility for developing an understanding "Conception of function" and to make clear the inclination of each school year. As the result, we confirmed that basic parts of "Conception of function" can be taught to the 4th grade pupils, that upper class of 3rd grade pupils are able to understand nearly to the extent that 4th grade pupils do, that lower class of 3rd grade pupils can be instructed as far as we give them basic items such as "one-to-one correspondence", and that for 2nd grade pupils it is appropriate to give them instruction of ground- preparing to such extent that "relation" is taught, and so on.
The authors have studied on the formation of the concepts on science. One of the most basic concepts on the electric current is its direction concept in a direct current circuit. In the present paper, we aimed at making clear the process of children's concept formation of its direction. The research was made by using the following three problems: (1) which asked the direction of electric current in words, (2) which asked it by illustrations, and (3) which asked the difference of the intensity of electric current at the three points in the circuit. The subjects were mainly the third to the ninth grade pupils. The result revealed that the degree of children's understanding had a close relation-ship to that of their study. Children's answers to Problem 1 fairly corresponded to those to Problem 2 and the rate of the correspondence increased with their study. By comparing their answers to Problem 3 with those to Problems 1 & 2, however, quite a number of the pupils, except the ninth grade, were found to have a subconscious idea that the electricity flowed from both poles of the cell.
Several ideas of electricity is difficult to comprehend. Because, it is invrisble to naked eyes and images of it various with a child. This study proved that the relation between the brightness of a miniature bulb and the consumption of energy of a dry cell in easy to understand, even by school children. In this unit "Connecting miniature bulbs" we have studied through several practices the possibility and degree of understanding by children of invisible electric current, noticing the consumption of energy. We obtaindid effective results. To give lessons to a class we laid stress on both stages of grasping problems and its generalization. At the stage of grasping problems, we gave children plenty of time to try and think concerning a miniature bulb with a dry cell. We should let each child try it freely in order to exhibit ones own image, at the stage of generalization. Throughout the unit, we set a standard to compare one dry-cell connecting with one miniature bulb.
Our previous paper has reported the measurement of cognitive structures of learners by using the I-WA Test (or Word Association Test of Iwate Form). In the present paper, we attempt to compare the I-WA Test with the GS-WA Test (or Word Association Test in Geeslin and Shavelson's paper (1975)) and to clarify validity and reliability of the I-WA Test. Then it is found that the I-WA Test is an instrument to measure the same objects as the GS-WA Test. Moreover, some results concerning with an S-P Table (or Student and Problem Table) for two WA tests are stated and discussed.
The author has discussed the associative inferences about English verb meanings since 1975: how the inferences about verb meanings are achieved by the native speakers of English (1977, 1978, and 1980) and how the inferences are useful for understanding the cultural differences between the native speakers of English and the TEFL students when they are applicable to the case of teaching English as a foreign language (1980). The purpose of the present paper is to report how the inferences about sentence meanings illustrated in English Learner's Dictionaries are achieved by the native speakers of English with the help of clue modifiers which are assumed to identify one of the syntactic and semantic features imposed by verbs. The modifiers were chosen from the several studies of word associations by Palermo and Jenkins (1964), Entwisle (1969), and Postman and Keppel (1970).
1) The NHK TV science program for primary school are designed by three component elements which we call phenomenon, meaning and cognition process. 2) The program offers not only phenomenon but also pursuit of meaning of phenomenon. 3) The pursuit of meaning is developed by the process of children's thinking. 4) We call that the process is the cognition process which produce scientific thinking and attitude of children.