Fifth and sixth graders were presented with 2 problems: (1) "Find the area of this triangle [base 8cm, height 5cm]," and (2) "How big is triangle B [an isosceles triangle] compared to triangle A [a right triangle]?" In figure accompanying the second question, the bases of the 2 triangles were equal, and triangle B was twice the height of triangle A. However, numerical values for the width of the base and the height were not provided. If the children were able to use the formula, "area of a triangle=base×height÷2", properly, they should have been able to realize that triangle B had twice the area of triangle A. This is called the "relational operation of a formula". Of the 135 children, 123 (91%) gave the correct answer to Question 1, but only 62 (46%) answered Question 2 correctly. In other words, the children who could calculate area by using the formula could not necessarily operate the variable in the formula. Further analysis suggested that prerequisites for giving the correct answer to Question 2 were: (a) grasping the relative, rather than absolute, difference in the areas of the 2 triangles, and (b) understanding the difference between "the difference in the area of 2 figures" and "their ratio".

Magara (2006) demonstrated that learners' notion that a rule that they had been taught might have some exceptions prevented them from applying the rule to new instances. However, those learners' notions of exceptions may have been influenced by their thinking of specific things. Another possible factor is their misinterpretation of the range of instances of the rule. In the present study, undergraduates (N=414) were given a scientific rule (e.g., the thermal conductivity of metal is higher than that of nonmetal), or a logical rule (e.g., all Xs are Q), and their estimation of the range of instances of the rules was investigated. Many participants discounted the range of instances of even the logical rules, not only the scientific ones. Those who discounted the range of instances of a rule did not apply the rule to new instances in the test session.

In Japanese sentences, the particle (wa) is used not only to indicate the subject of a sentence, but also to mark the topic (e. g., in English,"as for..."). Words preceding (wa)I in a Japanese sentence do not, therefore, consistently correspond to the subject of that sentence when translated into English. Furthermore, in Japanese sentences, the subject is often unstated. As a result, when native speakers of Japanese are asked to translate into English sentences in Japanese in which the particle is used as a topic indicator, they may misidentify the topic as the subject of those sentences. In Study 1, junior high school students (N=57) and high school students (N=114) were presented with incorrect English sentences in which words preceding the particle (wa) were incorrectly translated as the subject of the sentence (e. g., Yesterday was a part-time job; January is my birthday; All my shirts bring to the laundry). The participants were asked to judge whether each sentence was correct. Incorrect sentences were judged to be correct by 40%-80% of the participants, suggesting that their knowledge of Japanese had interfered with their understanding of the concept of the subject in English sentences. In Study 2, high school students (N=89) read an instructional text which explained the difference between words preceding the particle (wa) in Japanese sentences and the subject of English sentences. After reading this material, the students correctly evaluated the incorrect sentences as incorrect.

Statements taught to students can, in general, be described in proposition form, as "if it is p, then it implies q." Instances where the antecedent "p" is illustrated are known as substitution instances. In addition, it is possible to obtain another type of instances by illustrating the consequent "q." We will refer to this type of instances as symbolic instances. The aim of this study is to clarify the condition under which symbolic instances can have a positive effect on learning. We focused in our study on the teaching of history. We prepared three different texts that involved one of three symbolic instances concerning the Meiji era. Each text was presented to one of three groups of undergraduate participants in the learning session of the experiment. After the learning session, we presented them with a problem to which learners had previously given an incorrect answer due to their misconception. The problem could be solved correctly by referring to the symbolic instance presented in the learning session. In addition, we asked the participants to specify whether they had referred to the symbolic instance at the time of problem solving, and if they had not, to explain their reasons for failing to do so. We found that failure to refer to the instance had two causes: the symbolic instance had been given a different interpretation or the subjects had been unable to incorporate it into their cognitive structure. However, the symbolic instances that could be incorporated into learners' cognitive structure easily and did not allow another interpretation were effective. In the second experiment, we presented learners with two symbolic instances simultaneously. This treatment was revealed to be very effective in correcting learners' misconception.

Children and adults know that when sunlight converges with a convex lens, it makes a small round dot. They, however, tend to think that no other light than sunlight (e.g., from a fluorescent lamp) can converge with a convex lens, and that even if a fluorescent light converged it would form a small round dot. These facts perplex us because in junior high school, students learn that when a light converges with a convex lens, it forms an image of an object that emits or reflects the light. Analyzing science textbooks in junior high school, we found that the textbook emphasized the manner in which the size and position of the reflected image is modified by changes in the position of the source. We considered the possibility that this mode of presentation made it difficult for students to grasp the mechanism of image formation per se. In study 1, university students (N=28) were divided into two groups. After the explanation of an experiment using a convex lens and a candle, the rule per se was emphasized to one group (group 1), and the place and the size of the image were emphasized to the other group(group 2). The target problem was as follows; "Does the light from a fluorescent ceiling lamp converge with a convex lens, and if so, what will you see on the screen-" Although the number of students in Group 1 who gave a correct answer was higher than the corresponding number in Group 2, the overall score in Group 1 was not very high. In study 2, university students (N=48) were asked to draw the path of the light and the shapes of the images projected on a screen when different light sources were used. In spite of the fact that the rule was emphasized to them, their performance did not improve. In study 3, we asked the subjects in study 2 why it was difficult for them to apply the rule to the target problem. Analysis of their answers revealed their misconceptions. Some thought that only parallel light rays like the sun's could converge. Others thought that the small round dot which a convex lens made when sunlight converged was not the image of the sun. The article examines the manner in which these results can be used to improve the efficiency of science teaching for this topic.

Seed plants propagate by sexual and asexual reproduction. This study investigated to what extent undergraduates and junior high school students understand the merits of sexual reproduction of seed plants. Subjects were asked why the seed plant propagates by seed while it propagates ascxually by subterraneans. Many of them pointed out the extension of the habitat of the plant as a main merit of reproduction by seed. Only about 20% of the undergraduates and 10% of the junior high school students pointed out the variety of an inherited character and the possible chance of adaptation of the plant to various environments. This fact means most of undergraduates and junior high school students do not understand one of the fundamental reason why seed plants propagate by seed. Obtained results were discussed from the standpoint of class work study of science.

Magara (1999) proposed a strategy named the Double Reasoning Method in order to rectify learners' misconceptions. In this study the author aimed to examine the beneficial effects of this method by using different learning materials in a science classes. The Double Reasoning Method was exercised as follows. At the first stage, learners were presented with reading material contained useful information to help them answer correctly a target problem in physics. At the second stage the target problem was set and learners were asked two kinds of questions. One question them to solve the problem on the basis of their intuition. Their answers were generally incorrect because they were based on misconception. The second required them to answer the question on the basis of information with which they had already been presented. In the latter case, their answers were generally correct. At the third stage, the result of the physics experiment was presented and learners came to know the correct answer. Subsequently, a transferable problem was set. Most students could solve it successfully. Thus they could rectify their misconceptions and the efficacy of this method was confirmed.

Whereas Piaget established a conservation task to assess children's understanding of extensive quantity, this study aimed at establishing another kind of conservation task to assess children's understanding of the concept of intensive quantity, e.g. the thickness of paint on a board. The following study examined children's misconception by using our conservation task. Subjects were sixth graders and undergraduates. A typical question was asked in the conservation task : Which is thicker, the large part of a board or the small part, when it is painted uniformly? Although Subjects were taught in advance that the thickness of paint was given by its volume per unit area (1 cm^2) , commonly explained in school education, two-thirds of sixth graders and one-fourth of undergraduates failed to answer the question, suggesting they did not understand the concept of intensive quantity through the commonly given explanation. Results were discussed from the viewpoint of the method employed to teach the concept of intensive quantity.

It is widely accepted that in order to rectify learners' misconception it is necessary to make them encounter scientific evidence that contradicts their misconception. In this paper an alternative strategy is proposed and its effect examined. The strategy was as follows. At the first stage a reading material was presented to learners which contained useful information that would help them to make solve aproblem in physics. At the second stage the problem was set and learners were asked two kinds of questions. One question requested them to solve the problem on the basis of their intuition. Their answers were generally wrong because they were guided by a misconception. The other question requested them to solve it on the basis of the information they had already read. Their answers were generally correct. At the third stage the consequence of the experiment in physics was presented and therefore the learners came to know which solution was correct. After these steps a transferable problem was set. Most of them could solve it successfully, being able to rectify their misconception. This teaching strategy was named "double reasoning method", because two contradictory reasoning processes (and answers) were provoked in each learner before he observed the consequence of the experiment.

It is quite natural that a household electric appliance such as a television works in a electric circuit. But the author encountered several undergraduates who had the notion that an electric current was sent out one-sidedly from a power plant to a television and was consumed in it. This study investigated to what extent such a misconception was held by undergraduates and junior high school students. Subjects were presented several different figures illustrating schematically how an electric current flowed between a power plant and a television in a house, and then they were asked to select a correct one. About 55% of the undergraduates and 30% of the junior high school students selected a figure in which an electric current was illustrated as being sent out one-sidedly from a power plant to a television. Ss were then asked whether or not a man would be struck by electricity when he jumped and touched a transmission line that was torn off and dangling. Many subjects answered he would be struck. These results indicated that they pay no respect whether a load was incorporated into a circuit or not.