In this study, we clarified the learning effect of introducing the shape dependence of electrical resistance from quantitative analysis, based on practice, in lower secondary school science. The experiment using CNP (carbon nanotube paper) resistors allows for a study of the shape dependence of electrical resistance with the resistor adjusting its shape two-dimensionally. The inferences obtained from the results of the questionnaire survey are as follows: (1) it is effective in understanding the combined resistance of the parallel connection but not the series connection; (2) when studying the shape dependence of electrical resistance, the learning effect of the combined resistance is higher when using CNP resistors than when using cement resistors; (3) the effect of a different teacher cannot be confirmed. Introducing the shape dependence of resistance in lower secondary school science is effective in understanding combined resistance. Therefore, we emphasize the importance of discussion regarding the introduction and accumulation of such practices.

The need for dealing with uncertainty in today’s complex and changing society has led to renewed research attention toward informal statistical inferences (ISIs) from child early years. However, the actual status of ISIs of Japanese lower grade children and the possibilities for its promotion remain to be clarified. This study clarifies the role of models in ISIs of such children, focusing on data modeling processes. To do so, Japanese second grade (7–8 years old) lessons involving the data modeling process were analyzed. The results reveal that the models created through the data modeling processes, with the support of the teacher, can serve three roles in promoting ISI in early elementary school children who are beginners in statistics and ISI: (i) a descriptive means to represent the structure of data and stochastic variability, (ii) a referent to draw analogies with the structure, and (iii) an explanatory means to explain the structure in a unified and comprehensive manner. Finally, based on the results, the direction of teacher support in teaching to promote ISI of lower grade children was suggested.

This study aims to examine the possibility and significance of creating learning activities to deepen mathematical understanding through the promotion of metaphorical thinking. For this purpose it analyzes and discusses a case study in the “Expressions Representing Relationships among Quantities” unit in the fifth-grade elementary school class. Three perspectives were set for the expected deepening of understanding. Viewpoint 1 (understanding with conviction related to concrete experiences), was considered by the children to be easily understandable. Viewpoint 2 (understanding of mathematical concepts with multifaceted meanings), through the activity of interpreting multiple metaphorical expressions that extracted different elements, could provide a way to organize the multifaceted meanings of mathematical concepts, including meanings that were implicit until then. For Viewpoint 3 (understanding through the diversity of base selection), we found that by listening to different metaphorical expressions, students could select the expressions that were most accurately understood by them. Regarding the role of the teacher in creating learning activities, two aspects were identified: asking questions that encourage the children to examine the differences in the elements being extracted, and asking questions that focus on the issues according to the children’s understanding.

Based on an alkaline hydrolysis reaction of Prussian blue, we developed experiments for learning the difference in reaction rate depending on the reagent added to the Prussian blue suspension and the difference depending on the temperature of the suspension. A color change was observed when sodium hydroxide or potassium hydroxide was added to the suspension, which is used as commercial watercolor paint. In either case, the color changes from dark blue to light yellow, but the time required for the color to change varies significantly, and the students can visually confirm the difference in the reaction rate depending on the reagent added. As a preliminary experiment, a spectrophotometer was utilized to analyze the reaction rate of samples. The reaction rate of each alkaline hydrolysis reaction can be analyzed using a primary reaction formula. We were able to estimate the activation energy in each case using an Arrhenius plot. Based on these experimental results, teaching materials using the color change of the suspension were developed. From the results of the questionnaire on the class practice, it was clear that (1) the difference in reaction rate due to temperature change and (2) the difference in decomposition reaction rate between two alkaline solutions and can be learned.

To clarify the learning effect of classes using granular models, a model of concrete objects in which learners can represent and manipulate thermal phenomena dynamically, and an animation that shows the representational operations were created. Using these, we conducted a class on how water heats up (convection), analyzed the learners’ expressive manipulations to explain thermal phenomena, and investigated whether the convection concept was formed. The results indicated that some learners changed their convection concept into a scientific interpretation after the explanatory activity using the model and animation. Therefore, the results suggest that learning to manipulate scientific representations using animation with models is effective in promoting the elaboration of convection concepts.

This study clarifies aspects of utilization of proofs within the context of mathematical problem posing, by analyzing individual students’ processes of problem posing in a mathematics classroom. First, we establish a framework to analyze students’ processes of utilizing proofs in problem posing by focusing on functions of proofs. Second, we describe the methods of data collection and the outline of the whole class activities in the lesson on “numbers and algebraic expressions” for Japanese 8th graders. Third, we analyze two students’ processes of utilizing proofs in problem posing, which resulted in gaining the students’ insight into why the statement of the starting point is true. As a result, we clarify two aspects of utilizing proofs within the context of problem posing: (1) utilizing others’ proofs concerning different functions of the proofs properly based on their own conviction (or non-conviction) of the functions by reviewing the proofs. (2) Repeatedly utilizing the explanatory function of proofs while gradually expanding the extent of their consideration. Finally, we discuss educational implications, significance, and limitations of the analysis.

Students face difficulty in acquiring the methods required to decompose a force into two partial forces. This is because in the composition of two forces, the resultant force is compressed into a single force, but in the decomposition of a single force, the decomposed forces vary in direction and size. So, to understand the decomposition of force, students had to understand how to draw the vector arrow and recognize the force as the vector with the direction and size.

For this purpose, the students identified the relationship between the length of each arrow and each angle using the values computed from the experiment and found the change in the component force to be as large as the change in the degree of the angle. On the other hand, on decomposing the component force, most students found that the force size of the perpendicular direction to the original force changed by the angle of decomposition, but that the force size was in the same direction as the original force did not change.

The findings indicate that it is highly effective to decompose the component force and to use the values computed from the experiment in understanding the force as the vector and the relationship among the decomposed angle, the group of the direction, and the size of the component force.