Fractions of quantity are considered difficult to understand due to confusion with division fractions that were learned before. Therefore, this study focused on group learning when studying fractions where existing mathematical knowledge is superior. The aim was to characterize the mathematical negotiations influencing the selection of an original unit that is necessary to capture a fraction of quantity as a fraction of subordinate units. We conducted a survey on learning fractions of quantity in the third grade of elementary school. Further, we analyzed, both quantitatively and qualitatively, results of the pretests and intentions behind the discussions observed during group learning. Specifically, we extracted three groups from the experimental lesson and examined aspects of the discussions using an analytical framework we developed based on Searle’s speech act theory. The results showed two types of mathematical negotiations—integrated and distributed—which are necessary to select an original unit in a fraction of quantity. We also considered differences from discussions in which mathematical negotiations did not occur, and examined implications to provide learning guidance.

The teaching of two-way tables is becoming more and more important in Japanese school mathematics. In considering the teaching of two-way tables, the rubric for student responses to two-way table problems proposed in one previous study is suggestive. However, no study has examined a revision of the rubric as far as we know. Considering that developing a rubric with validity and reliability requires a lot of effort and time, we believe it necessary to study the rubric critically. That is the purpose of this paper. The methods are semi-structured interviews with university students and analysis of discussions of pairs of university students. As a result, [1] Students’ responses based on the size of the diagonal cell ratio are not taken into account in the rubric; [2] Students’ making sense is not properly categorized because the expressions indicating the object of investigation in the question text and the numerical values in the two-way table affect the students’ answers; [3] Being able to read properly in either row or column orientation does not imply being able to read properly in both row and column orientation.

The purpose of this paper is to obtain suggestions from sampling perspectives when grasping learners’ thoughts by collecting examples of the aspect of the learners’ description of reflection. In this paper, we specifically identify the aspects described in the “Examples” section to obtain suggestions on the sampling perspective. For this purpose, using the 5th grade elementary school unit “Volume of a Solid” as a case study, we identified aspects of the “Examples” mainly based on the Strauss & Corbin (1998) version of the grounded theory approach, and compared them with all of the students’ descriptions at each time period to determine the sampling. The viewpoints were then discussed.

As a result, we were able to identify the following types of “Examples”: i) those in which the students themselves came up with specific examples, ii) those in which they used problems or diagrams from the class and changed the numerical values, iii) those in which they showed specific examples of problems from the class, and iv) those in which they did not write anything. The results suggest that the identified aspects can be used as one of the perspectives for sampling.

Discussions on the connection between elementary school mathematics and lower secondary school mathematics in Japan have been conducted for many years. However, this has been confined to local discussions on the connection between the same domains, and there has been no global discussion on the connection between elementary school mathematics itself and lower secondary school mathematics itself. Therefore, the objective of this study is to clarify the similarities and differences between them.

To achieve this, we analysed mathematics textbooks from the perspective of semiotics. The results of a quantitative analysis show that there were almost no descriptive models using all three meta-languages in all grades, and that the proportion of descriptive models using at least meta-language with object-referential property was high in all grades. On the other hand, the proportion of descriptive models with figurative representation and expressive representation was lower in grade 5 than in grade 6 and onwards. The results of the qualitative analysis show that the data-driven domain was not connected to other domains in all grades, while there was a difference in that the number of nested models was three up to grade 6, but two from grade 1 in lower secondary school.

The purpose of this study is to identify Aspects and Grundvorstellungen in the learning process of the function y=ax² and obtain suggestions for teaching the function y=ax². For this purpose, we list implications through an identification of the Aspects and Grundvorstellungen, and give an explanation based on the mathematics textbook. As a result, we demonstrate the usefulness of Aspects and Grundvorstellungen. The focus on Grundvorstellungen allows us to make a concept image not only about content within mathematics, but also about content outside of mathematics. The relationship between Aspects and Grundvorstellungen points out some teaching considerations in the process of learning the function y=ax². It is also clear that other Grundvorstellungen are affected by the link of Aspects to Grundvorstellungen. A future task is to take into account the descriptive Grundvorstellungen. In this paper, we have focused only on the normative (prescriptive) Grundvorstellungen.

Sodium hydrogen carbonate and sodium carbonate are often used in chemistry experiments at junior and senior high schools. They are also occupying an important position in our daily lives. The ammonia soda method (Solvay process), an industrial process for sodium carbonate, is a subject of study in the “Properties of Inorganic Substances” section of senior high school chemistry. Teaching materials for students to conduct experiments about it have also been developed. However, most of them are demonstration experiments using ammonia solution or dry ice, and it is difficult to get students to make such experiments. In this study, we focused on the phenomenon that when ammonium hydrogen carbonate is added to a sodium chloride solution, precipitation of sodium hydrogen carbonate with low solubility is generated. This kind of phenomenon, in which the combination of ions varies, is called fractional crystallization. First, we explored the solutions and reagents suitable for the students’ experiment, and turned sodium hydrogen carbonate into sodium carbonate. Then, we developed an educational program that included a neutralization titration of sodium carbonate and an investigation of the properties of carbonates.

In order to understand the psychological safety of science groups, this study applied multilevel model to the analysis. As a result, the following four points were revealed. First, psychological safety is a psychological variable consisting of multiple levels. Second, the student-level variance accounts for half of the variance in psychological safety, while the science group-level variance is slight. Third, in many groups, there are numerous students who have relatively high psychological safety within the group, but some students have lower psychological safety than other members. Fourth, the higher the psychological safety of the observation/experimental group, the stronger the tendency for some students in the group to have relatively low psychological safety and for other students of the same group to have relatively high psychological safety.

The purpose of this research was to give an overview of Japanese science picture books by focusing on the relationship with the “environment”, as a basis for examining the roles and the potential uses of science picture books in early childhood science education. The subjects of the survey were two kinds of monthly science picture books published in the past 3 years, a total of 72 books. First, based on previous researches, they were analyzed according to the science fields they covered. As a result, it was shown that the proportion of animals and plants was large, as in previous researches. On the other hand, however, more than half of them also dealt with other fields. Then, they were analyzed according to the classification checklist of the science picture books based on the contents of “environment”. The result showed that the following topics were applicable to many science picture books; “5. Interest in their nature and organization”, “8. Interest in things surrounding them, such as nature”, “4. Contact with various things in their lives”, “14. Interest in surrounding things”, “22. Curiosity about the information that play an important role in their lives”, “16. Find a relationship”, and “15. Compare”.

In school mathematics, it is considered important to learn that the variation of relative frequency of an event is large when the number of trials is small, but that the variation decreases as the number of trials increases (the relationship between the number of trials and the variation of relative frequency), in order to understand the meaning of experimental probability. However, this is not considered very important in current Japanese school mathematics. Therefore, the purpose of this paper is to design a lesson and to examine whether or not the lesson produced learning of the relationship between the number of trials and the variation of relative frequencies of trials. A task was designed based on the hospital problem, and the lesson was designed to achieve learning in the sense of the Theory of Didactic Situations. It was hypothesized that learning of the relationship between the number of trials and the variation of relative frequencies in the sense of the Theory of Didactic Situations would occur through the designed lessons. As a result, we were able to confirm the students’ learning from their utterances and worksheet descriptions during the lesson.

In order to examine the learning support for visitors to a museum’s exhibits, it is necessary to clarify how the philosophy of an exhibition room is reflected in its exhibits. In this study, we attempted to clarify how the philosophy is reflected in developing an exhibition room for young children, by taking up “ComPaSS” in the National Museum of Nature and Science and one of its characteristic exhibits, “Kahaku-no-Mado”, as a case study. We conducted semi-structured interviews with museum staff and field surveys to determine how the museum tried to support the communication between children and parents and identify the means and intentions behind this support. The interviews show three ways to design exhibits to support communication between children and parents. First, select specimens that are attractive to young children. Second, position the specimens to take advantage of the differences in the perspectives of adults and children, and third, use exhibition labels with short conversational texts. We showed similarities with previous studies as well as findings not found in previous studies.

An early childhood education reform with emphasis on intellectual education is currently underway in Germany, and project works pertaining to this reform are attracting attention as an approach to promote children’s competencies and as a way of implementing appropriate learning for early childhood. In this paper, the themes and activities of 53 project works related to natural sciences were analyzed, and the following findings were obtained.

Approximately 60% of the themes were biological and about 40% were physical, chemical, and geological. The project works can be classified into 13 categories, such as “water,” “fire,” “energy,” “soil,” etc. Additionally, while children’s interests were the basis of the project themes, those regarding education for sustainable development (ESD) and Mathematik, Informatik, Naturwissenschaft, Technik (MINT) were set after support by teachers. The project works are characterized first by experiential activities that involve thoughts, feelings, and the five senses; second, they include free expressive activities; and finally, they develop activities that advocate personal lifestyles and social change. Given that the “process itself is the goal” of project works, there is value in participating in a certain situation or process, and this could be one way of “learning” in early childhood.

In this study, we developed experimental materials that can be used in high school polymer chemistry using photo-curable resins containing a polyethylene glycol dimethacrylate derivative as a monomer. By combining two-component monomers with varying chain lengths in various substance quantity ratio combinations, changes in the physical properties of the polymer because of the copolymerization reaction were studied. Consequently, the heat of reaction associated with the formation of the copolymer, elasticity of the product, and water absorption rate varied depending on the length of the chain portion estimated from the average value of the monomer distribution ratios. The results confirm the change in the physical properties of the polymer during polymerization of the single component monomer. The copolymerization reaction was performed without using organic solvents and highly safe reagents; however, experimental operations and the physical properties of the copolymer varied. Therefore, this study helps to understand the reaction of the two-component system and predict the physical characteristics of the product from the structure of the copolymer and the distribution ratio of monomers.

This paper constructs a framework for describing and analysing data-driven modelling (DDM) activities in school mathematics from the perspectives of mathematical and statistical models. Based on previous research, the framework mainly consists of three transitions between: (α) data/context and mathematical models, (β) data/context and statistical models, and (γ) mathematical and statistical models. We present a case study of group work of ninth graders, and illustrate that the crucial and dynamic DDM activities of learners that move between data/context, mathematical and statistical models for better prediction can be described and analysed in detail by diagramming them with three transitions. The framework also implies two types of DDM activities, “mathematics-oriented” and “statistics-oriented”, and the opportunities of teacher intervention to facilitate learners’ DDM activities. These implications may make a practical contribution to the linkage between mathematics education and statistics education in school mathematics.

The purpose of this research was to investigate the knowledge and skills necessary for lower secondary school students to study “the waxing and waning of the moon” by clarifying the causes of their struggling while studying this topic.

We found that the following information need to be fully emphasized:

1) Comprehension of the moon’s period of revolution and the moon’s rotating direction.

2) Estimation of the time of the observation based on the position of the sun.

3) Rotation of the horizon from the observer’s perspective along with the rotation of the Earth.

Acquiring this knowledge and these skills will promote the students’ comprehension of the waxing and waning of the moon.

Disaster and disaster risk reduction are emphasized under the on-going curriculum revision in Nepal. However, there is a gap between topics in the current textbook and in the draft curriculum. Under these circumstances, this study examines the present situation of students’ perceptions and scientific understanding concerning disaster education through trial lessons on landslide disasters. Two trial lessons, ‘the function of water’ and ‘landslide disaster’, were carried out for 47 students in Grade 11 at a secondary school. Data was collected through questionnaires, worksheets and records of blackboard-writing to analyze the student’s understanding of the lessons and their attitudes of the lessons. The results are as follows: First, many students could understand how water affects humans and animals and causes landslides through the ‘function of water’. Second, it was difficult for the students to explain the mechanism of landslides by applying knowledge from the experiments. Third, the increase in the number of students who became more interested in disasters was not statistically significant. Almost all the students could predict a suitable path for evacuation by observing the landslide model and they seemed to think of the disaster as their own.

The purpose of this study is to investigate fifth graders’ drawing and utilization of number line diagrams or relation diagrams in solving decimal multiplication and division word problems. The subjects decided on a correct operation by selecting one of two diagrams and drawing the diagram. There was no difference in the selectivity between the number line diagram and the relation diagram. In addition, there was no difference in the performance of the expressions in the two diagrams. However, the results of the formula were better in the relation diagram than in the number line diagram. When a correct diagram was drawn, there was no difference in the better performance of the formula between the line diagram with notation arithmetic operation and the relation diagram, but the performance of the line diagram without operation was worse. These results show that both a line diagram with operation and a relation diagram are useful to solve multiplication and division word problems, and the process of problem integration is more difficult when using the number line diagram.

Science play is held in many kindergartens, nursery centers, and science museums to increase children’s interest in science. Additionally, it is evaluated as an element of education in elementary school science classes, owing to the strange things that children think and the way they try to solve problems. Furthermore, it has been shown that continued support from guardians is effective in developing the interests gained by children through scientific play. However, in early childhood education, science play is less emphasized than words and numbers at home. One reason for this phenomenon is that parents have little interest in science. Therefore, guardians’ interest in science is an important factor for them and their young children to actively engage in science play at home. In this study, we investigated whether guardians’ attitudes toward science would change if they engaged in science play with their children. We also examined issues that were associated with the contents and methods of science play by guardians with their children at home.