This paper aims to clarify some viewpoints for analyzing the interactions using various proofs in mathematics lessons. Students who have already learnt basic mathematical proving can give various verifications to a theorem. In this paper, we propose a framework which has two viewpoints, which were invoked by Voigt (1995), “interaction patterns” and “thematic patterns of interactions.” Furthermore we divide the former viewpoint into “comparison pattern” and “discussion pattern,” and the latter into two thematic classifications, “ways of proof” and “structures of proof.”

　　Using the framework, we analyzed the lessons where 31 third graders at a junior high school tackled a proof problem. As a result, we get the following two findings in the interactions using various proofs in the mathematics lesson. i) To distinguish between the comparison and discussion patterns is available for us to analyze the complicated interactions. ii) To analyze the thematic patterns of interactions by distinguishing between ways and structures of proof is useful in describing the students’ processes of proving a theorem and generating another proof through their interactions. Especially it can be described the students’ interactions in generating various proofs by referring to the thematic patterns, integrating the thematic patterns of various proofs, and comparing themes with another theme of new proof.

　　This study aimed to explore the parents’ process of recognizing the value of physical education (PE). Participants were 10 parents with children in the 5th or 6th grades of elementary school with differences in their recognition compared to objectives of Physical Education in the Courses of Study. Data were collected through semi-structured interviews with the parents. Data were analyzed using a Modified-Grounded Theory Approach.

　　The results revealed that parents’ recognition of physical education is based on their “experiences as students” and that “parents’ views of physical education” are formed throughout ten to several decades. In particular, parents’ experiences of relative skill praise during their school years are a factor that reinforces the perception that motor skills are emphasized in physical education. In addition, the results also suggested that schools should appropriately inform parents of their children’s learning status in physical education and create social interactions between parents and children regarding physical education are important in reshaping parents’ recognition of physical education.

　　In the curriculum guidelines for elementary schools, junior high schools and, high schools revised in 2017 and 2018, it was shown that the education of competency bases would be promoted as a new direction of education. Previous studies have revealed that by having students who want to become home economics teachers compare home economics with other subjects, the view of subjects regarding home economics deepens. Therefore, in this report, classes that provide an opportunity to compare home economics with other subjects held in graduate schools are used to clarify the graduate students’ perceptions of home economics after participating in the classes, as well as their current educational practices and subject views as home economics teachers. As a result, it became clear that the lesson experience at the graduate school influenced the graduate students who aspired to be home economics teachers and deepened their understanding of the essential meaning of home economics. In addition, it was possible to catch the actual condition that the effect continued in the subject view and the guidance view in the fourth year of the teacher.

　　Using family learning materials (picture books and worksheets (WS)) in an elementary school home economics class, we conducted a class practice of Family and Life in the life studies class. Two types of worksheets were prepared: WS-I, in which students wrote in speech bubbles as family members in the picture book, and WS-II, where they wrote on ruled lines as advisors who improve their families and have studied life studies. The results showed that many children wrote about help with the housework to improve their family life in both WS-I and WS-II and generally achieved the learning goal of realizing the necessity of cooperation as a family member. Although the characteristics of the descriptions were both abstract, it was found that WS-I gave commands to the partner and WS-II provided suggestions to the partner more often. In the post-questionnaire, both groups showed an increase in the number of children who wrote words representing the cooperation category. In particular, the number of descriptions of helping with housework in the cooperation category was the largest, indicating a learning effect. In particular, the WS-I group was capable of describing many innovations in the WS, suggesting that it was effective for learning.

　　This study focused on the strategies and evaluation of the context-based approach, and developed the unit based on the context-based approach of disaster education at upper secondary school, and conducted trial lessons to develop attitudes toward disaster preparedness and understand the necessity of knowledge about science. As a result of the literature study revealed that the context-based approach is characterized by a “need-to-know” concept that defines the context of learning and incorporates relevant scientific knowledge as needed, a spiral content of a learning unit, and a drip-feed approach that repeatedly utilizes the same scientific concepts in other contexts. Based on the results of the aforementioned survey, we developed a new learning program that focused on a context-based approach for upper secondary schools. This unit included a storyline about natural disasters and consisted of seven units with different contexts, such as performing experiments as seismologists and providing geological and historical explanations to visitors of an area. Each unit included one to two lessons. We implemented one unit to include civic roleplaying. Then, we analyzed questionnaire responses from 110 students. The topic of this practice lesson was “positive and negative aspects of installing new weirs.” The one-hour class concerned whether weirs, which have been installed in the river for many years, should be modernized. Students were divided into groups, namely Residents A-C and Scientists, who read the materials prepared by the teacher to understand the various advantages and disadvantages of their respective areas of residence. Students in each group organized the points and decided whether they should accept the latest weir renovation. The analysis of the questionnaires before and after the lesson revealed changes in the attitude toward disaster preparedness and the recognition of the necessity of knowledge about science. The results showed that a mature attitude toward disaster preparedness would occur with the change and expansion of the connection between the words “investigate,” “know,” and “discuss.” It was inferred that reconstructing the network of these words would contribute to developing attitudes. Furthermore, by roleplaying as residents and scientists, students learned the necessity of getting scientifically correct information, knowing the history of their location and participating in local society-making. It was inferred that the recognition of the necessity of knowledge about science is improved by discussing with other students from different standpoints based on scientific views and ideas.

　　The present study aims to investigate how many letters of the alphabet 5th graders can write correctly and to classify the students based on their handwriting proficiency to obtain a deeper insight into an approach to the instruction of handwriting the English letters. Results show that regarding uppercase letters, Z, W, Y, C, E, and S were the easiest for children to write, whereas more difficulty was had with writing D, K, and P. Furthermore, among lowercase letters, a, s, o, and c were the easiest for children to write, and more difficulty was experienced with writing f, q, j, and l. Based on results from cluster analysis of their handwriting, the students can be divided into five error groups. Although some of the students were already able to write most English letters correctly, others had some problems with the shapes of lowercase letters and the correct positioning of letters according to the descender line, baseline, mid-line, and ascender line. The results suggest that it is necessary to instruct letter sounds first and familiarize the children with lowercase letters.