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Publishing type：Research paper (conference, symposium, etc.)  

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Society for Science Education  

Expectation is one of the most important concepts in learning probability. The purpose of this paper is to construct a process of conceptualization of expectation. The theoretical framework is a process of conceptualization based on negation theory. As a result, the process of conceptualization of expectation is developed as follows: [1] to recognize that the simple average may produce an average that is insufficient to be considered balanced; [2] to reconsider as expectation a model that does not assume that the certainty of each value is equal; [3] the simple average is, for example, “a model that does not consider the difference in certainty of each value” and “cannot be applied to situations where the certainty of each value is different”; [4] to recognize that the expectation may not allow selection taking into account variables (e.g., the amount of money won). In addition, we analyzed five Japanese high school mathematics A textbooks from the viewpoint of the process of forming the process of conceptualization of expectation that we constructed. We derived four issues in teaching expectation and proposed problems and activities to overcome them.

DOI： 10.14935/jssej.47.281

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Academic Society of Mathematics Education  

The probability we consider in our daily lives is conditional probability. For this reason, the teaching of conditional probability is important in school mathematics. However, some problems have been pointed out in teaching conditional probability. For example, although previous researches have pointed out the problems of tasks and lessons for the introduction of conditional probability, they have not led to the design and verification of specific tasks and lessons. Therefore, the purpose of this paper is to design and verify tasks and lessons for the introduction of conditional probability in school mathematics. The theoretical framework is the process of formulating the concept of conditional probability from the perspective of negation.

As a result, we first identified the hypotheses about tasks and classes. The hypotheses about tasks are: “If we use a question that asks for the probability of cause, which is the opposite of the probability of outcome, as an introductory question to conditional probability, students may realize that they cannot derive an appropriate model given the information they have”, and “If the question involves several people with different information about the same event, students may realize that probabilities apply to our information about the event”. The hypothesis about the lessons is that ［1］ students recognize that using unconditional probability, students recognize that they cannot derive an appropriate model in consideration of the information obtained, ［2］ they reinterpret the probability that does not ignore the condition as conditional probability, and ［3］ they avoid confusing unconditional and conditional probability by characterizing the former as a model that has no conditions related to the event. This course of instruction is effective as an introduction for students to formulate the concept of conditional probability. We then designed and implemented a task and a lesson to illustrate these hypotheses, targeting 10th grade students who had not studied conditional probability. As a result, we were able to illustrate three hypotheses.

DOI： 10.24529/jasme.29.1_69

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Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Academic Society of Mathematics Education  

The purpose of this theoretical discussion paper is to elaborate the concept of “teacher” in the context of lifelong learning of mathematics. In the existing literature on lifelong learning of mathematics, the absence of a teacher was seen as characteristic of good lifelong learning of mathematics. However, empirical research on voluntarily learning of mathematics was often conducted in the environments where mathematics teachers exist. An issue on the naïve use of the term “teacher” is raised.

This paper consists of the following four main sections. First, we introduce the concept of “mode” for capturing the fact that the same learner takes different learning styles. Second, we introduce the first philosophy of mathematics: Ethics. It is a key to reflection on the fundamental concept of “teacher.” Third, from this ethical perspective, we introduce the concept of “respectful learning” and argue that it provides the next theoretical orientation in research on lifelong learning of mathematics. Finally, we introduce the concept of “boundary object” and propose the following promising research questions in this field: For the purpose of realizing respectful learning, how and what can function as a boundary object? What conditions are necessary in learning environments for making something a boundary object?

DOI： 10.24529/jasme.28.2_1

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Society for Science Education  

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.

DOI： 10.14935/jssej.46.299

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Society for Science Education  

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.

DOI： 10.14935/jssej.46.371

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Academic Society of Mathematics Education  

In this paper, we discussed the implicit assumptions about elementary event of probability in Japanese high school, because the treatment of elementary event of probability in Japanese high school is different from it in probability theory. First, from the descriptions of elementary event and probability in probability theory, classical probability, and high school mathematics A textbooks, we identified the implicit assumption about elementary event of probability in Japanese high school as“each elementary event is equally likely.” Next, we posed the research question:“When asked about elementary event without the goal of defining probability and without knowing that they will later consider equally likely elementary event to define probability, will students be convinced that the answer is only if each root event is equally certain?” As a result of analyzing a class for high school students, it was confirmed that students were not convinced of this. Then, we pointed out that this result could happen even if we enhanced the explanation with examples or followed the development of other textbooks, and discussed the teaching of elementary event and probability to overcome this challenge.

DOI： 10.24529/jasme.28.1_41

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Authorship：Lead author   Publishing type：Research paper (scientific journal)   Publisher：Modestum Publishing Ltd  

DOI： 10.29333/iejme/12061

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Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：一般社団法人 日本科学教育学会  

DOI： 10.14935/jssej.46.221

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：一般社団法人 日本科学教育学会  

DOI： 10.14935/jssej.46.224

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Curriculum Research and Development Association  

In senior high school mathematics, the Monty Hall problem is sometimes used as teaching material for introducing probability and conditional probability. However, if the Monty Hall problem is handled without a sufficient understanding of conditional probability, students will focus on the solution method that focuses on the complementary event, and they may not recognize that the Monty Hall problem is a problem of conditional probability. In this study, we surveyed university students who had finished the survey of conditional probability to clarify the significance of the Monty Hall problem as teaching material for introducing probability and conditional probability. As a result, it was pointed out that focusing on the solution of the Monty Hall problem by focusing on the complementary event may not lead to the development of problem-solving skills using conditional probability. We then proposed the Falk phenomenon problem as new teaching material for probability and conditional probability.

DOI： 10.18993/jcrdajp.45.1_1

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Authorship：Lead author   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

DOI： 10.1016/j.jmathb.2022.100934

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Society for Science Education  

DOI： 10.14935/jssej.46.104

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Curriculum Research and Development Association  

Although critical thinking cannot be developed only in a specific subject or a specific unit, there have been few studies on developing critical thinking through cross-curricular learning. Therefore, this paper aims to develop learning activities to realize cross-curricular learning for the development of critical thinking. As a result, we developed a teaching material, “The difference between “0” (Rei) and “0” (Zero),” and developed learning activities using it. The developed learning activities were to be implemented in four hours of classes, mainly in Japanese language, home economics, and English, and cross-curricular learning activities were set up. We also set up all the specific learning activities for fostering critical thinking, such as critical reading, discussion, report writing, and group activities, which have been proposed in previous studies. From the above, we developed cross-curricular learning activities that are expected to foster critical thinking through the teaching material “The difference between “0” (Rei) and “0” (Zero).”

DOI： 10.18993/jcrdajp.44.2_51

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：公益社団法人 日本数学教育学会（旧 社団法人 日本数学教育会）  

DOI： 10.32296/jjsme.102.r116_3

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Society for Science Education  

<p>Probabilities apply not to events in the real world we are familiar with, but to our information about that world at any given moment in time. But students understand "equally likely" to be based not on the recognition that probabilities apply to our information about events, but the recognition that probabilities do not apply to events in the real world we are familiar with. The purpose of this study is to develop principles for teaching "equally likely" based on the recognition of probabilities applying to our information about events in probability education. As a result, we developed principles for teaching "equally likely", which consist of the following levels:</p><p>1. We introduce "equally likely" based on a large number of independent identical trials of a random experiment in the physical world.</p><p>2. We expand probability mathematically, and teach conditional probability.</p><p>3. We make students understand that:</p><p>• Probabilities apply not to events in the real world we are familiar with, but to our information about that world at any given moment in time.</p><p>• "Equally likely" is an assumption in a hypothetical world based on the principle of insufficient reason.</p><p>through problems about Bayesian updating.</p>

DOI： 10.14935/jssej.45.246

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Society for Science Education  

<p>Today's society is becoming increasingly complex. To effectively function and develop in this society, all citizens need to overcome misconceptions about probability, and foster an ability of probabilistic reasoning instead. According to previous research, both theory and experiment are essential for the development of such reasoning. Japanese high school probability lessons, however, do not place great importance on the link between theory and experiment. Consequently, the more Japanese high school students study probability, the more they fail to accept probabilistic reasoning. To address the aforementioned issue, this paper aims to develop a high school probability lesson that will encourage development of the ability of probabilistic reasoning. The teaching material used will be the problem of "Effect of sample size". To answer the research question, students need to think probabilistically and use the concept of repeated trials, which is a part of the high school probability curriculum. For the interplay between theory and experiment, we used TinkerPlots Software to visualize the process of data generation. As a result, we developed a lesson and showed that it is effective for the development of the ability of probabilistic reasoning.</p>

DOI： 10.14935/jssej.45.76

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：全国数学教育学会  

DOI： 10.24529/jasme.26.2_73

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Society of Mathematical Education  

DOI： 10.32296/jjsme.102.5_25

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Other Link： http://ousar.lib.okayama-u.ac.jp/58751

Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Society for Science Education  

The purpose of this paper was to clarify junior high school student validation processes in solving word problems for simultaneous equations. We proposed and demonstrated new hypotheses through the observation of an 8th-grade mathematics class from the following two viewpoints: validation of real results in solving word problems in mathematical modeling and an implicit requirement for learners referred to as the fictionality of word problems. Fictionality is described as the fact that when learners solve word problems, they cannot avoid constructing nonexistent fictional worlds in their minds from the problems and engage in modeling activities in these fictional worlds. Analyzing the classroom observations, we found that even if learners are aware of the fictionality of a word problem, it is when they obtain mutually exclusive multiple real results that they feel the necessity of validating their results. It is suggested that a condition of word problems as teaching materials for supporting learners’ realization of the necessity of validating their results is that the problems must allow them to generate multiple real models.

DOI： 10.14935/jssej.43.333

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：全国数学教育学会  

DOI： 10.24529/jasme.25.2_11

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (conference, symposium, etc.)   Publisher：日本数学教育学会  

本稿では，どのような教材と授業が，原因の確率の理解を目標とした条件付き確率の学習を支援するのかを明らかにすることを目的とした．まずは，原因の確率を理解するためには「主観的な確率解釈」と「主観的な確率解釈と条件付き確率の関連」が必要であることから，それぞれをどのように生徒が学習するべきであるかを示した．結果，「α：主観的な確率解釈は，頻度的な確率解釈が適用できないと認識することを契機として学習する」と「β：条件付き確率は，条件なし確率では，主観的な確率解釈をモデル化できないことを認識し，主観的な確率解釈をモデル化するものとして学習する」を，学習の原理として構築した．次に，原理α，β を支援する教材として，「a：事象に関する情報に対して確率は適用されると考えさせる」と「b：結果に対する原因の確率を考えさせる」を満たす教材を開発し，それを用いた授業を開発した．最後に，授業を実施・分析・考察した結果，原因の確率の理解を目標とした条件付き確率の授業では，原理α，β に基づいた学習の支援を目指した教材と授業が有効であることが確認された．本稿は，JSPS科研費(課題番号：18J10445)の助成を受けて行われた研究の一部である．第52回秋期研究大会, 令和元年11月16日(土)，17日(日), 於 東京学芸大学, 主催 : 日本数学教育学会, 共催 : 日本教育大学協会数学部門

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (conference, symposium, etc.)   Publisher：日本数学教育学会  

先行研究では，条件付き確率の困難性の要因として，条件付き確率とその関連概念との混同が指摘されている．そこで本研究では，2 つの概念間の関係を否定によって特徴づける否定論を用いることで，関連概念との繋がりを考慮した条件付き確率の概念形成の過程を明らかにすることを目的とする．考察の結果，条件付き確率の概念形成の過程は，次の通りである．最初に，①条件なし確率が「得られた条件(情報)を考慮した適切な確率モデルを導出することができない」ことから，②「それまで同様に確からしいと考えていた事象が同様に確からしくなくなる」ことで条件付き確率が必要となり，③「確率は事象に対する情報を定量化したものである」との見方によって条件付き確率の概念が再構成される．その後，④「得られた情報を考慮しても，考慮していないモデルから算出された確率値と変わらない場合(すなわち，𝑃𝐴(𝐵) = 𝑃(𝐵))」があることで，条件付き確率の適用範囲が明確にされる．さらにこの理論的考察から，適切な条件付き確率の指導に向けた課題を導出した．本研究はJSPS科研費(課題番号：18J10445)の助成を受けて行われた．第51回秋期研究大会, 平成30年11月17日(土)，18日(日), 於 岡山大学, 主催 : 日本数学教育学会, 共催 : 日本教育大学協会数学部門

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Other Link： http://ir.lib.hiroshima-u.ac.jp/00048203

Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Academic Society of Mathematics Education  

<p> In the current era, citizens are required to train risk literacy, which is the ability to grasp risk properly and make judgments appropriately. Since risk is represented as the product of the level of the damage and the probability, I believe it is the role of probability education that developing the ability to judge. Based on the above, the purpose of this paper is to identify the educational content of the probability towards development of risk literacy and decide its arrangement.</p><p> The results of this paper are the following three things:</p><p>・ From the definition of risk, expected value, expected utility and decision tree were identified as educational contents related to probability.</p><p>・There is statistical literacy as a subordinate concept of risk literacy, and it is learned in stages (Table. 1)</p><p><img align="middle" src="./Graphics/abst-24_1_1.jpg"/></p><p>・ From the viewpoint of Construction of knowledge, educational contents were arranged according to the qualitative level of statistical literacy (Table. 2)</p><p><img align="middle" src="./Graphics/abst-24_1_2.jpg"/></p><p>From the above, organizing such learning activities is expected to develop risk literacy, which is a decisionmaking ability in modern society.</p>

DOI： 10.24529/jasme.24.2_1

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Authorship：Lead author   Publishing type：Research paper (international conference proceedings)  

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Authorship：Lead author   Language：Japanese   Publisher：Japan Curriculum Research and Development Association  

The purpose of this paper is to consider the contents of instruction and its educational methods for understanding the concept of independence in probability education. In spite of the concept of independence becoming more important in present probability education, its difficulty of understanding has been pointed out for a long time by previous studies, and is still unsolved. Therefore, this study focused on the curriculum which might be an effective way to examine causations of the unsolved issue mentioned above. In this study, firstly, "the discrepancy between the concept of independence and intuition" and "the confusion of the concept of independence with mutually exclusive events" were examined as to causes of why students have difficulty understanding the concept of independence. Secondly, "emphasis on the understanding of the concept of randomness" and "distinction among mutually exclusive events, independent trials and independent events" were derived as the point of view that improves the above causes. Finally, this study pointed out that the current curriculum has some problems from the above point of view, and "teaching of probability by experiment in the higher classes at elementary school" and "introduction of independent events in mathematics A" were proposed on the vision of revising the curriculum and the level of formation of the student's concept of probability. Furthermore, "setting up the proposition" and "illustrative representation by Karnaugh map" were proposed as the teaching methods of independent events in this paper.

DOI： 10.18993/jcrdajp.40.3_37

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Academic Society of Mathematics Education  

<p> In society that change suddenly, citizens need to acquire competency in making decision in everyday and professional situations.  On making decision, they need to rate choices and judgement using probability is needed at that time.  That is, competency of judgement using probability is important as competency of decision making.  Therefore, the purposes of this paper are to: ・ Propose the contents of learning that consider training of competency of judgement using probability in making decision. ・Derive the task based on the contents of learning for revision of teaching probability. The results of this paper are the following three things: ・ From the development of history of probability, there are suggested that a way of mutual understanding of the frequency idea and the subjective idea are important, and citizens need to do judgement using probability  that follow Bayes rule in everyday and professional situations. ・ It is effective that students learn Bayes theorem that is methodology of Bayes rule to train the competency given above. ・ From result of the research on actual conditions in this paper, because the treatment of Bayes theorem is inadequate in the teaching probability currently being used in view of training the competency given above, it is needed that the overall revision to the teaching probability from the Bayes theorem on down from the current.</p>

DOI： 10.24529/jasme.23.2_83

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Academic Society of Mathematics Education  

<p> The purpose of this paper is to obtain implications to develop curriculum on probability from the point of view of formation of the student's concept of probability.</p><p> Firstly, I referred to the duality of classical probability and frequentistic probability from Otaki (2011) and the relation of the concept of probability and that of randomness from Kawasaki (1990).  Then, I pointed out that, to form the concept of probability, the followings are necessary: "understanding both classical probability and frequentistic probability, and mutual connection between them" and "understanding of the concept of randomness preceding that of probability, and connection between them".</p><p> Secondly, I considered the current curriculum critically from the point of view of formation of the concept of probability, and found that the current curriculum have some problems in this point of view.</p><p> Finally, I suggest "spiral curriculum" from this point of view based on "Principles in Setting and Arranging Teaching Contents" in "A Study on Constituent Principles of Curriculum in Mathematics Education" (Nakahara, 2008).  This paper shows that spiral curriculum is effective to form the student's concept of probability and is required in the current secondary education.</p>

DOI： 10.24529/jasme.22.2_133

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (conference, symposium, etc.)   Publisher：Japan Society for Science Education  

DOI： 10.14935/jsser.38.3_21

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (other academic)   Publisher：Japan Society for Science Education  

DOI： 10.14935/jsser.38.2_37

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (conference, symposium, etc.)   Publisher：Japan Society for Science Education  

DOI： 10.14935/jssep.47.0_609

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Publishing type：Research paper (international conference proceedings)   Publisher：International Association for Statistical Education  

Context plays a significant role in teaching probability and statistics; although its importance has been contended in previous studies, there is not sufficient research on the role of context. Therefore, this study aimed to clarify the actual use of context in problem solving through pre-service mathematics teachers. We focussed on the Tuesday Birthday Problem, which requires awareness of context. Data were obtained from surveys involving 98 teachers and analysed by classifying answers based on the answer types related to context. Results revealed that there are three hurdles related to context in this problem: ‘generation of the idea of conditional probability,’ ‘identification of the necessary and sufficient context for the condition,’ and ‘correct use of the context.’

DOI： 10.52041/iase.icots11.t6f2

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (conference, symposium, etc.)   Publisher：Japan Society for Science Education  

DOI： 10.14935/jssep.46.0_543

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Language：Japanese   Publishing type：Research paper (conference, symposium, etc.)   Publisher：Japan Society for Science Education  

DOI： 10.14935/jssep.46.0_547

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (conference, symposium, etc.)  

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (conference, symposium, etc.)   Publisher：Japan Society for Science Education  

DOI： 10.14935/jsser.36.2_209

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Language：English   Publishing type：Research paper (conference, symposium, etc.)   Publisher：Japan Society for Science Education  

<p>This study aims to identify a potential factor in students' narrow perspectives when engaging with trans-scientific issues. The main structure of this study is divided into the following two parts. First, based on existing empirical data, we reviewed the theoretical issue of conceptualizing critical thinking within mathematics education research and proposed a new conceptualization as equitable treatment of multiple perspectives from a superordinate ethical perspective. Second, from this perspective, we retrospectively analyzed whether students disrespected a probabilistic perspective in solving and a traditional word problem with conditional probability. Consequently, we found that students tended to take a probabilistic perspective in solving the traditional word problem. It is suggested that excessive information in word problems narrows their perspective rather than the authenticity of the problems.</p>

DOI： 10.14935/jsser.36.2_65

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Language：English   Publishing type：Research paper (conference, symposium, etc.)   Publisher：一般社団法人 日本科学教育学会  

<p>With the spread of the novel coronavirus disease， there is a need for mathematics education to deal with social issues that cannot be solved by scientific knowledge alone (trans-scientific issues).Therefore， this project focuses on socio-critical modeling， which aims to critically examine the role of mathematical modeling in students' daily and societal situations and the possibility of its implementation in mathematics classes. In critical mathematics education， which is the theoretical perspective of socio-critical modeling， both the everyday and the social are required simultaneously in the task context. However， it is difficult to create teaching materials for mathematics in children's daily and societal situations， which is neither only daily nor only societal. This project will examine this point from various perspectives such as a case study of students'research activity on the definition of recycling rate， risk communication， and socially open-ended problems.</p>

DOI： 10.14935/jssep.45.0_127

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Language：English   Publishing type：Research paper (conference, symposium, etc.)   Publisher：一般社団法人 日本科学教育学会  

<p>This study proposes a new problem context using students'daily and societal situations as teaching material for implementing socio-critical modeling in mathematics classes. We reviewed the practice of a thematic approach based on critical mathematics education-a theoretical perspective of socio-critical modeling-and reconsidered the framework of socially open-ended problems that emphasize students'daily and societal situations. Based on our research outcome， we propose a quasi-society， as the problem context. School based extracurricular activities such as election of the student body president can correspond to real-world elections. We see it as a quasi-society. This study critically examines the role of mathematics in addressing problems that are inherent in a quasi-society for effectively teaching socio-critical modeling. We used Taiwan's quadratic voting system as the teaching material.</p>

DOI： 10.14935/jssep.45.0_137

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Language：Japanese   Publishing type：Research paper (conference, symposium, etc.)   Publisher：Japan Society for Science Education  

DOI： 10.14935/jssep.45.0_491

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Language：English   Publishing type：Research paper (conference, symposium, etc.)   Publisher：一般社団法人 日本科学教育学会  

<p>The purpose of this paper is to determine practical implications for the effective implementation of a socio-critical modeling approach in mathematics lessons. We analyzed an activity undertaken by tenth-grade students from a school of educational research in Japan. In this activity， the students inquired about recycling efforts in their cities. They found differences in the definitions of "recycling rate" between the cities and asked the city officers about the different definitions. Until they realized there were multiple definitions， they uncritically accepted a definition. This episode， thus， implies the possibility that an intellectual need for critical consideration supports the effective implementation of a socio-critical modeling approach. However， the students uncritically accepted the officers' reply that the definitions in cities have the same meaning. Future research needs to further investigate how a socio-political perspective supports students' intellectual need.</p>

DOI： 10.14935/jssep.45.0_129

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Authorship：Lead author   Language：English   Publishing type：Research paper (conference, symposium, etc.)   Publisher：一般社団法人 日本科学教育学会  

<p>The purpose of this study is to explore teaching materials on socio-critical modeling for developing students' ability of critical consideration based on mathematical modeling to understand daily and societal situations. To this end， we focused on risk communication， which has reported difficulties in conveying risk information from experts to general citizens. As a result， it is suggested that the societal topics of "conveying relative risk (risk ratio) or odds ratio without baseline risk" or "mismatched framing" are suitable for teaching materials on socio-critical modeling. We found related societal topics in Japanese newspapers. Risk communication is effective in exploring socio-critical modeling teaching materials. In addition， because some of the risks increase with age， students can and should learn not only about their current positions in society but also about their future positions through lessons oriented toward socio-critical modeling.</p>

DOI： 10.14935/jssep.45.0_133

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Authorship：Lead author   Language：Japanese   Publishing type：Doctoral thesis   Publisher：公益社団法人 日本数学教育学会（旧 社団法人 日本数学教育会）  

DOI： 10.32296/jjsme.102.r115_21

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (conference, symposium, etc.)   Publisher：Japan Society for Science Education  

DOI： 10.14935/jsser.35.3_137

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Language：English   Publishing type：Research paper (conference, symposium, etc.)   Publisher：Japan Society for Science Education  

<p>The social need for negative result certificates of polymerase chain reaction (PCR) testing for COVID-19 has rapidly increased during the pandemic. Although the results of the test should be interpreted based on the concept of conditional probability like any other test, this is not an easy task for high school students in general. This study reports the thought process of Japanese tenth-grade students regarding the use of mathematics for social issues. Based on a design research approach, two experimental lessons have been conducted to investigate how the students perceive the necessity of certificates for PCR tests with the probabilistic concepts in a given fictional context. It has been observed that even intelligent students came to conclusive opinions, intentionally neglecting the results of probabilistic thinking. It is imperative to discuss how students' critical and mathematical thinking abilities can be developed in real-world contexts without appealing to the usefulness of mathematics.</p>

DOI： 10.14935/jsser.35.3_43

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Authorship：Lead author   Language：Japanese   Publishing type：Research paper (bulletin of university, research institution)  

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Other Link： http://ousar.lib.okayama-u.ac.jp/60999

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Authorship：Lead author   Publishing type：Master’s thesis  

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Language：Japanese

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