著者

和田 信哉

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.18, no.1, pp.31-41, 2012 (Released:2019-01-17)

参考文献数

34

---

This research aims at clarifying the transitional process from elementary mathematics to secondary one, especially arithmetic to algebra, and from the viewpoint of Early Algebra, we focus on algebraic reasoning at elementary grades. However, it does not yet become clear enough. The purposes of this paper, therefore, are to clarify algebraic reasoning through the semiotic analysis of classes of the multiplication and division with fractions, obtain the implications to promote algebraic reasoning, and obtain the implications for the classes. The results are followings. (1) Algebraic reasoning was identified by the semiotic analysis of the classes from the viewpoint of generalization and justification. The characteristic of the reasoning depends on deductive reasoning grounded on a property of numbers and operations or a pictorial expression. (2) From the viewpoint of justification, we regard deduction using a model and a specific case as deductive reasoning, in the case of deduction using a model, it is important that the model is made a tool, in the case of deduction using a specific case, it is important to examine whether become the generic example or the representative special case, and to draw various deductive explanations. (3) About the implications for the classes, at the time of classes of the multiplication at the second grade and the unifying partitive division with quotative division at the third grade, it is important to make students understand that the relation of multiplication to division is reverse operations from concrete operations. At the time of classes of the division with fractions, it is natural to understand the method of calculation from a property of operations.

著者

高淵 千香子

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.17, no.2, pp.143-157, 2011 (Released:2019-01-17)

参考文献数

16

---

The purpose of this paper is to suggest that the teaching focused on the extention of multiplication of fractions on the sixth grade is effective to promote learner's understanding of its meaning. In the teaching of multiplication of fractions, we adopted the following four activities in the lesson. (1) The first lesson was designed for the extention of the meaning of multiplication of fractions in comparison with multiplication of integers. (2) The classification activity of mathematical word problems was introduced to promote learner's awareness of the mathematical structure on multiplication of fractions. (3) The number line was introduced to support leaner's understanding when the ratio concept became the theme of the lessons. (4) We introduced the activity to organize the relationship among multiplication of integers, decimal fractions, and fractions. Through the implementation of these experimental designs into the lessons of the multiplication of fractions on the sixth grade, the performance of many children was improved. The result of the post evaluation showed that they were able to understand the meaning of multiplication of fractions. But, there were some difficulties for each learner to realize the extention of its meaning. We need to improve the lesson designs according to learner's situation of understanding. Especially, the standardization of the lesson of multiplication of fractions and the way of using the number line are two major tasks for now.

著者

渡邊 耕二

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.21, no.2, pp.73-87, 2015-07-28 (Released:2019-01-17)

参考文献数

56

---

This study is undertaken to better understand the relationship between mathematics and reading achievement focusing on PISA2003 and PISA2012.  In PISA, the mathematics and reading literacy are examined continuously every three years from the year 2000.  Therefore, the relationship between them can be analysed including its secular changes.  The research on the relationship between mathematics and reading ability has currently focused by researchers of mathematics education. In this study, the approach of international comparison will be adopted.  The countries which are performing high mathematical literacy tend to also have higher performance in reading literacy.  However, the relationship between them within the country is not always cleared.  In order to make this point clear, we will focus on not only the indexes of reflecting the level of students’ performance of mathematics and reading literacy such as the mean score, but also the indexes of reflecting the relationship between two variables have to be considered to capture the domestic feature of countries, for instance, such indexes are correlation coefficient and regression coefficient and so on. In this study, there are two points of view.  One is to focus on test score.  By using Hierarchical Linear Model (HLM), the international comparison of mathematics literacy test score will be conducted through controlling reading literacy test score.  Another one is to clarify the answer pattern of each country by focusing on item difficulties based on Items Response Theory (IRT). As a result, in the countries have gotten higher level mathematics literacy, the students’ mathematics and reading performance are more related domestically than in lower performed countries.  In addition, the differences of the level of reading literacy test score in higher performed mathematics literacy countries come to a head markedly on a particular item.  On the other hand, regarding lower performed countries, we could not make mention the same situation.  The results imply that the relationship between mathematics and reading achievement is different between higher and lower performed mathematical literacy countries.

著者

砂場 拓也

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.9, pp.141-152, 2003 (Released:2019-01-17)

参考文献数

19

---

When people think and deal mathematically with various real phenomena to solve the real problem, 'hypothesizing' is indispensable for the problem solving. However, the activity that requires simplification of the activity of real situations and also selection of essential variables in the situations is so hard that mathematics teachers have avoided dealing with it in mathematics class. Therefore, in this paper, we tried to construct mathematics class focused on 'hypothesizing' and to investigate the effectiveness of the class by practicing it. The following is the mathematics class focused on 'hypothesizing' that was suggested in this paper. 1. Show the real problem → 2. Solve the problem mathematically ((1)select some essential variables, (2)collect information from the distributed references → (3)hypothesize and solve the problem mathematically → (4)present the ideas and solutions each other → (5)correct each of the ideas if it is mistake) → 3. Investigate each of the solutions and write a report on the problem solving As a result of this investigation, most of the students could hypothesize and solve the real problem mathematically. However, in '(4)present the ideas and solutions each other', the students didn't discuss each of the ideas actively. In addition they couldn't investigate each of the solutions, because they had no time to do it.

著者

中西 隆

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.4, pp.37-44, 1998 (Released:2019-01-17)

参考文献数

14

---

The aim of this paper is to adopt the cultural approach to mathematics curriculum, referring to "Mathematical Enculturation" written by A. J. Bishop. He has described three components of the curriculum, which labeled the symbolic, societal, and cultural components. Those have two complementary values. He presents a curriculum structure which allows 'rationalism' to be stressed more than 'objectism', where 'progress' can be emphasised more than 'control' and where 'openness' can be more significant than 'mystery'. The societal and cultural component are necessary to adopt exemplifying to historical development of knowledge, which offer an individualising aspect of teaching. On the otherhand, the symbolic component generates concepts of mathematics through activities. I interpreted the significant on the cultural approach from a Vygotskian perspective in the following way. The symbolic component generates mainly an intermental category, and then the societal and cultural components generate an intramental category. Finally, I suggested as the cultural approach to the mathematics curriculum an alternative to the 'technique' curriculum.

著者

岩田 耕司 服部 裕一郎

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.14, pp.153-166, 2008 (Released:2019-01-17)

参考文献数

36

---

The purpose of this paper is to examine the possibility of the teaching via problem solving in high school mathematics. In this paper, we focused on the learning of the "addition theorems of trigonometric functions" in MAHTEMATICS II, and following was examined. 1) Through quantitative and qualitative investigations, the actual conditions of the activities of the students who worked on the theorems for the first time. 2) Through teaching practice, the effect and validity of the hypothetical ways of support based on the investigations. As a result, it has been understood that the hypothetical ways of support set in this paper worked effectively in the following three points: to understand the problem, to devise the plan for solving in the classroom, and to understand the proof method or meanings of the addition theorems of trigonometric functions. In a word, it is the main result of this paper to have suggested the possibility and the effectiveness of the teaching via problem solving in high school mathematics.

著者

濵中 裕明 川内 充延 吉川 昌慶 加藤 久恵

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 = Journal of JASME : research in mathematics education (ISSN:13412620)

巻号頁・発行日

vol.25, no.2, pp.1-9, 2019

著者

伊達 文治

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.13, pp.29-36, 2007 (Released:2019-01-17)

参考文献数

17

---

This paper is a part of "Research on Cultural Value in Mathematics Education". I grasped and surveyed "mathematics", particularly "the development of mathematics" as cultural elements, and brought their cultural nature into focus. What's more, I went on to examine the present status of Japanese mathematics education from the viewpoint of the cultural nature of development of mathematics in the world. The following issues emerged; (1) Present Japanese mathematics education doesn't grasp the development of mathematics as an organic whole paying attention to its cultural nature. (2) It isn't enough to discuss on the grounds that we did away with traditional Japanese mathematics "Wasan" and adopted only European mathematics from the various mathematics of the world. We should also reflect upon the extent that the learning material is explained haphazardly in the texts etc. without solving those issues. Concerning issue 1, it goes without saying that we must get down to reflecting concretely the development of mathematics into the development of mathematics education. In this paper, I considered issue 2 particularly by clarifying the property of "Wasan" and the decision to accept European mathematics in the Meiji Period and I explored a course for the future Japanese mathematics education. Consequently, I insisted that we need to consider "Wasan" under the spotlight of cultural sociology and that we must proceed to study what culture we appoint to the spirit base of future Japanese mathematics education.

著者

袴田 綾斗 上ヶ谷 友佑 早田 透

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.24, no.1, pp.161-168, 2018-03-23 (Released:2019-09-09)

参考文献数

17

---

The purpose of this paper is to elaborate effects of definitions of logical implication on the unit structure of logic in mathematics textbooks.  Especially, this study focuses on the effects of their definitions on indirect proof. For this purpose, we carried out praxeological analysis of a Japanese high school mathematics textbook within Anthropological Theory of the Didactic.  The analysis consists of two parts.  First, we briefly review a definition of implication by inclusive relationships of sets.  Second, we identify what types of tasks appear how many tasks each type has respectively.  As a result, we found that the definition of logical implication justified solutions for almost all of tasks.  Especially, we can explain and justify the validity of proof by contrapositive by using the definition.  On the other hand, we showed that the definition did not validate of the method of proof by contradiction.  Furthermore, we suggested that above differences were caused by the following three reasons: 1) The current conception of implication based on the concept of set in Japanese school mathematics does not subsume the conception of non-implicational proposition, that is, singular proposition; 2) As long as following the description of the textbook, we cannot define negation for any propositions (we can define negation only for open sentences); nevertheless, 3) The textbook does not explicitly describe some other concepts, such as a logical consequence, required for explaining the validity of proof by contradiction.

著者

杉野本 勇気

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.17, no.1, pp.53-59, 2011

---

Recently, the lesson plan from a constructivist perspective is central problem of mathematics education. Therefore teachers must have belief from constructivist perspective in mathematical teaching. In this paper I consider the impact of mathematics teacher's view of mathematics on practice. View of mathematics as conception of mathematics has been brought to light by Dossey (1992). Teachers need to take Aristotle's, and Fallibilist's views of mathematics. We can assume the hypothetical teaching trajectory for the way to consider the impact of mathematics teacher's view of mathematics on practice. It is formed the basis for Simon's hypothetical learning trajectory, and thought of the hypotheses about the teacher's prediction as to the path by which learning might proceed. The hypothetical teaching trajectory is also made up of three components: teacher's supposition about the learning goal, the learning activities, and the learning process. In this paper, while considering the factor of mathematics teacher's view of mathematics on practice, I constructed a framework of teacher's belief System based on the View of Mathematics for the hypotheses of these components.

著者

加藤 久恵

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.9, pp.153-162, 2003

---

Recently, learning with the portfolio assessment is paid attention to in Japan, because it focuses on the processes of children's learning. The portfolio assessment is one of the way of assessing children's activities and learning processes with their portfolios. The purpose of this study is to discuss the portfolio assessment on mathematical learning to develop the metacognitive ability. For the purpose of this study, this article proposed the framework of a rubric on mathematical learning with metacognitive perspectives. The rubric of portfolios refers to the scale of assessment of portfolios. Using this framework, you will be able to identify children's metacognitive activities, and use the portfolio assessment to develop the metacognitive ability. The characteristics of this framework are the followings; (1) it is two dimensions which are criteria and standards. (2) its criteria include four aspects. (3) its standards include the metacognitive aspects, and 5 levels. : Metacognition requires targets because of its definition (Flavell, 1976). So metacognitive aspects refer to its standers on this framework.

著者

中和 渚

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.22, no.2, pp.37-49, 2016-08-30 (Released:2019-01-17)

参考文献数

21

---

The article discusses the challenges of a lesson study activity held in Serenje, Zambia, dealing with 1-digit multiplication, particularly focusing on teaching and learning including Kyozai Kenkyu and contents of discussion in lesson study.  Fourteen teachers for grade two and three gathered and planned two lessons.  Two trainers in the ministry were the facilitators of the lesson study.  The qualitative analysis was underpinned, utilising the transcription of lessons and lesson study, short interviews to children and the data of participatory observation in Grade 2 and 3 lessons.  First, the analysis showed that students did not understand how to count and recognise points shown in array diagrams in lesson.  Moreover, the array diagram was not effectively used for them to understand the concept of multiplication.Second, teachers did not succeed in guiding students’ better understanding in multiplication since they did not explain well when students did not understand in lesson.  Third, the analysis of the discussion revealed that some teachers did not fully understand the meaning of the order of two numbers in multiplication, discovered in the reflective discussion in lesson study. Conclusions for the improvement of lesson study are two points: Kyozai Kenkyu should be more focused in the whole group of participants by taking time; Discussion should hold the gap between the planning and the implementation in a concrete manner.

著者

後藤 佳太

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.21, no.1, pp.53-61, 2015-01-31 (Released:2019-01-17)

参考文献数

12

---

In mathematics learning, we expect students’ activity that they create meaningful mathematical knowledge and make use of it by themselves.  In such activities, we need to distinguish the stage of guess and justification and we focus on the stage of guess.  Wada (2009) pointed out the importance role of the reasoning of abduction in the stage of guess. However, it is not fully clarified what types thinking are the basis of abduction.  Thus, we focus on the Yonemori (2007) because he argues about the nature of abduction.  According to him, there are the stage of insight and inference in the process of abduction, and both of them play essential role for to form a hypothesis. In the stage of inference, there are four criteria for to choose a hypothesis. When subjects form and choose a hypothesis, s/he use the criterion consciously and reflectively.  For this reason, we argue the criteria by to analyze examples and to compare Nakazima (1981). As a result, we propose three criteria (the criterion of the hypothesis formation) that played primary role for abduction.

著者

松本 菜苗 二宮 裕之

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.21, no.2, pp.187-201, 2015-07-28 (Released:2019-01-17)

参考文献数

31

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As nature of mathematics activity, there are two aspects as “adopting mathematics onto daily life situation” and “creating mathematics from daily life situation”.  Even though many people believe that such connections are important, it is still difficult to make them in good use, because of the NOISES in real life situation.  In this paper, the “Mathematics Problem in Real Life Situation” was examined from the view point of “Mathematical Situation Theory” by Prof. Hirabayashi. First of all, “Social Open-ended Problem”, which has been presented by Shimada & Baba (2013), is examined as the typical example of “Mathematics Problem in Real Life Situation”.  Finding the major characteristics of it, “Open-Closed Continuum” theory by Dienes, Mathematical Modeling theory, explicit and implicit mathematics theory by Chevallard, are also examined to establish the framework of Mathematics activities with Open-Closed Continuum situation. By using this framework, a proposal for the lesson is presented, with the procedure of ①Socially Closed situation, ②Socially Open situation, ③Mathematically Open-Closed situation, and ④Socially Closed situation. (Fig.15)  Finally, some advantages for “Mathematics Problem in Real Life Situation” were concluded as follows:  1) Smooth connection between real world and mathematics world, 2) Supporting for students’ motivations for finding rules, 3) Making good use of the value of problem solving, and 4) Getting deeper understanding of mathematics contents.

著者

竺沙 敏彦

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.6, pp.119-124, 2000 (Released:2019-01-17)

参考文献数

12

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When solving real-world problems through mathematical modeling, the interpretation of solutions is important. Greer, B. (1993) was pointed out students' tendency to exclude real-world knowledge and realistic considerations on the problem solving. The purpose of this paper is to examine how Japanese junior high school students consider real-world knowledge and realistic considerations during the realistic problem solving. In this investigation, I confirmed the same results as Greer, B. (1993) in Japanese junior high school students, that is they tend to exclude real-world knowledge and realistic considerations from their problem solutions.

著者

河村 真由美

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.22, no.2, pp.47-57, 2016-08-30 (Released:2019-01-17)

参考文献数

17

---

The purpose of this research is to propose the methodology to design and conduct a mathematics lesson through students’ activities with examples. In this paper, I made the lesson design model to enhance and use their activities with examples and then, conducted a series of experiment lessons based on it about a logarithm function in high school mathematics to analyze empirically. In principle, the model consists of three stages of students’ activities - operation, reflection, and application -  and a concrete teaching way to change them effectively.  Students form their own typical example at each stage  and change the stage by making use of it.  The teaching way with the model is necessary for a teacher to have the students’ activity stage increase. I designed a series of lessons based on the model and conducted it.  And then, I analyzed it qualitatively what typical examples students had and how students’ activities changed.  As a result, I argued that students had their own typical examples and changed their activities by using them.  Students had their own typical examples that the inequality is the example of inequality including exponent, because students calculated directly inequality 2x > (6.37 × 108)2 in the class of first time. In the class of the eighth time, students solved the same problem using common logarithm and they had their own typical examples that the problem or inequality is the example that they solve the problem using common logarithm.  In the class of the ninth time, students changed the activities that they utilize a typical example of the eighth time as for it and consider the structure of other problems. I suggest that when students change the activities, they change the formation of their own typical examples, too.  Therefore, the result implies that students change the examples while being activities by learning of mathematics lessons and I could demonstrate the effectiveness of the model.

著者

山口 武志 影山 和也 中原 忠男 岡崎 正和 前田 一誠

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.23, no.1, pp.1-20, 2017-01-27 (Released:2019-01-17)

参考文献数

20

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It is still very difficult for children to understand the meaning of division although various efforts for the improvement of teaching division have been implemented. Therefore overall researches which both capture difficulties and misconceptions of various kinds of division systematically and propose better way of teaching and learning of it to overcome them are required. From this perspective, as the first step of our research, we developed six sets of test of division, for fifth and sixth graders in the elementary school and first graders in the junior high school, which could reveal difficulties of understanding the meaning of division systematically. In six sets of test, various factors of story problems of division which will be expected to affect the percentage of correct answers, such as effect of the order or value of the dividend and the divisor, effect of figures, number lines, word expressions, key words and so on, were taken into account. It is the main reason for us to develop new tests why most of previous test or studies of division only focused on specific grade or specific kind of division such as division with fractions which children have difficulties. We conducted the longitudinal and cross-sectional survey with six tests for children at both elementary schools and junior high schools located in three prefectures: Okayama, Hiroshima and Kagoshima. This article reported results of children’s performance of solving problems of “partitive division and the extension of its meaning”, and analyzed children’s difficulties and misconceptions of them in terms of various factors of story problems of division.

著者

岩崎 秀樹 杉野本 勇気 大滝 孝治 岩知道 秀樹

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.23, no.2, pp.1-13, 2017-07-31 (Released:2019-09-09)

参考文献数

36

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This paper simply aims at development of teaching materials on mathematical proof based upon the theory of substantial learning environment proposed by Wittmann.  We think proof attitude and proving skills will become a core for new literacy in future days after modern times.  Mathematics education has to play a big role to realize it. So far mathematics education research, however, paid much attention to the entrance of school mathematics, i.e. arithmetic teaching in Japan.  She missed the exit of school mathematics, especially high school mathematics.  In other words the issue has not been problematized academically on secondary mathematics throughout six years although almost all of students go up to senior high school after graduation of compulsory junior level.  Oncoming mathematics education research, therefore, should focus on the exit of school mathematics from the various angles as well as the entrance.   On the other hand, senior high school mathematics still seems to be a cluster of teaching materials or collection of new instructional resources.  They are not always examined and surveyed carefully and academically.  They need to be scrutinized another angle besides mathematics because mathematics in senior high school stands at the exit of whole school mathematics.  That is to say institutional angle, cultural angle, and societal angle are inevitable.  Many students more than half launch out society with relevant citizenship after graduation of senior high school.  Moreover they must engage in lifelong learning and highly advanced information society whether they like it or not.   In this paper, “Sylvester’s  partition theorem” is chosen as a throughout proof teaching material.  She will be prepared and considered in terms of substantial learning environments as an authentic teaching material first.  She will be analyzed by means of the core of mathematics education as a scientific discipline proposed by Wittmann second.  As consequences, some methodological techniques for developing instructional materials are identified.  The techniques imply not only developmental methods in mathematics education research, but also new direction of training-system for mathematics teachers in educational practice.

著者

川内 充延 渡邊 公夫

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.24, no.1, pp.61-69, 2018-03-23 (Released:2019-09-09)

参考文献数

19

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Seven companies publish mathematics textbooks for use in junior high schools in Japan. Introducing square roots in mathematics class, all of them discuss the relationship between the area and the side of a square. For example, there is a description of “If the area of a square is 2cm2, how many centimeters is the length of one side of a square?” Hitotsumatsu (1990) casts doubt upon the description of “The solution of x2 - 2 = 0 is + √2 and - √2 ” (p.7). The aim of this paper is to develop a new approach to introduce square roots in teaching for readiness. That lies hidden in Square Dotty Grid and Isometric Grid. Our idea is based on the figures of “If a segment is multiplied by a and one more time running, then it is multiplied by 2 and 5 on Square Dotty Grid, 3 and 7 on Isometric Grid” We carried out classwork study and realized that the approach will succeed. 67 second-grade students in junior high school made three squares or three rhombuses using a diagonal’ length of a square or a rhombus, and responded to a question in worksheets during class. As a result of the survey, their notes gave us three suggestions. First, there is a possibility that students consider with the ratio in length between each one side of three squares or three rhombuses. Second, these teaching materials provide learning opportunities of inductive, analogical and deductive inference for students. Third, students may notice irrationalness themselves.

著者

アーネスト・コヒィ・ デイビス 馬場 卓也

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.11, pp.241-257, 2005

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本研究は,ガーナにおける現職教員夜間研修プログラムが基礎学校教員の教科知識に与えた影響について,事例研究を行うことを目的としている。また同時に,教師がこの研修への参加動機を,自らを高めることとしていることについても確認しようというものである。この研修プログラムは,教員の質やその不足の問題を解決することが目的で,1998年に始められた。本プログラムの良い点は,研修を受講する教師が教壇に立ちながら,同時に研修も受けることができるということである。したがって教師は研修の中で新しく学習したことを,授業の中ですぐさま活用する事ができるのである。ところがこの研修プログラムの効果について,未だ研究がなされておらず,より良い研修を求めていく上で,まだ為すべきことは多数存在する。<br> そこで本研究では,ガーナ国中央州における現地調査を実施した。質問紙調査において,研修受講者58名,研修未受講者54名,校長40名,指導主事20名の有効回答を得た。さらに研修受講者の内6名が選出され,さらに6名の未受講者と合わせて計12名の教師の授業が観察され,さらにその内の受講者1名と未受講者3名より授業についてコメントを得た。このようにして収集されたデータに対して,平均や標準偏差などの記述統計による量的分析と,コメントの内容分析を行った。これらを通じて本事例では,この研修プログラムにおいて基礎学校教師の数学教科知識が高まったが,他方で未だに分数を指導する上での問題が存在していることが分かった。