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The Taisei Sankei is an encyclopaedic work of Japanese mathematics compiled by three mathematicians, Seki Takakazu and his disciples, the Tatebe brothers. The compilation project began in 1683 on the initiative of the younger Takebe, Katahiro, and was completed by the elder Takebe, Kata'akira, in 1710. An interim edition in twelve volumes, entitled Sanpō Taisei, was drafted by Katahiro around 1695, but no manuscript of this edition survives. However, it is important to study the Sanpō Taisei because it is considered to be the culmination of Seki Takakazu's mathematical works. By studying the mathematical manuscripts left behind by the three mathematicians, this paper deduces which volumes of the Taisei Sankei succeed the Sanpō Taisei and how the Sanpō Taisei was compiled. We also identify the author(s) of the four manuscripts Kyūketsu Henkeisōkai, Kyūseki, Kaihō Sanshiki and Kaihō whose contents are common to some parts of the Taisei Sankei.

Following a decision of the Ministry of Education, “the Experimental Classes for Science Education” were formed in four cities of Japan in the near end of the World War II. The one of the Experimental classes were established in the Kyoto-Prefectural Kyoto First Secondary School, one each in the 3rd, 2nd and 1st year. In addition to the actual management of the class, the content of the lessons and the career paths of pupils in the class are described. I will once again shed light on the Experimental Class for Science Education, and make use of a part of science and technology education in Japan in the future., 本稿は，京都における特別科学教育学級について調査したものであり，「京都における特別科学教育学級の記録」（田中，2021）の追調査報告である., 【RIMS講究録別冊B85修正について】P114.4行目「湯川氏は京都帝国大学の学生については特攻隊の係で，自分の学生たちは戦争に送り出しつつ，科学組には駒井氏と共に頻繁に足を運び，非常に熱心だったことは，当時の状況から考えると異常なまでだろう．近くで関わっていた元教師は後に「湯川先生の御執心は教育無視の時代への憤りとも拝察された．」と述べている．」との記載は誤りであり，正しくは「湯川氏は京都帝国大学学徒隊組織表によると，理学部特技隊の隊附であった(京都帝国大学理学部，1945）．同時期に科学組には駒井氏と共に頻繁に足を運び，非常に熱心だった．近くで関わっていた元教師は後に「湯川先生の御執心は教育無視の時代への憤りとも拝察された．」と述べている．」です．

The Takuma School is a school in Osaka that produced Kamata Toshikiyo (the 3rd), whose achievements should be comparable to those of Seki Takakazu, Tatebe Takahiro, and his brother Kataakira, and Matsuoka Yoshikazu (the 5th), who wrote one of the most important textbooks of the 19th century, the Complete book for arithmetic practice. In this paper, we discuss the Methods of transformation of equations written by Oka Shichibei Yukitada, who was a student of Matsuoka. After a brief overview of the Takuma School in Section 2, Sections 3 to 6 discuss the characteristics of Takuma School mathematics through an analysis of Oka's book. It has long been known that the style of expression in the Takuma school differs from that in the Seki school, but in Section 4 we discuss in more detail some of the important terms in the Takuma school (or, more precisely, in Oka's mathematics). In particular, section 5 describes Oka's transition methods of equations in detail. Section 7 briefly mentions Oka's student Asaoka Uhei, whose existence became known in 2021.

このノートは、2021年2月2日に数理解析研究所での講演（『四元玉鑑』と『四元玉鑑細草』について）の記録である。RIMS共同研究（公開型）『数学史の研究』の報告集（RIMS Kôkyûroku Bessatsu B85) に載せることになっていたが、原稿の完成が締め切りに間に合わず、今回の講究録に載せて頂くことになった。

Seki Takakazu, Takebe Kata'akira and Takebe Katahiro compiled the 20 volumes encyclopedia called the Taisei Sankei for 28 years (1683-1710). The first three volumes treat elementary arithmetic. We will review these volumes with special attention to Volume 3. This volume can be divided in two parts. We will show how fundamental rules of arithmetic were conceived and expressed in the traditional Chinese format of problem-answer-procedure in the first part of Volume 3. We will discuss then how Takebe Kataakira constructed the second part of Volume 3 on the basis of Seki Takakazu's two notes, the Kaihō-sanshiki and the Kaihō-honhen-no-hō.

Mikami Yoshio, as a famous Japanese historian of mathematics and science in the 20th century, is one of the founders of modern mathematical history research in the East and West, and is also regarded by some scholars as the creator of the theory of external history. He is famous domestically and internationally for his research on traditional Chinese and Japanese mathematics. His research on Chinese arithmetic has not only introduced the traditional mathematics as one of the treasures of Chinese history and culture to the West, but has also laid foundation for the study of traditional mathematics in China. Since the 1990s, scholars in China have carried out the study on Mikami Yoshio. A brief survey of the research on him conducted by domestic scholars over the past three decades is presented in this article from five aspects categorized and discussed, including an early introductory study of him, a study of his thoughts on the history of mathematics and science, a rediscovery of the outstanding achievements of traditional Chinese mathematics with the help of his research, an analysis of the different stages and characteristics of his research on the history of mathematics, and an observation of his relationship with Western scholars.

As for the text book “Kōzangaku” edited by the Imperial Japanese Army Academy, it is well known that there are no evidence of who is the author and when it was published. In this paper we propose that a new candidate of the author must be Masahide Kawatani, Army Artillery Lieutenant, and the year of publication is possibly 1887 which is one year earlier than its common view.

To activate the study on the history of Mathematics in Japan, the author proposed to organize some memorial events for the year 2022, the 314th year after his death of SEKI Takakazu (?-1708), the 300th anniversary of TAKEBE Katahiro's “Tetsujjutsu-Sankei”, and so on. We propose to build a stone monument near his tomb in Jorinji Temple, because of his significant work concerning to Pi., 数学，数学教育，数学史の教育・研究の活性化のために2022年に関孝和314年祭開催等を（建部賢弘が「綴術算経」の序文を書いてから300年の記念の年でもあり）提唱している．関先生の円周率の近似計算に関する世界的な業績を記念して石碑を墓のある浄輪寺に設置することを思いつき準備していることを報告する．

In the early Meiji period, the mathematical probability concept will be supposed to be very difficult to understand or accept at Japanese Army. In this paper, we investigate how the Japanese had understood or accepted the classical probability theory founded by Laplace, comparing several Japanese text books on probability theory with those of some European ones. Especially we focus on the words“ total probability” which is a little bit curious words from the point of view in the modern probability theory., "Study of the History of Mathematics 2020". February 1-3, 2021. edited by Naoki Osada. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

In this short note, we treat some commemorative events of mathematicians, societies, books etc. concerning to the mathematics in Japan. As a by-product, we are able to build the following hypothes.is: SEKI Takakazu was born in “Kansei 20”. We are planning to organize some anniversary events in 2022 and those will be useful to activate the study on the history of Mathematics in Japan., 数学，数学教育，数学史の教育・研究の活性化のために2022年に関孝和314年祭開催等を提唱しているが，その概要を記してある．副産物としては，関孝和の誕生年を祝い年に出版があったと考えると寛永20年（1643年2月19日から1644年2月7日）になると推測されることに気付いたことである．, "Study of the History of Mathematics 2020". February 1-3, 2021. edited by Naoki Osada. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

Following a decision of the Ministry of Education, “the Experimental Classes for Science Education” were formed in four cities of Japan in the near end of the World War II. The one of the Experimental classes were established in the Kyoto-Prefectural Kyoto First Secondary School, one each in the 3rd, 2nd and 1st year. The origins of the classes, entrance examinations, contents of the courses, teachers are described together until the abolition. The significance of the classes and why the class was abolished are considered., "Study of the History of Mathematics 2020". February 1-3, 2021. edited by Naoki Osada. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

The lattice multiplication (格子乗算) was probably discovered in the Western Asia or Southern Asia, then it was introduced to the East and West. In Japan, two types lattice multiplication were arrived at the Edo period. Chen Wen (陳雯) introduced the lattice multiplication system and Napier’s bones from Western mathematical arts, and he used ‘Suzhou Numerals’. But Japanese mathematicians at the Edo period already studied the Lattice Multiplication system of ‘Xie Suan’ (or ‘Pudijin’, 写算, 鋪地錦) and Suzhou Numerals (蘇州号瑪) by Chinese mathematical arts at the Ming dynasty (明朝) such as the Suanfa Tongzong (算法統宗), (Cheng Dawei (程大位), 1592) before Western mathematics arrived into China. Japanese medical doctors had never studied Chinese mathematical arts at the Ming dynasty. Therefore, there were two types of mathematics in that time, that is to say, ‘Jikata’ Wasan (rich farmers’ mathematics) and ‘Komozan’ (Western Mathematics, 地方紅毛算和算期)., "Study of the History of Mathematics 2020". February 1-3, 2021. edited by Naoki Osada. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

Four letters from Confucian Ogyū Sorai (1666-1728) to calendrical calculator Nakane Genkei (1662-1733) have been preserved in the Kansai University Library. In each of these letters, the date and month are only written, but not the year. Although it is not clear when the two met, it is likely that the letters were written between the 10th and 12th year of Kyōhō period (1725-1727). The main content of the letter is related to the request for a preface to Genkei's work, the Kowa-tsūreki (the Japanese Emperor's Almanac) and the Chinese literature, the Jun shi that Genkei planned to publish. The letter also mentions that the two had a disagreement over the evaluation of the Gakuritsu zensho (the Complete Works of Chinese classical Music and Calendrer) written by Zhū zǎi yù (1536 - 1611), which was introduced to Japan from China in July of 10th year of Kyōhō period (1725). In this paper, we will first introduce the contents of the letter, converted into modern printing, as well as the process of writing the preface for the two books and the conflicts between the two sides regarding the value of 𝜋 discovered by Zhū zǎi yù., "Study of the History of Mathematics 2020". February 1-3, 2021. edited by Naoki Osada. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

Kyouzaikenkyuu (translated as instructional materials research) is said to be a crucial part of successful Japanese lesson study. Kyouzaikenkyuu is described as the planning portion of the research lesson during lesson study. Kyouzaikenkyuu is also said to be done on a daily basis by Japanese teachers; however, there is very little written about this process in the literature. This study takes an in-depth look into what Japanese junior high mathematics teachers do during their daily kyouzaikenkyuu, and why they do it. Through interviews, observations, and participation in kyouzaikenkyuu, we explain the process and key ideas that many Japanese mathematics teachers go through to prepare their lessons. We document two different approaches to kyouzaikenkyuu. We also found that for some teachers there is a large difference between what they do during kyouzaikenkyuu for a research lesson compared to the kyouzaikenkyuu of a daily lesson. If teachers outside of Japan wish to engage in kyouzaikenkyuu and lesson study, these approaches are a good place to start.

In the 1620s, two books on mathematics were published in Kyoto. This article describes the cultural, religious, and commercial activities surrounding their publications and examines their contents,...

Rikitaro Fujisawa who was the second Japanese professor of mathematics of the Imperial University insists in the preface of his book that he wrote his book for repaying an obligation to the country. In this paper, we show that really he made the best effort to apply the life insurance to the society by using of talent of the self from the world level documents concerning life insurance. Especially we show that he refers De Morgan's book([3]) and the article the Life Insurance written by Kenzo Wadagaki([26]) who is appreciated in the preface of Fujisawa's book., Study of the History of Mathematics 2019. September 2-4, 2019. edited by Naoki Osada. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

The open problems of Kazuyuki Sawaguchi's Kokon Sampōki are famous for being solved in Hatsubi Sampō by Takakazu Seki using the method of elimination of unknowns. In this paper, we consider how Sawaguchi solved the open problems proposed by Masaoki Satō in the Sampō Kongenki , and how he made the open problems his book, Kokon Sampōki. We will reveal what kind of solutions Sawaguchi had expected. We will also describe Sawaguchi's contribution to the development of early-modern Japanese mathematics (wasan) that were beyond Chinese traditional mathematics of that time., Study of the History of Mathematics 2019. September 2-4, 2019. edited by Naoki Osada. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

Seki Takakazu (?-1708) has long been known as one of the founders of mathematics in Pre- modern Japan. His personal profile, documentary legacy, and view of mathematics have been studied by numerous scholars in numerous papers. Here, I confrm that his primary interest was in the theory of algebraic equations, a topic on which he left several manuscripts. He was the first person to grasp equations systematically and abstractly as mathematical objects per se. His theory was based on the side writing" system that he developed to solve the problems set in Sawaguchi Kazuyuki's Mathematical Method Old and New (Kokon Sanpouki, 1671). It has previously been pointed out that this side writing system allowed problems to be resolved into simultaneous equations of differing degrees (simple, quadratic, etc.) which led immediately to elimination theory as a new subject of study. Seki's theory on algebraic equations has two aspects. One is still of mathematical interest today while the other belongs more to the historical context. I discuss the former quickly and the latter in rather more detail, referring to a problem treated in Seki's Method for Restoring Defective Problems (Byoudai Meichi)., Study of the History of Mathematics 2019. September 2-4, 2019. edited by Naoki Osada. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

This paper introduces a mathematical puzzle book, Gobanjo, rediscovered on 2008. The radiocarbon dating on this book suggests that this puzzle book had been written on 15th century, which could be the oldest mathematical book in Japan. The Gobanjo shows us 6 types of puzzle utilizing go stones. The author summaries and translates these 6 types of puzzle into modern Japanese, i.e. Hyakugogenzan (Chinese Remainder Theorem), Shihoseki (counting the sides of square), Tonitarazu (addition and subtraction), Sassadate (simultaneous equations), Metsukeishi (guessing a hidden go stone), and Jugodate (3×3 magic square). Hitherto, as we had some knowledge about these puzzles except Metsukeishi, the author presumes the reconstruction of Metsukeishi utilizing the transposed matrix.

“Wasan” is the collective name given to a set of mathematical texts written in Japan in the Edo period (1603–1867). These documents represent a unique type of mathematics and amalgamate the mathematical knowledge of a time and place where major advances where reached. Due to these facts, Wasan documents are considered to be of great historical and cultural significance. This paper presents a fully automatic algorithmic process to first detect the kanji characters in Wasan documents and subsequently classify them using deep learning networks. We pay special attention to the results concerning one particular kanji character, the “ima” kanji, as it is of special importance for the interpretation of Wasan documents. As our database is made up of manual scans of real historical documents, it presents scanning artifacts in the form of image noise and page misalignment. First, we use two preprocessing steps to ameliorate these artifacts. Then we use three different blob detector algorithms to determine what parts of each image belong to kanji Characters. Finally, we use five deep learning networks to classify the detected kanji. All the steps of the pipeline are thoroughly evaluated, and several options are compared for the kanji detection and classification steps. As ancient kanji database are rare and often include relatively few images, we explore the possibility of using modern kanji databases for kanji classification. Experiments are run on a dataset containing 100 Wasan book pages. We compare the performance of three blob detector algorithms for kanji detection obtaining 79.60% success rate with 7.88% false positive detections. Furthermore, we study the performance of five well-known deep learning networks and obtain 99.75% classification accuracy for modern kanji and 90.4% for classical kanji. Finally, our full pipeline obtains 95% correct detection and classification of the “ima” kanji with 3% False positives.

In recent years, construction of databases from digitized documents of Japanese mathematics (wasan) has been progressing. We can search documents individually by keywords such as titles and authors in these databases. On the other hand, it is unable to cross-search them from contents such as problems in the documents. To realize this cross-searching based on problems, the authors propose a system to tag images of geometric problems in wasan automatically. In addition, the authors consider generating vector based on tags to evaluate the similarity of geometric problems., "The study of the history of mathematics 2018". September 18-21, 2018. edited by Shigeru Jochi. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

The Taisei Sankei (1710) is an encyclopedic work of mathematics written by Seki Takakazu (?-1708), Takebe Katahiro (1663-1739) and Takebe Kata'akira (1661 - 1716). The authors tried to expound all the mathematics in the Chinese and Japanese tradition and their own discoveries in a systematic way. This work was conceived in 1683 by Takebe Katahiro and, around 1695, reached an interim work (12 volumes) called Sanpō Taisei. The final version (20 volumes) was completed after 10 years editorial endeavor by Takebe Kata'akira. The Taisei Sankei was not published but there have been more than twenty manuscripts of the monograph. Hikosaburo Komatsu listed all the manuscripts known to him (see [2]) and he himselfedited a collated version of the Taisei Sankei [4], [5], [6] and [7]. In [2] the manuscripts enumerated by the numbers which we propose to call the Komatsu numbers. The first aim of this article is to overview the present state and availability of the manuscripts according to the Komatsu numbers. Second, in 2018 we investigated a manuscript of the Taisei Sankei preserved at Tsu City Library, Mie Prefecture. We show pictures of its pages and are happy to say the manuscript are in a good condition. Third we sketch our speculation on the interim edition, the Sanpō Taisei, which left no trace at all but the title. We propose here what 12 volumes out of the 20 volumes of the Taisei Sankei consisted the Sanpō Taisei. Lastly, the proceedings [8] of the Takebe Conference 2014 was published on December 25, 2018. Ogawa's survey article in English [9] will provide the background information on Takebe Katahiro, the initiative author ofthe Taisei Sankei. Volumes 12, 17 and 19 ofthe Taisei Sankei were translated in English in [10], [11] and [12], respectively., "The study of the history of mathematics 2018". September 18-21, 2018. edited by Shigeru Jochi. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

This study aimed to analyze boundaries of the community of teachers’ imple- menting the mathematics textbooks with Lesson Study and Open Approach. For this study, Mathematics textbooks were Japanese mathematics textbooks (Thai version), consisting of mathematics problems, flow of lesson, and students’ mathematical ideas. The participants were 2 expert teachers who use the textbooks in the classroom using Lesson Study and Open Approach since 2013. The data were collected in 2017 school year by using interview andclassroom observation with video recording. The data were analyzed based on Wenger, McDermott, & Snyder (2002)’s framework of community of practice. The results showed that the teachers practiced in 3 boundariesof the community: 1) within school—every week, they use the textbooks to design mathematical problems and anticipating students’ ideas with their school team, then they teach the lesson and observe students’ ideas in the classroom, and they reflect on students’ ideas that occurred in their classroom, 2) across schools—every semester, they form team with teachers who work in different schools of the project to design/observe/reflect a classroom by using the textbooks in school open class activity, and 3) across organization boundaries —every year, they and their school network participated in the activities, the national open class, the workshop for school teachers, the national and international conference, that help them to understand students’ ideas via classroom by using the textbooks and sharing with their school teachers and university experts.

This study was aimed to analyze how students’ mathematical ideas emerged through a flow of lesson in mathematics classroom using Lesson Study and Open Approach. A context of the study was the Open Approach as a teaching approach and the Lesson Study as a way to improve the quality of teaching (Inprasitha, 2015a). The flow of lesson, likewise, is considered to be a tool for accessing to students’ ideas when the students are involved in problem solving and connection between students’ real world and mathematical real world (Inprasitha, 2017b). Ethnographic study was employed as a research methodology in this qualitative study by using a participative research design to form a lesson study team for collaborative designing of lesson plans guided by Thai version of Japanese mathematics textbooks. Research results were shown that the students’ mathematical ideas emerged, through the flow of lesson, when the students’ ideas of a problem solving were mathematized as follows: 1) the mathematical ideas were extended through representations of real world, 2) the mathematical ideas were extended and generalized through semi-concrete aids, and 3) the mathematical ideas were generalized through representations of mathematical world. The processes of mathematization (Isoda & Katagiri, 2012), furthermore, were accomplished when the students’ mathematical ideas become “how to” or tools for learning for the next lessons.

This research aims to analyze how and what teachers learn in community of implementing mathematics textbooks with Lesson Study and Open Approach about addition in number and operations for first grade. The participants were 2 teachers who use the textbook in the classroom using Lesson Study and Open Approach. The mathematics textbooks for this study were Japanese mathematics textbooks (Thai version), and consist of mathematics activities, flow of lesson, and students’ mathematical ideas (Inprasitha, 2015b). The data were collected in October 2015 by interview and classroom observation with video recording. The data were analyzed based on communities of practice (CoP) from Wenger, McDermott, & Snyder (2002), and Shulman & Shulman (2004). The result of this research found that how and what teachers learned in community of implementing mathematics textbooks with Lesson Study and Open Approach, are 2 aspects: 1) teachers learned about the content of mathematics from their sharing on the textbook and students’ ideas together, and 2) teachers learned how to teach the content, through using the textbook for sharing anticipating students’ ideas, observing students’ ideas, and reflecting by using evidence from students’ ideas that appeared in classroom.

Paul Lévy (1886-1971)had left a rich and deep performance in probability theory. Paul Lévy's probability theory included a novelty that was not in the previous stochastic theory, and inspired the two mathematicians of Japan, Kiyoshi Itô (1915 - 2008) and Takeyuki Hida (1927 - 2017). I would like to glimpse some of Paul Lévy's charms and his mathematical charms from the materials such as the words that the two Japanese mathematicians spoke about Lévy, what Lévy himself wrote, and the letters exchanged by Lévy and Hida. I feel the insight of Paul Lévy's mathematical approach to the Brownian movement, and I would like to close to the source., "The study of the history of mathematics 2017". September 19-22, 2017. edited by Shigeru Jochi. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

We discuss tekijin-shokyū (method of vanishing a polynomial and its certain derivative), shokyū-taisū (in literal, replacement of each coefficient to obtain a root), and shishō-kyokusū (in literal, find the common root of a given polynomial and its derivative ) in Kaihō honhen no Hō (Methods of Equation Modifications) re-revised by Seki Takakazu in 1685. We show that the algorithm of taisū consists of five procedures of Kaihō honhen no Hō. We declare tekijin-renkyūhō, which has been considerd to be purposeless, is available to use taisū. We also demonstrate that tekijin-renkyūhō and tekijin-karenkyūhō provide useful information on roots of real cubic and quartic equations, respectively., "The study of the history of mathematics 2016". August 29～September 1, 2016. edited by Shigeru Jochi. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

In Wasan which is old mathematics in Japan, Steiner chain was studied by Ajima Naonobu (1732-1798) earlier than Jakob Steiner (1796-1863). Geometry was the major areas of Wasan. Now in practice, it takes a lot of time to solve beautiful geometry problems in the time of the method, but it is difficult to explain them using sophisticated way. If we can show the relevance among the problems clearly in a simple way, we can show more charm of Wasan. This paper will be such an experimental approach. The second purpose of this paper is related to the fact that one of the invariant holds on Steiner chain problems in Japan. This fact is known among people who are interested to solve Wasan geometry problems. Probably for the first time, it was submitted collectively in Tatsuhiko Kobayashi's paper. Although it has passed more than 30 years from that pointing out, the elucidation of it has not been made. We already made another simple proof to Ikeda's theorem and Kenmochi's theorem, using the inversion method. Now, the idea of proof and the other one have been found to be effective to clarify that. This paper will be an effort to answer the problem., "The study of the history of mathematics 2016". August 29～September 1, 2016. edited by Shigeru Jochi. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

In this chapter, we analyse three fundamental practices of Japanese mathematics teachers to better understand the set of community values that influence their work as teachers. The three fundamental practices are: writing detailed lesson plans, kyozaikenkyu (a planning practice), and emphasizing student mathematical reasoning in instruction. An analysis of these community practices resulted in eight potential values of the Japanese mathematics teacher community. These values help the field better understand why Japanese teachers engage in the work of teaching the way that they do.

Japanese lesson study was introduced to the West in the late 1990s. Certain widely disseminated publications and classroom videos, and also reports on international surveys of students achievement, led many to consider that Japanese mathematics teaching is highly creative and effective, with lesson study as a main explanatory factor. As a result, substantial efforts have been deployed in many countries to engage mathematics teachers in lesson study. In this paper, we argue that lesson study is but one element of a comprehensive Japanese “infrastructure” for developing teacher knowledge, both personal and shared, and that the functions and workings of any particular element in this infrastructure cannot be fully understood when viewed in isolation. In this paper, we offer a systemic (institutional) analysis of how these “infrastructure” elements interact in crucial ways. Specifically we study two episodes where a teacher’s “practice research” is clearly motivated and supported by other infrastructural conditions, such as the possibility to present the outcomes at a regional teacher conference, and in a publication. Moreover, a central prerequisite for the creative part of “lesson planning” is a much more limited activity: the patient study and discussion of mathematical tasks and materials. This activity is also crucially supported by elements of the infrastructure.