{{Short description|Misunderstanding in Japanese education}} {{Pi box}} "'''Pi is 3'''" is a misconception that the Japanese public once believed that, due to the revision of the Japanese Curriculum guideline in 2002, the approximate value of pi (π), which had previously been taught as 3.14, is now taught as 3 in arithmetic education.{{R|曽我2001|細野2001}}{{Sfn|朝日新聞|2012}}{{R|山下2001}} In fact, this is not true, and even after the revision, the approximate value of pi is still taught as 3.14.

In the Japanese Curriculum guideline published in December 1998 and implemented in 2002, regulations such as the limitation on the number of digits for decimal multiplication were changed. Although the new regulations did not change the fact that pi was to be calculated using "3.14," they added the statement that "3 is used for the purpose."

At that time, many people believed elementary school students were forced to hand calculate pi as "3", and believed that is a typical example of the negative effects of a relaxed education.{{Sfn|関沢正躬|2000|pp=8-9}}{{Sfn|黒木哲徳|2001|p=25}}{{Sfn|大西俊弘|2002|p=18}} This misunderstanding was not easily resolved.{{Sfn|木村寛治|2004|p=138}}{{Sfn|神永正博|2008}}{{Sfn|池上彰|2013}}

== Origin == In the fall of 1999, a major cram school company launched a major campaign with advertisements that read "The formula for finding the area of a circle: radius x radius x 3!", "Calculate the quadrature of a circle with pi as approximately 3 instead of 3.14."{{Sfn|朝日新聞|2012}}

The mass media also picked up on this issue, and it wrongly became widely believed in society that "as a result of the relaxed education system, pi is now taught as 3".{{R|産経20080218}}{{Sfn|木村寛治|2004}}

As a criticism of the decline in scholastic achievement and the relaxed education system, "Pi is 3" was widely covered in weekly{{R|週刊新潮2001|週刊文春2000|週刊朝日2001}} and monthly{{R|細野2001|プレジデント2002}} magazines and other mathematics-related journals.{{R|曽我2001|山下2001}}

== Details == === "Use 3 if fits your purpose" guideline === The Japanese Curriculum guideline was started as a guide only, but at some point, they came to be considered legally binding. In addition to this, there was also a so-called "restrictive provision" that "has to teach without excesses or deficiencies of what the guidelines say."<ref>{{Cite news |url=http://www.nishinippon.co.jp/wordbox/display/881/ |title=歯止め規定 |newspaper=西日本新聞 |date=2003-10-07 |archiveurl=https://web.archive.org/web/20090221152207/http://www.nishinippon.co.jp/wordbox/display/881/ |archivedate=2009-02-21|trans-title=Regulations for Prevention Purposes}}</ref> This statement was carried over to the 1998 revision (implemented in 2002 for elementary schools.)

{{Quote frame|(1) c) of "section B: Quantity and Measurement" and (1) d) of "section C: Figures"in the contents, while 3.14 is used for pi, consideration should be given to the ability to process using 3 for the purposes.|Curriculum guideline published in 1989{{Sfn|木村寛治|2004|p=138}} }}

"To process using 3 for the purpose" assumed for, *If you want to make an estimate, calculate quickly by 3.<ref name="monkasho_Q">{{Cite web|url=https://www.mext.go.jp/a_menu/shotou/gakuryoku/faq/001.htm#19 |title=Q「円周率は3」で教えていると聞きましたが、本当ですか。|publisher=文部科学省 |date= |accessdate=2014-02-26|trans-title=Q: I heard they're teaching that pi is 3. Is that true?}}</ref> *The decimal point is not calculated from the beginning, and a rough guess is made with 3 to reduce the possibility of calculation errors. *When want to approximate the perimeter or area of an object that is similar to a circle, calculate the circumference and area of the circle using pi as 3.{{Sfn|木村寛治|2004|p=138}} One interpretation is that they expect to develop the ability to make appropriate judgments and process the information according to the situation and application.{{Sfn|木村寛治|2004|p=138}}

=== Issues with the 1998 Revised Guidelines === As part of the so-called "relaxed education," the content of arithmetic learning in multiplication, division, and decimals was reduced, while calculators were allowed to be used from the arithmetic learning stage.

On the other hand, because relaxed education reduced the time for learning but not the areas of learning, many people believed that, students were forced by guideline to use 3 instead of 3.14 as the approximate number of Pi for calculating. However, it was a misunderstanding.{{Sfn|関沢正躬|2000|p=}}{{Sfn|黒木哲徳|2001|pp=25-26}}<ref name="鴨志田2007">{{cite journal|author=鴨志田英樹|journal=日本ロボット学会誌|title=ロボットを通した実学 ―教育とロボットの融合―|trans-title=Practical Learning Through Robotics: The Integration of Education and Robotics|year=2007|pages=57–59|url=https://doi.org/10.7210/jrsj.25.57|volume=25|doi=10.7210/jrsj.25.57 |url-access=subscription|doi-access=free}}</ref>

In addition, the use of calculators, which was allowed from the 5th grade under the previous teaching guidelines, was allowed from the 4th grade{{Sfn|大西俊弘|2002}}{{Sfn|黒木哲徳|2001|pp=24-25}}{{R|原田2003}}<ref>{{Cite journal|url=http://repository.lib.tottori-u.ac.jp/Repository/detail/276820100210061523 |format=PDF |title=（卒業論文要約）小学校算数科教育における計算指導－電卓の利用のあり方－|author=西村宏太|editor=指導教官：溝口達也|journal=鳥取大学数学教育研究|number=7|date=2005|trans-title=Teaching Computation in Elementary School Mathematics Education: Approaches to Calculator Use}}</ref> and calculations using 3.14 were possible even with a calculator.{{Sfn|大西俊弘|2002}}

=== Limit the number of decimal digits ===

In the 1998 Revised Curriculum guideline in Japan, the calculation of decimals in the fifth grade of elementary school is as follows,

{{Quote frame|1= 2. Details{{Sfn|木村寛治|2004|p=138}} :A. Numbers and Calculations. ::(3) Understand the meaning of multiplication and division of decimals and be able to use them appropriately. :::(3c) The student should be able to think about how to multiply and divide decimals and be able to perform those calculations. Also, to understand the magnitude of the remainder. ::::(note 3c) The calculation of decimals to the nearest 1/10th of a place shall be handled.{{Sfn|木村寛治|2004|p=138}}}}

Because of the above limitation, this led to the misunderstanding that 3 must be used as pi. But even if decimals were limited to 1/10th of a place, the pi used would still be 3.1, which does not define pi as 3.

=== The misunderstanding that "pi is approximately 3" ===

At that time, in the fall of 1999, a major cram school company released the following advertisement.

{{Quote frame|1= The formula for finding the area of a circle is radius x radius x 3? In 2002, fifth-grade students will be doing a quadrature calculation of circles with pi as "approximately 3" instead of 3.14. It's real. {{Sfn|朝日新聞|2012}} }}

They conducted a major campaign in the Tokyo metropolitan area,{{Sfn|朝日新聞|2012}} and the media covered it extensively.{{R|本田2002}}

This led to widespread public awareness of the misunderstanding that pi is now taught as 3 because of the relaxed education system.{{Sfn|朝日新聞|2012}}{{Sfn|池上彰|2013}}{{R|産経20080218}}{{Sfn|木村寛治|2004}}

Akito Arima, who promoted "relaxed education" as the Minister of Education at the time, repeatedly said, "I was stunned by that," and regretted "my failure to go around the country and explain it in detail."<ref name="arima">{{Cite web|url=https://digital.asahi.com/articles/ASND764BSND7UTIL034.html |title=ゆとり教育貫いた有馬朗人さん 怖い目をした2つの話題|publisher=朝日新聞 |date=2020-12-07 |accessdate=2022-07-09|trans-title=Mr. Akihiro Arima, who championed the “yutori” education policy Two topics with a scary look}}</ref>

=== Disappearance of the sentence === In the second report of the Japanese Central Council for Education on February 23, 2003, the policy of emphasizing scholastic ability was formulated.{{R|原田2003}}

In December 2003, the Curriculum guideline was partially revised to remove the limitation that they must be taught without excesses or deficiencies and changed to a minimum standard that allows teaching in more detail than what is written in the Curriculum guideline, if necessary.<ref>{{Cite web|title=小学校、中学校、高等学校等の学習指導要領の一部改正等について（通知）15文科初第923号 平成15年12月26日 |author=文部科学事務次官 御手洗康 |publisher=文部科学省|url=https://www.mext.go.jp/a_menu/shotou/cs/1320953.htm |accessdate=2014-03-01|trans-title=Partial Revision of the Curriculum Guidelines for Elementary Schools, Junior High Schools, High Schools, etc. (Notice) No. 15 Bunka-Sho-923}}</ref><ref>{{cite journal|author=板谷裕子|journal=岡山医学会雑誌|title=医学教育概説 教育評価とその運用|year=2004|volume=116 |pages=29–38|doi=10.4044/joma1947.116.1_29|doi-access=free|trans-title=Overview of Medical Education: Educational Evaluation and Its Implementation}}</ref>

On February 15, 2008, the Japanese Ministry of Education released the new Curriculum guideline (effective in 2011 for elementary schools), the first after the complete revision of the Fundamental Law of Education, and the ''restrictive provision'' was eliminated.<ref>{{Cite web|url=https://www.mext.go.jp/b_menu/shingi/tosho/003/gijiroku/08090901/004.htm |title=新学習指導要領における、いわゆる「はどめ規定」について |publisher=文部科学省 |author=初等中等教育局教科書課 |accessdate=2014-02-26|trans-title=Regarding the so-called “restrictive provisions” in the new curriculum guidelines}}</ref><ref>{{cite journal|author=鵜澤武俊、文有彬|journal=環境技術|title=環境教育に有用な電気泳動を用いたDNA検出法の開発|year=2014|pages=286–292|volume=43|issue=5 |doi=10.5956/jriet.43.286 |bibcode=2014JECE...43..286U |doi-access=free}}</ref>

As a result of the increase in the content of the study, the content has become such that have already learned how to calculate the decimal point by the time they use pi, and the section on pi now states only that "pi shall be 3.14" and the statement "3 is used for the purpose" has been deleted.{{Sfn|学習指導要領|2009}}

== Impact == === Science and education professionals === The issue of "pi is 3" was discussed in mathematics-related journals{{R|曽我2001|山下2001}} and various academic journals.{{R|原田2003}}<ref>{{cite journal|author=霍見芳浩、高田博和|journal=経営行動科学|title=インタビュー|year=2005|pages=157–174|volume=18|issue=2 |doi=10.5651/jaas.18.157 |doi-access=free|trans-title=Interview}}</ref> This misunderstanding was not easily resolved, and there were many misunderstandings even among those involved in education.{{Sfn|木村寛治|2004|p=138}}

In response to this situation, Masahiro Kaminaga, an associate professor of the Department of Electrical and Computer Engineering in Tohoku Gakuin University, confessed that he had been convinced that "relaxed education is a foolish reform that teaches pi as 3." And he said, "I usually said, 'Go and do your own research until you are satisfied,' but if teachers are like this, it must be a problem before educational reform."{{Sfn|神永正博|2008|pp=19-20}}

Other issues with treating pi as approximately 3 that were discussed, included "pi is an irrational number, so it is neither exactly 3 nor 3.14. Thus, while the former and the latter are essentially equivalent in learning the procedure, there is a clear difference in approximate accuracy,"{{R|藤原2005}} "if pi is calculated as 3, the perimeter is the same for the circle and the regular hexagon inscribed in it,"{{R|藤原2005}} and "for the circumference of a circle with a diameter of 10 cm, the error would be 1.4 cm"{{Sfn|大西俊弘|2002|p=26}} were point out.

It also points out the danger of adding ".14" in vain in terms of significant figures.{{Sfn|木村寛治|2004|p=138}}<ref>{{cite journal|author=熊谷正朗|journal=プラントエンジニア|title=身の回りに見つけるメカトロ雑学 ―「円周率は3」と有効数字―|year=2013|pages=74–75|url=http://id.nii.ac.jp/1204/00000187/|volume=45|trans-title=Mechatronics Trivia Found Around You ― “Pi is 3” and Significant Digits ―}}</ref>

=== The public === The misunderstanding that "they teach pi as 3 in elementary school" was seen in weekly{{R|週刊新潮2001|週刊文春2000|週刊朝日2001}} and monthly{{R|細野2001|プレジデント2002}} magazines as well. This has resulted in a distrust of public school education.{{Sfn|朝日新聞|2012}}

In Nisio Isin's novel Zaregoto, a scene appeared in which the truncated decimal point is introduced as "the tragedy of 0.14".<ref name="kubiki">{{Cite book |author=NISIOISIN|title=Decapitation Kubikiri Cycle |publisher=Kodansha USA |year=2017|isbn=9781945054211}}</ref>

On one TV program, five comedians presented a skit in which they used "Pi is OK at 3" as a key line.{{R|朝日20120408}}

The theme song of "Yutori-chan," an animation about Japan's "Yutori" generation, includes the lyrics "3.1415 pi is approximately 3."<ref>{{Cite web |author=yozuca* |url=https://j-lyric.net/artist/a053b0a/l0202d2.html |title=「ゆとりのゆとり」歌詞 |accessdate=2023-07-02|trans-title=“Leisure Within Leisure” Lyrics}}</ref>

The misunderstanding of teaching pi as 3 was also introduced by Akira Ikegami in a 2013 TV program.{{Sfn|池上彰|2013}}

=== University entrance examination questions === In 2003, in the sixth question of the first semester of science at the University of Tokyo, a question asking "Prove that pi is greater than 3.05" was included and it became famous as a question with a message opposing the government's stance of teaching pi as 3.<ref>{{Cite book |author=早田幸政|title=国立大学法人化の衝撃と私大の挑戦 |publisher=エイデル研究所 |year=2007|page=249|isbn=9784871683845|trans-title=The Impact of National University Corporation Reform and the Challenges Facing Private Universities}}</ref>

;Example of a solution To solve this problem, to prove that the perimeter of the regular dodecagon inscribed in the circle of diameter 1 is greater than 3.05.<ref>{{Cite web |author=原圭助 |date=2023-06-13 |url=https://toshin-wasedaschool.com/suizenji/9751/ |title=旧帝大の魅力その２２～円周率が3.05より大きいことを証明せよ |accessdate=2023-07-02|trans-title=The Charm of the Former Imperial Universities #22: Prove that Pi is greater than 3.05}}</ref>

:First, consider a circle {{Math|C}} of diameter {{Math|1}} and a regular dodecagon inscribed in circle {{Math|C}}. Since the length of the circumference of a circle of radius {{Mvar|r}} is {{Math|2{{Pi}}''r''}}, the length of the circumference {{Mvar|l}} of circle {{Math|C}} whose radius {{Math|1/2}} is ::<math>l=2\pi \cdot \frac{1}{2}=\pi</math>.

:Also, if the perimeter of the regular dodecagon inscribed in circle {{Math|C}} is defined as {{Mvar|L}}, ::<math>L=12 \sin 15^{\circ} =12\sqrt{\frac{1- \cos {30^{\circ}} }{2}}=6\sqrt{2-\sqrt{3}}</math> ::<math>L^2=36\left(2-\sqrt{3}\right)>36(2-1.74)=9.36>9.3025=3.05^2</math>.

:Thus, the circumference {{Mvar|L}} of a regular dodecagon are greater than 3.05. Then ::<math>\pi=l >L>3.05</math> ::<math>\pi>3.05</math>.

==See also== * Indiana pi bill * Yutori education * Curriculum guideline (Japan) * Approximations of π

==References== {{Reflist|2|refs= <ref name="原田2003">{{cite journal|author=原田昭治|journal=工学教育|title=大学が目指す及び企業が求める技術者教育地殻変動する教育環境と今後の産学連携|trans-title=Engineers universities aim to cultivate and companies seek. Educational landscape shifting amid evolving educational environments and future industry-academia collaboration.|year=2003|pages=9–17|volume=51|issue=3 |doi=10.4307/jsee.51.3_9 |doi-access=free}}</ref> <ref name="曽我2001">{{cite journal|author=曽我昇平|url=https://ci.nii.ac.jp/naid/40004890952|journal=数学セミナー|title=円周率「3」の子どもたち|trans-title=Children of Pi “3”|volume=40|year=2001|pages=23}}</ref> <ref name="山下2001">{{cite journal|author=山下純一|url=https://iss.ndl.go.jp/books/R000000004-I5799863-00|journal=理系への数学|title=入試問題からの旅立ち/円周率は「およそ3」|trans-title=Departure from Entrance Exam Questions / Pi is “Approximately 3”|year=2001|volume=7 |pages=81–85}}</ref> <ref name="本田2002">{{cite journal|author=本田由紀|journal=教育社会学研究|title=90年代におけるカリキュラムと学力|trans-title=Curriculum and Academic Achievement in the 1990s|year=2002|pages=105–123|volume=70|doi=10.11151/eds1951.70.105 |doi-access=free}}</ref> <ref name="藤原2005">{{Cite book |author=藤原正彦|title=祖国とは国語 |trans-title=Motherland is the national language|publisher=新潮社 |year=2005|pages=55–56|isbn=9784101248080}}</ref> <ref name="週刊新潮2001">「[https://ci.nii.ac.jp/naid/40001694884 円周率はちゃんと「3.14」と教えろ]」、『週刊新潮』第46巻第16号、2001年4月、48-49頁。</ref> <ref name="週刊文春2000">「[https://ci.nii.ac.jp/naid/40001711022 新学習指導要領で 「円周率は3」「必須英単語は100個」日本の生徒がバカになる!?]」、『週刊文春』第42巻第9号、2000年3月、35-37頁。</ref> <ref name="週刊朝日2001">{{cite journal|author=|journal=週刊朝日|title=それでも聞きたい「円周率」はやっぱり「3」で教える?|url=https://ci.nii.ac.jp/naid/40001687037|year=2001|pages=182–183|volume=106}}</ref> <ref name="細野2001">細野真宏「[https://ci.nii.ac.jp/naid/40003428389 「円周率3」時代の勉強法]」(Study Methods for the “Pi Equals 3” Era)、『Bungeishunjū』vol. 79(3), Mar. 2001, pp. 156-160</ref> <ref name="プレジデント2002">{{cite journal|journal=プレジデント|title=緊急特集 円周率=3の教育システムは、吉と出るか凶と出るか 「ゆとり教育」開始!わが子はどうなる|trans-title=Emergency Special Feature: Will the “Pi=3” Education System Bring Good Fortune or Misfortune? “Relaxed Education” Begins! What Will Happen to My Child?|date=2002-04-15|pages=133–142}}</ref> <ref name="朝日20120408">“[http://www.asahi.com/national/intro/TKY201204070228.html ミスターゆとり教育の反論 元文部官僚・寺脇研さん]”. ''朝日新聞デジタル'' (2012年4月8日). 2017年3月25日閲覧。</ref> <ref name="産経20080218">{{Cite news|url=http://sankei.jp.msn.com/life/education/080218/edc0802182202000-n1.htm |title=「総合学習」進化する塾 |newspaper=msn産経ニュース |archiveurl=https://web.archive.org/web/20080327203544/http://sankei.jp.msn.com/life/education/080218/edc0802182202000-n1.htm |archivedate=2008-03-27}}</ref> }} {{Go to top}}

*{{Cite book |title=朝日新聞縮刷版（2012年9月号） |section=「脱ゆとり」の真相：中〉円周率「3」の波紋 06 Sep. 2012 (The Truth Behind “Abandoning the ‘Yutori’ Education Policy”: Part 2 - The Ripples Caused by Pi Being “3”)|publisher=朝日新聞出版 |year=2012|page=33|asin=B00OABTKZ6|ref={{Sfnref|朝日新聞|2012}}}} * {{Cite web|url=https://datazoo.jp/w/%e5%86%86%e5%91%a8%e7%8e%87/14236359 |title=2013年4月4日放送 19:00-21:48 テレビ朝日 池上×マツコ ニュースな話 池上×マツコ 教育問題を考える |work=「円周率」に関するテレビ情報 |publisher=テレビでた蔵 |accessdate=2017-03-25 |trans-title=April 4, 2013 Broadcast 7:00 PM - 9:48 PM TV Asahi Ikegami × Matsuko: News Talk Ikegami × Matsuko: Considering Education Issues|ref={{SfnRef|池上彰|2013}} }} * {{Cite book|url=http://www.sbrain.co.jp/theme/T-30188.htm|author=伊藤敏雄|title=誰も教えてくれない教育のホントがよくわかる本 -ゆとり教育になって学校はどうなった?-|publisher=文芸社|year=2006|isbn=978-4286009544|trans-title=The Book That Clearly Explains the Truth About Education Nobody Tells You - What Happened to Schools After the Relaxed Education Policy?}} * {{Cite journal|url=http://www.math.ryukoku.ac.jp/~t-onishi/sj231422.pdf|title=「学力低下」問題と新学習指導要領|author=大西俊弘|journal=Sigma Journal|number=23|publisher=文英堂|date=2002|pages=14–22|trans-title=The Issue of “Declining Academic Performance” and the New Curriculum Guidelines}} * {{Cite book|author=神永正博|title=学力低下は錯覚である|publisher=森北出版|year=2008|isbn=978-4-627-97511-8|trans-title=The decline in academic ability is an illusion.}} * {{Cite journal|title=小学校算数教科書から3.14は消えたか|author=木村寛治|journal=工学教育|volume=52|number=1|year=2004|pages=138–139|trans-title=Has 3.14 Disappeared from Elementary School Math Textbooks?}} * {{Cite book|url=http://www.iwanami.co.jp/.BOOKS/02/5/0255520.html|title=理科・数学教育の危機と再生|editor=左巻健男、苅谷剛彦|year=2001|publisher=岩波書店|isbn=4-00-025552-5|chapter=算数，数学の教育の時間と内容はこれだけでいいのか|author=黒木哲徳|pages=20–30|trans-title=The Crisis and Revival of Science and Mathematics Education}} * {{Cite book|url=https://www.iwanami.co.jp/.BOOKS/00/8/0092130.html|title=算数があぶない|series=岩波ブックレット|author=関沢正躬|year=2000|publisher=岩波書店|isbn=978-4000092135|trans-title=Math is getting shaky.}} * {{Cite book|title=小学校学習指導要領 第4版―平成20年3月告示|trans-title=Elementary School Curriculum Guidelines, 4th Edition—Announced in March 2008|author=文部科学省|authorlink=文部科学省|publisher=東京書籍|year=2009|isbn=978-4487286959|ref={{SfnRef|学習指導要領|2009}} }} * {{Cite book|title=小学校学習指導要領解説 算数編|trans-title=Explanation of the Elementary School Curriculum Guidelines: Mathematics|author=文部省|authorlink=文部省|publisher=東洋館出版社|year=1999|isbn=978-4491015507|ref={{SfnRef|学習指導要領|1999}} }}

Category:Pi Category:Education in Japan Category:Misconceptions Category:2002 in education Category:3 (number)