8. The Parrot's TheoremUse this thread to discuss The Parrot's Theorem by Denis Guedj.http://www.scientix.eu/cs_CZ/c/message_boards/find_category?p_l_id=&mbCategoryId=6011092019-08-25T07:24:11Z2019-08-25T07:24:11ZRE: Share your classroom ideas hereNatalija Budinskihttp://www.scientix.eu/cs_CZ/c/message_boards/find_message?p_l_id=&messageId=6053372017-04-30T20:15:53Z2017-04-30T20:15:53ZMy name is Natalija Budinski, and I am a math teacher in Primary and secondary school "Petro Kuzmjak" in Ruski Krstur in Serbia. I have become a Scientix ambassador in March 2017. In my opinion STEM is the future of education and I am giving my best to implement it as much as possible to my classes. Also, I am sharing my ideas with colleagues on my blog www.math4all4math.blogspot.com. There is one of the example how could Denis Guedj's book "Parrot Theorem" be applied in math classes in order to teach students the fundaments of mathematics, and open new frontiers to them, as well.<br />There is no doubt that Pythagoras and Euclid are two important figures of both, ancient and contemporary mathematics. The book describes many interesting facts about their lives, but also reveals that their teaching was approach similar to STEM principles. In the chapter dedicated to the Pythagoras, students can learn about the connection between fractions and music, or area and space object called lunule. <br />The main topic that I would teach my students following the book chapters would be irrational numbers. This real numbers troubled Pythagoras and during his time it was an unexplored topic. Besides the fact that the hypotenuse of right isosceles triangle is represented with square root of two, not much was known. The book describes the proof of the fact that the square root is an irrational number in the form of dialog, which is easy to follow and useful in the today classroom.<br />As the story in book develops, Euclid "tamed" irrational numbers. The Euclid's comprehensive work assembled in thirteen books called "Elements" is still relevant. Basics of Euclid's geometry are part of mathematical curriculums worldwide. Among many concepts that Elements elaborate, they provide the explanation how to find the square root of a number. Even though, Elements are rich well of mathematical concepts, they fail in solving problems such as doubling the cube or trisection of an angle.<br />Mr Ruche noted in the book: "Consider later three major problems of Greek mathematics, squaring the circle, doubling the cube and angle trisection". And later on, at the end of the book, mr Ruche officially announced that those problems are not solvable with compass and straightedge. That can lead lesson to the process of examining Euclidian geometry limitation.<br />Inspired by the book, I would tackle students with a question if the doubling the cube or trisection of an angle are really unsolvable? Or maybe there are solutions of three famous problems? The story developed in the book would be an excellent introduction to the contemporary mathematical research which provides the solution for mentioned unsolvable problems. What is more the solutions are elegant and can be followed with the high school- mathematical knowledge. They rely on origami techniques and paper folding. At the end of 20th century, origami was axiomatized which made him a mathematical discipline. What is more, origami axioms and theorems provided the solutions for problems of doubling the cube and angle trisection. That means that construction of third root of two became possible with origami.<br />On the one hand, Euclid's quotation in the book that "There are not royal road to mathematics", reminds us how sometimes mathematics can be hard, but on the other hand, there are interesting ways to explore mathematics. The "Parrot's theorem" led as through history of mathematics, but also opens the door for new enquires which can provide us with interesting lessons based on contemporary mathematical discoveries. Natalija Budinski2017-04-30T20:15:53ZRE: Share your classroom ideas hereRobert Baldurssonhttp://www.scientix.eu/cs_CZ/c/message_boards/find_message?p_l_id=&messageId=6051072017-04-30T16:02:08Z2017-04-30T16:02:08ZThank you for sharing Konstantinos <img alt="emoticon" src="http://www.scientix.eu/scientix-theme/images/emoticons/happy.gif" >Robert Baldursson2017-04-30T16:02:08ZRE: Share your classroom ideas hereKonstantinos Manolakishttp://www.scientix.eu/cs_CZ/c/message_boards/find_message?p_l_id=&messageId=6047902017-04-29T16:39:23Z2017-04-29T16:10:51Z<span style="font-size: 16px"></span><span style="font-size: 16px"><span style="font-family: Cambria">Greetings! My name is Konstantinos Manolakis, I am a newly recruited Scientix Ambassador (since March 2017). I am also a teacher and the director at a primary school in Chania, Crete. As I was reading the Parrot’s Theorem, I tried to think up ways of how this book could have pedagogical use as a whole. Additionally, I wanted the whole of the educational community (students, teachers, parents) to become involved in this process, in this way suggesting an alternative approach to the science of Mathematics. In primary school, Math is taught by conveying concepts such as those of numbers, calculations (algorithms), problem solving, geometric issues, etc. as well as any symbols or mental tools we utilize, all these are readily accepted as a fact, “sent from heaven”; we rarely concern ourselves or investigate the origin of their use. We very often ignore the fact that behind these ideas are people who initially introduced them to the field of Mathematics. The editor of the Greek translation of the book, Tefkros Michaelides, very aptly points out: <em>“… the history of mathematics is an inspiration of ideas, problems, devises. It is, however, most importantly a story about people. Enlightened individuals, who through the mist, were able to distinguish the opposite bank and slowly find the passage that led them there” (pg. 709).</em>Moreover, at some point, a heroine of the novel, Lea, surprised by the absence of the equals symbol before 1557, wonders: <em>“Someone was forced to die on the other side of the world when trying to uncover and ascertain where this symbol originated. Why has nobody ever told us these things in the classroom?”</em></span><span style="font-family: Cambria"> </span><span style="font-family: Cambria">Based on all of this, my personal idea is to try and include the history of mathematics in a collaborative project that will run throughout the school year and involve all the grades of the primary school. </span><span style="font-family: Cambria">Amelion- Mamagena, the Amazonian parrot, can become the mascot that will inspire the children, teachers, parents and anyone else who is interested in creating the historical line of mathematics, by exhibiting and bring forward the people who were behind the ideas and symbols. This historical line will be a specially shaped belt that will run through the corridors of the school and will begin from ancient times- all the way to our era. Each class, depending on the chosen subject they will assume, will look into and try to solve a riddle (through some research) within Denis Geudj’s book. </span><span style="font-family: Cambria">For example: Why are fractions considered broken figures? </span><span style="font-family: Cambria"><em>“Al-Khwarizmi accepts only positive, inertial (whole) or fractional numbers. This is where the word ‘fractions’ was coined. The Latin word fractiones is the translation of the Arabic kasser, do you know what kasser means? It means broken! Thus, fractions are broken numbers!” </em></span><span style="font-family: Cambria">(pg. 309) So, with fractions as a triggering topic the historical line will be enriched with the Arabic contribution to the propagation and development of mathematics. Another example is through teaching the maximum common divisor/ highest common factor: Which numbers are friendly according to Pythagoras? </span><span style="font-family: Cambria"><em>“When he was asked what a friend is, he answered “he who is your other self, such as the numbers 220 and 284”. Two numbers are “friends” or “friendly with each other” when the sum of the numbers that divide the one number equal the sum of the second number (therefore divide)</em></span><span style="font-family: Cambria">.” </span><span style="font-family: Cambria">And so on the occasion of the divisors the reference to Pythagoras will offer new learning possibilities. </span><span style="font-family: Cambria">Depending on the age and the potential of the students, the historical line will have its own dynamic. The young students will create the mascot of the project, the parrot who “knows” math and therefore, the students will be given the opportunity to understand the difference between “holding” knowledge and merely “parroting” that knowledge. The older students will partake in researching and enriching the historical line. Teachers will guide and motivate the students by providing stimuli for exploratory- research learning. Parents will also be able to contribute according to their interests as guests in projects or presentations while working with their children. Finally, the result will be multimodal (text, images, and symbols) collective work and there will be a personal touch from all the participants. It will unite the lessons of mathematics, history and literature! </span><span style="font-family: Cambria">It would also be highly beneficial to collaborate with other schools, even with older children in high schools and lyceums, through the digital advancement of the historical line. Tools that would be helpful in this endeavor are (thehistoryproject.com, timeglider.com, padlet.com etc.) </span><br /><span style="font-family: Cambria">References: </span><span style="font-family: Cambria">Guedj, D. (2010), </span><span style="font-family: Cambria"><em>The Parrot’s Theorem</em></span><span style="font-family: Cambria">, Kedros (greek edition)</span><br /><a href="http://www.kidsmathgamesonline.com/facts/history.html"><span style="color: #1155cc"><span style="font-family: Cambria">http://www.kidsmathgamesonline.com/facts/history.html</span></span></a><a href="http://www.storyofmathematics.com/"><span style="color: #1155cc"><span style="font-family: Cambria">http://www.storyofmathematics.com/</span></span></a><a href="http://www-history.mcs.st-and.ac.uk/Chronology/full.html"><span style="color: #1155cc"><span style="font-family: Cambria">http://www-history.mcs.st-and.ac.uk/Chronology/full.html</span></span></a></span>Konstantinos Manolakis2017-04-29T16:10:51ZRE: Share your classroom ideas hereRobert Baldurssonhttp://www.scientix.eu/cs_CZ/c/message_boards/find_message?p_l_id=&messageId=6032212017-04-27T10:10:52Z2017-04-27T10:10:52ZPanagiota, thank you so much for sharing your geometry lesson and materials with us. Very cool how you managed to integrate it with the Thales chapter of the Parrot's Theorem <img alt="emoticon" src="http://www.scientix.eu/scientix-theme/images/emoticons/happy.gif" ><br />In the past we had books for the lessons, which was portrayed by the regular book discussions in the Parrot's Theorem, but you also show how technology can nowadays enhance learning experience what used to be more limited in the past.Robert Baldursson2017-04-27T10:10:52ZRE: Share your classroom ideas herePanagiota Argyrihttp://www.scientix.eu/cs_CZ/c/message_boards/find_message?p_l_id=&messageId=6026682017-04-25T22:37:38Z2017-04-25T22:31:10ZMy name is Panagiota Argyri, I am mathematician to Model High School Evangeliki of Smyrni <br />(Athens , Greece). I am Scientix ambassador from 2014. I am exciting with this discussion forum. I love challenges based on science literature. <br />Chapter 3 : Dedicated to Thales.<br />Playing with shadows for calculate the height of pyramid of Cheops.<br /><u>Mathematical and Geometrical concepts based on Chapter 3 for teaching Geometry : <br /></u>Theorem of Thale for parallels lines, similarity of triangles and polygons, equal rates <br />for analogy ammounts. <br />An iquiry lesson plan based on chapter 3 :<br /><a href="https://www.slideshare.net/PanagiotaArgiri/thales-75406760">https://www.slideshare.net/PanagiotaArgiri/thales-75406760<br /><br /></a>Using mathematical software Geogebra for activities and exercises based on Chapter 3 Parrot's Theorem <br /><br /><a href="https://ggbm.at/EhPe2t6N">https://ggbm.at/EhPe2t6N<br /><br /></a><a href="https://ggbm.at/n2QWdStV">https://ggbm.at/n2QWdStV<br /></a><br /><a href="https://ggbm.at/y4SerXBN">https://ggbm.at/y4SerXBN</a><br /><br /><a href="https://ggbm.at/zhtXCzjr">https://ggbm.at/zhtXCzjr</a><br /><br />Video reviewing chapter 3 :<br /><a href="https://youtu.be/0P1Nc1t8vWg">https://youtu.be/0P1Nc1t8vWg</a><br /><br />(Note : Not only Thales..but also..Eratoshenes playied with shadows for calculate the cirtumance of Earth)Panagiota Argyri2017-04-25T22:31:10ZShare your classroom ideas hereRobert Baldurssonhttp://www.scientix.eu/cs_CZ/c/message_boards/find_message?p_l_id=&messageId=6011682017-04-23T07:01:27Z2017-04-23T07:01:27ZUse this thread to share your classroom ideas inspired by the Parrot's Theorem by <span style="font-size: 16px">Denis Guedj. Looking forward to hearing your ideas!<br /><img src="http://www.scientix.eu/documents/10137/595389/Parrot%27s+Theroem.jpg/f443ff28-6a16-45a6-bf26-edf8db724c32?t=1491206213000" style="height: 300px; width: 200px;" /></span>Robert Baldursson2017-04-23T07:01:27Z