PRESCHOOL, AGE 3 TO 5
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Early Years Foundation Stage
The University of Cambridge
http://nrich.maths.org/early-years
The 'Early Years Foundation Stage', for children age 3 to 5, is a project that is "an innovative collaboration between the Faculties of Mathematics and Education at the University of Cambridge which focuses on problem-solving and on creating opportunities for students to learn mathematics through exploration and discussion."
Baskets
https://nrich.maths.org/content/id/9716/Baskets%202020.pdf
OR https://nrich.maths.org/9716
Counting reliably. Solving problems, including doubling, halving and sharing. Using everyday language to talk about size, capacity, position and distance.
The Activity
Place some baskets (probably 3 to 8) in the middle of a suitable space along with the objects which should be near to, but not in, the baskets.
The Mathematical Journey
Properties of shapes:
• choosing particular baskets for particular objects having analysed the properties of the shapes involved
Position and spatial properties:
• using positional language, for example: on top of, next to, underneath, in front of, behind, between, left, right, etc., to describe the items in the baskets and the positions of the baskets themselves
Number:
• counting and cardinality – progressing from knowing some number words, to saying one number for each object, then knowing the number of the whole group
"Children's Basket-Making Class, Upper Arlington, Ohio, 1918."
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3RD - 5TH GRADE
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Math in Basketry: Basketry Kit
Grade Level: Upper Elementary: Third Grade through Fifth Grade
Subject: Math, Social Studies
https://www.nps.gov/teachers/classrooms/basketry-kit.htm
A kit for making and studying baskets.
This kit blends culture with math. Students learn the mathematical properties of shapes, patterns, angles, and symmetry used in Tlingit basketry [ED: Native American Indian]. Kit includes basket, weaving books, and references for borrowing museum items for school use.
National School of Wickerwork and Basketry of Fayl-Billot, making large baskets, 1910.
__________________________________4TH GRADE
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Math In A Basket
In-School 4th Grade
https://dramaticresults.org/our_program/math-in-a-basket/
Students integrate math, social studies, and the arts when learning to make reed baskets from scratch. This unique program meets Common Core Content Standards for both Visual Art and Mathematics. By finding the surface area, perimeter, and volume of their baskets students practice measurement. Furthermore, the process of planning, designing, and creating helps students become familiar with engineering concepts. Rudiments of algebra and geometry are integrated into Math in a Basket curriculum.
Student Impact:
The latest evaluation results show that over 3 years, the program:
Improved math and art skills for nearly 900 students.
Increased teachers’ abilities to integrate the arts in class.
Benefitted social-emotional learning for students and teachers.
"Basket makers, Industrial School, Baguio, Philippines, 1911."
https://commons.wikimedia.org/wiki/File:Basket_makers,_Industrial_School,_Baguio,_P.I_(NYPL_Hades-2359625-4044390).tiff
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6TH GRADE
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Building Baskets, Benchmark Style
https://www.benchmarkschool.org/news/news/news-detail/~board/news/post/building-baskets-benchmark-style
Consider what you might need to survive in a hunter-gatherer society. What tools would you need, and how would you get them?
Nicole Scali asked her students to create functional hunter-gatherer baskets using only glue, 80 strips of paper, brushes, and a plan. Would their baskets hold up? The class intended to find out, holding a competition to see which baskets could carry the most weight for the longest time.
Prior to beginning construction, the class brainstormed. What obstacles might they encounter? They considered that the paper might rip, they might run out of paper, and they might be stymied by not having an example to follow.
Next came planning. Working in teams of two, students sketched their designs. When construction began...it became clear that no two basket designs were alike. Some teams made woven designs, some layered, and some used twisted paper.
When the baskets were completed and the day for testing arrived, they...ran into a problem they hadn’t anticipated: what to do with baskets that broke in some way prior to testing? Falling back on hunter-gatherer methods, Nicole allowed the students whose baskets needed fixing to go out into the playground and use objects found in nature, including bark and stems from leaves, to make repairs.
Nicole... says, “I was very impressed with how creative the kids were, both in their designs and in their flexibility. They did a great job and were pleased with the outcome.”
Basket weaving with the Sisters; Karlshof nursing home, Germany.
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5TH - 12TH GRADE
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Math for Real: Weaving Mathematical Concepts
Grades 5 - 12
Funding provided by the Canadian federal government
https://theconversation.com/indigenous-basket-weaving-makes-an-excellent-digital-math-lesson-110094
Indigenous Basket-Weaving Makes An Excellent Digital Math Lesson
By Veselin Jungic, Professor, Simon Fraser University
The Tla’amin baskets are examples of functional mathematics and art. Baskets of all shapes and sizes are built with the purpose of packing food, storing goods or even as baby cribs. Building a basket is a small bio-engineering project that requires mathematical thinking and math-related skills. These skills include precise measurement, the creation of appropriate shapes, and adhering to certain well-established patterns.
Digital classroom learning
Callysto is a multimodal learning platform available to grades 5-12 students across Canada at no charge. It was launched in fall 2017 by the Pacific Institute for Mathematical Sciences (PIMS) and Cybera, an Alberta-based digital infrastructure non-profit organization. The Callysto program lists as its main goal “help[ing] young learners complete high school with the fundamental skills — computational and design thinking — required to be able to tackle any challenge they might face.” The funding was provided by the Canadian federal government through the CanCode program.
"Country School- Everyday Life at Baldock County Council School, Baldock, Hertfordshire, England, UK, 1944."
"Classes, Department of the Interior, Bureau of Indian Affairs, Pierre Agency, (1954 - 1972)."
"Illustration from 1911 Encyclopædia Britannica, article BASKET."
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AN INSTRUCTION BOOK
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The Basket Maker
Author: Turner, Luther Weston.
Worchester, Mass.: The Davis Press, 1909.
https://archive.org/details/basketmaker00turniala
"A pupil should not be allowed to progress who cannot make the bottom of a basket and have it strong and closely woven. He must understand that no basket can be firmly made unless its foundation is right."
"But the expression of thought through basketry requires almost no tools (a knife and scratch-awl), has variety as to form and color and almost unlimited possibilities in design."
(RIGHT) "Wicker basket starting."
The geometry of melon-shaped baskets.
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LEARNING WITHOUT A LANGUAGE OR WORDS
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Learning And Teaching Via Imitation
According to an article in the Evolution of Culture [2], very few animals possess the ability to learn via imitation. But the genus Homo was/is one of them. Susan Blackmore of the Department of Psychology, University of the West of England, Bristol, United Kingdom wrote the following:
"The first obvious signs of imitation are the stone tools made by Homo habilis about 2.5 million years ago, although their form did not change very much for another million years. It seems likely that less durable tools were made before then, possibly carrying baskets, slings, wooden tools and so on." [3]
"What was it these early stone-knappers knew that chimpanzees can't get? I think one thing was that early hominids were much better at copying motor procedures — we can watch an individual perform a motor task and mimic it. Chimpanzees are terrible at that — they see a task and have to reinvent the wheel. This gets back to mirror neurons and the copying of behavior."
Quotation from paleoanthropologist Thomas Wynn of the University of Colorado at Colorado Springs in an article by Charles Choi. entitled "Human Evolution: The Origin of Tool Use." [4]
So my final example of teaching comes from a study of the lives of the African Aka hunter-gatherer women by Bonnie Hewlett [5]:
Bonnie Hewlett asked women to teach her how to be an Aka woman. In order to show her how to make a basket, a woman sat next to her, touching her and never left her side. The woman started the basket, ripped it apart, then asked her to try it on her own. As she tried to weave, some Aka laughed and commented; after a short time, a 12-year-old girl came over, sat next to her in the same way as the adult woman, demonstrated again how to do it, and then handed it back for her to try. Hewlett was not weaving correctly so the girl took her hand and helped her weave the twine. The mother and the 12-year-old spent three weeks, hours at a time, sitting right next to Hewlett until she completed the small children’s basket. Both the Aka mother and young girl had pedagogic skills, knew how to use demonstration, pointing, feedback, and scaffolding.
(LEFT) Germany, 1860.
https://commons.wikimedia.org/wiki/File:Die_Gartenlaube_(1860)_b_429_3.jpg
(RIGHT) "Basketweaving at Fort Ross State Historic Park, Jenner, California."
https://commons.wikimedia.org/wiki/File:Basketweaving_at_Fort_Ross_State_Historic_Park_-_Jenner,_California_-_Stierch_1.jpg
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TEACHERS, COMBAT SOLDIER REHAB & BLIND WORKERS
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"Public Instruction Activities at the Teachers' Training College, Art Section, Basket Work Class, Brisbane City, Australia, April 1951."
https://commons.wikimedia.org/wiki/File:Queensland_State_Archives_1624_Public_Instruction_Activities_at_the_Teachers_Training_College_Art_Section_Basket_Work_Class_April_1951.png
(LEFT) "Reconstruction: occupational therapy, Walter Reed General Hospital, Washington, D.C., World War I."
(RIGHT) "The War on War Nerves- Rehabilitation at Mill Hill Hospital, England, 1942."
"Blind Basket-makers," 19th century.
https://commons.wikimedia.org/wiki/File:Blind_Basket-makers_Wellcome_L0000904.jpg
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ESSAY ON ZULU BASKET MAKING:
AN EXPLANATION OF THE COGNITIVE ASPECTS OF TRADITIONAL BASKET-WEAVING
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Juxtaposing Form, Function, and Social Symbolism:
An Ethnomathematical Analysis of Indigenous Technologies in the Zulu Culture
Project: Ethnomathematics and Indigenous Knowledge Systems
https://www.researchgate.net/publication/316089427_Juxtaposing_Form_Function_and_Social_Symbolism_An_Ethnomathematical_Analysis_of_Indigenous_Technologies_in_the_Zulu_Culture
"Zulu basket with cover."
The following is quoted from the above website.
"For the Zulu culture, basketry technology requires thinking in terms of form, functionality, and the process of handling the vegetal materials. The materials, which are confined to the local vegetation of the Zululand, determine the kind of construction and consequently influence the shape of the baskets.
"In response to the delicate nature of the elements, the process of bending and folding gently but firmly follows a methodical configuration that adheres to certain specifications in the dimensions of the piece, to the flexibility of the design, and to the strength of the structure. The basket is composed of systematically repeated modular units or repeated sequences of units.
"The basket begins its existence as a flat surface and progressively takes a three dimensional shape, a kind of hemisphere in many variations. To get the desired dimensions, the basket maker resorts to successive subtractions, reducing the size of the materials used without interrupting the iterative patterns and the structural organization of the elements.
"Measuring, counting, timing, devising and structuring patterns, bending and folding according to afforded dimensions, and decision making are all examples of activity-situated ethnomathematical ideas.
"We contend hitherto that such technologies embody indigenous knowledges and skills that are methodically systematized yet ORALLY-BASED [ED: my emphasis]."
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COGNITIVE DEVELOPMENT AND BASKET-WEAVING
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Just how could basketry have affected thought and culture? We can point to one specific example in the early days of human civilizations.
Basket-weaving was central to the first civilization of Sumer. And without it, this first civilization could not have functioned -- as it needed baskets for agricultural work and for the transporting, distributing, and storing of crops. In addition, basket-weaving was used for a variety of items from reed mats to fences, grass houses, and large reed boats.
In the Elementary Sumerian Glossary [6], a basket weaver is defined as:" a reed craftsman, basket, and mat weaver." In this same glossary, there are 19 words relating to basketry and reed craftsmanship showing how important and pervasive it was within Sumerian society.
Moreover, basket-weaving was a highly revered skill. In a Sumerian creation myth the principal god, Enlil, declared that "the pickax and the basket build cities." [7] The 'craft of basket-weaving' was specifically mentioned in the about 100 MEs of Sumer, a list of the most important values, beliefs, and skills of Sumerian culture. [8]
In Africa, the Dogons equated a basket with the sky.
"The Dogon of West Africa tell how their first ancestor received a square-bottomed basket with a round mouth like those still used there in the 20th century. This basket, upended, served him as a model on which to erect a world system with a circular base representing the sun and a square terrace representing the sky."
Dogon basket.
https://commons.wikimedia.org/wiki/File:ASC_Leiden_-_W.E.A._van_Beek_Collection_-_Dogon_daily_life_03_-_Jauire_takes_the_millet_from_the_granary_for_the_daily_meal._In_principle,_only_men_can_get_millet_from_the_granary,_Tireli,_Mali_1980.jpg
"The Babylonian god Marduk “plaited [wove] a wicker hurdle [mat] on the surface of the waters. He created dust and spread it on the hurdle.” Thus ancient Mesopotamian myth describes the creation of the Earth using a reed mat."
"Neolithic reed mat, Hemudu Culture, Zhejiang, China."
https://commons.wikimedia.org/wiki/File:Neolithic_reed_mat,_Hemudu_Culture,_Zhejiang,_1974.jpg
Furthermore, the basket was so important the king was required to perform a basket-bearing ceremony [9] when a new religious temple, called a ziggurat, was to be constructed. He carried the basket on his head during a ceremony to dedicate the start of construction and then later metal figures of the king with a basket on his head, known as foundation pegs, were buried at key points during the construction of the building. [10] The ziggurat was a high temple made of bricks that was designed to bring religious clerics nearer to the sky so they could be closer to the gods in the heavens.
"Partially reconstructed facade and access staircase of the Ziggurat of Ur, originally built by Ur-Nammu, circa 2100 BCE."
(LEFT) King "Ashurbanipal as High Priest."
(RIGHT) "Computer reconstruction of the Zugurat of Ur-Nammu, currently located on the outskirts of Nasiriyah and built at the beginning of the 21st century BC."
"Foundation Figure in the form of a peg surmounted by the bust of King Ur-Namma, Neo-Sumerian, Ur III period, reign of Ur-Namma, c. 2112–2094 BCE."
https://commons.wikimedia.org/wiki/File:Foundation_figure_of_Ur-Namma_holding_a_basket_MET_DP375097.jpg
And because of the Sumerian familiarity with basketry, it is highly likely that it became a model for mapping out the night sky.
But how did this map of the stars and planets specifically relate to basket weaving?
Generally speaking, a basket is made up of two parts: vertical spokes and the horizontal weaver. This forms a regular grid that defines a space that can be expressed in mathematical terms. Basketry was so much a part of this culture it is likely that basket structure led to the Sumerian and then the later Babylonian concepts and maps of the stars and planets that were located by declination and right ascension which today can be thought of as latitude and longitude on the Earth projected into the sky.
"Markfelder Straße at the Canal Festival 2011 in Datteln" Germany.
The Babylonians developed a system to map out the stars in the sky based on a circular grid that was divided into 360 degrees. The sky was then further divided into hours, minutes, and seconds which both pinpointed the position of a star or a planet and also related to the movement and rotation of the heavens or the moving planets in the night sky. In other words, it added the element of time. In short, they had created a human model that defined space and time and that was so accurate and useful we still use it today.
"The Babylonian GU text arranges stars in 'strings' that lie along declination circles and thus measure right-ascensions or time intervals, and also employs the stars of the zenith, which are also separated by given right-ascensional differences."
Reading: Babylonia. LibreTexts [11]
This 360-degree circle of the stars is still how the night sky is understood in astronomy today. In this picture, you can also see the vertical and horizontal grid lines.
"Map of the night sky: star positions from the Bright Stars Catalog, 5th Edition. Rasterized." 2006.
So it is possible that the basket was a model for a mathematical spatial pattern that also included time.
Commenting on a new recent understanding of the precision of this Babylonian math, Alexander Jones, a historian at New York University, said it showed:
"a more abstract and profound conception of a geometrical object in which one dimension represents time, It's much earlier than these concepts have ever been found before, he said, and "their presence … testifies to the revolutionary brilliance of the unknown Mesopotamian scholars who constructed Babylonian mathematical astronomy." [12]
As I said this system is still in use today and utilizes the same mathematical system such as 360 degrees divided into hours, minutes, and seconds. It defined a 'grid' not unlike today's Cartesian coordinate system which is essential to our modern way of life and, for example, forms the basis of computer graphs and modeling.
In fact, a recent study of the Babylonian system corresponded exactly with a calculation using modern graphing. Mathieu Ossendrijver, an astroarchaeologist at Humboldt University of Berlin who could also read ancient cuneiform Sumerian tablets, said in an interview with Space.com [12] that:
The process of measuring that geometric shape [ED: regarding the planet Jupiter as it was indicated on the Babylonian grid] was described on the Babylonian tablets. Although the tablets did not have any visible graphs, the calculations done matched this technique precisely.
Michael Lombardi, a metrologist in the Time and Frequency Division at the National Institute of Standards and Technology in Boulder, Colorado wrote the following for Scientific American:
Although it is no longer used for general computation, the sexagesimal system [ED: base 60] is still used to measure angles, geographic coordinates and time. In fact, both the circular face of a clock and the sphere of a globe owe their divisions to a 4,000-year-old numeric system of the Babylonians.[13]
CONCLUSION
I believe it is clear from this article, that basket-weaving would have been possible even with the limited brain capacity of Homo habilis or other early hominins. And it could have led to increased cognitive skills as basketry became more complex, the same dynamic that has been hypothesized for the evolution of stone tools, from Oldowan to Acheulean, for example. And these in turn may have led to an evolution that favored a larger brain which again appears to be the case with the development of stone tools.
Ancient Egyptian "Toy Basket with Contents, From Egypt, Upper Egypt, Thebes, Deir el-Bahri, Temple of Mentuhotep II, circa 712–525 B.C."
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AFTERWORD
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This is my 10th article about the possibility that basket-weaving could have been an early technology of hominins in the Lower Paleolithic era. My first article in September 2019 listed a number of reasons that this was likely. But now a year and a half later, I have explored many different aspects of this hypothesis which has made my case much stronger. For example, I have found evidence that hominins lived in close proximity to weaverbirds who made elaborate woven nests that could have been a model for early basket weaving. And I have examined the later discovery of right-angle construction which opened the door to an almost limitless number of well-made functional designs and constructions from small to large. I have also examined a number of assumptions that have turned out to be false, but which, in the past, have prevented research into the early existence of basketry in human cultures.
But now with this 10th article, I have in a sense, come full circle. Since this is a blog about the human experience of time, I believe that baskets and the process of making baskets may have been models for time itself. The steps for making a basket could have eventually become time metaphors, for example. And so I ended this article with an example of a space-time grid, the map of the sky, designed by the avid basket makers of Sumer and Babylon, which may have been based on basket construction.
Since time is invisible, cultures have needed metaphors to describe it, such as time is like a flowing river, or the past is behind us and the future ahead of us. Some physical constructs have also been useful such as the hourglass in which the sand at the top is the future, the sand that has fallen to the bottom is the past and the sand that is flowing from top to bottom is the present. The expression "the sands of time" comes from the hourglass.
Basketry could also have been a visible metaphor for time. This is because making the basket involved creating a regular grid that took a specific amount of time to construct. Furthermore, the construction and the time element could be further divided as each row took a specific amount of time. Therefore a basket might have been thought of as a physical visual representation of time and, moreover, it was a representation that would have been easily understood.
"Bamboo basket making."
https://commons.wikimedia.org/wiki/File:A_bamboo_basket_making.JPG
As I said almost ten years ago in the first post on this blog, an understanding of time was/is essential for human cognition. Without it we could not plan or build or develop -- and words about time are present in all languages. How we developed that sense of time, of past, present, future, and duration -- which only we have and which the animals do not have -- is one of the great achievements of humankind, and without it, civilization could not exist. The gradual human understanding of time and how it came about is one of the great mysteries and one whose importance has been virtually ignored.
Hourglass icon on the computer.
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FOOTNOTES
[1] Bahn, Dr. Paul. (2001). "Palaeolithic weaving – a contribution from Chauvet." Antiquity, 75:271-272.
[2] Blackmore, Susan. "The Origins of Imitation." The Evolution of Culture: Volume IV (The International Library of Essays on Evolutionary Thought), Stefan Linquist (Editor). No page numbers. Routledge, July 28, 2010.
[3] Blackmore, Susan. "Evolution and Memes: The Human Brain as a Selective Imitation Device." Cybernetics and Systems, Vol 32:1, 225-255, 2001,
[5] Boyette, Adam; Hewlett, Barry. "Teaching in Hunter-Gatherers." Washington State University. # Springer Science+Business Media Dordrecht 2017.
DOI 10.1007/s13164-017-0347-2.
BoyetteHewlett_teaching_in_HG_tYq6NC7.pdf
[6] Foxvog, Daniel A. Elementary Sumerian Glossary. University of California at Berkeley revised 2008. SumerianGlossaryFoxvog.pdf
[7] Kramer, Samuel Noah. Sumerian Mythology, Revised Edition. University of Pennsylvania Press, 1961, page 53.
[8] Kramer, 1961, p. 116.
[9] Porter, Barbara Nevling. Trees, Kings, and Politics Studies in Assyrian Iconography. Academic Press Fribourg Vandenhoeck & Ruprecht Göttingen, 2003, pp. 50-51. Porter_2003_Trees_Kings_and_Politics.pdf
[10] Foundation figures and foundation pegs are explained in this description of a particular one.
"Foundation Figurine Dedicated to Ninmarki." CDLI entry: P231800. Credit: Werwie, Katherine; image credit: Wagensonner, Klaus. Cuneiform Digital Library Initiative: A joint project of the University of California, Los Angeles, the University of Oxford, and the Max Planck Institute for the History of Science, Berlin.
[11] Reading: Babylonia. LibreTexts (Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot). Last updated Aug 8, 2020.
[12] Lewin, Sarah. "Ancient Astronomy: Babylonians Used Surprising Math Leap to Track Jupiter." New York, Future US, Inc., January 28, 2016.
[13] Lombardi, Michael. (Metrologist in the Time and Frequency Division at the National Institute of Standards and Technology in Boulder, Colorado.) "Why is a minute divided into 60 seconds, an hour into 60 minutes, yet there are only 24 hours in a day?" Scientific American. Scientificamerican.com, March 5, 2007. Accessed 2/13/2021.
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