Women and the Origin of Mathematics in Africa

8/13/2019 Women and the Origin of Mathematics in Africa

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African Women and the Origin ofMathematics

Lesson 1

Vocabulary Words: archeology, excavation, radiocarbon dating, lunar

The Ishango Bone

In the late 1950s , an archeologist from Belgium named Jean De Heinzelin conductedan archeological excavation in the Ishango District of Congo, Central Africa. De

Heinzelin found many interesting harpoon heads and a bone that captured his attentionimmediately because it contained groups of particular markings. This very interestingbone would become known as the Ishango Bone. Originally, De Heinzlin dated the bonevia a carbon-dating process to be 8500 BCE (Before the Common Era). However, laterdating with more sensitive radiocarbon instruments found that the Ishango Bone datesto 25,000 years old! It should be noted that since that time, a much older bone, withsimilar markings known as the Lembombo bone has been discovered in modern daySwaziland. It easily dates to 35,000 BCE. However, much more study has been doneon the Ishango Bone, so it remains the focus of this lesson

What is so fascinating about the Ishango Bone?The markings on the Ishango Bone were intentionally set in a mathematical pattern.When De Heinzlin did a close examination of the Ishango bone, he was relativelycertain that whoever made the bone was familiar with prime numbers, decimals andaddition by duplication. The Ishango Bone was studied by the Harvard Universityarcheologist, Alexander Marshack. Marshack did not believe that there was a high level


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Activity One

Geography Discuss the reading. Have students fill in the exact location of the LakeEdward/ Ishango District in Congo on the attached map (Appendix A).

Activity Two

Recall Have students answer the following questions:

1. What is the Ishango Bone?2. What is the significance of the bone?3. What is the possible role of women in the origin of mathematics?

Activity Three

Portfolio Creation of a Portfolio Submission. Gain access to the book In Praise ofBlack Women Volume 1: Ancient African Queens by Simone Schwarz-Bart. Based onthe book, students should choose one black woman from antiquity on which to create aone-page report. The report should highlight the black womans contribution to earlycivilization in Africa. The report should also include pictures of the woman. The picturesmay be hand drawn or they can be researched and copied from a book or onlinesource.

Activity Four

Science Students will learn what radiocarbon dating is by exploring the website athttp://www.kidspot.org/discover/creation/carbon4.html. Once students have gonethrough the definition a couple of times they should gather into groups of two or three.Each group should discuss what they understood by the definition given and theyshould submit the definition in their own words. It should not be longer than oneparagraph.

Activity Five

Science Students should visit the website

http://africa.si.edu/exhibits/cosmos/moon.html There they will learn about the Africanproverb which states, Without the Moon there is no life. After reading the information,students should share the ways that African people respect and celebrate the moon. Inorder to have students develop awareness of the moon, the entire class can be involvedin the creation of a moon calendar. Each day a student is assigned to observe the moonthat evening. The next day they will draw in on a blank calendar the exact formation ofthe moon as it appeared in the night sky. If there is no moon in the night sky, students
http://www.amazon.com/Simone-Schwarz-Bart/e/B001ITPKAW/ref=sr_ntt_srch_lnk_1?qid=1370284401&sr=8-1http://www.kidspot.org/discover/creation/carbon4.htmlhttp://www.kidspot.org/discover/creation/carbon4.htmlhttp://africa.si.edu/exhibits/cosmos/moon.htmlhttp://africa.si.edu/exhibits/cosmos/moon.htmlhttp://africa.si.edu/exhibits/cosmos/moon.htmlhttp://www.kidspot.org/discover/creation/carbon4.htmlhttp://www.amazon.com/Simone-Schwarz-Bart/e/B001ITPKAW/ref=sr_ntt_srch_lnk_1?qid=1370284401&sr=8-1


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should leave those dates blank. At the end of a 28 30-day cycle, students shouldanalyze the calendar and point out moon patterns such as the new moon, the waxingmoon, the full moon and the waning moon.

Resources

For Teachers

Nile Genesis: Continuity of Culture from theGreat Lakes to the Delta by CharlesFinch, in the book Egypt: Child of Africa, edited by Ivan Van Sertima.

Africa Counts: Numbers and Patterns in African Culture by Claudia Zaslavsky

Tracing the Roots of Civilization by Robert Trotter, Science News, Vol. 101, No.8 (Feb.19,1972) pp. 124 126.

African Fractals: Modern Computing and Indigenous Design by Ron Eglash

Blacks in Science: Ancient and Modern (Journal of African Civilization) edited by IvanVan Sertima

Diloggn Tales of the Natural World: How the Moon Fooled the Sun and Other SanteraStories by cha'ni Lele.

African Cosmos by Christine Mullen Kreamer

Moon Gazers Wheel by Bob Crelin

For Students

African Cosmos by Christine Mullen Kreamer

Moon Gazers Wheel by Bob Crelin

Math Games & Activities from Around the Worldby Claudia Zaslavsky
http://www.amazon.com/Math-Games-Activities-Around-World/dp/1556522878/ref=sr_1_3?ie=UTF8&qid=1373222841&sr=8-3&keywords=math+africa+for+childrenhttp://www.amazon.com/Claudia-Zaslavsky/e/B001HD2WQ4/ref=sr_ntt_srch_lnk_3?qid=1373222841&sr=8-3http://www.amazon.com/Claudia-Zaslavsky/e/B001HD2WQ4/ref=sr_ntt_srch_lnk_3?qid=1373222841&sr=8-3http://www.amazon.com/Math-Games-Activities-Around-World/dp/1556522878/ref=sr_1_3?ie=UTF8&qid=1373222841&sr=8-3&keywords=math+africa+for+children


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Blank Map of Africa

(Appendix A)


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Lesson Plan

Unit Social JusticeGoals/Standards:

African Women and the Origin of Mathematics

RATIONALE :

Illinois LearningStandards:

Lesson Objectives: SWBAT Identify and discuss the possible role of women inthe origin of mathematics.

SWBAT identify and understand the significance of theIshango Bone. SWBAT find the exact location of the Lake Edward/

Ishango District in Congo on the attached map. SWBAT understand the processes involved in radiocarbon

dating. SWBAT understand that the workings of the lunar calendar

based on the moon.

Materials/Resources Nile Genesis: Continuity of Culture from the Great Lakes tothe Delta by Charles Finch in the book Egypt Child of Africa(edited by Ivan van Sertima)

Africa Counts: Number and Patterns in African Culture(Claudia Zaslavsky)

Tracing the Roots of Civilization (Robert Trotter)

GradeLevel(s):

Grade 6 Unit & TimeFrame: 2 fiftyminute periods

Unit 1: Amistad

African Women and the

Origin of Mathematics(Wadie)


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African Fractals: Modern Computing and Indigenous Design(Ron Eglash)

Blacks in Science: Ancient and Modern (Journal of AfricanCivilization) edited by Ivan Van Sertima

Diloggun Tales of the Natural World: How the Moon Fooledthe Sun and Other Santeria Stories (Ochani Lele) Math Games & Activities from Around the World (Claudia

Zaslavsky) African Cosmos (Christine Mullen Kreamer) Moon Gazers Wheel (Bob Crelin)

Key Terms andVocabulary:

Social Justice:

KEY TERMS/KEY PLACES/KEY PEOPLE

Ishango Bone The Ishango bone is an ancient bone tool.Some scientists have suggested that the groupings of notchesindicate a mathematical understanding that goes beyondcounting.

Jean De Heinzlin Jean de Heinzelin was a geologist and aremarkable observer. Africa was his main area of work but healso worked in the Middle East, Europe, and the United States.His discovery of the Ishango bone brought him internationalfame.

Archeology - the scientific study of material remains (as fossilrelics, artifacts, and monuments) of past human life and activities

Charles S. Finch III Scholar, Author, Doctor, Researcher,Master Teacher. Dr. Finch has conducted independent studies in

African antiquities, comparative religion, anthropology, and


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ancient science since 1971.

Excavation to dig out and remove a covering or surface withthe intention of viewing what is underneath.

Lunar Something that relates to or is based on the moon.

Alexander Marshack he studied the Ishangobone microscopically, and concluded that it may represent a six-month lunar calendar.

Radiocarbon Dating The determination of the approximate ageof an ancient object, such as an archaeological specimen, bymeasuring the amount of carbon 14 it contains.

InterdisciplinaryConnections:

Geography/Comprehension/Math/Science:

Geography Teacher will discuss reading with students.Teacher will have students fill in the exact location of the LakeEdward/ Ishango District in Congo on the attached map.

Comprehension - Have students answer the followingquestions. 1. What is the Ishango Bone? What is thesignificance of the bone? What is the possible role of women inthe origin of mathematics?


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Activity Three-Creation of a Portfolio Submission- Gainaccess to the book In Pra ise of Black Wom en Volum e 1:Anc ien t Af r ican Queens b y Simone Schwarz-Bart. Based onthe book, students should choose one black woman fromantiquity to create a one page report on. The report shouldhighlight the black womans contribution to early civilization in

Africa. The report should also include pictures of the women.The pictures may be hand drawn or they can be researched andcopied from a book or online source.

Science - Student will learn what radiocarbon dating is byexploring websitehttp://www.kidspot.org/discover/creation/carbon4.html Once students have gone through the definition a couple of timesstudents should break up in to groups of two or three. Eachgroup should discuss what they understood by the definitiongiven, and they should submit definition in their own word, not belonger than one paragraph.

Science

- Students should visit the websitehttp://africa.si.edu/exhibits/cosmos/moon.html There they willlearn about the African proverb which states, Without the Moonthere is no life. After reading the information students shouldshare the ways that African people respect and celebrate themoon. In order to have students develop awareness of themoon, the entire class can be involved in the creation of a mooncalendar. Each day a student is assigned to observe the moonthat evening. The next day they will draw in on a blank calendarthe exact formation of the moon as it appeared in the night sky.If there is no moon in the night sky, students should leave thosedates blank. At the end of a 28-30 day cycle, students should
http://www.amazon.com/Simone-Schwarz-Bart/e/B001ITPKAW/ref=sr_ntt_srch_lnk_1?qid=1370284401&sr=8-1http://www.amazon.com/Simone-Schwarz-Bart/e/B001ITPKAW/ref=sr_ntt_srch_lnk_1?qid=1370284401&sr=8-1http://www.kidspot.org/discover/creation/carbon4.htmlhttp://www.kidspot.org/discover/creation/carbon4.htmlhttp://africa.si.edu/exhibits/cosmos/moon.htmlhttp://africa.si.edu/exhibits/cosmos/moon.htmlhttp://africa.si.edu/exhibits/cosmos/moon.htmlhttp://www.kidspot.org/discover/creation/carbon4.htmlhttp://www.amazon.com/Simone-Schwarz-Bart/e/B001ITPKAW/ref=sr_ntt_srch_lnk_1?qid=1370284401&sr=8-1


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analyze the calendar and point out moon patterns such as thenew moon, the waxing moon, the full moon and the waningmoon.

Lesson Schedule: 05 minutes: Anticipatory Set (Opening)

15 minutes: Introduction to New Material

20 minutes: Guided Practice (Discussion)

15 minutes: Independent Practice (Critical Reflection Activity)

05 minutes: Closing

Anticipatory Set(Opening)

Teacher will set the scene by stating that many ancient societieshad excellent astronomers and also had calendars, and builders,skills which required the knowledge of mathematics. Teacher willintroduce the Ishango bone and why it is highly probable that itwas used as a calendar.

Introduction to NewMaterial:

MAIN IDEA

Foundations in mathematics were created in Africa (and Asia).Mathematics is not an exclusively European product.

Activate Prior Knowledge

Teacher will ask students if they think they use mathematics intheir day to day activities. Teacher will discuss the importance ofmathematics in the lives of humans, both ancient andcontemporary.


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The Ishango Bone

In the late 1950s an archeologist from Belgium named Jean DeHeinzlin conducted excavation in the Ishango District of Congo,

Central Africa. De Heinzelin found many interested harpoonheads and a bone which captured his interest because itcontained groups of particular markings. This very interestingbone would become known as the Ishango Bone. Originally, DeHeinzlin dated the bone via a carbon-dating process to be 8500BCE (Before the Common Era) , however later dating with moresensitive radiocarbon instruments found that the Ishango Bonedates to 25,000 years old; making it over 27,000 years old! Itshould be noted that since the time a much older bone, withsimilar markings known as the Lembombo bone has beendiscovered in modern day Swaziland. It easily dates to 35,000BCE. However, much more study has been done on theIshango Bone, so it remains the focus of this lesson

What is fascinating about the Ishango Bone?

The markings on the Ishango were intentionally set in amathematical pattern. When De Heinzlin did a close examinationof the Ishango bone he was relatively certain that whoever madethe bone was familiar with prime numbers, decimals, and additionby duplication. The Ishango Bone was studied by the HarvardUniversity archeologist, Alexander Marshack. Marshack did notbelieve that there was a high level of mathematics in Africa27,000 years ago, but he did conclude that the markings on theIshango Bone constituted the charting of a lunar (moon) cycle.The Egyptian scholar Charles S. Finch, M.D. states that there isno reason why the Ishango Bone cannot be both a lunar calendarand sophisticated math tool.

Although there are some researchers who feel that the markingson the Ishango Bone and other such bones are just decorative,


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more evidence to the contrary is being reveled. Dr. CharlesFinch reports that later versions of the Ishango Bone are foundall way up the Nile River, in even the area of Syrio-Palestine.Based on these findings De Heinzlin concludes that thetechnology of the Ishango Bone began in Central Africa andspread northward to Egypt and the Near East.

What does this all mean?

Whereas the birth of mathematics has been previouslythought to be in Mesopotamia and Egypt, accuratemathematical history must begin in Central Africa andSouth Africa.

The method of addition by duplication, which thearcheologist Jean De Heinzlin found to be on the Ishangobone, is also utilized in the Rind Papyrus of Egypt, whichdates back to 4000 BCE. It is at least possible that themathematicians of central Africa carried their mathematicalgenius up the Nile River and into Ancient Egypt.

If Alexander Marshack is right that the Ishango Bonerecords lunar cycles, then African women may be theoriginators of mathematics in Africa. Women have a veryunmistakable connection to the moon. A womansmenstrual cycle like the moon re-occurs every 28 days.This is the most obvious reason why lunar or mooncharting would be necessary for early humans. It is quiteprobable that by Africanwomen charting their own bodyscycles, which are directly connected to the moons cycles,they very well may have developed the timeconsciousness, and time sensitivity that is necessary for


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agriculture to occur.

Dr. Charles Finch reports that when the pre-dynasticgraves of Ancient Egypt were opened the field researchersnoted the superior wealth in the graves of the females. Inaddition, the female figurines out-numbered the malefigurines that were added to the graves of the deceased.There has been speculation that this is because of role andwork that women do in a family setting. However, it mayalso be because women were greatly honored by Africanpeople for having introduced basic mathematicalunderstanding.

Guided Practice(Discussion)

What is the possible role of women in the origin ofmathematics?

What is the Ishango bone and why is it significant?IndependentPractice (CriticalReflection Activity)

Define (a) Radiocarbon Dating, (b) Excavation, (c) Lunar. Describe the Ishango bone and explain its significance. Identify the following people and their contributions to the

study of the Ishango Bone (a) Alexander Von Wuthenau (b)Ivan Van Sertima (c) Jean De Heinzlin (d) AlexanderMarshack

In your own words, discuss the possible role of women inthe origin of mathematics.

Closing: Teacher will reiterate the highlights of the lesson.

Assessment: Observation, Critical Reflection Activity, Participation in classdiscussion, Writing, Geography, and Math/Science Activities.

Extensions(Homework,Projects):

Observation, Critical Reflection Activity, Participation inclass discussion, Writing, Geography, and Math/Science Activities.


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Women and the Origin of Mathematics in Africa

Documents

Transcript of Women and the Origin of Mathematics in Africa