Read supplementary readings #1 & #2 : Ethnomathematics (Ascher and D'Ambrosio)

Questions for discussion.

1. What is ethnomathematics according to Ascher?

2. What is ethnomathematics according to D'Ambrosio?

Jan. 21 (M)

Jan. 22 (T)

Jan. 23 (W)

Jan. 24 (Th)

Read Asher's Introduction and pp.5-16 and

Supplementary Readings #3: Counting Sheep in Basque  and

#4: Numbers and Counting in Loboda

Questions for discussion

1. Give 5 additional examples of the Western belief that numbers carry a great deal of information.
2. Describe in modern notation the structure of the Nahuatl number words for 65, 394, 506, and 8543.
3. Why do the Yuki say that their numeral words based on cycles of 8 refer to human fingers?
4. What kinds of information about Gilbert Island culture are suggested by their categories of numeral classifiers?
5. What kinds of information about Dioi culture are suggested by their categories of numeral classifiers?
6. What problems are associated with counting sheep on the hoof? 
7. Write the following numbers in Basque: 22, 67, 735.
8. How many sheep are there if the last number said aloud is hamalau and there are 3 stones and 5 notches?
9. What is the meaning of the word “gumorai” in the phrase “nima toi gumorai” ?
10. How would you say 62 in Loboda?
11. Why are the Loboda disinterested in using large numbers?

Jan. 28 (M)

Jan. 29 (T)

Read Ascher pp.17-26

Hand in your responses to these:

1. What is a quipu?
2. What are the six aspects of quipu construction that are part of the logical-numerical recording?
3. What are the three types of quipu knots and how are they interpreted?
4. How does a quipu represent zero?

Jan. 30 (W)

Jan. 31 (Th)

Read Code of the Quipu handout.

Feb. 4 (M)

Feb. 5 (T)

Read Supplementary reading # 8: Considering Quipus

Hand in your solution to this:

Three sheds are being built. They are different sizes but each has walls made of cinder block and a floor and roof made of wooden boards.  The materials used for the first shed are: 284 cinder blocks, 100 pounds of mortar, 28 boards, and 200 pounds of nails.  For the second and third sheds, respectively the materials are: 244 cinder blocks, 85 pounds of mortar, 24 boards, 170 pounds of nails; and 364 cinder blocks, 150 pounds of mortar, 51 boards and 400 pounds of nails.  Design a quipu and record on it the amount of each material used for each shed and their sums.  Show the quipu on a schematic including relative cord placement, cord color, knot types (use Ascher’s notation), and relative knot placement.

Feb. 6 (W)

Feb.7  (Th)

Read Ascher pp.31-43

Feb. 11  (M)

Feb. 12  (T)

Hand in your responses to these:

1. What is a connected graph?  A planar graph?
2. What is the degree of a vertex in a graph?
3. Why do the Bushoong decorate daily utilitarian objects?
4. Under what conditions will a graph have an Eulerian path?
5. Draw a Bushoong figure using the algorithm on the bottom of page 36 with N = 8.
6. Prove that the sona in Figure 2.7 (p.40) are isomorphic.
7. Draw a sona on a 9 by 10 grid of dots that corresponds to the one shown in Figure 2.13b on page 42.

Feb. 13 (W)

Feb. 14  (Th)

Read Ascher pp.48-62

Questions for class discussion.

1. What is the challenge posed by the guardian of the entrance to the Land of the Dead?

2.  Following the notation presented on pp.48-49, draw the nitus AAASBBB. 

3. Make up three simple initial procedures A, B and C.  Use these procedures to draw the three stage nitus .

4. Draw the A component of  “two fishes head to tail” (Figure 2.28, p.60).

Feb. 18 (M)

Feb. 19 (T)

Read Ascher pp. 67-72

For class discussion:

Solve the kin relation puzzles posed on the top of page 69.

Feb. 20 (W)

Feb. 21  (Th)

Read Ascher pp. 72-81

Class discussion:  symmetries of square and triangle

Feb. 25 (M)

Feb. 26 (T)

Read Supplementary Reading #11: Marlujarrakurlu

Class discussion: The Dreaming and the two kangaroos

Hand in your responses to these:

1. In the Warlpiri kinship system, if your mother’s sister is in section 6, in what section is your father’s brother’s daughter?
2. Use table 3.1 (p.73) to calculate the section corresponding to
3. Use table 3.2 (p.79) to calculate the section corresponding to

Feb. 27 (W)

Feb. 28(Th)

Read Supplementary Reading #10: Aboriginal Mathematical Concepts

For class discussion:

1. Why doesn't the Aboriginal want to count?

2.  Why would an Aboriginal refuse to shoot a kangaroo when a man of kangaroo totem is missing in the bush?

3. How do Aboriginal notions of measurement differ from that of the white man?

4. How do Aurukun children recognize cards?

5.  What is "threeness"?

6.  What does this sentence tell us about Wik-Mungan measurement concepts?  "Signpost alangan waa'an ngant aak kech nath or nath ya' "

Mar. 3 (M)

Mar. 4 (T)

Read Ascher pp.85-94, 109-116

For class discussion:

1. How are games expressions of culture?

2. Why do you think Ascher says “the spiritual and communal embedding of this game stands in stark contrast to games of chance as they are most often currently played in Western culture”?  Do you agree with her?

3.  What is your favorite game?  What aspects of your culture does the game express?

4.  Extend the Cayuga game tree to a fourth toss and recalculate the probabilities. (See p.92)

5. Can the Kpelle, Swahili, and Ila crossing puzzles be solved by all three of Ascher's solutions?

Mar. 5 (W)

Mar. 6  (Th)

Hand in:

1.  Here is a description of a Cree game pahkasahkimac.  “The playing pieces are 8 objects made of bone. Four are hook shaped and four are diamond shaped. Each object has one side painted white and the other black.  The dice are tossed in a bowl.  The count is determines as follows: All white counts 100; all black counts 80; 7 white and 1 black counts 30; all hooked shaped white and one diamond white counts 10; all hooked shaped black and one diamond black counts 8; all diamond white with 1 hooked white counts 6; all diamond black with one hooked black counts 4. All other outcomes count 0.”  Compute the expected value of a toss. Show how you obtained your answer.

2.  Essay Question:  Discuss the mathematical ideas explicit or implicit in Warlpiri culture. (1-2 pages)

Mar. 10 (M)

Mar. 11 (T)

Read Ascher 123-132  and

Supplementary Reading #12: Comparing Time and Temporality in Cultures

R U thinking about your project?

Questions for discussion:

1.   What is meant by "sa'ah naghai bik'eh hozhoon" ?

2.  What is a minimal set of problems for all human cultures?

3.   Compare and contrast cosmological time with human time.

4.   Does the universe change?

5.  Give some examples of how western culture treats time as a commodity.

6.   How would your day be different under a Navajo notion of time and knowledge?

Mar. 12 (W)

Mar. 13  (Th)

Read Ascher 132-140

Hand in your responses to these:

1.   Essay Question: It what ways would your view of your world change if you saw the universe as processes rather than objects and situations? (1 page)

2. Art Question: Draw a sketch of a basketball game in progress as an Inuit would sketch it. 

3. Math Question:  Find the Maya date which is 100 days after 12.19.15.13.15  13 Men 18 Yax.  Show your work.

4.  Math Question: Calculate the date of Easter for the year 2010. Show your work.

Mar. 24 (M)

Mar.26 (W)

Read Supplementary Reading #13: The Kewa Calendar

Hand in your responses to these:

1.  Suppose today is Wednesday April 2, 2008.   How would the Kewa refer to  April 3, 2008?  April 5, 2008?  March 31, 2008?

2. Translate these Kewa words into English:  eke, kegali, mindi, nare,ropa, kuli, pondea.

3. Suppose that you were sailing from Elato to Satawal (see p.141 in Ascher). Select a reference island. Now describe the way a Caroline Islander would navigate the journey. Give specific star references (see p.144 in Ascher)

Mar. 31 (M)

Read Supplementary Reading #13: The Kewa Calendar

Hand in your responses to these:

1.  Suppose today is Wednesday April 2, 2008.   How would the Kewa refer to  April 3, 2008?  April 5, 2008?  March 31, 2008?

2. Translate these Kewa words into English: eke, kegali, mindi, nare, ropa, kuli, pondea.

3. Suppose that you were sailing from Elato to Satawal (see p.141 in Ascher). Select a reference island. Now describe the way a Caroline Islander would navigate the journey. Give specific star references (see p.144 in Ascher)

No Class Today -- Advising Day

Frieze pattern links:

http://nrich.maths.org/content/98/11/art1/thumb_gallery1.html

http://www.felber.net/products/friezes_moldings/friezes_1.html

http://www.protozone.net/ASHOCK/AJBord.html

http://www.scienceu.com/geometry/handson/kali/kali.html

Apr. 2 (W)

Apr. 3 (Th)

Read Ascher pp.155-165

Hand in your reponses to these:

Using this figure

as the base pattern. Draw each of the following strip patterns.

a.  p111

b.  pm11

c.  p1m1

d.  p112

e.  pmm2

f.  p1a1

g. pma2

h. p'111

i.  pma'2'

j.  pm'm2'

Apr. 7 (M)

Apr. 8 (T)

Read Ascher pp.166-172 and

Supplementary Reading #14: Symmetry and Antisymmetry in Maori Rafter Designs

Apr. 9 (W)

Apr. 10   (Th)

No Class Today: Use the time for your project.

Turn in your assignment to me in my office (SH203J) before class time.

Read Ascher pp. 172-180

Hand in:

Classify each of the following Inca pottery designs. Indicate the base pattern for each.

1. 

2.

3.

4.

5.

6.

7.

Apr. 14 (M)

Apr. 15 (T)

Apr. 16 (W)

Apr. 17   (Th)

No Class Today: Use the time for your project.

Turn in your assignment to me in my office (SH203J) before class time.

Hand in :

Show the steps in the construction of the Lindisfarne Gospel pattern (p.38, Fig. 6a, Supplementary Reading #15). Specifically, draw the grid and break markers, the paths of the strings, the paths outlined and background filled in, and the added interlacing.

Apr. 21 (M)

Apr. 22 (T)

Apr. 23   (W)

Apr. 24   (Th)

Read Ascher pp. 185-196

  Hand in your responses to these:

1. Essay question: Identify an instance of mathematics in your culture. Describe how it can viewed decontextualized and in context. Do the same with an instance of mathematics in one of the cultures we've studied this semester (Malekula, Kewa, Maori, Maya, Warlpiri, Cayuga, Navajo, etc.).  (2-3 pages)
2.  Math question: Here is a description of a Sauk game called gusigonogi.  “The playing pieces are 8 bone disks. Six have circles marked on one side and the other two have stars marked on one side. The other side of each disk is plain. The dice are tossed in a bowl.  The count is determines as follows: Eight marked sides up counts 4; eight plain sides up counts 4; seven marked sides and 1 plain side counts 2; seven plain sides and one marked side counts 2; seven plain sides and one star counts 5; six plain sides and two stars count 10; all other outcomes count 0.”  Compute the expected value of a toss. Show how you obtained your answer.

Apr. 28 (M)

Apr. 30(W)

May 5 (M)