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Joseph Mano: Multicultural History of Mathematics

Three Lesson Plans
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Three Lesson Plans
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Lesson Plan 5a: Mathematics in Social Context

 

Title: The Not Always Steady Marriage of Mathematics and Society

 

Content: This lesson will begin by focusing on the conflict between Galileo and the Catholic Church in the 17th Century, chiefly concerning Galileo’s scientific evidence that the Earth revolved around the Sun (the Copernican view), against the Church’s belief that the Sun rotated around the Earth (the Ptolemaic view); and then relating this conflict to possible conflicts of our current age, as imagined by the students.

 

Objective: Students will be able to identify the role that social structures play in the perception of truth, especially in science and mathematics; then, students will identify ways in which our current social structures might possibly lead to a denial, at least initially, of potential new mathematical/scientific evidence that challenge these structures.

 

Materials:

---handouts for each student of a Biography of Galileo (http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Galileo.html) (possibly edited for time constraints / pertinence)

---rubric for group dramatization of a potential current conflict between a social structure and math/science.

 

Procedures:

1) Daily Procedures: entry problem, homework correcting, etc.

 

2)  Lesson Introduction: Have you ever known something to be true, and yet have someone not believe you in the slightest?  Why didn't they believe you?

 

3)  Statement of Purpose: Today, we will learn about the social circumstances that precluded Galileo from receiving acclaim for his proofs that the Earth revolved around the Sun, and not vice versa as was popularly believed at the time; and then we will gather in groups to create and perform dramatizations of how such a conflict, between society and mathematics/science, might potentially play out today.

 

4)  Reading of Galileo Biography: Individuals take turns reading the Galileo Biography aloud to the class, as the teacher interjects salient questions (along the range of Bloom’s taxonomy) as a means of fostering thought and discussion, with a special focus on the conflict between Galileo’s mathematics and the Church’s Doctrines, and Galileo's proposed resolutions of that conflict.

 

5)  Groups:  Introduction to activity: group dramatization of imagined conflict in a current social structure with an imagined mathematical/scientific finding; discussion of rubric; breaking up into groups of 3 – 5 students; groups meet and brainstorm ideas, rehearse dramatizations.

 

6)  Dramatizations:  Either later that period, or the next day, groups perform their dramatizations for the entire class.

 

7)  Closure:  Student-led re-statement of the lesson objective; pertinent discussion.

 

Evaluation: Students will be evaluated by their group dramatizations in accordance with the distributed rubric, which will include points on group-wide participation, the length and quality of the drama, as well as the appropriateness and relevance to both Galileo’s problems and identification of current social structures.

 

 

Lesson Plan 5b: Women in Mathematics

 

Title: Biographies of Women in Mathematics

 

Content:  This lesson will focus on the history the contributions that some women have made in the history of mathematics, especially focusing on the bias and prejudice that most of them had to face in order to succeed in their field.

 

Objective:  In groups, students will read and understand biographies of women in mathematics; then each group will present their findings to the whole class, using both speech and visual media.  Students will understand the importance of women in the history of mathematics, and understand some of the social barriers existing against women, in both history and contemporary times.

 

Materials:

---biographies of several women in mathematics (possibly using http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Women.html or other resources)

---other math history references for students to research their mathematician and/or their specialty area

---poster paper

---colored markers

---rubric for group presentations

 

Procedures:

1) Daily Procedures: entry problem, homework correcting, etc.

 

2)  Lesson Introduction/Discussion: Do you think mathematics comes easier to men or women?  What do you know about famous mathematicians?  What do you know about famous women mathematicians?

 

3)  Statement of Purpose:  Today we are going to look at the contributions of individual women in the history of mathematics, and the social obstacles they had to overcome or sidestep to further their studies.

 

4)  Groups / Distribution of Materials: Division of groups of 4 or so; distribution of poster paper, markers, biographies.

 

5)  Explanation of Presentations: In accordance to the rubric, which will include specific benchmarks to include in both the speech and the poster, including: social context; discussion of the mathematician’s contributions to their field, especially specific on the type of mathematics they specialized in, or perhaps the way in which they contributed to mathematics overall (e.g., Hypatia); poster graphics furthering understanding of the mathematician; overall group participation; and quality of summary of biography and poster.

 

6)  Group Work: Groups will be given time to read biographies of their mathematicians, and conduct further research on the mathematician and their field of study, as a group; and then to organize an oral and visual presentation of the contributions of that female mathematician.  This may take a day or two, depending on the length of the period.

 

7)  Presentations: Students will present their mathematician, both orally and visually.

 

8)  Exam:  Groups will create and submit questions relevant to their presentation of a woman mathematician.  The class will then take an exam comprised of all the groups’ questions, plus a teacher-generated extended-response question on the role of women in the history of mathematics, requiring students to reflect on the origin and existence of restrictions on women in academic mathematics, both in the past and the present day.

 

9)  Closure: student-led re-statement of the lesson objective; pertinent discussion.

 

Evaluation:  Students will be evaluated relative to the quality of their group presentations, in accordance with the distributed rubric; as well as in their exams (see above).

 

 

Lesson Plan 5c: Current Issues in Mathematics

 

Title: Chaos Theory

 

Content: This lesson will focus on the history and development of “Chaos Theory,” from its beginnings in 1961, to current applications and extensions.

 

Objective: Students will understand the basic history of Chaos Theory, its fundamental tenets, and some of its far-reaching applications in modern life.  

 

Materials:

---copies of an equilateral triangle on white paper

---rulers

---a die for each pair of students

 

Procedures:

1) Daily Procedures: entry problem, homework correcting, etc.

 

2)  Lesson Introduction / Discussion: Have you ever wondered why they can’t predict the weather?  Have you ever heard of “The Butterfly Effect”?

 

3) Statement of Purpose: Today we will learn about an accidental discovery by a meteorologist in 1961of something called Chaos Theory, what it means, and how it applies to the world as we know it.

 

4) Lecture / Discussion: The teacher will begin by providing a history of Chaos Theory; an explanation of what Chaos Theory is (characteristics: deterministic, Lorenz attractor, the quantum world, its infinity, etc.) and its difference from other known types of “order”; and how it applies to a wide-range of phenomena (weather, stock markets, population growth, the “infinite” coastline of Europe, quantum physics, epistemology, etc.).

 

5) Activity: Next, students will engage in an activity that will demonstrate how chaos theory works (taken from the following website: http://www.germantownacademy.org/academics/US/Math/Geometry/stwk99/danc/activity.htm):

a. To play the Chaos game, take your piece of paper and draw a triangle on it, preferably an isosceles triangle or an equilateral triangle. Mark the numbers 1 and 2 next to the top vertex. Mark the bottom left vertex 3 and 4. Mark the bottom right vertex 5 and 6.

b. Each number that comes up on the die will correspond to one of the numbers on the triangle's vertices.

c. First, place a random dot anywhere inside the triangle

d. Then, roll the die. Take your ruler and place one end on the vertex which matches the number on the die. Mark a dot at the midpoint of the point and the vertex. DO NOT DRAW ANY LINES!

e. Using the new dot, roll the die again and repeat the process.

f. Eventually, after many, many rolls of the die, a pattern will arise; the students will be required to describe this pattern in writing.

6) Closure: student-led re-statement of the lesson objective; an examination of the patterns discovered in the activity and its relation to Chaos Theory; pertinent discussion.

 

7) Assignment: Students will then be given an assignment, for either an in-class activity or as homework, in which they will have to conduct web-research on Chaos Theory, finding and explaining in detail at least three applications of it in contemporary life, and listing the websites they used for this purpose.

 

Evaluation: Students will be evaluated in accordance to their participation in the activity; as well as by the quality and completion of their assignment (see above).