**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 17^{th} 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).