SOCRATIC SEMINAR: WHY STUDY MATHEMATICS?

1. Meaghan Smith Roger Williams University msmith886@hawks.rwu.edu SOCRATICSEMINAR:WHY STUDY MATHEMATICS? Mathematics Lesson Any Class for Grades 9-12

2. Learning Goals and Expectations: Students will think critically about the purpose of taking this class Students will feel comfortable questioning the goals of learning Students will feel comfortable questioning the instructor Standards: This lesson does not address any standards directly. This lesson is designed to be used during the first week of classes, as an introductory lesson prior to exposing students to any class content. This lesson will allow students to think about why they are taking the class as opposed to just learning the material with no context. Although this lesson does not directly address any specific mathematics standards, I do think that it is extremely important for the students so that they begin the year with the understanding that it is encouraged that they take their learning into their own hands and really think about and question what they are really there for. FOCUS

3. IMPLEMENTING THE LESSON Students will be placed in two groups of nine (ideally) and each student will be asked to pick an essay to read. This way students are coming to the Socratic Seminar with different information and new ideas. • The readings for this lesson were taken from the website http://www.math.uakron.edu/~norfolk/why223f03.pdf. • Students will complete a Facts, Questions, Responses graphic organizer while reading the assigned essay. • During the Socratic Seminar, the students will be put into inner and outer circles. The groups will switch halfway through to ensure equal opportunity to contribute. • Students will be instructed of their roles and the ground rules. • The role of the inner circle is to discuss the guiding questions. • The role of the outer circle is to listen and take notes on key speaking points. • This Socratic Seminar will last one entire class period, with a halfway point designated from the beginning as the time in which the inner and outer circles will switch. • Formative assessment will be assigned following the Seminar.

4. This collection of student essays has the following introduction, which should be shared with the students as background information regarding their readings: “In Fall 2003, I gave the question above (Why should anyone have to study mathematics?) to my Honors Calculus III students. After some lively discussion, they were asked to write a paper on it. The requirements on the paper were very lax in terms of length and format. The main requirement was that I expected reasoned answers, whether the argument was pro- or con-. I then solicited those students who were interested and willing to submit their papers, without correction, for this web page, with the understanding that their gender, but not their names, would appear. Below are some of the 33 essays that I received, all of which had interesting points to make. I have only changed the formatting, since I was working in LaTeX, and most submissions were in Microsoft WORD.” WHY SHOULD ANYONE HAVE TO STUDY MATHEMATICS?

5. GEORGE WASHINGTON’S QUOTE “The investigation of mathematical truths accustoms the mind to method and correctness in reasoning, and is an employment peculiarly worthy of rational beings.” – George Washington as quoted in William Dunham’s The Mathematical Universe (http://letsplaymath.wordpress.com/2006/12/31/why-study-mathematics/) This quote should be written on the board throughout the Socratic Seminar. Following the Socratic Seminar, students will be asked to write an essay in which they are asked to react to this quote.

6. Key Question: Why should anyone have to study mathematics? Why is it important to think about why anyone should or should not have to learn mathematics? What real life applications does mathematics have? Are these valid reasons as to why mathematics should be mandatory in high schools? What other ways, besides learning high levels of mathematics, can students build problem solving skills? How do these ways of learning problem solving skills compare to learning through mathematics? How many years / how much mathematics should students be required to take in high school (if any)? How did you reach this conclusion? All the essays that were read for this discussion were written by students in an Honors Calculus III class. In what ways, if at all, do you think this affected their responses? One essay states, “Arguments against taking required mathematics courses can be easily dismissed as nothing more than complaints”. In what ways is this claim valid / not valid? Why do you think that the gender of the author was given for each essay? GUIDING QUESTIONS

7. IMPLEMENTATION TIPS • Students will be reading different essays, which will encourage and allow for different opinions to be offered throughout the discussion • Students should be engaged throughout; possibly have students ‘play devils advocate’ toward one another FORMATIVE ASSESSMENT Students will be asked to complete a Facts, Questions, Responses on their assigned essay. (On the next slide) In the Seminar, after students leave the inner circle, they will be asked to complete a one sentence summary of the discussion they were a part of. As more of a summative assessment, students will be asked to write an essay, with the topic being a reaction to the quote by George Washington Students will be asked to react to the ideas behind the quote and how this quote relates to the Seminar that the students participated in. Students will be asked to make at least two references to what they heard in the Socratic Seminar, and give proper credit to their classmates for shared ideas. This essay will serve as a test grade. This way, students that do this assignment well will start the year with a strong test grade. IMPLEMENTATION, MATERIALS, AND ASSESSMENT MATERIALS • Students will need the readings from the link provided previously.

8. FACTS, QUESTIONS, RESPONSES • Students will be asked to complete this graphic while reading their assigned essay the night prior to our Seminar. • While reading, students should take notes in the appropriate category: • Facts: Materials presented as truthful items. Students can also include items in this category that they want to verify or have clarified. • Questions: Items from the text that are confusing or for which further information is needed. • Responses: Personal reactions to specific sections of the reading. 3. Students will be encouraged to use this graphic during the Seminar.

9. For those students that are not able, for any reason, to read the assigned essay, I will ask them to participate in an alternative assignment in order to come to the Socratic Seminar prepared. I would have those students conduct an interview with a family member or friend outside of school in which the student examines why or why not this person feels it is necessary to study mathematics in high school. The students will need to establish credibility for their interviewee (such as previous mathematics courses he/she has taken, highest level of education, profession, etc.) and be sure to ask for clear and concise answers. These students, if capable, will be asked to take notes on the interview and still will be required to fill in the Facts, Questions, Responses graphic prior to the Seminar. ACCESSIBILITY

10. SOCRATIC SEMINAR RESOURCES Curriki Socratic Seminars Socratic Seminars: Journey to Excellence Socratic Seminars International Socratic Seminar Grading Rubric Socratic Seminar Overview Socratic Seminar Study Guide The Paideia Philosophy CREDITS: Norfolk, T. S. (2003). Why Study Mathematics (2003)? Retrieved November 30, 2008, from Dr. Timothy S. Norfolk Web site: http://www.math.uakron.edu/~norfolk/. RESOURCES & CREDITS

11. Socrates had no syllabus. He wanted Athenians to think for themselves. No wonder the local authorities were disturbed.… Inevitably, they decided that Socrates was subversive.” Gray • All members of the inner circle are expected to participate in the discussion. • Anyone who doesn’t wish to answer a question should so indicate by saying, “I’d like to pass.” • Try to direct your comments and questions to each other and not to the Seminar leader. • Please maintain rules of “civil discourse” It’s OK to disagree with a person’s ideas, but never to criticize the person offering them. • Members of the outer circle must maintain silent until the seminar is concluded. STUDENT GROUND RULES