This class has been good.  I enjoyed learning about websites as resources.  The teaching experiences were good, and working with Geometer Sketchpad was fun.  But the best part of this class for me was the research paper.  At first when I found out that we would be required to do a research paper I wasn’t very thrilled but it turned out to be a very good thing for me.

I was reading a professional article for another class when I ran across the mention of Socratic Seminars.  The phrase caught my attention; the article did not explain it however.  As soon as I could I began doing research to find out what Socratic Seminars are and the more I learned the more fascinated I became with the idea and it became the subject of my research paper.

Socratic Seminars are the result of the work of Mortimer Adler, Director of the Institute for Philosophical Research in Chicago.  Socratic Seminars are something that I am very interested in using in the classroom and a copy of my research paper follows:

           

“The need to understand and be able to use mathematics in everyday life and in the workplace has never been greater” (NCTM). Math is not just for the mathematician or scientist or accountant; it is relevant to everyone. Math is the foundation for most facets of life, for instance making purchase decisions, choosing insurance or health plans, using credit cards, investing, voting knowledgably, and problem solving in the work place. Anyone who understands and can do mathematics will have increased opportunities and options for shaping their futures.   And so it is the responsibility of educators to help students learn to make conjectures, experiment with various approaches to solving problems, construct mathematical arguments and respond to others’ arguments (NCTM). An effective way to meet these goals is to use the Socratic Seminar. 

The Socratic Seminar method is based on Socrates’ theory that “it is more important to enable students to think for themselves than to merely fill their heads with ‘right’ answers” (Adams). 

“I don’t understand this.”

“What is the answer?”

“I don’t get it.”

These are common questions and phrases heard in math classrooms across the country, but it is not good enough to just give the answers to the problems or to re-explain the math procedures.  It is far more productive to use questioning to lead the student to learn for him or herself what the answer is. The Socratic seminar is a method of using questions to lead the students to think about what they know, why they know it and how to explain what they know.  If students can do that, then you can be assured that they have learned the concepts.  According to the National Council of Teachers of Mathematics, “Students need opportunities to test their ideas on the basis of shared knowledge in the mathematical community of the classroom to see where they can be understood and if they are sufficiently convincing.  When such ideas are worked out in public, students can profit from being part of the discussion, and the teacher can monitor their learning.” (NCTM 61)  

History of the Socratic Seminar

Socratic Seminars are the result of the work of Mortimer Adler, Director of the Institute for Philosophical Research in Chicago.  In his published works, The Paideia Proposal (1982) and Paideia Problems and Possibilities (1983) Adler argued that education should be rooted in three goals: the acquisition of knowledge, the development of intellectual skills, and the enlarged understanding of ideas and values.  The acquisition of knowledge is gained by using textbooks and instructor lectures and demonstrations.  The development of intellectual skills is accomplished through exercises, coaching, and practice.  The third, an enlarged understanding of ideas and values, can be achieved by using Socratic Seminars (Journey).

            Socratic Seminars may be used in grades K-12, and in all subject areas. It is usually most effective if used once a week; although in math classrooms, once a month is sufficient.

Guidelines for using a Socratic Seminar

            First, the instructor should choose a problem on which to apply previously learned concepts. This ensures that the students have skills and language in which to communicate and draw from during the discussion.  It also prevents the need for teachers to stop the conversation and clarify or provide additional information. 

It is important to choose questions wisely so as to promote good discussion.   Choose questions that “arise from genuine interest or curiosity on the part of the teacher, are open to interpretation (no right or wrong answer), foster analysis and a greater understanding of the text, are supportable by the text (answered by reference to the text), and are framed in such a way that they generate dialogue from the students” (Journey).  

Next, it is important that there is enough time allowed for the dialogue, at least 45 to 50 minutes is a good guide.  The students should be seated in a circle with the teacher among them, at their same level, an equal participant in the dialogue.  The role of the instructor is to keep the discussion moving, not to be the recipient of the answers, or to be the one to give answers or explanations.  After the teacher poses the question it may be a good idea to avoid eye contact with the students, or even keep her eyes down cast so that the students will take seriously that it is their conversation.  It is also okay for the teacher to allow silence; the students will quickly become uncomfortable and begin speaking. The instructor allows the students to discover the truth through their own questions and explanations. 

Before the seminar begins it is a good idea to talk about the purpose of the seminar and to set rules and guidelines to be followed.  Some suggestions for these guidelines came from Forrest Park High School, Forrest Park, Georgia, where Socratic Seminars were tested in eight math classrooms. 

·         Participants must respect one another’s opinions.

·         Participants do not have to raise their hands to speak, but they must not interrupt (use body language and eye contact).

·         Participants address their fellow classmates by name (name cards can be placed on the desks, if necessary) and should take notes.

·         Participants’ comments address the topic and do not digress.

·         Participants settle points of disagreement among themselves.  The teacher is not used as a resource. (Koeliner-clark)

During the seminar it is wise for the teacher to make assessments, not only about understanding of the subject being discussed, but about the seminar process.  This will allow the teacher and students to make each succeeding seminar better and more effective.   An example of assessment questions are as follows: did the participants…

·         Speak loudly and clearly?

·         Cite reasons and evidence for their statements?

·         Use the text to find support?

·         Listen respectfully?

·         Stick with the subject?

·         Talk to each other, not just to the leader?

·         Paraphrase accurately?

·         Ask for help to clear up confusion?

·         Support each other?

·         Avoid hostile exchanges?

·         Question others in a civil manner?

·         Seem prepared?

Another suggestion might be for three or four students to sit on the sidelines and instead of participating in the dialogue they conduct the assessment. Lynda Tredway, who wrote an article in Educational Leadership, suggests students “Use an observation form, [to] tally how many and what kind of contributions classmates make, whether they use evidence to support ideas and ask questions of others, and whether they yield to others when several wish to speak at once - in short, whether they demonstrate habits of conversation and mind that educators seek in students” (Tredway). By having students take turns being the observers they will become improved contributors to future discussions.

Example Questions for Mathematical Seminars

            The following sample questions are a few that came from Higher Order thinking Questions: Secondary Mathematics by Robyn Silbey and published by Socratic Seminars International.

Problem Solving:

·         What are some things common to all solvable problems?

·         In your own words, and in your life, what is problem solving?

Number Patterns and Relationships:

·         The number 64 can be represented as the product of 16 and 4.  What are some other ways to represent the number 64? What is the relationship among these representations?

·         What are some ways number properties, such as, commutative, associative, and distributive, describe the relationships among numbers?

Fraction Addition and Subtraction

·         What are some instances that and exact sum or difference is needed, rather than an estimate?

·         There is a sequence of steps used to add and subtract fractions.  What parts of the sequence could be changed, and what parts must remain the same? Explain your reasoning using examples.

Algebra: Solving Equations and Inequalities

·         What are some visual representations of equations and inequalities?

·         What connections can you make between the equation of a line and a line graph?

Geometry Concepts

·         Is geometry more valuable to an architect, engineer, or astronomer? Why?

·         Are you more like a circle, a square, a triangle, or a pentagon? Why?

Conclusion

            The national mathematics communication standards are that “Instructional programs from prekindergarten through grade 12 should enable all students to—

·         Organize and consolidate their mathematical thinking through communication;

·         Communicate their mathematical thinking coherently and clearly to peers, teachers, and others;

·         Analyze and evaluate the mathematical thinking and strategies of others;

·         And use language of mathematics to express mathematical ideas precisely” (NCTM).

There are perhaps many ways to meet these standards, writing being one of them, and perhaps the most commonly used, but the Socratic Seminar is another effective tool to use in reaching these standards.  According to Blooms Taxonomy students learn in different ways and using the Socratic seminar allows those students who learn orally, to fully participate in understanding the principles being taught.  It gives those who may not be strong writers a way to think and solidify their knowledge. 

            Teachers, who have participated in Socratic Seminars, like those at Forest Park High School, find that students tend to understand concepts better after having participated. And as they participated in the discussions they would continually refine, and improve their ideas so that they were willing and able to teach and explain concepts to their peers.  What more could educators hope for than students who actively take part in their learning, are able to communicate with others, and are willing to help those around them.  The Socratic Seminar is a tool that should be added to every teacher’s tool chest. 

 

Bibliography

 

Adams, Mrs. (2002). “Socratic Seminars.” Studyguide.org. http://www.studyguide.org/socratic_seminar.htm

 

Graybill, O. (2008).  Socratic Seminars International.  “Coaching best practices to ehance student engagement and critical thinking in mathematics.  www.CocraticSeminars.com

 

Keviin (2008).  Hubpages Inc. Socratic Seminars 74. http://hubpages.com/hub/Socratic_Seminars

 

Koeliner-Clark K., L Lynn Stallings, Sue A Hoover.  The Mathematics Teacher. Reston: Dec 2002.  Vol.95, Iss.9; pg 682. Proquest data base, retrieved November 1, 2008.

 

National Council of Teachers of Mathematics (2000).  Principles and Standards for School Mathematics. NCTM Reston, VA.

 

North American division office of Education (2004-2008). Journey to Excellence; Socratic Seminars.  http://www.journeytoexcellence.org/practice/instruction/theories/miscideas/socratic/

 

Socratic Seminar. Prince William County Schools.  http://www.pwcs.edu/curriculum/sol/socratic.htm

 

Tredway, L. (1995). “Socratic Seminars: Engaging Students in Intellectual Discourse.”  Educational Leadership. 53,1, 26-29.  http://www.middleweb.com/Socratic.html

               

 

 

As I was substituting in a math class today, it was a struggle to teach story problems involving percents.  After the class was done and I had time to reflect, I thought that a method of teaching math problems (not just story problems), is to present the problem and give them the answer to the problem and then have the students figure out how to get the right answer and why it is the right answer.  Sometimes this is how I have been able to learn math problems.  I look at the answer and then work backwards using all that I know.  I want to remember this.