I hear and it helps a little
I see and ideas begin to form.
I do and the ideas become real to me.
I do, see, and hear, and I understand.
I talk about it and I understand more.
I apply it and I see its value.

                                                                              - ancient Chinese proverb-
 

Description:  This course is designed for students who seek Pennsylvania certification in teaching secondary and/or middle school mathematics.  In addition to reviewing numerous concepts of mathematics and learning methods of teaching them, you will learn and/or relearn the complex background necessary to become a good teacher of mathematics.

 
Instructor:  Dr. Warren Hickman, HSC 158, Phone ext. 7285

Text:  Teaching Secondary School Mathematics, 6^th Edition, by Posamentier and Stepelman
            Reference books:  (1) The NCTM Standards (3 volumes) Curriculum & Evaluation,
            Professional, and Assessment.  (2)  Principles and Standards for School Mathematics
            Copies of (1) and (2) are on reserve in the Hoyt Library

Goals/Philosophy in Mathematics Education

Preservice teachers of mathematics must master a certain body of mathematics and be aware of its increasing relevance in our technological age.  They must be able to stimulate students to understand and to use mathematics and appreciate the significance of mathematical concepts.  Furthermore, the preservice teachers must be concerned not only with mathematical ideas, but also with the communication of those ideas to students of different sociological, cultural, psychological, and economic backgrounds.

Objectives:  The primary objective of this course is to make you aware of how mathematics is taught and what is taught.  To accomplish this:

1)     We will cover chapters 1- 6 in the text.  In addition, you will receive numerous
       articles to peruse, to critique and to discuss. 

      2)     You are to purchase a 3 ring binder and divide it into two sections:  “Journal” and “Exposition”.  In the journal  part you are to record your perceptions and opinions of what we do in class.  It can  be of a personal nature if you wish or ask me questions, etc.  The exposition part is explained on pages 89 and 90 of the text.  These are to be submitted to me every Monday (except the weeks of fall and Thanksgiving breaks) before noon.  I will return them to you at class time on Tuesday. 

3)  You are to become acquainted with and consult other sources to enhance your
                  knowledge of teaching mathematics.  Included are:  The Mathematics Teacher, 
                 Mathematics Teaching in the Middle School, Journal for Research in Mathematics
                 Education, NCTM yearbooks and the numerous Web Resources distributed to you in
                class.

          4)   You are to become acquainted with and refer to the Pennsylvania's Department of
                  Education's Academic Standards for Mathematics. 

5)   We consider the current reforms in mathematics and the vast amount of research
       articles pertinent to it, with special attention given to the NCTM Standards.                                                  

6)  You “teach” selected topics in mathematics, including some from the College
      Geometry material.  Note the "Enrichment Units for the Secondary School
      Classroom" in your text.  There is a wealth of good suggestions contained therein
      pertaining to topics in mathematics and the teaching of these topics. 

7)  We view, critique, and discuss two videos pertaining to teaching and learning. These
      are "Stand and Deliver" and "The Search for Bobby Fisher."

Your Grade:  There are no tests or quizzes.  You begin with an A in the course.  Class participation is extremely important.  More than one unexcused absence will drop your grade to a B (or lower). 

You are "learning" to be a mathematics teacher, therefore by the end of the semester you should be exhibiting those attributes of a well-prepared teacher.

These include:

1)  Preparing a well-constructed lesson plan.  These should steadily improve over the course of
     the semester.

2)  Implementing your lesson plan in a time-restricted setting.

3)  Using active learning activities in your "teaching presentations" including, on occasion,
     Geometer's Sketchpad and the TI-83 calculator.

 4)  Assessing your classmates' "teaching presentations" with constructive comments.

 
5)  Using Geometer's Sketchpad to give a "professional" teaching presentation during Finals
      Week.

 
6)  Assessing your over-all performance in this course.  This is part of your "final exam".

I, of course, will be assessing your work in the course.  If at any time, I think you are in danger of losing you’re A, I will tell you and expect you to improve upon the weak area(s).  If there is no improvement, I will inform you, in writing, that your grade is no longer an A and why.

 Personal Comments:  There is so much to consider, to learn and to experience in order to become an excellent teacher of mathematics.  In the limited time of this course, there is no way to discuss every topic or concern related to teaching mathematics, so we must choose what we believe to be important to us.  We are in this together!  Each of us must be open and honest with the group and participate in our discussions.  You are not being graded or judged on what you say.  Use the journal and exposition described above to enhance the group's and your growth.  If

you do teach on the secondary or middle school level, give yourself three years before deciding to stay in the profession or not.  I think the following paragraphs give to us the keystone to teaching mathematics. 

A View of Learning Mathematics

Educational research findings from cognitive psychology and mathematics education indicate that learning does not occur by passive absorption and imitation (Davis, 1984; Case & Bereiter 1984; Cobb & Steffe, 1983; Hiebert, 1986; Lampert, 1986; Lesh, 1983; Schoenfeld, 1987).  Rather, learning occurs as students actively assimilate new information and experiences and construct their own meanings.  This is a major shift from learning mathematics as accumulating facts and procedures to learning mathematics as an integrated set of intellectual tools for making sense of mathematical situations (Resnick, 1987).  This view of learning is summarized in Everybody Counts (Mathematical Science Education Board 1989, pp. 58-59).
 

            In reality, no one can teach mathematics.  Effective teachers are those who can stimulate students to learn mathematics.  Educational research offers compelling evidence that students learn mathematics well only when they construct their own mathematical  understanding.  To understand what they learn, they must enact for themselves verbs that permeate the mathematics curriculum:  “examine,” “represent,” “transform,” “solve,” “apply,” “prove,” “communicate.”  This happens most readily when students work in groups, engage in discussion, make presentations, and in other ways take charge of their    own learning. 

            All students engage in a great deal of invention as they learn mathematics; they impose    their own interpretation on what is presented to create a theory that makes sense to them.  Students do not learn simply a subset of what they have been shown.  Instead, they use new information to modify their prior beliefs.  As a consequence, each student’s  knowledge of mathematics is uniquely personal.
 

Every time I facilitate this course, I learn something new about teaching, so I look forward to our meetings.

All parts of this syllabus are subject to change. 

WARREN D. HICKMAN 

Professor of Mathematics

                                                                              Westminster College
 
 

(A glimpse of why I teach.  I share it with you.)

 
THE BRIDGE BUILDER

 An old man going a lone highway

Came at the evening cold and gray

To a chasm vast and deep and wide.

The old man crossed in the twilight dim.

The sullen stream had no fears for him;

But he turned when safe on the other side

And built a bridge to span the tide.

“Old man,” said a pilgrim near,

You are wasting your strength building here;

Your journey will end at the ending day,

You never again will pass this way;

You’ve crossed the chasm deep and wide,

Why build this bridge at evening tide?”

 
The builder lifted his old gray head-

“Good friend, in the path I have come,” he said,

“There followeth after me today

A youth whose feet must pass this way, 

This chasm that has been as naught to me

To that fair-headed youth may a pitfall be,

He too, must cross in the twilight dim,

Good friend, I am building this bridge for him.”

                            Will Allen Dromgoole