| Clint Erb 535 Waterman 656-3356 cerb@zoo.uvm.edu | Karen Rich Essex Junction High School 879-5533 |
Course Theme: Teaching for Understanding
Prerequisites: Acceptance into the Secondary Teacher Education Program, and prior or simultaneous enrollment in EDSC 216 "General Methods for Secondary Teachers".
Purpose: The purpose of this course is to help prepare mathematics teachers to meet the mathematics educational goals for their students as reflected in the following statement from the NCTM curriculum standards. "Educational goals for students must reflect the importance of mathematical literacy. Toward this end, the K-12 standards articulate five general goals for all students: (1) that they learn to value mathematics, (2) that they become confident in their ability to do mathematics, (3) that they become mathematical problem solvers, (4) that they learn to communicate mathematically, and (5) that they learn to reason mathematically. These goals imply that students should be exposed to numerous and varied interrelated experiences that encourage them to value the mathematical enterprise, to develop mathematical habits of mind, and to understand and appreciate the role of mathematics in human affairs; that they should be encourage to explore, to guess, and even to make and correct errors so that they gain confidence in their ability to solve complex problems; that they should read, write, and discuss mathematics; and that they should conjecture, test, and build arguments about a conjecture's validity." [NCTM Standards, p. 5]
Objectives: To enable students to take the ideas and concepts developed in the general methods course, EDSC 216: "General Methods for Secondary Teachers" and apply them to instruction in mathematics; To become familiar with the research in the teaching of mathematics; To address specific teaching problems within mathematics; To be able to develop planning formats and lessons within mathematics; To develop skills in setting instructional goals and objectives, curriculum planning and design, instructional techniques, instructional technology, and collaborative and consultative skills.
CESS Common Goals: To make use of professional concepts, theoretical terms and scholarly understandings to communicate with colleagues about professional matters; To engage in the study of practice and to address professional problems by making use of rigorous procedures of inquiry; To participate fully in the obligations of professional roles; To collaborate with colleagues in working toward common goals.
State Competencies for Mathematics Teachers:
The work you will do in this course will be divided into two main sections - - the work you do in class and what you do out of class. The homework assignments are designed in part to acquaint you with the sources of information that are available to the teacher. The in-class discussions will center around current issues of importance to the mathematics educator such as problem solving, curriculum, and the use of calculators and computers. We will look at the question of evaluation including testing, test construction and grading. Most secondary math courses are taught from a deductive approach so we will look at some examples of teaching using induction along with the use of patterns. Micro-teaching will also be an activity that is central to this course. An important aspect of this course is for you to clarify and refine your "educational philosophy" regarding the teaching of mathematics.
In addition to, or possibly in place of any of the above, I would like to follow up any special interests that you might have so be sure to make your desires and interests known.
Major Course Requirements:
Readings - Students will be assigned readings from the text and the NCTM Standards. For all the readings in the Standards each student will write a one page reaction to the standard. All levels of any standard will be read if that standard is covered at more than one level.
It is expected that any assignment from the text will be read and every student will come to class prepared to talk about the material in that assignment.
Observations - You will observe a different classroom teacher once every two weeks for a total of 7 observations. You will write a one page summary of the observation along with any comments. The observation may be general in nature or look at an assigned aspect of teaching.
Journal - The post-bac students will track two of their students, one male and one female, looking at their progress in their course, their performance and/or behavior and what seems to influence same, and any other aspects that seems appropriate. Do not use names in keeping this journal or make up false names.
The undergraduates will follow the two interns at Essex Junction. They will observe the intern 3 times over the course of the semester and interview them every week regarding their experiences or anything else which seems appropriate.
More direction will follow in class.
Five-Minute Activities - You will prepare ten activities that can be presented to a class in five minutes. They can be used when your lesson has ended early and there is a little time left in the period. It can be something that can stand on its own merit or some activity to supplement a lesson.
Put each activity on a 4x6 or 5x8 card (not 3x5). Include the following on each card: name of activity, concept being developed, materials needed (if any), procedure, and the source of the idea.
Unit Plan - You will write a unit plan for a topic which extends over a period of at least 2 weeks. This unit plan will be the context for many of the other assignments for this course (lesson plan, micro-teaching, test construction, and student portfolio project). This unit plan and all of its parts should be something which will be appropriate for your professional portfolio.
Lesson Plan - You will write a complete lesson plan which is one of the lessons from your unit. This lesson will also be the lesson you will present for your micro-teaching.
Book Review - You will read a book of your own choosing about a topic related to teaching math or one that could be used in teaching math. You are not to use a book that you are reading for another class. Some suggestions are:
Mindstorms - Seymour Papert
How Children Fail - John Holt
Why Johnny Can't Add - Morris Kline
How To Solve It - George Polya
Flatland - Edwin Abbott
Don't consider this list exhaustive. If you know of a book you would like to read, just clear it with me first. After reading the book write a 2-3 page report which gives a summary of the book, your personal opinion of it, and how it relates to teaching and your professional development.
Research Paper - Identify an issue which is pertinent to mathematics education today and write a 1000-1500 (4-6 typed pages) research paper about that issue. Follow proper form with appropriate footnotes and bibliographic references. State the issue, the opinions of professionals on the issue and then your position.
Some suggestions are:
Writing in the Mathematics Classroom
The Use of History in Math Classes
Should Algebra be Taught to Eighth Graders?
Women and Mathematics
Computers and the Mathematics Teacher
Hetrogeneous Grouping in Math Classes
Using Cooperative Learning in Math Class
Multiculturalism and Maathematics
Micro-teaching - You will teach one 15 minute lesson to the class. The material that is developed in the lesson plan above will be the subject that is presented.
Instructions for micro-teaching:
Test Construction - You will construct an objective math test that will include a variety of types of items (true/false, multiple choice, completion, etc.). The test will be the test which will cover all the material in your unit. More details will be given when test construction is the topic of discussion.
| Date | Topics | Assignments due |
|---|---|---|
| 1/24 | Introduction - handouts Standards - Introduction | Mathematics questions - quiz |
| 1/31 | Issues and resources Standards - Problem Solving | Math Understanding - Skemp article Standard 1 - Intro & Problem Solving |
| 2/7 | Problem solving | Problem solving handouts |
| 2/14 | Standards - Communication Modes of Instruction | Standard 2 - Communication Ch. 1 Farrell - Modes of Instruction Ch. 2 Farrell - Feedback |
| 2/21 | Standards - Reasoning Objectives of tching math Lesson Planning | Standard 3 - Reasoning Ch. 5 Farrell - Instructional Obj. Ch. 6 Farrell - The Lrning of Math. |
| 2/28 | Standards - Connections Design of Instruction Lesson Planning | Standard 4 - Connections Ch. 7 Farrell - Design of Inst. Strat. |
| 3/6 | Test construction Grading | Ch. 8 Farrell - Evaluation of Inst. Grade sample test Book reports due |
| 3/13 | Portfolios, Evaluation | Standards - Evaluation |
| 3/20 | UVM Spring recess - No Class | |
| 3/31 | Manipulatives in Secondary Math classes | Test assignment due |
| 4/3 | Graphing calculators | |
| 4/17 | Micro-teaching | Lesson plans if teaching |
| 4/24 | Micro-teaching | Lesson plans if teaching |
| 4/10 | Micro-teaching | Lesson plans if teaching |
| 5/2 | Share papers (in groups) | Research papers due |
Evaluation Criteria: The grade in this course will be a composite of your work on the assignments and your participation in the class sessions. Students will develop a professional portfolio which could include a resume, transcript, lessons plans, tests, plus any other work of significance.
Required Texts:
Readings: