I already know this stuff...  

Engaging Students in Geometry
A Senior High Syllabus


prepared by Mike Yansak

     

 

     
 

SAMPLE SYLLABUS

Geometry is much more than just shapes and sizes. In this course, we'll also learn to use Socratic methods for understanding logic and proof. Some of this you'll remember from Algebra. Sometimes, you'll need reminders. We'll pace ourselves. Breathe deep, trust in yourselves and each other, and prepare to learn:

* narrative forms of logic and proof
* 2-column methods for steps and theorems
* intuitive experiments
* how to work with pictures and manipulatives

 

WHY YOU TAKE THIS COURSE

Geometry is far more than theorems and shapes. In fact, geo means "earth," and as we each perceive the world about us through some combination of spatial relationships, geometry is very much the study of our world. In this class, you will gain experience in using shapes and their properties in real-world situations. The use of figures, pictures, and manipulatives may be one of the most powerful tools in problem-solving. In this class, you will also gain further skills in implementing inductive and deductive reasoning, to reach logical solutions to problems. This combination of experiential, hands-on learning and mathematical reasoning, you will become a better person, because you'll be a better problem solver in real-world situations.

HOW THIS COURSE WORKS

You will be using manipulatives; engaging in group and individual experiments; doing a little work with transformations in moving shapes around on the coordinate plane; getting some mathematical history and biographical information about our heroes in geometry, including René Descartes and his spider; introductions to early Euclidean postulates; comparative study of non-Euclidean geometry; and contemporary chaos theories, in the area of fractals geometry.

A BREAK-DOWN OF THE GRADING

* Writing Assignments

Journal: You are required to keep a regular journal telling me how your experiences with geometry shapes up in this course. Yes, you can include some diagrams or drawings. A more complete description of my expectations will be discussed during the first full week of classes. (Journal = 100 points)

Paper: A research/writing assignment will be given around the middle of the semester. You'll be comparing early Euclidean models of geometry to mathematical precepts of today. I'll need to approve your specific topic. More detailed information on the paper will be given to you when timely, but be thinking of a topic that you find really interesting. (Paper = 100 points)

* In-class Assignments and Homework

Individual: Periodically, you will be given homework assignments to be turned in; quizzes in class (sometimes without warning); and various other individual projects, to be announced. All this brainstorming will total 200 points.

Group: You will be spending a lot of time in groups in this course. And a lot of group assignments, group projects, etc., will arise from this group work. Altogether, the group stuff will total 150 points.

* Tests

A total of 3 rather traditional assessment devices, just like in Algebra, will be given during the semester; the points will be divided as follows:

Test 1: 100 points
Test 2: 150 points
Final Exam: 200 points

So, the overall grading structure is measured like this:

Written assignments, 200 points = 20 %
In-class and homework, 350 points = 35%
Tests, 450 points = 45%
TOTAL: 1,000 points = 100%

With this structure in mind, the grading scale will look like this:

A = 90-100%
B = 78-89%
C = 66-77%
F = 65% and below

OTHER IMPORTANT STUFF

* Attendance. I already know this stuff. If you don't, you need to be here, so I can teach it to you. If you do, I need you here to help your classmates who don't get it. If you're bored, let me know. We'll try to get you into the TA program at the school. If you're lost, tell me, and I'll work with you individually. Any way you look at it, we're in this together, so be here.

* Make-Ups. Just like in Algebra, make-up work does not exist in this class. Get to know School policies on excused and unexcused absences.

* Reading. I'd really appreciate it if you'd study the sections of all reading assignments before we discuss them in class. This is your final core requirement in mathematics, and I'd hate to see you trip up here.

* Cheating. As always: don't do it. School policy will be followed.

* Important dates. Will be announced by the second week of classes.

* Class structure. We get to move around and play with stuff a lot in this class. This as an intellectual adventure, and we're partners. Work with your groups fairly; contribute equally; and expect to stay focused.

* Your standard reminder: I am a public servant. This is your final mathematics requirement. Keep in touch with me. Let me know how the course can improve. Let's all stay on our toes.

 
     

 

 

 Text © 1997 by Mike Yansak
 
     
 

 Original Graphic © 1997 by Jim Davis-Rosenthal
 

 

 

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