Math 3610
Introduction to Geometry
Dr. Sarah J. Greenwald

Where to Get Help

  • Office Hours 326 Walker Hall, 262-2363. I am always happy to help you in office hours. An open door means that I am on the floor somewhere, so come look for me.
  • Check the main web page often.
  • The WebCT Bulletin Board is the easiest way to ask a math question outside of class and office hours. I prefer that you use office hours since it is easier to discuss material in person, but if you can not make them, then the newsgroup is a great alternative.

    Required Resources

  • The Geometric Viewpoint: A Survey of Geometries by Thomas Q. Sibley     text available for rental from the bookstore
  • Roads to Geometry by Edward C. Wallace and Stephen F. West     text available for rental from the bookstore
  • access to a web-browser at least once every 48 hours
  • 3-ring binder notebook and a hole puncher to organize handouts, notes and your work
  • printouts of your work - see for information about ASU charging for print services.
  • manipulatives required to complete projects

    Course Goals

  • An introduction to the foundations of geometry through mathematical reasoning and proofs, manipulatives, dynamic geometry software, and the historical progression of geometry.
  • To model various ways of teaching and learning geometry.
  • Develop problem solving, visualization and proof-writing skills.
  • Math 3610 has been designated as a speaking course. In order to satisfy the speaking designator, presentations will occur during the semester and during a final project.


    This is a mathematics content course, which means that it will stimulate the intellectual growth of each student. While many of you are future teachers and some of the mathematics covered in the course will be related in meaningful ways to materials that can be taken into the classroom (for example, various ways of teaching and learning geometry will be modeled), the primary purpose of this course is your mathematical development.

    Catalog Description

    A study of the development of Euclidean geometry including both the synthetic and the metric approach. Topics to be considered include parallelism and similarity, measurements, ruler and compass constructions, and consideration of at least one non-Euclidean geometry.


  • Participation in Classroom Activities 15% You are expected to contribute to discussions, read messages from Dr. Sarah on the WebCT bulletin board, and complete homework. You are also expected to actively engage the material in class and lab. These kinds of baseline activities will result in a participation grade of 12/15. Other activities can increase or decrease this grade. Asking and answering thought provoking questions, coming up with creative ways of thinking about the material, and explaining the material to others are some examples of positive participation that will increase your grade. On the other hand, doing work or holding conversations unrelated to the class, sleeping in class, letting your cell phone ring in class, talking to your neighbors instead of engaging the material, challenging authority instead of looking for answers within yourself, leaving the classroom, refusing to engage in the baseline activities and performing other activities that detract from the professional classroom environment will result in a lowered participation grade.
  • Attendance Policy There will be days when the activities are designed to be completed during class. Thus, attendance is required at ALL classes. If the university is open and you miss part or all of a class, then that counts as an absence. If you must be late to a class, or must leave early, then do still attend, although you can expect that the portion of the class that you miss will be deducted from your attendance allowance. You will receive (-.5*credit hours of absences + 1.5) / 100 added onto or subtracted from your final average. Missing more than 6 classes will result in an automatic grade of F in the class.
  • Projects 35% Work will not be accepted without explanation and must also be turned in on or before the due date. May occur the last week of classes. If there is some reason you must miss a class, then obtain the assignment from the web pages. The lowest project will be dropped - save this for emergencies. Every other project will be equally weighted regardless of the total number of points. If all of your projects are turned in on time AND you have received at least a grade of C (above 73%) for all work, then you will receive and on-time credit of +1 added on to your final average. No lates allowed.
  • Tests 25% Tests may be oral, written or on WebCT. Tests are not only an opportunity for you to demonstrate your mastery of the material, but are also an opportunity for you to be challenged with new material in order for you to make new connections. No make-ups allowed. May occur the last week of classes.
  • Final Project Presentations 15% will occur on Dec 13 from 12-2:30. No make-ups allowed.
  • Professional Development 10% Two (no repetition) of the following activities are expected from each student outside of class. Personal reflection containing a written description and evaluation of each activity is required. This should be no more than three pages long and must include the dates, times and duration of each activity. The first report must be turned in no later than November 10. The second report must be turned in by Dec 8.
                Attend two seminars or colloquia in the mathematics department. Dr. Sarah will post info on WebCT.
                Help out in the math lab by volunteering as a tutor for two hours.
                Participate in three meetings of the math club (student chapter of the Mathematics Association of America).
                Participate in three meetings of PTMA (Prospective Teachers of Mathematics Association).
                Participate for three hours in the faculty-student tea.
                Attend a professional meeting (mathematics or mathematics education) at the national, state, or regional level.
                Design a small interview and use it with at least two high school mathematics teachers of geometry.
                Observe two high school geometry classes.
  • Extra credit There will extra credit opportunities during the semester for which points will accumulate. When final grades are given, extra credit points are taken into account in the determination of -, nothing, or + attached to a letter grade.

    Other Policies and Methodology

    Plan to spend 5-7 hours per week, out of class, on average, on this course. You are responsible for all material covered and all announcements and assignments made at each class, whether you are present or not. You are also responsible for announcements made on the web pages, so check them often.

    Asking questions, and explaining things to others, in or out of class, is one of the best ways to improve your understanding of the material. This course is to be an environment in which everyone feels comfortable asking questions, making mistakes, offering good guesses and ideas, and is respectful to one another. Turn in projects or prepare to present problems even if it they are not complete, even if only to say, "I do not understand such and such" or "I am stuck here." Be as specific as possible. When writing up work, be sure to give acknowledgment where it is due. Submitting someone else's work as your own (PLAGIARISM) is a serious violation of the University's Academic Integrity Code.

    In this course, you will be challenged with problems that you have never seen before. I do not expect you to be able to solve all the issues immediately. Instead, I want to see what you can do on your own. Out in the real world, this is important, since no matter what job you have, you will be expected to seek out information and answers to new topics you have not seen before. This may feel uncomfortable and frustrating. I understand this and want to help you through the process. It helps to remember that there are no mathematical dead-ends! Each time we get stuck, it teaches us something about the problem we are working on, and leads us to a deeper understanding of the mathematics.

    In the real world though, you are not expected to face your work alone. You will be allowed to talk to other people and you may even be expected to work with other people. In this class, you are also not expected to face your work alone. I am always happy to help you in class, during office hours (or by appointment), or on the WebCT bulletin board, and will try to give you hints and direction. At times though, to encourage the exploration process, I may direct you to rethink a problem and to come back to discuss it with me again afterwards. This occurs when I believe that the struggle to understand is imperative for your deep understanding of the material.