M 316L (Unique #55980)- Foundations of Geometry, Statistics, and Probability
Meeting time/place: MWF 10-11 am, RLM 6.116
Instructor:
Altha Rodin, RLM 11.110, 475-9517
[email protected]
Office hours:
MWF 2:00-3:00 pm and by appointment
Text: Reconceptualizing Mathematics for Elementary School Teachers; Sowder, Sowder, and
Nickerson
Course objectives:
This is an inquiry based course in the mathematics relevant to future teachers of elementary school
students. The goal is to provide you with the background and tools necessary to teach elementary
school mathematics in such a way as to ensure that your students learn good problem-solving skills,
gain the self-confidence needed to tackle non-routine problems, and have a sense of mathematics as
a connected body of knowledge that is consistent, relevant, and enjoyable. You will be asked to
reflect on your own approaches as well as those of your classmates. You will also be presenting
problems in oral and written form. You will get experience in giving and receiving feedback on
your mathematical communications (both oral and written.)
In order for you to get as much as you can from this class, it is essential that you attend class
regularly. In addition to being here, you must participate actively in class by presenting exercises,
being attentive to solutions presented by other students, allowing others to speak freely, asking
questions and offering constructive feedback to fellow students, accepting feedback and
constructive criticism offered to you, and generally contributing to a healthy learning environment.
More than two unexcused absences will negatively affect your participation grade.
Policy on Collaboration: Since unauthorized collaboration is considered academic dishonesty, it is
important that you know what kinds of collaboration are and are not authorized in this class.
1. The following activities are not only authorized but encouraged:
 Working on a problem with someone when neither of you has yet solved the problem
 Asking someone for a small hint if you have given a problem a serious try and are stuck.
 Giving a student who asks for help the smallest hint that you possibly can.
 Asking someone to listen to and critique your ideas on a problem.
 Listening to a student's ideas on a problem and critiquing them without giving away the
solution.
 Asking another person to read and critique your write-up of a problem.
 Reading and critiquing another student's write-up of a problem, pointing out errors but not
correcting major errors.
2. Unauthorized collaboration includes:
 Asking someone to show you the solution to a problem that hasn't been handed in or discussed
in class yet.
 Showing a student in the class a solution to a problem they have not yet solved and that hasn't
been handed in or discussed in class yet.
 Copying, either word for word or by rewording, a solution that you have not played a
significant part in obtaining. This includes a solution found in a book, a solution obtained by a
student or group of students in this class, a solution originating in this class in a previous year,
or any other source.
 Writing up a solution together with someone else, whether or not you have worked out the
solution together.
Authorized collaboration provides a learning experience for both parties. Unauthorized
collaboration benefits no one and, in fact, is educationally detrimental. Please do not put your
classmates in a difficult position by asking to copy their work.
Prerequisites: To enroll in this class, it is necessary that you have at least a grade of C- in M316K.
This prerequisite will be waived for students seeking Math Middle Grades Certification.
Exams: There will be three mid-semester exams (during regular class time) and a comprehensive
final exam. The dates for the mid-semester exams are:
Exam 1 – Wednesday, February 23
Exam 2 – Wednesday, March 30
Exam 3 – Wednesday, April 27
Final Exam – Friday, May 13, 9 am- 12 noon
The mid-semester exams have two components. You will be given 50 minutes to work the exam in
class. After class, you may rework at home any problems you think you have missed and complete
the ones you did not finish in class. You will turn in test corrections/completions the day after the
exam. No late corrections will be accepted. You can earn up to half credit back on any part of the
exam that you missed by working the problems correctly at home. No collaboration is allowed on
the take-home portion of the exam. Makeup exams will only be given with a valid, substantiated
excuse. The final exam is a three hour, in–class exam.
Homework Assignments: Homework will be assigned weekly. The homework consists of text
problems and problems that I will write up and post on Blackboard. You must keep your solutions
to the text problems in a homework folder or notebook. I will pick these up periodically and you
will get a completion grade for these problems. The problems posted on Blackboard will be picked
up on Fridays and will be graded. Solutions to these problems must be written up clearly and with
all work completely justified. No late homework will be accepted. If extenuating circumstances
prevent you from coming to class on days that homework is due, you can either send your work
with a classmate or email your work to me. Two assignment grades will be dropped.
Journal: As part of your coursework for this class, you are required to keep a class-related journal.
The journal will serve several purposes, including: encouraging you to reflect on your problem
solving behavior and other topics related to mathematics and teaching, giving you practice writing
about mathematics, providing feedback to me, and providing another means for me to give
feedback to you.
You are expected to make journal entries at least once a week, with each entry being at least
one half of a handwritten, standard sized page, or the equivalent word processed. Feel free to write
more than half a page per entry if you have more to say. Please date each entry and keep them in
chronological order. I will pick up journals every other week.
I will usually ask you to write on a specific topic. If I have not made a journal assignment, the
choice will be up to you. Possibilities include:
 Your reactions (thoughts, and feelings if you wish) to topics in the readings or discussed in
class.
 Analysis of how you go about solving problems (e.g., what strategies you most often use), and
how you might do so better.
 Insights you have had into various mathematical concepts.
 Comparing and contrasting how you and other students go about solving problems.
 Comparing and contrasting different solutions to the same problem.
 How you have used ideas discussed in this class in other classes or other situations in your life,
or how these relate to what we've discussed in class. (Students who have an extended field
experience or are student teaching this semester may have lots of comments related to those
experiences.)
 How you might incorporate ideas in this class in your own teaching.
 How you might use what you learned in solving one problem in solving another.
 Suggesting generalizations of problems we have discussed in class or in the homework.
 Describing problems you have made up, and why, when, and how they might be good teaching
problems.
 Asking questions about concepts you don't yet understand fully.
 Requests for specific kinds of feedback.
 Suggestions on how to improve this class.
 Discussion of what types of problems you like best, and why.
 Comments on your progress in any of the areas of the course objectives.
(Don't limit yourself to just one of these topics, however. Anything related to mathematics and
teaching mathematics is appropriate.)
Grading: Course grades will be based on all relevant information I have about you: performance
in class discussion and problem solving, homework turned in, exams, journal, and any other
information I have pertaining to your work in this class and its effect outside this class. Homework,
exams, journals, and quality of class participation will be weighted as follows:
Homework:
 graded homework - 15%
 text problems – 5%
Semester Exams - 15% each
Final - 20%
Class participation - 10%
Journal - 5%
Topics/Schedule: (Schedule subject to change)
Week 1 Problem Solving
Week 2: Introduction to Statistics
Week 3: Representing and Interpreting Data
Week 4: Dealing with Multiple Data Sets or Multiple Variables
Week 5: Introduction to Probability
Weeks 6&7: Computing more complicated probabilities
Week 8: Introduction to Geometry
Weeks 9&10: Polygons and Polyhedra
Week 11: Congruence and Similarity
Week 12: Perimeter, Area, and Volume
Week 13: The Pythagorean Theorem
Week 14: Symmetry
STUDENTS WITH DISABILITIES:
The University of Austin provides upon request appropriate academic accommodations for
qualified students with disabilities. For more information, contact the Office of the Dean of
Students at 471-6259, 471-6441 TTY.