Longwood University
Department of Mathematics & Computer Science
MATH 313 (Geometry & Reasoning, Fall 2011)
Instructor: Dr. Wendy Hageman Smith
Email: smithwh@longwood.edu
Office: 346 Ruffner; Phone 395-2992
Math Office: 395-2194, 395-2865(fax)
Class Time: Lecture: TR (12:30 – 1:45), Room G54 Ruffner Lab: G56 Ruffner
Dr. Hageman Smith – OFFICE HOURS
Monday and Wednesday; 3:00-4:00
Tuesday &Thursday; 3:30-4:30
Friday: by appointment
Texts:
Beckmann, Sybilla (2008). Mathematics for Elementary Teachers (With accompanying
workbook) 3rd ed. Pearson/Addison Wesley. (ISBN: 978-0-321-65427-4 )
Mobius Education Group (2007). Virginia Procedural Fluency Workbook
(ISBN : 1-60120-016-1)
Smith, B. and Smith, W. (2006) Studying Math : pathways to success, 2nd ed. Thompson Publ.
(ISBN : 0-7593-9002-9)
Other Required Materials :
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Computer disks, CD’s or jump-drives to save course material & computer files
Colored pencils, Patty paper, Compass, Protractor/StraightEdge
Geometer’s Sketchpad software (available in most campus labs; purchasing the student
edition of Geometer’s Sketchpad, is optional but suggested. The software may be
purchased online for $39.95 at www.keypress.com . There is a second dynamic
geometry software program called GeoGebra that is downloadable for free from the
world wide web. Either of these programs are recommended for this class.
Course Description: . Geometry and Reasoning. Examines properties of and relationships
between geometric figures, measurement, concepts of perimeter, area, and volume of two- and
three-dimensional figures, transformations and coordinate geometry, constructions, the
Pythagorean Theorem and trigonometric ratios, and geometric reasoning both deductive and
inductive in a problem-solving environment through student investigations and hands-on
activities.
COURSE CONTENT AND GOALS:
The first week of the 313 class will be spent learning about and reflecting upon Math Anxiety.
Not only do many teachers (and future teachers) suffer from some form of math anxiety, but also
more importantly, negative feelings are transferable to elementary students via teacher attitudes
about mathematics and methods of teaching mathematics. In an effort to address this
phenomenon, it is important to discuss in class those attitudes. Read the booklet Studying Math:
Pathways to Success and be prepared to discuss the material in class.
For the remainder of the semester, come to class prepared to explore and refine your knowledge
of chapter content as the accompanying schedule dictates. “Prepared” means you have read the
chapter before coming to class. You have already seen/learned the mathematics in this book – it
is elementary school mathematics. However, this class is not about simply “doing the math
problem”, but developing a deeper knowledge of the structures that give rise to “doing the
math.” This includes methods and philosophical/research-based ideas on the teaching of
mathematics. For much of class-time, you will be exploring and refining your knowledge for the
assigned chapter content. The activities manual for the class will be used for most in-class
activities except labs. So then, the course has three primary goals:
1) To re-examine the content knowledge of the mathematics that you will teach and improve
your math skill.
2) To give you the skills and knowledge you need to pass the mathematics section of the Praxis I
exam.
3) Develop knowledge about pedagogical methods and will also be included in the math
Anxiety portion of the class and then modeled throughout the semester in class via discussion
and in-class activities.
Lectures will usually be brief, as I think you will get more out of working problems than
watching me do so. Discussions will include whole-class participation and small group
participation. Your attendance is mandatory, so if you do not think you can attend class
regularly, DROP NOW.
YOUR INSTRUCTOR:
Please do not hesitate to come and get help if you need it. I am here to help facilitate your
learning mathematics. The most important thing to remember is that I am available to help, that
is my job, so do not wait until problems reach critical mass. He who hesitates is lost, so don't
hesitate.
You are responsible for everything that happens in class. I am of course willing to help you, but I
am not willing to re-teach the course in my office. If you miss class, get the notes from someone,
try the problems, and then come get help.
If you have specific physical, psychiatric, or learning disabilities and require accommodations,
please let me know early in the semester so that your learning needs may be appropriately met.
You will need to provide documentation of your disability to the Disability Services Office.
YOUR GRADE:
Your grade for the class will be figured on in-class assignments, homework, tests and any
projects you may be assigned. I have provided all the particulars on how much each assignment
is worth, so you should be able to find a percentage given how much each assignment is worth
and how many points you received on the assignment. In the “General Grading Overview”
section on this syllabus is a breakdown of how grades are decided. If you are going to be
teachers, I think it is necessary that you are able to find an average (percent) and figure grades.
If you have any questions please feel free to come to office hours and I will assist you.
In-class work:
There will often be in-class work. You can only get one of two scores on in-class work: one
point for having made a serious attempt to do it, or zero. By serious I mean that I want to see all
work shown for the problem(s) you work on in class; do not just give me an answer. At the end
of the semester your grade for in-class work will be the number of points you have made divided
by the number of available points minus two assignments – up to a score of 100%. (That is, you
can miss two in-class assignments without penalty.)
You will be doing in-class assignments for just about every class. I do this to help your final
grade so please do not say that there is a lot of work for which you don’t receive credit as you do
receive credit and since it is not graded – per se – you have opportunity to “boost” you grade for
the class by coming and participating so you can learn the material without penalty.
FORMAT for in-class assignments: When you hand in in-class work EVERYONE does all the
problems and hands in their work. Whenever you hand in your in-class work, staple all group
members' work together and include a cover sheet with the date and SIGNATURES of all group
members included. For obvious reasons in-class assignments may not be made up. This is why I
drop two assignments.
At the beginning of the semester you will take a pre-test. This test will allow me to offer group
leader status to those who wish to be a group leader. The benefits and specifics of this will be
reviewed in class the first week of classes.
Homework: I do not grade homework for correctness. I will, however, assign homework on a
regular basis; if you do not practice mathematics you will not become proficient, homework is
your opportunity to become proficient. Homework comes in two flavors:
1) Weekly homework (up to three points total):
For any assigned homework, I will collect homework and give you a credit point
provided you have completed at least 80% of the assignment which INCLUDES
explaining your reasoning and showing YOUR WORK. Completion of these criteria is
the qualification for the 80% required to obtain a credit point for the homework
assignment. A homework assignment may include problems assigned from three
sources: Problems assigned from the textbook (0-1pt): You may also have a piece of the
homework assignment that includes problem(s) from the workbook. This portion of the
homework will also be worth 0-1pt. as for the portion from the textbook, but the same
rules apply for its completion. A third portion might include something from the web (or
some other source) and it will also be worth 0-1pt. and must be completed in the same
manner as specified above.
This flavor of homework is always due on the Tuesday after the week during which the
homework was assigned. (example: Homework for sections 10.1 and 10.2 would be
assigned the week of Sept. 6. That homework assignment would then be due the following
Tuesday Sept 13.)
2)
A second flavor of homework may sometimes be assigned and graded; I will advise you
when I assign this type of homework assignment.
The solutions for any homework assignment will be posted on the web page for the class the
day I hand back the homework assignment. This is so you can check your work to be sure you
understand the material. If you think you might still not understand the material, please come
to office hours and get help.
NOTE: I can assure you that the only students who do badly in my class are those I never see in
office hours (OK; also those who don’t hand in any work or do incomplete work).
Homework and in-class assignments combined constitute 20% of your course grade.
Projects:
This semester I will be introducing you to a geometry drawing program. We will meet in Ruffner
G56 for this introduction and a project will be assigned using the software. This project will be
completed individually but handed in as a group. I will give you a class day to complete the
project and so I want you to work on it together, as a group.
You will also have a second project that will have to do with creating a lesson using the materials
you are introduced to in class – the second project will not be based in Geometer’s Sketchpad.
Projects assigned are worth 15% of your grade.
NO STUDENT IS ALLOWED TO DO A GROUP PROJECT WITHOUT MY ASSIGNNING
THEM TO A GROUP.
Tests:
There will be two tests and a comprehensive final for this class. The two tests count as 40% of
your grade. You will be able to earn credit points for fixing the two tests but these opportunities
will ONLY BE OFFERED IN CLASS THE DAY THE TESTS ARE RETURNED. The
schedule included in the final pages of this syllabus shows the two tests take a week each. You
will take the test on the Tuesday of the test week and have the opportunity to fix your answers on
the following Thursday.
You will be required to create a “Dictionary” of terms in the textbook. The dictionary needs to
be created separately from your regular notebook as you can use it for the two tests. You will
NOT be able to use your dictionary for the final – you should know the terms very well by then.
The words for the dictionary come from the main body of text in each section of your textbook.
These words are in green in the margins and sometimes bolded in the text. I will give you
requirements for the dictionary the third week of class and post the requirements on Blackboard.
I will give to you a review sheet the week before the test that will list the chapters and problems
you should know for the test and your tests will consist of:
1) Any special problems identified and gone over in class.
2) Homework problems comparable to those assigned.
3) In-class problems comparable to those assigned in class.
Final: This course has a comprehensive final exam; will consist of mathematics content from the
entire semester including mathematics problems and discussion information based on in-class
activities and notes. The final counts as 25% of your grade.
General Grading Overview
Course Grades will be calculated using a 10 point scale as follows:
A = 90 ~ 100
B = 80 ~ 90
C = 70 ~ 80
D = 60 ~ 70
F = 0 ~ 60
Plus and minus grades are given at the discretion of the instructor.
In general, the achievement of a student in a course indicates the following:
A: Superior work
B: Above average work
C: Average work
D: Below average
I’m sure you have all seen this scaling and description before, but what does it mean?
I will award a grade of A only to a student who meets every standard of learning in the course,
and who in addition consistently exhibits excellence (0-2 mathematical errors and no
typographic/grammatical/directional errors) in their work. Absent consistent excellence (3-4
mathematical errors and minimal typographic/grammatical/directional errors), I award a B to the
student who meets every standard. I award a C to the student who has met most of the standards
of learning, but continues to struggle in acquiring some key skills or concepts. I award a grade
of D to a student who is capable but appears, based on their performance and effort, unable to
commit themselves to achieving a minimum acceptable standard. I reserve a failing grade only
for those students who do not meet minimum standards of learning, and who seem unable to do
so at the level of the course. This indicates that the student must, if he or she is to continue to
pursue the same educational goals, be prepared to repeat coursework and – most critical –
thoughtfully reexamine their goals and priorities with an eye towards reinventing themselves as a
student.
ADDITIONAL INFORMATION
Students are responsible for checking the ANNOUNCEMENTS in Blackboard in advance of
each class period as there will be important information regarding assignments, due dates, items
that must be brought to the next class session, etc. Also, students are responsible for
downloading all needed course documents from Blackboard, printing them if hardcopies are
desired, and knowing the information contained therein.
Class Attendance
As implied above in course content and goals and in the in-class assignments sections, students
are required to attend all classes. Due to the nature of this course, participation in activities and
discussion is vital to learning content and methods. Thus, missing class will hurt your
opportunity to succeed!
The following attendance policies are in effect for this course:
 A grade of “0” or “F” may be given on work missed because of unexcused absences
 A course grade of “F” may be assigned when the student has missed a total (excused and
unexcused) of 25 percent of the scheduled class meeting times (more than 5 absences)
 Acceptable excused absences (as listed in the Longwood catalog) will be taken into
consideration for missed tests; however, except in VERY EXTREME circumstances, be
sure to make PRIOR arrangements.
Longwood’s Honor System
A strong tradition of honor is fundamental to the quality of living and learning in the Longwood
community. The Honor System was founded in 1910, and its purpose is to create and sustain a
community in which all persons are treated with trust, respect, and dignity. Longwood affirms
the value and necessity of integrity in all intellectual community endeavors. Students are
expected to assume full responsibility for their actions and to refrain from lying, cheating,
stealing, and plagiarism.
The Longwood Honor Code applies to all work for the course as follows:
 Any out-of-class practice work or hand-in assignment can include using text information,
discussion with other class members, and/or discussion with instructor BUT, the final
product handed-in for the grade must be the student’s own work.
 Any in-class activities that involve teamwork allows for discussion within your team as
directed by the instructor.
 All tests are to be completed individually (unless otherwise noted in directions from
instructor). Please sign the honor code on all exams indicating that: “I have neither
given nor received help on this work, nor am I aware of any infraction of the Honor
Code.”
Schedule Outline
Note: This schedule is tentative, small changes may be made to this schedule through the
semester, according to how the class progresses, and will be announced in class before any
changes to the syllabus are initiated.
Week of
Chapter/Sec
Assignments/Tests
August 23
MA
On Tuesday we will start the section on Math Anxiety in class.
On Thursday we will be doing a Pre-test.
Aug 30
On Thursday we will finish the Math Anxiety unit.
Polya’s problem-solving posted on Blackboard.
September
6
10.1; 10.2
Sept 13
Sept 20
10.4; 10.5;
10.6
14.1; 14.2
Sept 27
14.2; 14.3
Start your vocabulary pages on a separate set of papers than in your
notebook.
On Thursday we will meet in the lab and start using GSP.
ACCTM theory posted on Blackboard.
Project1 Assigned
Van Hiele levels and Bloom’s taxonomy posted on Blackboard
October 4
Test1
Oct 13
Project 1 due
Oct 18
Oct 25
November
1
November
8
Nov 15
11.1; 11.2;
11.4; 14.4
14.5; 12.1;
12.2
12.3; 12.4;
12.6
12.7; 12.8;
12.9
Five Strands of Mathematical thinking posted on Blackboard.
Project 2 assigned
Test2
Nov 22
13.1; 13.2
Nov 29
13.3
Presentations of Project 2
Dec 5
Final Exams
Wednesday December 7