Mathematics for Elementary Teachers I

MATH 112, Fall 2006

Benedictine University


Basic Information

Team Homework

Academic Honesty

Course Description

Learning Logs

Academic Accommodations For Religious Obligations (AAFRO) Honesty

Course Goals


Other Information



Assignment Schedule

Evaluation Final Assignment and Oral Exam Dr. Tim Comar's Homepage

Technology Requirement

Attendance and Tardiness

Basic Information:

Instructor: Dr. Timothy D. Comar

Location: BK 226

Office: Birck 128

Phone: 829 - 6555

Time: Monday, Wednesday, Friday: 8:00 a.m. – 9:10 a.m.


Web Site:

WebCT login:

Office Hours:


10:45 a.m. - 11:45 a.m.

1:30 p.m. - 3:00 p.m.


10:45 a.m. - 11:45 a.m.

1:30 p.m. - 3:00 p.m.


10:45 a.m. - 11:45 a.m.
Also: by appointment


T. Bassarear, Mathematics for Elementary School Teachers, 3e, Houghton Mifflin Company, 2005.

T. Bassarear, Mathematics for Elementary School Teachers: Explorations, 3e, Houghton Mifflin Company, 2005.

Bassarear's Student Manipulative Kit, ETA/Cuisenaire®.

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Course Description:

This course is designed to deeply explore mathematical content of elementary school mathematics.  Specifically, we will focus on problem solving, numeration, arithmetic operations, estimation, number theory, integers, fractions, proportions, and percents.  Our approach will primarily consist of cooperative, exploratory activities. This course is designed to reflect the NCTM's Principles and Standards,  the Illinois State Board of Education's Content-Area Standards for Educators, and the Conference Board of the Mathematical Science publication, the Mathematical Education of Teachers.

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Course Goals:

This course is designed to enable you to become a confident and successful teacher of elementary mathematics. This course is specifically designed to help you develop and expand your mathematical compentency, understand the mathematical issues and complexities relevant to elementary school mathematics, and learn to apply the course material through improved thinking and problem solving. This course is also concerned with reinforcing and expanding your knowledge and understanding of fundamental mathematical principles.By the end of this course, you should be expected to develop a deep, confident, and working understanding of the aforementioned topics in elementary mathematics, appreciation of how the mathematical content appears in the elementary classroom and in society, and the increased problem solving abilities, which will enable you to develop a similarly deep understanding of other topics in elementary mathematics. 

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Core Goals:

This course contributes to the science component of the core. The course is intended to enable students to continue to meet the following core goals:

1.      Demonstrate an effective level of cognitive, communicative (oral and written), and research skills;

2.      Achieve a college level of computational skills and an ability to understand and interpret numerical data;

3.      Acquire a knowledge of the history and heritage of western civilization to include: c) scientific literacy through a knowledge of the history, the methods, and the impact of science on the individual, society, and the environment;

5.      Apply liberal learning in problem solving contexts as preparation for active participation in society;

6.      Make informed ethical decisions that promote personal integrity, the legitimate rights and aspirations of individuals and groups, and the common good.

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Learner Outcomes:

To successfully complete this course, the student will:

  1. Demonstrate ability to successfully approach mathematics problems four different ways: geometrically, algebraically, numerically, and verbally (oral and written forms); this will be achieved through homework assignments, group explorations, in-class discussions, exams, the learning log, and the final assignment.
  2. Evidence mastery of problem-solving techniques through homework assignments, group explorations, in-class discussions, exams, the learning log, and the final assignment.
  3. Evidence mastery of numeration, estimation, arithmetic algorithms through homework assignments, group explorations, in-class discussions, and exams.
  4. Evidence mastery of fractions and proportional reasoning through homework assignments, explorations, and the final assignment.
  5. Engage in mathematical dialogue through posing and addressing mathematical questions through group explorations, in-class discussions, and the learning log.
  6. Develop group work skills. This is achieved by student participation in classroom activities and group homework explorations.
  7. Develop enhanced written and oral communication skills in the area of scientific communication. This will be achieved through classroom participation, group work in the classroom and outside of class, homework assignments, explorations, the learning log, the oral exam, and the final assignment.

    IDEA Objectives:

    1. Developing specific skills, competencies, and points of view needed by professionals in the field most closely related to this course. (Essential)
    2. Learning to apply course material (to improve thinking, problem solving, and decisions). (Essential)
    3. Learning fundamental principles, generalizations, or theories. (Important)

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Your are expected to come to class regularly and on time.  You will not be admitted if you arrive more than fifteen minutes late. You are expected to work collaboratively or independently as assignments dictate and submit all required work on time.  Late papers will not be accepted. I would expect that you will need to spend at least eight hours per week outside of class on this course.  Be prepared to assimilate concepts over time, look at content from different perspectives, reflect upon your learning as the course proceeds.  Ask questions!  If there is material with which you are not fully comfortable, you are expected to ask questions either during class or during office hours.

Even though this course addresses the content of elementary school mathematics, "elementary" does not imply that the course content is easy or trivial. It is our goal to develop a deeper understanding of the content elementary school mathematics so that you can become successful, effective, and vertisatile teachers and become life-long learners. There is a significant amount of homework in this course. If you are struggling with the content, you may need to devote more than the recommended number of hours. Please seek appropriate assistance to help you complete your work within a reasonable amount of time.

This course is specifically designed to help you become a successful professional as an elementary (or middle) school teacher. Therefore, professional conduct is expected in all aspects of this course inside and outside of the classroom. Respect for fellow classmates, the instructor, and the content is expected. As a positive attitude will be necessary part of your success as a teacher, a positive attitude is necessary in this course. Cell phones and pagers must be turned off. If yours rings during class, you will be expected to take your possessions and leave class for the day.

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Technology Requirement:

Students are expected to use WebCT for all course communications, accessing notes and course information, and the completion of certain assignments as indicated in this syllabus. Learing Log Reflections are to be prepared using word processing software. A calculator may be needed for some activities and homework. Written homework is expected to be completed using MS Word.

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Team Homework


Individual Homework 15%

Learning Log (Other than Individual HW)




Exam I


Exam II


Final Oral Exam


Final Assignment



The grading scale is 90% for A, 80% for B, 70% for C, and 60% for a D.  It is the student’s responsibility to seek clarification of the course requirements and evaluation policy.

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Team Homework:

Homework problems from the text are assigned to reinforce concepts addressed in the explorations and in the text. Success with the these problems may also improve your performance on the Basic Skills Test. Problems will be collected on the dates listed on the syllabus. You are still responsible for including the other problems in your learning log, the content of which may appear on exams.  You will be evaluated primarily on the quality and correctness of your team and individual homework solutions. You will have the opportunity to resubmit homework until the instructor is satisfied with the quality, clarity, and correctness of the solution.  Only one paper will be collected from each homework team.  The grading rubric for team homework problems is as follows:


Correct answer and solution with appropriate details and labeling


Incorrect but close answer due to minor computational or miscopying error


Incorrect answer, but solution is generally on track; problems with one aspect of problem


Incorrect, but work shows some understanding of problem


Incorrect, but shows evidence of work beyond simply copying the given information


Problem not submitted on time


Studying mathematics is a social process. Much benefit can be gained by sharing insights and by struggling through problems with your peers.  Learn to work with each other and learn from each other. Some activities may require follow-up work and re-writing outside of class.   You are strongly encouraged to study and work with other class members. You are also strongly encouraged to consult Dr. Comar outside of the class periods either during office hours or via e-mail at

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Learning Logs:

The learning log is your record of your thinking process, ideas, and reflections on various homework questions and problems.  Here, the goal to concentrate on "making sense of ideas" rather than trying "to get it."  This is an appropriate place to focus of the fourth step in Polya's problem-solving strategy:  "looking back." This is also a good place to record your thoughts on why problem solutions work rather than just on how they work and connections between topics and discussions throughout the course. This is also a good place to pose questions, to which you can return and answer at a later time.  The learning log is designed for you to think deeply about the ideas and concepts in the course, to reflect on your understanding of these concepts, and to record your intellectual growth throughout the course.  To help with this, some additional questions will be posted on the course website for you to respond to in your learning log. Your final entries in your learning log will consist of documentation of your intellectual growth in this course; please keep track of all your and your progress throughout the term to prepare these entries. There will we three main sections in your learning logs: Exploration Reflections, Text and Problem Reflections, Individual Homework Problems.

Exploration Reflections:

For each exploration, BRIEFLY reflect on the following questions in your learning log:

  1. What content standards were addressed?
  2. What process standards were addressed?
  3. What new insights did the exploration or activity help you make? Were any connections made between different mathematical concepts?
  4. What problem solving tools did you use in this exploration?
  5. What did you find difficult about the exploration?
  6. What is the relavance of the exploration?
  7. What thoughts do you have on implementing this content and a similar style activity?
  8. What further questions do you have? (You are REQUIRED to pose at least ONE question.)

Text and Problem Reflections:

For each section of the text and its corresponding exercise set, reflect on the following questions in your learning log:

  1. What key mathematical ideas are addressed?
  2. What new insights do you have about the content?
  3. What is the relevance of the content? Describe any "classroom connections" in the section.
  4. What did you find difficult about the content?
  5. What further questions do you have? (You are REQUIRED to pose at least ONE question.)


Please organize your reflections by numbering your responses according to the question listed above. One point will be awarded for each of the questions listed above. Occasionally, additional questions will be added to your reflections and will be awarded points for answering. You will be required to submit Exploration Reflections with your "SELF" homework problems for each Exploration completed in class since your last submission. You will be required to to submit Text and Problem Reflections with your "SELF" homework for the text section containing the problem set. As you develop your questions, you will likely raise good, pedagogical questions, which would will be addressed in your methods courses. Keep track of these questions in addition to your mathematical content questions, as you will be able to answer them down the road. Extra credit may be granted at the instructor's discretion for any of the following:  unsolicited connections between various aspects and topics, unsolicited answers to your own questions, unsolicited insights that you develop. 

Individual Homework:

Your learning logs will also contain your complete solutions for your individual homework problems. The same grading rubric and correction policy applies to both the individual and team problems. Corrected problems should be kept in this section as well. Please see above for details. Only six "self" problems will be collected per assignment. You may choose which six problems you will submit. Additional problems will count for extra credit if you have completed at least five problems correctly. Resubmission of problems for additional credit is strongly encouraged.

Your learning log is your record of your learning and growth throughout this course. Please organize your complete learning log in the following manner. Use a 3-ring binder. Separate your binder into 4 sections: Exploration Reflections, Text and Problem Reflections, Individual Problems, and Team Problems. Each component should be stapled and submitted in the grading box separately. Please staple your in class Exploration work to the corresponding reflection. Reflections should be typed so that both you and the instructor can read them. You are encouraged but not required to electronically prepare your homework assignments as well.

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A significant part of your learning in this course, inside and outside of the classroom, will occur through working on discovery-based activities in the Explorations volume of the text.  These activities will consist of exploratory team activities, discussions, and written work. Significant portions of the explorations will be submitted for evaluation, which will follow the same grading rubric as for the team homework problems.

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There will two in-class exams during the semester. The in-class exam dates are 10/2/06 and 11/10/06.  Exams cannot be made up or retaken.  If you miss an exam, your total exam score will be based on your performance on the other exams including the final.  The instructor may choose to allow calculators on particular exams. Calculators with computer algebra systems including the TI-89, TI-92, and the TI-92+ are never permitted on exams. The instructor reserves the right to delete all calculator memory prior to an exam.

Final Assignment and Oral Exam:

This assignment is designed to allow you explore some mathematical content, synthesize the content, and present a portion of your work to the class.  You will be given the assignment (a take home exam) the last day of class. The oral exam will be scheduled for 10 minute period during the final exam period for this course: Friday, 12/15/05 at 7:30 am - 10:00 am. This written assigment will be due by the later of your scheduled oral exam and 8:00 am on 12/15/05.

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Absence and Tardiness:

Absence due to documented illness, participation in Benedictine University athletic activities, religious observance, or other extenuating circumstances will be excused according to the AAFRO policy below.  It is your responsibility to inform Dr. Comar in the event of such absences.  Class attendance is very important.  Others will depend on you to be to participate in group exercises.  It is incumbent upon you to obtain class notes and updated assignments for missed classes. Tardiness will interfere with your time to complete homework quizzes and exams.  No student shall be admitted fifteen minutes after the scheduled classtime.

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Academic Honesty:

The search for truth and the dissemination of knowledge are the central missions of a university. Benedictine University pursues these missions in an environment guided by our Roman Catholic tradition and our Benedictine heritage. Integrity and honesty are therefore expected of all members of the University community, including students, faculty members, administration, and staff. Actions such as cheating, plagiarism, collusion, fabrication, forgery, falsification, destruction, multiple submission, solicitation, and misrepresentation, are violations of these expectations and constitute unacceptable behavior in the University community. The penalties for such actions can range from a private verbal warning, all the way to expulsion from the University. The University's Academic Honesty Policy is available at , and students are expected to read it. Acts of any sort of academic dishonesty will not be tolerated.  All instances will be pursued.  The first case of any academic dishonesty will result in a grade of zero for the assignment.  A second case will result in failure of the course. Any incident of academic honesty on the final exam will result in failure of the course.

Your name should appear on all of your submissions of your work.  If collaboration is allowed, you must state with whom you have collaborated. You are responsible for understanding any authorized collaboriation policies on specific assignments. You must also properly reference any other print, electronic, or human resource that you consult. Using unauthorized electronic media during exams and quizzes is a violations of this policy. Plagiarism of any sort--from print, online, other electronic media or from your peers--is a violation of this policy. If your submitted homework appears identical in whole or in part to that of another student in the course, plagiarism will be assumed.

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Academic Accommodations For Religious Obligations (AAFRO)

A student whose religious obligation conflicts with a course requirement may request an academic accommodation from the instructor. Students must make such requests in writing by the end of the first week of the class.

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Other Information:

If you have a documented learning, psychological or physical disability, you may be eligible for reasonable academic accommodations or services. To request accommodations or services, please contact Tina Sonderby in the Academic Resource Center, 249 Kindlon Hall, 630-829-6512. All students are expected to fulfill essential course requirements. The University will not waive any essential skill or requirement of a course or degree program.

Final Drop Date: November 17, 2006

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This syllabus is subject to change. Any changes will be communicated to all class members electronically.

Contact Dr. Comar:

 Dr. Tim Comar's Homepage 

Benedictine University Homepage | Department of Mathematics | Faculty Profiles