Mathematics for Elementary Teachers I

MATH 112A, Fall 2014

Benedictine University


Basic Information

Team Homework

Academic Honesty

Course Description

Learning Logs

Academic Accommodations For Religious Obligations (AAFRO)

Course Goals


Electronic Devices Policy



Other Information


Final Assignment and Oral Exam

Assignment Schedule

Technology Requirement

Attendance and Tardiness

Dr. Tim Comar's Homepage

Basic Information:

Instructor: Dr. Timothy D. Comar

Location:  Kindlon 125

Office: Birck 128

Phone: 829 - 6555

Time: MW 3:00 p.m. - 4:40 p.m.


Web Site:

D2L login:

Office Hours:


10:30 a.m. -12:30 p.m.


11:00 a.m.-12:15 p.m.


11:00 a.m.-12:15 p.m.


10:30 a.m. -12:30 p.m.


by appointment


T. Bassarear, Mathematics for Elementary School Teachers, 5e, Houghton Mifflin Company, 2012.

T. Bassarear, Mathematics for Elementary School Teachers: Explorations, 5e, Houghton Mifflin Company, 2012.

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 Common Core State Standards for Mathematics, the NCTM's Principles and Standards, the Illinois State Board of Education's Standards for Endorsements in Elementary Education, and the Conference Board of the Mathematical Science publication, the Mathematical Education of Teachers. For subject to the 2014-2015 or later catalog, this course is the first of three mathematics courses required of all Elementary Education majors. (Math 112, Math 222 (offered each spring semester), and Math 223 (to be offered for the first time during the 2015-2016 academic year). All Elementary Education majors are required to take Math 112 and Math 222.

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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 competency, 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 (2013-2014 Catalog or Earlier Catalog):

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. Know, understand, and implement the NCTM Process Standards and Common Core Standards for Mathematical Practice. (c.1)
  2. Be prepared to develop student proficiency and address common misconceptions related to counting and cardinality. (c.2)
  3. Be prepared to develop student proficiency and address common misconceptions related to operations and algebraic thinking. (c.3)
  4. Be prepared to develop student proficiency and address common misconceptions related to operations in base 10. (c.4)
  5. Be prepared to develop student proficiency and address common misconceptions related to numbers and operations involving fractions. (c.5)

These objectives will be achieved through readings, group and individual homework assignments, in class explorations, reflective writing, and exams. The codes next to the objectives refer to Title 23: Education and Cultural Resources, Subtitle A: Education, Chapter I: State Board of Education, Subchapter b: Personnel, Part 20: Standards for Endorsements in Elementary Education. A detailed description of these learner outcomes, which are broken down into specific objectives with specific assignments and connections to state and national standards, can be found on the Objectives Grid. Mastery of these learner outcomes is important beyond this course.  You will be responsible for demonstrating the course’s content and practices in the Elementary Education Licensure Exam, your mathematics methods courses, and your field experiences, including student teaching. Additionally, portions of the content appear on the Test for Academic Proficiency.

Links to standards documents, which elaborate on the listed standards in the Objectives Grid can be found at the following websites:

Part 20:
Licensure Exam Website:
National Council of Teachers of Mathematics (NCTM):
Illinois Learning Standards and Common Core Standards:



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.

You are expected to bring your Explorations Manual and your Student Manipulative Kit to each class.

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Technology Requirement:

Students are expected to be able to communicate with the instructor through email. Learing Log Reflections are to be prepared using MS Word. A calculator may be needed for some activities and homework There will be occasional use of Excel.. The Student Manipulative Kit will be required for activities in class; students are required to bring this kit to class regularly. Written homework is expected to be completed using MS Word.

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Team Homework


Individual Homework


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:

(As this course is an independent version, the usual team homework will be completeed independently.) 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 NCTM and Common Core standards were addressed? Explain how they were addressed.
  2. What NCTM process standards and Common Core Standards for Mathematical Practice were addressed? Explain how they 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 abou the mathematical content? (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. (Following the direction of the instructor, you may be ask to submit a single exploration response for one or more Explorations completed in a given week.) 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 Math 112 grading boxes separately. There is one box labeled "Homework" and another labeled "Reflections." 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 required to electronically prepare your homework assignments as well. (Figures and tables may be created by hand as needed.)

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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 exam dates are Monday, 9/29 and Monday, 11/3.. The instructor may choose to allow calculators or the Student Manipulative Kit 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 a 10 minute period during the final exam period of December 10, 3:15 pm. - 5:15 p.m. The written assigment will be due at the time of your scheduled oral exam.

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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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Electronic Devices Policy

One aspect of being a member of a community of scholars is to show respect for others by the way you behave. One way of showing respect for others in the educational community is to do your part to create or maintain an environment that is conducive to learning. That being said, allowing your cell phone to ring in class is completely inappropriate because it distracts your classmates and thus degrades their overall classroom experience. For the sake of your classmates, you are expected to turn off your cell phone or set it to mute/silence BEFORE you enter class-every class. Furthermore, if you use your cell phone in any manner during class (e.g. text messaging, games, etc.), you will be dismissed from class and will forfeit any points you might have earned in the remainder of the period. If you use your cell phone in any manner during a test or quiz, you will receive a zero for that test or quiz. (This policy also applies to pagers, iPODs, BlackBerrys, PDAs, Treos, MP3 players and all other electronic communication and/or data storage devices.)

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Other Information:

Americans with Disabilities Act (ADA):

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 Jennifer Rigor-Golminas in the Student Success Center, 012 Krasa Student Center, (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: Sunday, November 16, 2014

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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