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Mathematics 1011, Spring 2012
Dimensions of Mathematical Understanding

Course Description: This course focuses on the understanding of mathematical properties of real numbers and problem solving skills. Multiple representations will be used including algebraic. Emphasis is placed on verbal and written communication of mathematical concepts.

Welcome to Dimensions of Mathematical Understanding


This course is designed to develop your understanding of mathematics by providing opportunities for you to experience what it means to problem solve and reason about mathematics. Emphasis is on problem solving (investigating, conjecturing, and justifying), on understanding of concepts, on connections among concepts, and on written and verbal communication of strategies and reasoning.  This requires practice and commitment to sense making on the part of the student. 


It is important that you realize that you cannot solve with understanding mathematical problems by observing and mimicking others doing mathematics.  You must participate mentally in the learning process.  This participation includes studying the material; working with others; struggling with non-routine problems; using calculators for exploring, reasoning about, and solving problems; symbolically representing mathematical thinking and reasoning; listening to others; reflecting about what you are doing; as well as the more typical tasks of taking examinations and doing homework.  The emphasis in this course will be on problem solving and reasoning with understanding rather than memorizing and using equations or algorithms. As a consequence you will be expected to provide complete explanations of the reasoning you used to solve problems.


Too often our previous experiences with mathematics have caused us to focus on memorization and finding correct answers.  Consequently our understanding of what mathematics is and what it means to do mathematics is shaped by these experiences and is rather limited and narrow.  And yet, mathematical problem solving consists of so much more.  In this course we will focus on problem situations as described in different guises: visual, quantitative, graphic, abstract, and concrete.  From these we will focus on the various dimensions of mathematical problem solving: investigating and exploring, reasoning and conjecturing, justifying and verifying, connecting, and communicating.

Professor: Ms. Cynthia Schultz
: 224-0431

Office hours (E304)
Monday:  10:00 am -10:50 am, 1:00 pm - 1:30 pm
Tuesday:  10:00 am -10:50 am
Wednesday:  11:00 am -noon
Thursday:  10:00 am -10:50 am
Friday:  10:00 am -10:50 am

Required supplies: Base-10 blocks, fraction circle pieces, pattern blocks, multi-color set of dry-erase (such as expo) markers (I suggest at least one black and 4 bright colors) and colored pencils.  All these items are available in the bookstore.

Suggested supplies: A three-ring binder, loose leaf paper, a container to carry supplies, and the book Math for the Anxious by Rosanne Proga (available in the bookstore) 

Calculator:  Scientific calculators may be used on exams, but no graphing calculators, cell phones, etc.  are allowed. 

Prerequisite:  Math 0907 with a grade of C or better, or appropriate placement score.

Expected Learning Outcomes:

  1. Fraction representations
  2. Addition of fractions
  3. Subtraction of fractions
  4. Multiplication of fractions
  5. Division of fractions
  6. Base-10 number system
  7. Decimal system
  8. Percentages
  9. Written communication of mathematical concepts
  10. Oral communication of mathematical concepts
  11. Problem solving


Grading (Subject to change)


90 -100 %


Quiz 1:  25 points

Quiz 2:  30 points

Quiz 3:  35 points

Quiz 4:  40 points

Checkpoints: 50 points (Collectively)

Midterm: 100 points
Final exam: 100 points

Class participation: 40 points










Course Schedule:  For the most recently classroom schedule, visit this webpage:  Math 1011 Schedule.

Discussion Problems:  You will be required to work on the problems from the handouts outside of class.  It is expected and required that you will come to class prepared to present your solutions and explanations to the class.  Class discussion will be most meaningful when you have worked on the problems beforehand.  You will better understand the solutions presented by your classmates as well as able to participate by asking and answering questions.  In addition, you will be preparing for exams by working on your own solutions.

Exams and quizzes:  The exams and quizzes in this course consist of short answer, computational, and essay questions.  Emphasis of this course is on problem solving, sense making, and reasoning with understanding of concepts, on connections among concepts, and on verbal and written communications of your strategies and ideas.  Thus, you will be expected to provide complete explanations of the reasoning you use to solve problems and the explanations should make sense to both you and me.

Attendance: You are expected to attend all classes.  Your participation in class activities and discussions is important not only for your own learning, but also for the learning of others.  You are expected to attend class and be a collaborative participant in the work of the class.  Because much of the learning that will take place during class cannot be effectively transmitted through notes, it is recommended that you attend class regularly. 

Class handouts:  Handouts are distributed on a regular basis.  If you miss class, it is your responsibility to login to blackboard and print your needed handouts.

Participation:  This class is built around student participation.  You are expected to present solutions to problems, answer questions posed by the instructor and classmates, and ask questions of your classmates. Each student has the potential to earn 40 points participation. The points will be awarded according to the following rubric:

35-40 points:  You have excellent attendance. You have missed no more than 1 class.  You have volunteered to present multiple solutions to the class.  You ask questions of others and voluntarily answer questions posed to you or the class in general.  

25-35 points:  You have good attendance. You have missed no more than 2 classes.  You have presented multiple solutions voluntarily or when requested.  You ask questions and answer questions when called upon.  

15-24 points:  You have fair attendance.  You have missed no more than 3 classes.  You have presented as at least once.  You answer questions when class upon, but might not volunteer.   

11-14 points:  You have attendance problems. You may have missed at least 3 classes.   You might not have presented solutions to the class.  You do not ask questions or answer questions unless prodded.  

0-10 points.  You have excessive absences.  You have virtually no participation. 

Please note that using a cell phone, ipod, laptop, or similar device during class without permission will be recorded as an absence.

Study group:  You will find it beneficial to form study groups of 3 students.  Your study group can be used to work on problems to be presented in class, devise solutions for graded problem sets and prepare for exams. You will also find that your own understanding is strengthened by "teaching" your classmates during your study sessions.

Retakes of Exams and/or extra credit: I do not allow retakes of any assignment or assign extra credit to individuals to raise grades.  

Checkpoints:  Checkpoints are given periodically during the semester.  These must be completed in class.  To accommodate absences, you may miss one checkpoint without any effect on your grade, regardless of why you were absent. 

Testing policy:   You are expected to take each exam and quiz at the scheduled times.  However, if you have an unavoidable absence you may request to take the test at an alternative time provided you contact your professor before the exam/quiz begins and explain your absence.  I will decide if and when you take your makeup exam/quiz, which is generally no later than 2 business days.   If you request a makeup via email or voice mail, it is your responsibility to check your messages for my response.  If you do not receive a response from me within a reasonable amount of time, you MUST follow up with another attempt to contact me.  Failure to follow the policy will result in denial of your request.

Exceptions to the above policy will only be given for situations including, but not limited to, jury duty, military orders, serious medical problems (yourself or immediate family member) or a death of an immediate family member.  You MUST be able to provide documentation. (Acceptable documentation include such things as an accident report, doctor's note or hospital discharge papers.) Immediate family member is defined to be a spouse, partner, parent, grandparent, child, grandchild, sibling, or your spouse's/partner's immediate family member. These requests will be considered on a individual basis.

Repeated requests for makeup exams WILL REQUIRE that you provide documentation.

Requests to take exams/quizzes early are generally approved.

If for any reason, you do not take an exam or quiz, your midterm exam or final exam score will replace one missed exam/quiz.  (Scaled to the appropriate amount)  If the missed quiz precedes the midterm, the midterm will be used to replace the score.  Otherwise, the final will be used. Any other missed exam/quiz will earn a score of zero.

Cheating: A score of zero will be given on any assignment where cheating occurs. Examples of cheating are copying answers off other studentsí tests, submitting another personís work as your own, and having crib sheets during a test.  Repeated acts of cheating may result in a course withdrawal.

Classroom etiquette:  Please be courteous of others' rights in the classroom.  Do not disrupt their right to learn by  inappropriate talking  (talking during presentations or while others are asking or answering questions), whispering, or other immature acts.  Please turn cell phones to silent and do not text message or play games during class.  If you need your cell phone for emergency purposes (EMT, firefighters, sick family member, etc.) this is certainly allowed.  Each student is also held to "Student Code of Conduct" as specified in the student handbook. Violation of this student code may result in withdrawal from the course.

Withdrawals: Withdrawal from this course is not automatic.  You will need to initiate a withdrawal from this course by completing the form in the Records Office or through webadvisor.  IVCC has the right to rescind a withdrawal in cases of academic dishonesty or at the professorís discretion. If you do not initiate a withdrawal, you may receive a grade for this course, which in most cases, is an F.

Students should be aware of the impact of a withdrawal on full-time status for insurance purposes and for financial aid. It is highly recommended that students meet with their instructor or with a counselor before withdrawing from a class to discuss if a withdrawal is the best course of action for that particular student.


Please see your course schedule for the last day to withdraw.

Financial Aid:  Withdrawal from a course can affect financial aid.Students who receive financial aid should see an advisor in the Financial Aid Office before withdrawing from a course.

Cancelled class:  Every effort will be made to announce class cancellations in a timely manner.  Unexpected cancellations will be posted on the IVCC website.  (http://www.ivcc.edu/cancellations/)  You may wish to consider checking this webpage each morning before traveling to the college.  In the event that class is cancelled on an exam day, the exam will be moved to the next class day.  You may also sign up to receive text messages or emails when the college is closed for weather or emergencies.(https://www.ivcc.edu/forms/IVCCAlerts.aspx  )

Inclement weather:  In the event of bad weather, please listen to your local radio station for school closings.  If school has not been cancelled, use your own judgment as to the feasibility of traveling to school.

Grading process:  If you do not understand how I graded your work or you disagree with the number of points earned, you have the right and responsibility to initiate contact with me about the matter within 4 class days of the material being returned to you.  These matters will be discussed in my office by appointment. 

Graded materials:  You are to keep all graded materials for this course until after you receive your final grade.  If there is a clerical error, and you do not receive the grade you earned, these materials will be needed to resolve this issue.  In the absence of these materials, the professor's record will be assumed to be correct. If you are absent when an assignment is returned, you are responsible to visit my office during office hours to retrieve your assignment.

Special Needs Educational Support ServicesIf you are a student with a documented cognitive, physical or psychiatric disability you may be eligible for academic support services such as extended test time, texts on disc, notetaking services, etc...  If you are interested in learning if you can receive these academic support services, please contact either Tina Hardy (tina_hardy@ivcc.edu, or 224-0284) or Judy Mika (224-0350), or stop by the Disability Services Office in B-204. 

This course outline is subject to change to meet the needs of the instructor and/or students.