MTH 5020

Basics

Office Hours

  • MW: 10am-11am
  • TH: 2pm-3pm
  • or by appointment

Prerequisites:

Successful completion of MTH 1610 or successful completion of the MTH 1610 Place-Out Test administered by the Department of Mathematical and Computer Sciences, or successful completion of a course accepted for transfer as MTH 1610 by the Department of Mathematical and Computer Sciences or the College.

Requirements:

Pens preferred; graph paper, and a scientific calculator; that is, a calculator that can handle numbers in scientific notation and has [yx], [π], and [!] keys. (Cell-phone calculators, generally, are not scientific.) CELL PHONES ARE TO BE SHUT OFF AT THE BEGINNING OF CLASS (unless a prior arrangement with me has been made).

Required Text:

Hiebert, J., et.al, (1997) Making Sense: Teaching and Learning Mathematics With Understanding. Portsmouth, New Hampshire: Heinemann.

Optional Texts:

Van de Walle, J. A. Elementary and Middle School Mathematics: Teaching Developmentally (5th, 6th or 7th editions). White Plains, NY: Longman. [This is an excellent mathematics teaching methods text.] You will need to purchase it for EDU 4120 and ECE 4330.

Course Overview:

This graduate course is designed to deepen and extend prospective teachers’ understanding of the concepts underlying the school mathematics curriculum in grades PK-5. Teachers working in the diverse contexts of school mathematics classrooms must possess not only sound understanding of mathematical ideas, but of the processes by which this understanding develops and in which this understanding is applied. Therefore, how one does mathematics in this class is as important as the mathematical ideas themselves.

In this course, students will:

  • Pose and solve problems, individually, and in groups, in class and outside of class;
  • Describe and analyze their work and the work of others, including the mathematical thinking of children as seen in written and video cases drawn from elementary classrooms, both orally and in writing;
  • Use a variety of tools, including manipulative models and technology, to solve problems;
  • Demonstrate working knowledge of the big mathematical ideas of the course.
  • Examine records of elementary classroom practice – videos and samples of children’s written work – to analyze children’s understanding of the mathematical ideas listed in above.

Classroom Environment:

It is absolutely critical that we create a productive classroom environment that is friendly, non-judgmental, gentle and relaxed so that all class members will feel sufficiently safe to offer suggestions even when they are not absolutely sure that they are correct. So, take care with each other’s feelings. Give each other permission to be unsure, and encouragement to take chances and make guesses. That’s how we will all learn best. And besides, it is more fun that way.

We will be doing mathematics "one problem at a time." A "problem" is a mathematical situation for which you know no solution. An "exercise" is an opportunity to practice a known procedure. We will be exploring a lot of problems, and in the process will learn many useful strategies for solving them. The goal is to understand and explain why things are true, often in several different ways. After each class, your task is to review your notes, make sense of as much as you can and mark the parts about which you are still confused. Then ask about them with your groupmates or me. In this class, everything can make sense! ! This course does not follow a textbook, so I suggest that you keep a loose-leaf notebook that contains an accurate record of all in and out of class activities. You will refer to it frequently as your prepare your assignments and use it for the in-class exams. They are open-book!

The Mathematical “Big Ideas” of This Course:

  1. Mathematical problem-solving, reasoning, and communication;
  2. Proportional Reasoning;
  3. Patterns and their identification, representation, analysis, generalization, and use;
  4. Descriptive Statistics;
  5. Probability;
  6. Mathematical Disposition (This is, participating in the individual, small-group, and whole-class activities and discussions that constitute the daily work of the course; offering mathematical ideas for discussion and analysis by others, both orally and in writing; demonstrating intellectual commitment to learning and teaching mathematics.

As part of the learning process in our classroom, everyone is expected to observe the professional skills you make use of every day in your workplace. The classroom environment is one where a feeling of safety and security is necessary. Being considerate of others, their opinions and points of view is essential and expected. An atmosphere of equality, respect and consideration are all considered part of professionalism. Behaviors that would indicate you are acting in a professional manner would include (and are not limited to):

  1. relevant and appropriate participation in class discussions;
  2. avoiding the use of iPods, computers, cell phones and text messaging;
  3. preparation for class through reading all assigned material and handing assignments in on time;
  4. use of active listening skills (even if you disagree with someone’s point of view);
  5. attentiveness when someone else is speaking and
  6. an attitude that reflects openness and receptivity to learning and the learning process.

Part of your responsibilities as members of this classroom community includes recognizing the importance and responsibility you hold in facilitating the learning of your fellow classmates.

Attendance:

Successful completion of this course does not depend only on scores on assessments. It depends, in large part, on having participated in the set of class activities that comprise the course. Therefore, prompt attendance is required. I do understand that there might be times when you must miss class. If you must miss all or part of a class, use the office hours, phone number or e-mail address provided on page 1 to discuss the reasons with me beforehand. Whenever you miss class, you must do a 2 - 3 page "make-up" of the material that was missed. This involves writing your own set of notes about what happened that day and the results that were found in class. (This way, your personal set of class notes will be complete for use on the exams.) The "make-up" must be completed within a couple weeks of the absence. More than three absences will lower your grade by one letter, unless special arrangements are made with the instructor.

(Regular tardiness will be interpreted as a lack of intellectual commitment to the course, and will prevent a student from earning an “A.”) Assessment and Grading: Assessment in any mathematics class is the process of gathering and reporting evidence of students’ developing mathematical proficiency. In this class a database of evidence, collected from a variety of sources and built throughout the semester, will be summarized as a letter grade, as described next.

1. What are the characteristics of a student who will earn a grade of “B” or better in this class? Such a student will have, by the end of the course, provided consistent evidence of having reached an appropriate level of mathematical proficiency. Mathematical proficiency is defined as:

  • Conceptual understanding of the big ideas that underlie the school mathematics curriculum, and fluency with the procedures, skills and tools used to do mathematics.
  • The strategic competence needed to tackle novel mathematical problems, including the problems of understanding the mathematical thinking of children, and the adaptive reasoning needed to explain and justify one’s own methods and solutions, and the methods and solutions offered by others;
  • A productive disposition toward doing and learning mathematics. A prospective teacher has a productive disposition if she views mathematics as a sensible and meaningful discipline, and if she sees herself as capable of making sense of her own mathematical ideas and those offered by children, through persistent and diligent effort.

2. How does an “A” student differ from a “B” student?

An “A” student will have distinguished herself by:

  • Providing convincing evidence of a level of mathematical proficiency that goes well beyond the standard set for the course;
  • Participating consistently in the individual, small-group, and whole-class activities and discussions that constitute the daily work of the course;
  • Regularly offering mathematical ideas for discussion and analysis by others, both orally and in writing;
  • Demonstrating, through attendance, promptness, and attitude, the intellectual commitment to learning at the heart of outstanding teaching.

3. What are the characteristics of a “C” student? Such a student will have, by the end of the course, provided some evidence of mathematical proficiency, but not at the consistent level required to earn a grade of “B” or better. She might fall short of that standard, and earn the minimum passing grade for the course, if she:

  • Demonstrates proficiency in some but not all of the sections of the course;
  • Participates, but only intermittently, in class activities and discussions;
  • Demonstrates, through poor attendance, excessive tardiness, missing or late written work, or poor attitude, a lack of intellectual commitment to learning and, by extension, to teaching.

4. Why no “D” grades?

This course is required for prospective teachers, and a licensure recommendation is based on, among other things, grades of “C” or better in all required courses. A student who does not earn a grade of “C” or better will have to repeat the course, so a grade of “D” would be meaningless. A student who does not demonstrate the minimum characteristics of a “C” student, as described above, will receive a grade of “F.”

5. How can a student in this class provide evidence of mathematical proficiency and commitment to teaching? The instructor will give students opportunities throughout the semester to demonstrate mathematical proficiency, by assigning mathematical tasks to be completed in writing. The students’ written work will be assessed using the attached scoring guides. These mathematical tasks will be of five types:

  • Embedded tasks: instructional tasks for which the student composes an individual, written response in class.
  • Analysis of Mathematical Thinking (AMTs): summaries and analyses, composed outside of class, of case-based examples of children’s mathematical thinking.
  • A Midterm and Comprehensive Final comprised of tasks similar to the embedded tasks described above.

Homework:

Homework will be assigned when appropriate. Sometimes, homework will be graded for completion, other times it will be graded more rigorously. Reading Responses: Students will be assigned weekly readings that will usually be about 15-20 pages. Students will be asked to respond to the readings in writing either on-line through “Just In Time Teaching” or through a written assignment. The instructor will also gather, in a systematic if not exhaustive way, evidence of mathematical proficiency from students’ daily work in class. Therefore, participation in class discussions is a good way to meet or exceed the requirements of the course.

Grading Criteria for MTH 2620

Here is how the final course grade will be calculated. Performance on the AMTs and the Final Exam are weighted very heavily. If your actual assessments don’t fit into the attached rubric then the instructor will make a judgment call.

AMT “M” or “IP” grade

An AMT will be given a grade of M when all problems meet expectations. AMTs that do not meet this standard will be given a grade of IP. Students are expected to revise and resubmit their work until they get a grade of M for each of their AMTs. Revisions will be considered late if they are turned in more than a week after they are returned. Late papers, including late revisions, will cause the numeric grade for the assignment to be lowered.

Numeric Grade: The following two components will determine a student’s numeric grade for the semester.

  • AMTs: Each problem on the first submission will be graded using the attached rubric. The numeric score for the AMT will be the average of the scores for the first submission. Re-writes of the AMT will not affect the numeric score. The semester AMT numeric score will be the average of the individual AMT scores.
  • Exams: Exam problems will also be graded on the attached rubric. The exam numeric score for the semester will be the average of the scores for the individual problems. The semester exam numeric score will be the average of the two individual exam scores.

Religious Holidays:

Observance of religious holidays follows College policy, which is posted on the web at http://handbook.mscd.edu in the Academic and Campus Policies for Students section. Each student is responsible for understanding and abiding by the policy.

Americans with Disabilities Accommodations:

The Metropolitan State College of Denver is committed to making reasonable accommodations to assist individuals with disabilities in reaching their academic potential. If you have a disability which may impact your performance, attendance, or grades in this class and are requesting accommodations, then you must first register with the Access Center, located in the Auraria Library, Suite 116, 303-556-8387.

The Access Center is the designated department responsible for coordinating accommodations and services for students with disabilities. Accommodations will not be granted prior to my receipt of your faculty notification letter from the Access Center. Please note that accommodations are never provided retroactively (i.e., prior to the receipt of your faculty notification letter.) Once I am in receipt of your official Access Center faculty notification letter, I would be happy to meet with you to discuss your accommodations. All discussions will remain confidential. Further information is available by visiting the Access center website www.mscd.edu/~access.

Academic Dishonesty:

An act of Academic Dishonesty may lead to sanctions including a reduction in grade, probation, suspension or expulsion. See the Student Handbook at http://handbook.mscd.edu in the Academic and Campus Policies for Students section.

Page last modified on August 16, 2012, at 11:09 AM EST