|Math 105/115/116 Student's Guide|
As part of a nationwide movement, the Mathematics Department has changed its approach to teaching mathematics to one which is "leaner, livelier, and more relevant to real-life problems." The main purpose of this fresh approach is to help you learn to think about mathematics. The text, as you will see, emphasizes understanding concepts and de-emphasizes rote memorization. Since our goal is to prepare you for further study in all mathematical subjects, there will be a strong emphasis on mathematics in everyday life and many of the applications will come from the physical and social sciences.
In addition to the text, we will be using graphing calculators to help us better visualize the fundamental ideas, to do routine computations, and to make the course more interesting. You will find the graphing calculator very easy to learn and to use. Former students have consistently said that the use of calculators was a "big plus."
In all of our department's introductory courses there is an emphasis on cooperative learning. Your instructor will be facilitating group activities and discussion rather than just repeating the content of the text to you at the blackboard. This means that we will be asking you to read the material and attempt the homework before it is "covered" in class. There will be times when you will have to learn topics which will not be formally discussed in the classroom.
Along with your individual homework, another feature of the course will be team homework assignments. Each of the team problems will require considerable thought and a complete, well-written solution. You will often find that team homework problems are best solved in a cooperative environment. Your grade for each team homework assignment will be assigned to the team as a whole, so everyone in your group will be responsible for each other's learning of the material. Most students using homework teams in previous terms have found them helpful. Typical student comments include:
You will be cooperating with other students; not competing. Your course grade will depend on achievement and effort, and there is no limit to the number of students who can receive good grades in this course.
We are excited about this new approach to teaching and learning mathematics, and we hope that you will join us in this excitement. Have a good semester!
Back to Top
Back to Top
Here's what a principal aerodynamics engineer from The Boeing Company and members of the Washington State Software Alliance have to say.
What do we look for in employees? We hire those who have demonstrated that they:
Back to Top
Students often ask, "Why do we have to do all this writing? Writing has nothing to do with mathematics!" The purpose of having you write explanations of your work is to improve your understanding. The more carefully and clearly you write your mathematics, the more likely it is to be correct, and the more likely you will be to remember it. Writing is a crucial part of the thinking process itself.
As you are solving problems in this course, remember that getting the "answer" is only one of the steps. Don't think of what you write as just showing your instructor that you have done the homework. Think of writing as part of the process of learning.
Back to Top
During this course you will have to do a significant amount of group work. It is a growing trend in professional schools and business to have teams work on various projects. For the team homework in this course, each member of the team has an important role. These roles are to be rotated each week so that everyone has the opportunity to try each role. The roles are the scribe, the clarifier, the reporter, and the manager.
We recommend that all students go through the team homework tutorial at http://instruct.math.lsa.umich.edu/support/teamhomework/. This page is also linked from the course web page for your convenience.
Back to Top
The goal of team homework is to ensure that everyone learns with and from the other members of the group. This means that when the work is completed and submitted, every member of the group should be able to explain how to solve all the problems. Here are some ideas that past students have come up with to help your group function at its full potential.
Back to Top
In this course, it is absolutely essential that you do the reading assignments. Your experience with previous math courses may make it seem unlikely, since it may have been possible to avoid reading the text, yet do adequately well by copying down examples the instructor did in class and then doing the homework exercises by just changing the numbers in those "pattern examples" and the pattern examples given in the text. Also, older-style texts subtly encouraged students to skip the reading assignments by putting procedures for doing exercises in boxes, thereby essentially telling the students that "everything you really need to know to do the exercises can be found inside the boxes; you might as well skip reading everything else."
Unfortunately, this approach resulted in students being able to do the mechanical computations quite well, but having no real understanding of the material and no real ability to apply it in situations that are even a little bit different from that covered by the pattern examples. In essence, students were only being programmed like computers to do computations that computers can do faster and more accurately anyway. It is this deficiency in the old-style math courses that led to the national movement toward reformed courses, like this one, which stress understanding. This modern approach to learning requires new methods in the classroom emphasizing learning rather than lecturing, as well as new texts such as the one for this course.
The difference between the text for this course and an old-style math text is apparent from even a cursory scanning of the first chapter. If you open the text and just begin turning pages, you will probably be struck by the following:
Doing the exercises requires an understanding of the material in the text, not just the ability to change numbers in pattern examples. Also, your instructor will be counting on you to read the text, since he or she will not be lecturing very much and will be relying on you to have seen the material before you work with it in class. Like other courses outside mathematics (but perhaps unlike other mathematics you have taken), not every small point on which you will be tested will be covered by in-class examples. Since the reading is so very important, some hints on how to it might be helpful. You may find that slight variations on the following scheme will work well for you.
If you do not understand something during the second reading, put the book aside awhile and return to it later when your mind is fresher. If you still do not understand it after returning to it, ask your instructor or your homework group members about it. Do make sure you eventually understand all of the material. You will probably get tripped up in later reading, in doing the homework, or on test if you treat material you don't quite understand as "probably not all that important."
Do not get discouraged if some points require some time to understand. It is not uncommon to have to think about a point in a math test for a half hour (or more, for more complicated concepts) before it becomes clear what is really going on.
Back to Top
Back to Top
Grades in this math course. All sections of this course use the same grading guidelines to ensure a fair, standardized evaluation process. Your grade in this course will be determined primarily by your work on the "uniform component," which is the same for all sections of the course. The majority of this component comes from your scores on the uniform exams. Your grade as determined by the uniform component may be influenced by the "section component" of the course, which includes your work in your class-section. In some cases, your section component may adjust your grade up or down (as explained below). In addition, there is a "gateway component" to your grade which may also adjust your grade downward. The details follow.
1. The uniform component. This includes two uniform midterm exams, a uniform final exam, and your scores on web homework. Each of the exams will be taken by all students in all sections at the same time, and are graded by all the instructors working together. Your uniform component score will be determined from your scores on each exam as follows:
|Midterm Exam 1||25% of uniform component score|
|Midterm Exam 2||30% of uniform component score|
|Final Exam||40% of uniform component score|
|Web HW||5% of uniform component score|
After each exam, a letter grade will be assigned to your uniform component score using a scale determined by the course coordinator specifically for that exam. We do not use the "10-point scale" often seen in high school courses in which scores in the 90's get an A, in the 80's get a B, and so forth; the level of difficulty of the exams will be considered. The scale for the uniform component score will apply to all students in all sections. The scale for final course grades will be set by the coordinator based upon the above percents for each component. Most students will receive the course grade assigned by that scale.
2. The section component. To help you learn the material, you will be given a variety of reading assignments, team homework, quizzes and other in-class activities. Your instructor will decide how the section component is determined for your particular section and grade the section work.
If, at the end of the term, your rankings on the section component and uniform component differ significantly from one another, your course grade will be examined to see if an adjustment should be made. If you have participated in section activities but your section component is significantly lower than your uniform grade, your course grade may be lowered by one third of a letter grade. Students who have not seriously attempted to contribute to the section component of the course (i.e., quizzes, team homework, etc.) may have their final course grade lowered by up to a full letter grade. If, on the other hand, you have struggled on an exam and your in-class performance is significantly higher than the uniform component grade, your instructor may in some cases adjust your grade upward by one-third of a letter grade. This raise is generally only given for students whose uniform component places them near the top (or at the "cusp") of a letter grade category. The majority of students will find that their in-class performance and their exam scores are quite reflective of one another. Thus, in the majority of cases, no adjustment is made to the uniform course grade.
The best way to gauge your in-class performance is to keep an eye on the median grade in your section for each assignment and quiz. It is not useful to compare quiz and homework grades with students from other sections, because instructors write their own quizzes and determine the grading rubric for homework in a section.
3. The gateway component. There will be one or two (depending on the course you are taking) online basic skills gateway test(s) which you need to pass by the deadline announced in the course schedule. These tests may be taken multiple times, and cover skills that every student who passes the course should have. Therefore, students who are keeping up with the course work can and will pass the gateway---if they start taking it early enough! You may practice each test online as many times as you like, and you may take a test for a score as often as twice per day without penalty until the deadline. Because the gateway tests cover skills that every student must have, the gateway tests do not raise your baseline grade; instead, if they are not passed by the deadline, your final grade in the course will be automatically reduced. Opening dates, deadlines and grade penalties will be announced in your class. All sections of your course have the same open/closing dates and penalties assigned to the gateway component.
Section averages. Course policy is that a section's average final letter grade cannot differ too much from that section's average baseline letter grades. This means that the better your entire section does on the uniform exams, the higher average letter grade your instructor can assign in your section. It is therefore in your best interest to help your fellow students in your section do well in this course. In other words, cooperation counts!
Grades at the university. Many students who come to the University of Michigan have to adjust themselves to college grading standards. The mean high school grade point average (recalculated using only strictly academic classes) of our entering students is around 3.6, so many of you were accustomed to getting "straight A's" in high school. Students' first reaction to college grades is often, "I've never gotten grades like these." However, a grade of 15/20 on a team homework assignment (which you might previously have converted to 75% - a high school C) may well be a good score in a college math course. Your own instructor is your best source of information on your progress in the class.
Back to Top
Back to Top
Students at the University of Michigan are expected to exhibit academic integrity. Each College has its own standards for treating cases of academic misconduct, but in all Colleges there can be serious consequences for violating the Code of Academic Conduct. Sanctions can include: suspension, disciplinary probation, and receiving a failing grade. Some examples of cheating, as stated in the LS&A Code of Academic Conduct, include:
Back to Top
Back to Top