The nature of this course, and what this course is not

The adage "Math is not a Spectator Sport" appears, word for word, on hundreds of university syllabi on the web, and for good reason; one doesn't learn how to ride a bike or swim by watching others do it. This adage applies to any math course -- but applies even more to courses like Math 130 and Math 230. In these courses, the goal is not only to develop deep, teacher-level understanding of 'elementary' mathematics, but also helping preservice teachers gain the tools, habits, confidence, and disposition for life-long learning and growth well beyond the undergraduate years, and decades into their teaching career in an increasingly high-tech, and quantitative world.

This course is not a repeat of elementary and middle school mathematics. It is about gaining a higher, conceptual (rather than merely "mechanical manipulation") level of understanding of how and why elementary/middle school math works, including high-school and college level mathematical sophistication that will be expected of you as necessary for gaining this level of mastery required by local, state, and national bodies for those in the teaching profession which is so critical to our nation's future. In this course we are concerned more with meaning than in 'memorized mechanical manipulation' Getting the right answer is certainly important; but even more value is put in this course on students communicating mathematical clearly and precisely, explaining how and why, defining one's terms, giving and careful exposition

Course Structure

Since this university level class is not merely a review and repeat of Elementary School material, but one requiring higher-order analysis, synthesis, and thinking and communicating about "how" and "why" (as well as being able to carry out the "what"), you will want to be fully involved and engaged both in class and outside of class. Outside of class you will carefully read assigned sections, -- re-reading and reviewing them as necessary -- and work through assigned homework exercises as well as other written assignments.

During class I will introduce new material, including through lectures, which will often be brief; the rest of our time together in class will consist of cooperative working in groups on problems and activities; whole-class discussions in which you will be expected to participate; and students presenting solutions to assigned problems at the board -- with the rest of the class listening attentively, lending a helping hand if needed, and (in a polite, respectful, and collegial way) finding errors if there are any. I will give guidance and if the whole class is stumped, will provide either a solution or (more often) a hint for students to use to try again for next time.

The Role of Homework and Problem-Solving

The purpose of homework exercises is to build up your "mathematical muscles" in much the same way as athletic exercises prepare your for sports events. In other words, the purpose of homework is to gain practice and strengthen your understanding (and to discover what questions you need help with). We will have regular Homework Presentations (see below) in which students will solve problems on the board. Homework will not be normally collected and graded; you will receive credit for diligent work at home mostly by means of doing better on the tests, but also partly through the points awarded to you for making homework presentations (HWPs), as well as to a lesser extent, via Homework Quizzes, should we have any). While exam questions will not be carbon-copies (with only the numbers changed) of homework questions, they will build on homework and class work, so it will be difficult to do well on exams without regularly solving all assigned exercises; working conscientiously on weekly homework exercises should result in better performance on exams.

Should you need help with the homework outside of class many avenues exist to provide you with such support: the free tutoring center in Henson 117; as well as through office hours, speaking with me after class or emailing me a question. However, the most common, helpful, and frequent way to get help with the assigned exercises -- other than working in groups outside of class, as encouraged with our Class List contact sheet -- are the regular Homework Presentations.

Homework Presentations (HWP)

Each week, usually in the first half, you will come to class with a prepared list -- in writing in your notebook -- of which homework exercises, if any, you were unable to fully complete or comprehend, despite your significant time and effort, and a list of which problems you are able to present at the board. We will proceed as follows:

→ Presentations Protocol

1. Upon arriving in class with the above lists of problems already written down in your notebook, we will have a Designated Area of the blackboard where each student upon entering the class, will write down the section and problem number of any exercises you genuinely tried to solve but were unable to ("requests")

2. You should do this during the period 2 to 5 minutes before the official start of class and (if you sincerely cannot get to class before official starting time) no later than 2 minutes into the class (e.g. by 3:02 if the class tarts at 3:00pm) In other words, you are not to arrive in class and only then start to open your book to start picking questions; you are to already have written down a "need help with" (or "requests") list and a "can present on board" list.

3. If someone ahead of you already wrote a certain problem or part of problem on the board (e.g. "Sec. 2.3 #4b") and you too had that problem as "need help with" put a check mark next to that problem. This will help us prioritize which problems to have presented, that is to prioritize the requested problems.

4. If you are able to solve one of the "requested problems" being put up (wait during the first minute or so to see how many check marks each such question receives) write your initials next to the requested problem to claim it, and start solving that problem on the board in another area which will also be designated for this purpose. If you are somewhat shy about presenting, keep in mind that you will not be alone but part of a group, and that the rest of your classmates will be expected to serve not merely as 'audience' but as friendly, respectful and supportive colleagues at all times.

5. When you solve a HW problem. If you volunteered and were then called to present: after you write your full solution on the board, print your full name at the end of your solution. You may either stand (prefered) or return to your seat, but be ready to get back to the board when we review the solutions together as a class, if there are any student questions.

6. You should volunteer to present not for points, but in order to help your classmates, and help increase your own level of understanding and mathematical communication abilities. Nevertheless, in addition to helping boost your general Classroom Participation (worth 5%, see below) course portion, your printing your full name will give you a "plus" (+) for any such problem you put on the board and present to the class. For each four (+) you have, you will receive a full point added to your Final Exam score. If you were original, solved a hard problem, and needed no help, you might receive two pluses (equivalent to a ½ point added to your Final).

Grading, Participation, and Exams

Although some modification the following might be made later in the semester due to unforeseen circumstances, the course grade will tentatively be based on the following components:

Attendance and Participation (5%). Attendance will be taken every day at the beginning of the semester and regularly thereafter throughout the course. "Participation" includes actively participating in groupwork, whole-class discussion, and presenting at the board. These will count towards 5% of your grade. Conscientious attendance and effort makes it possible for almost any student to earn an "A" (i.e. 4.4 or more out of 5) for this portion, while skipping classes or less than full-hearted participation will lower the A&P grade.

Tests (50%). We will have three in-class exams. The exam with the lowest score will be dropped (this assumes you do not just skip a test). The average of the other two exams will count for 50% of your grade. You may bring one standard sized index card with handwritten (not typed or photocopied) notes on both sides to each exam, since exams will test not just memorization but conceptual reasoning.

Final Exam (25%) The Final will be comprehensive and cumulative; you will be expected to have retained the material from the entire semester. Instead of an index car you may bring an 8½ by 11 sheet with hand-written notes. Like the index card, you may use both sides. Highlighter pens ok.

The remaining 20% is the course grade is described in the section below. Note however that the activities below will count for much more than 20% of your learning After all, most of your learning will come before and after -- not during -- your sitting down to take exams, so most the learning must take place based on everything you do besides taking exams.

Along with regular careful reading of the textbook, problem solving, and studying outside of class, these activities, and your work preparing for them, require your full effort, and regular efforts -- the dividends repeated are in both course grade, and a lifelong pay-off for your comfort level and success in your career as teacher, as you can gather from speaking with any current elementary teacher who wishes they had a stronger mathematical foundation. This is the time to build that strong foundation!

Homework Quizzes (HWQs) will be given, often (but not restricted to) the second half of each week. They will be related to material on the homework and range in difficulty from easier (identical to a HW problems other than perhaps some changed numbers) to more challenging (an idea or method similar to the one you used to solve one of the recent HW problems). The lowest HWQ score will be dropped.

Written Assignments Required typed expositions and professional solution narratives.

Other We may have a Portfolio and/or Class Journal assignment required or options. Details TBD.

The above components will account for the remaining 20% of your grade.

In addition, you may earn extra points via:

• Pop Extra-Credit. These will be unannounced quizzes which cannot hurt your grade but which may earn you a point or more to be added to your test or Final scores.