• Notes from the President's Desk
• Notes from the 2003 AP Calculus Reading
• Mean & Adjusted Mean Scores for the 2003 Examinations
• Reading Opening Remarks
• Reading for AP Calculus and AP Statistics
• Finally an Acorn!
• New Reader Thoughts
• Thoughts of a TL (Table Leader) and QL (Question Leader)
• NCAAPMT Board Minutes, June 2003
• Treasurer & Membership Reports
• Report from the Test Development Committee
• 2003 Professional Night
• Regrouping the Alternating Harmonic Series
• Calculator Issue
• AP Reading Conventions
• AP Reading Terminology
• Calculus & Factorials
• Notes of Interest from the Editor

NOTES FROM THE PRESIDENT'S DESK
Sue Sams - Providence High School - Charlotte, NC

By the time you read this newsletter, school will have opened in most counties of North Carolina. I trust your summer was restful and that you are ready for another great year in the world of calculus!

The reading/grading of the 2003 Advanced Placement Calculus test was completed on June 8th with more than 208,000 student papers being scrutinized. I hope that your scores were among the best!

At the fall meeting (October 9-10, 2003) of NCCTM in Greensboro, several of our Board members will discuss four of the 2003 free response questions and will shed some light on their grading. In addition, Stephen Davis will give an update on slopefields, a topic that will be on the 2004 AB test. Please make plans to attend our session.

Our organization needs members like you! Make it a goal this year to get one new member who is interested in the future of calculus in North Carolina. Our dues are only $5.00 per year and the two newsletters are worth a lot more than that! Send check (payable to NCAAPMT) to Jeff Lucia, 718 Lansdowne Road, Charlotte, NC 28270. His e-mail address is: Jeff.lucia@Providenceday.org. My thanks to Deborah Britt and Jeff Lucia for all the work they do so willingly to keep our organization functioning so well.

Please keep in touch with us. Deborah Britt, our Executive Secretary, wants your ideas, articles and other information for our newsletter. Contact her at dgb531@aol.com.

Have a wonderful school year! I hope to see you in October in Greensboro.

NOTES FROM THE 2003 AP CALCULUS READING
Stephen Davis - Davidson College - Davidson, NC

There were an estimated 208,100 "operational" exams this year (163,200 AB; 44,900 BC), with an additional 2200 (1760 + 440) Form B exams and 2560 (2010 + 550) Alternate exams, nearly 213,00 exams in all. These were graded by approximately 640 readers, about the same number as the previous year.

The reading was extended a half day to a full seven days this year. Once again we were at Colorado State University in Fort Collins, CO, but unlike recent years, we toiled during the first reading session, from Monday, June 2, through Sunday, June 8, with the leadership arriving several days earlier.

This was Larry Riddle's final year as Chief Reader, with Caren Diefenderfer of Hollins College serving as Chief Reader Designate. The early reading proved to be a logistical challenge as only about 40% of the exams were on site at the beginning of the reading. The other exams arrived (so we hope) in several shipments during the week. This produced some interruptions in the process as "closed out" questions were re-opened for grading on late arriving papers.

Readers mourned the passing of our colleague Shrinivas Dalal of Embry-Riddle Aeronautical University in Florida. Prof. Dalal suffered an apparent heart attack on Saturday morning. He was treated on site and transported to a local hospital where he died later that day. A brief memorial service for Prof. Dalal was held Sunday evening; memorial gifts can be made to the Shrinivas Dalal Memorial Scholarship Fund, c/o Development Office, Embry-Riddle Aeronautical University, 600 South Clyde Morris Blvd., Daytona Beach, Florida 32114.

An issue of calculator accuracy arose with problem AB-2(c) where the correct answer of 4.3338 could be computed as 4.338 from the graphing environment of one TI calculator. The latter answer arose because the calculator uses a higher error tolerance for numeric integration when in graphing mode. Some accommodation was made for this answer at this reading, but teachers and students are advised to know their calculator and to use routines that produce the required three decimal place accuracy on future problems.

Finally, hints were given during the Discussion with the Test Development Committee that the Committee will advocate that more writing be expected for explanation or justification of answers. The effect of this advocacy was already evident this year where unsupported ("bald") answers received no credit in some instances where they may have received a token 1 point previously. The Committee also pointed to the familiar standby sign chart in optimization problems, indicating that these (labeled appropriately) will be less likely to stand alone as justification---appropriate context-sensitive interpretation of sign charts will be needed.

UNOFFICIAL MEAN SCORES AND ADJUSTED MEAN SCORES
FOR THE 2003 EXAMINATIONS

Each question on the free-response section of the examination is worth nine (9) points.  If a student does no work of a mathematical nature on a question, the student is given a - (dash) for this question on the grading form.  If a student does some work of a mathematical nature on a question, but this work earns no points, the student is given a 0 (zero) for this question on the grading form.  The following table shows the unofficial mean score on each free-response question on both the AB and BC examinations including -'s and 0's and the adjusted mean score on each question based on grades of at least a one (1) point on the question.

READING OPENING REMARKS
Deborah Britt - Asheville High School - Asheville, NC

I found it interesting that 30% of the total number of all exams given (since the 1st exam was given in the 1950s) were administered within the last 4 years. The only state not represented by a Reader was Wyoming. Readers were also there from Mexico, England, Turkey and Canada. There were 95 new Readers. 50% of all readers were college and 50% were high school. Bald answers are not going to get lots of points. The students must learn to "communicate." Calculus has the highest accuracy rate of all subjects. If you haven't heard the Terrorist Alert, I'll repeat it here for hopefully the last and final time: Apparently a math teacher was arrested at Gatwick Airport in London, UK for being in possession of a compass, protractor, and a straight edge. It is claimed that she was a member of the AL Gebra movement and was arrested for carrying weapons of math instruction.

READING FOR AP CALCULUS AND AP STATISTICS
Jeff Lucia - Providence Day School - Charlotte, NC

What do you do when Educational Testing Service (ETS) "retires" you from Calculus after twelve years as a reader and table leader? Sit at home during June and wish that the policy were different? Wait the mandatory minimum of three years and put your name back on the waiting list? Move on to something else? For me, it was an easy decision: try to read for AP Statistics. When I first read for Calculus, I had taught the AP course for six years, so I had experience. But I didn't yet have the big picture - the awareness of developments with calculus reform, the AP syllabus, grading policy, where technology fit into the course, etc. In short, I wasn't "plugged into the network." I'm not really sure I even knew just how much of a network there was.

Four years ago AP Statistics was added to my teaching schedule. That meant, as is the case for many of us, that I would have to learn to teach the course on the fly. I had resources - an AP Institute, a group of local teachers with similar circumstances, numerous statistics-related talks at math conferences, AP Central, and the AP Statistics on-line discussion list. But something was missing - the opportunity to spend a week in June with several hundred of my closest friends, learning first-hand some of the finer details of the syllabus, the teaching philosophy, and - of course - holistic scoring, all as we crank out the scores for thousands of student tests. So after spending a year on the waiting list, I was delighted this spring when my invitation for the 2003 AP Statistics reading at the University of Nebraska arrived in the mail.

The transition from being a table leader in Calculus to being an Acorn (first-year) reader in Statistics is a bit humbling. In Calculus I got to be part of the discussions that help to establish the rubric for each question, and then I helped teach that rubric to the readers in my room. In Statistics I had to listen, learn, try to internalize a new and somewhat different grading approach, and resist the temptation to ask "what if" questions in the briefings.

In Calculus, the rubric is defined as "a roadmap for awarding partial credit," and most student responses can be fairly well mapped to a score from 0 to 9. Not all are easy to read, however, and usually there is room for professional judgement for a difference of one point in the interpretation of the scoring. If different readers score a paper with a difference of two or more points, there is concern, and often the table leader will help to make a final interpretation.

In Statistics, however, the scores are Complete (4), Substantial (3), Developing (2), Minimal (1) or No Credit (0) for each question. Usually each component of each question is scored as E (essentially correct), P (partially correct), or I (incorrect), and a list of combinations of E, P and I accompanies each rubric to award a final score. A scale factor of almost 2 is applied for Questions 1 - 5, and a scale factor of over 3 is applied for Question 6, the investigative task. That means that in Statistics there is no such thing as a one-point swing in grading. A point missed is worth about two from the student's raw score, and a point missed on Question 6 costs the student more than three. (Note to teachers: be sure your students practice some investigative task-type questions and go into their exams prepared to earn some points on #6). So consistent interpretation of a student's paper by different readers is really crucial, and yet it is more difficult because of the wide variation of verbal responses to any question. Scores of 2 1/2 or 3 1/2, for example, are often a consequence of the combination of E, P, and I. The rubric sometimes says those half-points get truncated (2003 #4) and sometimes the score can go up or down, depending on the quality of communication in the student's answer (2003 #6). And frequently the interpretation by the rubric is sufficiently unclear that the reader just has to sit back, look at the overall response, and decide that it is "substantial" or "developing" or whatever. This is called holistic scoring, and it's the part of the grading process that I had the hardest time learning.

After grading countless Statistics papers myself and watching others do the same, some things became clear: it's really hard to get a 4, and hard for the student who attempts an answer to get a 0. The most frequent scores are 1, 2 and 3, and by far the majority of those are 2. The difference between a 3 and a 4 is usually the details of a problem, like verifying the assumptions for a test or confidence interval, stating anything about a problem in specific context or using absolute terms such as "eliminates" bias or "is" normal. In Calculus there continues to be emphasis on communication and verbal interpretations, but the nature of the questions is still such that most of what students write is mathematical syntax. In Statistics well over half of each exam is written text, including nearly all of the content on which credit is based. Thus it takes much more time to grade Statistics papers than Calculus papers, and it's harder (at least for me at this stage) to feel that each paper has been consistently assessed. ETS takes this into account by (this year) hiring about 650 readers to grade 208,000 Calculus exams (320 exams per reader) and 280 readers to grade about 59000 Statistics exams (211 exams per reader).

At Nebraska this year I encountered several readers whom I had known from my Calculus years. One said "You'll like this, it's much more relaxed," while another shared my opinion that there can be much less clarity in the grading process in Statistics, even though all papers are graded using the same system. The much smaller size of the Statistics reading leads to the more informal feeling I got. But the program is only seven years old, so developments like large briefing rooms, overhead projectors and wireless microphones will undoubtedly come along if the reading keeps growing. The authors of most of the major high school Statistics textbooks are part of the leadership team at the reading. That gives me confidence that, if I follow one of these books fairly well, my students will cover appropriate content so as to be well prepared for the AP Exam.

Upon looking back, I know what being a Calculus reader did for my teaching and for my students. I can see after only one year reading Statistics that the benefits there will be somewhat the same. I'm ready right now to go back to school and start sharing new insights into the teaching of Statistics with my next class. I just hope that they are ready to go with the same enthusiasm. And to anyone who teaches either AP Calculus or AP Statistics, I would strongly urge you to consider taking part in the reading. There is nothing else I have done which has had as much impact on my professional development as the AP reading. I can only hope I'll be invited back next year.

FINALLY AN ACORN!!
Rhea Caldwell - Providence Day School - Charlotte, NC

The notification arrives in late December. After 25 years of teaching, 20 years teaching Calculus, and 7 years on the waiting list for readers, I am finally invited to my first AP Calculus Reading. My husband thinks I am crazy wanting to go to "Calculus Camp" and grade papers for seven days, particularly with the mad rush that comes at the end of every school year. My daughter, married and pregnant for the third time, is disappointed that I will be out of town and unable to be on hand in case her baby comes early (due June 30th) like the first two. As the Mathematics Department Chairman at Providence Day School I have lots of end-of-the-year details to take care of, but my department members quickly offer to take over. With the hardy endorsement of Administrators, I make the plane reservations. Although a silly stumble down a flight of stairs in April did leave me hobbling with a twisted ankle and broken bone in my foot, I have waited a professional lifetime, it seems, for this experience and nothing will keep me from this opportunity. Taking the advice of other readers from Providence Day School, I decide that casual and comfortable is the attire for the week and my pair of tennis shoes, necessary for the twisted ankle that doesn't want to heal, will be perfect. Throwing a warm jacket and an OSU National Football Champions sweatshirt into my suitcase I am packed and on my way to Colorado State.

In many ways, I am off to camp for the first time. I don't feel like I know anyone, but several people of the plane are going to the reading and we talk briefly. Waiting for the bus that will take us from Denver to Fort Collins, people quickly introduce themselves, chatting easily, getting to know each other. The first day is spent getting settled into the dorms, having a light dinner and an official welcome for the first year readers from the chief reader, Larry Riddle. I am impressed with the lack of titles, the diversity of ages and backgrounds, the camaraderie between the experienced readers and the new people, and the many similarities and yet the many differences of our working situations. I still feel like I don't really know anyone, but I do recognize some friendly faces from North Carolina schools: Trish Morris, Steve Davis, Ben Klein, and Ken Collins, to mention a few. Once I find my way around and start to work, I am sure that I will feel part of all of this. Tomorrow is the first reading day. We'll see how that goes.

Monday morning the 650 readers gather for the welcome, explanation of terms used in the grading standards, and the briefing on the first problem. Many try to second guess some of the standards presented, but we are assured again and again that all the details have been discussed prior to our arrival and that we will all have to abide by the decisions made, and grade accordingly. It is a tough audience and Caren Diefenderfer, Chief Reader-Designate, handles the questions and comments expertly, while "grieving" for students' answers that will not be accepted.

I thought that I knew and understood the first problem. It seems straightforward enough. Just the standard area and volume problem, using of the calculator for the intersection point and for the evaluation of the integrals. Having small classes, just 8 to 10 students, who are typically good at mathematics, I am surprised by some of the responses in the papers that are presented to the group. I quickly obtain a new insight into the thinking of a far larger and more diverse population that takes AP Calculus all over the United States and in foreign countries. I also have a renewed appreciation for the task that many teachers have with large classes, and with students who are truly not as prepared for this college level course as they should be.

After the morning snack, we are off to our assigned rooms and the work begins. The table leaders set a calm tone, offering help and assistance whenever it is needed. Their ability to ask questions of my thought processes in the grading of the problem help me to appreciate the standards and to become a consistent grader. A good table partner is also essential to quickly getting acclimated to the reading process. My table partner couldn't have been more patient and helpful. Her discussions through that first day made all the difference in my comfort with the process for the rest of the week. She emphasized the philosophy for the question and helped me understand the standards that were presented in the briefing. I will know what to listen for tomorrow when problem 5 is presented.

Over the next three days we are briefed on more problems. Each room will grade two of the common problems and two others over the course of the week. I am lucky to have the chance to grade both AB and BC tests the first two days. There are 208,000 tests to do this week: 45,000 BC and 163,000 AB tests. The process, by which the boxes of tests are brought in, graded, checked and moved to the next room, is amazing, but not surprising. The exam leaders are experienced at every aspect of the process and in control, or so it seems, of the entire operation.

By the third day I feel like an expert, well almost. It is surprising to me that I feel so energized by grading the same problem again and again. There is so much to learn by the incomplete and incorrect responses that I see. As any teacher knows, I learn more about how to teach from the mistakes of my students, their false interpretations, their algebraic and conceptual errors, and their uncertainties about how and when to best use the calculator.

How I wish that every first year Calculus teacher could be part of this reading. While most new AP teachers go to workshops, all the details for teaching the course come so quickly that the internalization of the concepts and the philosophy can't possibly be complete. Working with young teachers in my own school has certainly shown me what a wonderful program can be developed with a team approach and a constant dialog about curriculum. Programs like the AP Reading, AP Central and the AP Calculus electronic discussion list are a wonderful way for veteran teachers to provide mentorship to those with less experience. It's just too bad that it takes so long to become a reader.

The passion for mathematics and teaching, quality teaching, is everywhere this week. It permeates every conversation at some point. It seems to be in the very air I breathe. It is probably a good thing for my Precalculus and AB Calculus students that the school year is over, because I feel ready to get back in the classroom and "crank it up a notch", as Emeril Lagasse, of Food Network fame, would say. My head is spinning from all the ideas of how to revamp what and how I teach. I will never be the same and I am already looking forward to next year.

NEW READER THOUGHTS
Norma Royster - UNCC - Charlotte, NC

Five years waiting for the opportunity to participate in an AP Calculus reading! The time had come to make it a reality. Was it worth it? You bet!

On Sunday, June 1st, 630+ gurus and would-be-gurus converged on Ft. Collins, Colorado to start a fun-filled week of grading 208,000+ AB and BC exams. I kept telling myself that the vibrations I felt was not the brain power around me but the fluttering of a zillion moths. The days were cool and the nights were cooler and the view of the Rockies was spectacular.

The first thing to catch my eye was the tee shirts. I had to have one. But, alas, they were now polo shirts. I got one anyway. My shirt did not have a slogan like:

Some people said I was average---I said they were mean,
... And then there are the backreaders,
Mighty readers from little acorns grow,
Clemson readers .. Nations Teachers

Soon I settled into understanding the lingo. Yes, we had to understand how to communicate:

Back-reader

one who double-checks and makes sure you are not making mistakes.

Inoculate

If a student makes a mistake you don't penalize twice.

Read with

If a student makes a mistake, penalize accordingly but continue to read the rest.

Table Scrapping

some people aren't finished and it's nearly time to end this session so let's divide up the package and get done.

By reading the students' solutions to problems I learned rather cool ways to do calculus and I also learned that some students will be taking calculus again in college. There were pleas, email addresses, drawings - some quite good, short stories-entertaining, statistical solutions to problems and poems. Many of those received the "other grade" the dash!

After packs and packs of grading the novice graders were called up to the head of the table. What have I done? Did I give too many "0's" or "9's"? Was my back-reader mad? "Fear not little acorn you are no longer an acorn but you are now free to grow into a mighty oak." My back-readers Sharon and Ben were smiling and so was I. They made my first experience a very good one. George my table partner was very patient with all my questions. The dorms, well they were dorms. The staff, consisting mostly of students, was great and always pleasant. Do I want to go next year! You bet!

THOUGHTS OF A TL (TABLE LEADER) AND QL (QUESTION LEADER)
John F. Mahoney - Benjamin Banneker Academic High School - Washington, DC

First, and for many most important, what a Table Leader does is: get to come back to the AP Reading. I was quite sad when I retired after my six years as a reader because I didn't expect to get invited back as a table leader. In fact, I didn't get asked to come back the following year. I was thrilled the year after that to get the ETS envelope containing the invitation to be a table leader. Then I had to explain to my wife what that role meant.

Those table leaders, who are not Question Leaders, come to the reading three days before the rest of the readers. During the first two days the question leaders brief the rest of the table leaders on the problems and entertain questions and comments from them on the Standards and a large bunch of samples. Typically, table leaders concentrate on the four problems that they will actually be grading during the reading and therefore concentrate on just two problems per day. Table leaders also are each asked to go through about 50 books to look for examples of student work that don't seem to follow the roadmap suggested by the standard for that problem. Post-it notes are put on these books, which are then read by the question leaders. These discussions with table leaders are quite open and sometimes argumentative. The question leaders use what they've learned from their discussions with the table leaders to improve their briefings.

Table leaders are partnered and work together on the seating arrangement in their rooms to make sure that new readers are paired up with experienced ones. New table leaders, by the way, are also paired up with experienced table leaders. There is a special briefing for new table leaders.

Eighteen table leaders, two per problem, have the roles of "Collector" and "Writer." These two work with the question leader for each problem to help prepare the briefing on the third day. The collector collects sample papers that will be used for consultant sample packets and ones that will be posted on the web. The writer prepares a report on how the problem was graded and how particular issues were dealt with. The reports go into large notebooks that serve as references for future years. As a question leader, I rely heavily on the collector and writer and feel that I'm just the spokesperson for the team of three.

On the third day, those table leaders who aren't involved with a briefing spend the day grading the Form B and sometimes the Alternate exams. Many table leaders attend evening rehearsals of the briefings to help ensure they go smoothly.

During the actual reading, the table leaders continue the briefings by answering questions from the readers in the rooms and by back reading folders of tests. The table leaders help all the readers reach a high level of consistency in grading. As a table leader, I try to make sure that all the readers in my room are comfortable asking questions. I work hard to make sure that those readers who are new are particularly comfortable and have the support of the two experienced readers on either side of them. I make sure to back read a folder from every reader on every problem. I try to give as much positive feedback as possible when I talk to a reader about a folder of theirs that I've read. Sometimes probably at least once a day a reader will convince me that I've made a mistake. I love it when that happens, because it emphasizes the fact that we all make mistakes. If table leaders have questions about a particular problem, they frequently will search out a question leader, collector, or writer for that problem. Each morning, the table leaders meet with the chief reader for 15 minutes.

Table leaders, themselves, actually read folders and score them! Table leaders help readers resolve difficulties. Some books need to be taken to the exam leaders room because they contain, for example, offensive material. Table leaders grade the large print versions of the exam. They also are often, by exam leaders, to grade particular folders or books for a variety of reasons. This year, as the Form B exam leader, I asked the table leaders to grade many Form B exams which arrived late to Fort Collins.

Some table leaders are asked to become Question Leaders. When I got the e-mail four years ago asking me to be a question leader, I was elated. I ran downstairs and told my wife that I was asked to be a question leader at the AP reading. She just started laughing: "Question Leader? When are they going to make you an ïAnswer Leader?'"

MINUTES OF
THE NORTH CAROLINA ASSOCIATION OF ADVANCED PLACEMENT MATHEMATICS TEACHERS
MEETING OF THE BOARD OF DIRECTORS
Davidson College, Davidson, North Carolina
21 June 2003

Members Present

Sue Sams (presiding), Jeff Lucia, Stephen Davis, Trish Morris, Deborah Britt, Ray Jernigan, Ed Tharrington, and Rona Schriber

Members Absent

Ben Klein, Betty Anne Shearin, and Martha Ray

1. Ms. Sams called the meeting to order at 10:10 a.m.
2. The minutes of the previous meeting of the Board on 3 August 2002 were approved as written in the Winter 2003 newsletter.
3. Mr. Lucia presented a Treasurer's report. He noted that as of 20 June 2003, our balance is $1348.38. This is down $622.67 from a year ago. This lesser balance for 2003 was due to three factors: 1. Extra mailing needed to clarify College Board copyright rules; 2. The size of the newsletters has increased resulting in added postage and printing costs; and 3. The Board meeting is earlier this year and not all of our renewals that come in over the summer are included. It was recommended that attempts be made to obtain grant monies to cover costs rather than raise dues. The following Board members also volunteered to seek additional funding: Both Rona and Ed would use contacts at SASS; Ray would contact the NCCTM Board to explore our affiliate connection; and Sue would contact PENC, as her husband is a member.
4. Mr. Lucia, without relinquishing the floor, presented a Membership Chair report, which shows that the Association has 344 members on its roll, but 70 of those have not renewed their membership for 2003-04. One hundred twenty-five members are from NC; two hundred sixteen are from 37 other states with New York, Virginia and California having the most. Three members are from foreign countries Belgium, China and Switzerland.
5. Ed Tharrington inquired about the idea of raising dues. It was decided that this was not yet needed and that grants would be investigated first. It was also noted that dues have only been raised once in our history and that this was fairly recent.
6. Deb Britt reported that all assignments for articles in the Summer 2003 Newsletter have been made. She expressed thanks to Rona, Trish, and Ben for their prompt writing. Jeff Lucia will be writing a comparison on the AP Statistics and AP Calculus readings, as he was a new reader in AP Stats after numerous years as an AP Calc reader. Stephen Davis is writing an article on the overall reading this year from his perspective as Alternate Exam Leader. Sue Sams will write the President's desk article and Deb Britt will write an article from the Executive Secretary/Editor. If all articles are in by the 1 July 03 deadline, then the newsletter should be ready for printing by 15 July 03.
7. Rona and Sue provided an update on progress being made on a NCA²PMT logo that would be included on our products. Several designs were discussed and it was decided to try to select a logo in Black/White that could be easily created and used electronically. Several students have helped with this project and a final logo will be ready for the next Board meeting.
8. Readers on the Board (Deb, Stephen, Trish and Rona) gave an overall report on the 2003 reading. Points emphasized were: The number of exams is growing; the number of readers was about the same as last year but readers read for a FULL seven days; the early reading dates this year caused some book flow problems as not all exams were there at the beginning; the on-line scoring field test report indicated that it could be done with good reliability but costlier and required more time (also, the on-line scoring worked better because there had been a n actual reading that was used to predict problems and produce the grading materials; ETS is exploring other reading options as we continue to grow and costs are increasing but most readers felt the teacher training during the reader was too worthwhile to give up the experience; On-line scorers expressed frustration with the process.
9. The NCCTM annual meeting was discussed. Our session is presently on Thursday, 9 October 03. Trish volunteered to present AB 4/BC 4, Rona will present AB2, Ben will present AB 3 and Deb will present AB 5. Stephen will give a slopefield lesson or related information as an update to last year's handout. The Board agreed that the Business meeting session would be moved to the end and that if time is an issue, one of the questions will not be discussed.
10. Ms. Britt brought up the issue of our continuing problems with the group in Florida that used grant money to set up our web site. Since the web site is not being maintained promptly, it was decided that Steve Davis would pursue the idea of having Davidson College be the host for our web site. Possible web site managers might be Davidson College students, high school students working on Senior Exit projects, AP Calculus teachers who also teach computer science or web site design. David Green, Jordan HS in Durham, was suggested as a possible manager.
11. The idea of getting slopefield materials together for members was suggested. These will be included in the newsletters.
12. Ms. Sams read a letter from the AP Statistics group that is forming. The letter asked for our monetary help in forming their organization. It was decided to reply that we would love to help but our own financing is not strong enough.
13. Teacher Resources were mentioned. These included: APCD with new worksheets to be downloaded from AP Central; the new manual developed by College Board (now in draft form) that will be presented at one day conferences; the Highland Mystery prep for the exam; and Audrey Week's Calculus in Motion as well as her Free Response animations. These will be mentioned and explained in our newsletters.
14. Ben Klein's present two-year cycle on the board expired at the end of the meeting and President Sue Sams stated that she was appointing him to another two-year term to expire in 2005.
15. It was decided that the Summer 2004 Board Meeting would be around the 26th of June. Attempts to avoid Father's Day weekend would be made as well as investigating the idea of a weekday meeting rather than Saturday. The 2004 meeting will also be held after both the AP Statistics and AP Calculus readings are complete since board members are involved in both.
16. Gratitude was expressed to Sue Sams for a well-conducted meeting and for her refreshments. Thanks were also given to Stephen Davis for hosting the site and providing such a nice meeting room.
17. The meeting adjourned at approximately 12:30 p.m.

NCA²PMT REPORT FROM THE TREASURER/MEMBERSHIP CHAIR

The above loss is due primarily to three factors: 1. The extra mailing, which was to communicate with members following the incomplete documentation of College Board material printed in the Summer 2002 Newsletter; 2. The size of the Summer 2002 Newsletter (52 pages) and the associated printing and postage costs; 3. The cycle for this statement is only about 10 months, and I anticipate dues payments for 30--40 of the people who are currently in arrears. I have found a bulk mailing service which can save us about 1/3 on postage costs (approximately $350 per year?) We should also not need to send out an extra mailing in the future, because we now understand the exact format of the documentation we must use for College Board material in future newsletters. I do not particularly want to recommend that we increase dues, but instead I think we should solicit grants and/or sponsorships in the amount of about $500 to help with overall expenses. We should probably once again discuss the concept of our newsletter, given that AP Central has begun to offer an AP Calculus E-Newsletter.

Current membership is 344, including 70 whose membership expired 3/03 who will receive a reminder but will not get the summer newsletter unless they renew. We continue to send 8 newsletters (professional courtesy exchange) to the officers of the SCA2PMT. Two of them are paid members of the NCA2PMT anyway. A breakdown of our membership is as follows:

North Carolina	Other States
Eastern - 36	New York - 27	Utah - 3
Central - 43	Virginia - 25	Alabama - 2
Western - 46	California - 19	Delaware - 2
TOTAL - 125	Georgia -15	Idaho - 2
	South Carolina - 13	Indiana - 2
	New Jersey - 12	Arizona - 1
	Florida - 10	Hawaii - 1
	Maryland - 10	Illinois - 1
	Texas - 10	Kansas - 1
	Michigan - 8	Maine - 1
	Colorado - 7	Missouri - 1
	Washington - 6	Nevada - 1
	Pennsylvania - 5	New Hampshire - 1
	Tennessee - 5	New Mexico - 1
Foreign	Connecticut - 4	Oklahoma - 1
Belgium - 1	Kentucky - 4	Vermont - 1
China - 1	Massachusetts - 4	Wisconsin - 1
Switzerland - 1	Ohio - 4	Wyoming - 1
TOTAL - 3	Oregon - 4
	TOTAL OTHER STATES - 216 (NC plus 37 states)
None from: Alaska, Arkansas, Iowa, Louisiana, Minnesota, Mississippi, Montana, Nebraska, North Dakota, Rhode Island, South Dakota, West Virginia

Submitted by Jeff Lucia, Treasurer/Membership Chair, June 21, 2003

REPORT FROM THE TEST DEVELOPMENT COMMITTEE, June 2003
Ben Klein, Davidson College, Davidson, NC

This report will focus on the conversation that took place between the Test Development Committee and about 150 readers on "Committee Night," Wednesday, 4 June, during this year's reading. All but one of the Committee's members were on the stage in the theater in the Lory Student Center.

The evening began with some remarks from the chair of the Committee, David Bressoud. David then opened up the floor for questions and comments. In the paragraphs below, I will try to summarize David's remarks and then summarize the comments and the questions (and their answers, without attribution, from various members of the Committee) that followed David's observations.

David began by introducing the members of the Committee, i.e.

• Janet Beery, University of Redlands, Redlands, CA
• David Bressoud, Macalester College, Saint Paul, MN
• Ben Klein, Davidson College, Davidson, NC, whose tenure on the Committee ends with its July 2003 meeting
• Maria Perez Randle, Bishop Kenney High School, Jacksonville, FL
• Nancy Stephenson, Clements High School, Houston, TX, whose tenure on the Committee ends with its July 2003 meeting
• Mike White, Pennridge High School, Perkaskie, PA, who could not attend the Reading

David also introduced the two teachers who will formally join the Committee in October when Ben Klein and Nancy Stephenson rotate off. The new members, both of whom were on the stage with the current members of the Committee, are

• David Lomen, University of Arizona, Tuscon, AZ
• Carol Miller, Glenbrook North High School, Northbrook, IL

David also noted that both the Chief Reader Larry Riddle, Agnes Scott College, Decatur, GA and the Chief Reader Designate Caren Diefenderfer, Hollins University, Roanoke, VA were, ex officio, members of the Committee and attend its meetings. Both Larry and Caren were present in the audience. David gave special thanks to Larry Riddle for his years of service on the Committee, during his tenure as Chief Reader. Larry's last meeting with the Committee will be in July of this year. Caren's term on the Committee began in July of 2002.

Finally David introduced the two ETS staffers who work with the Committee and attend its meetings, Craig Wright and Fred Kluempen. The introductions complete, David reminded the audience that, effective in the 2003-04 academic year, slope fields had been added as a topic in the AB curriculum. He suggested that the Committee took the addition seriously and students might well expect to find questions about slope fields on the 2004 examination. David went on to reassure the audience that the Committee did not have any other additions/deletions in mind for the next few years, in part because the curriculum had been so thoroughly revised in the late 90's.

David then suggested that, during the next ten years, the Committee would be grappling with a number of issues. Among these would be the advancing technology of handheld calculating tools. He predicted that, ten years out, the age of the graphing calculator would be over and students would be using handheld computers with full computer algebra capabilities. The examinations will need to adapt to the changes in technology.

Another issue that the Committee needs to wrestle with is writing in calculus courses. The course description for AP Calculus currently emphasizes that communication of mathematics is important, and the Committee has demonstrated, through a number of free response items in recent years, that writing, particularly clear explanations of mathematical concepts, is expected of students in AP Calculus. David predicted that this emphasis is likely to continue, if not to increase.

David next predicted that the content of first semester calculus is not likely to change much in the next ten years, and, correspondingly, the AB topic outline will not change dramatically either. However, the content of second semester calculus is now quite variable from one college to another. Some schools continue to teach a "standard" second semester course, incorporating a list of topics virtually identical to the non-AB topics in BC Calculus. Others (Davidson College, for example) teach what is essentially a multi-variable calculus course. Still others are somewhere in between. David noted that The College Board and ETS plan to survey a group of college and university mathematics departments within the next twelve months to try to find out how many different versions of second semester calculus exist and how popular each is.

[A teacher asked later whether the survey described above could be administered at the reading, and the consensus from the Committee and the ETS staff was that this would not be possible in 2003. However, the survey might be distributed during the 2004 reading.]

David concluded his remarks by noting that the Committee was concerned about the growing number of students who complete BC Calculus during their junior years in high school. He noted that AP Statistics was one possibly appropriate senior year option for these students but that the Committee will be thinking about introducing alternative AP courses, which do not now exist.

The following is a partial list of questions and comments that were made during the "open mike" period that followed David's remarks.

• How is the AB subscore working? [Answer (from Larry Riddle and the ETS staffers): Very well indeed. The reliability of the subscore is very high.]
• What are the trends in the awarding of credit for AP courses by colleges and universities? [Summary of answers (from members of the Committee, the ETS staff and members of the audience): While there have been a few well publicized examples of schools refusing to grant credit for AP scores of 3, 4 or even 5, there is no hard data about how many schools have similar policies. The College Board and ETS are, of course, concerned about this issue and intend to survey a collection of colleges and universities to try to get some clearer view of what policies are actually in place.]
• There were a number of questions about the mechanics of AP test construction. [Answers (from members of the Committee): While each free response problem begins as the construct of one, or in some cases, several members of the Committee, or, in others cases, external problem writers, each problem is reworked by the Committee to such an extent that the final product may well be essentially unrecognizable to the person who created it. Thus, free response problems are, always, the product of the Committee as a whole. Multiple-choice problems are created by either members of the Committee or external problem writers. Each multiple-choice problem candidate is run by the entire committee and those that are accepted by the Committee go into a pool from which problems are selected for individual examinations. The selection of multiple-choice problems in a given year is dictated to some extent by the free response problems that appear on the examination. Topics from the course description that do not appear in the free response section would typically be included in the multiple-choice section.]

Following the question and comment period, the Committee and the audience retired to the lobby of the Theatre for refreshments. For many of us, the refreshments constituted a second, if not a third or fourth, dessert.

2003 PROFESSIONAL NIGHT
Trish Morris - Greensboro Day - Greensboro, NC

"Who Wants To Be A Mathematician" is a mathematical game show similar to the popular TV show "Who Wants to be a Millionaire." Its creators are Mike Breen from the American Mathematical Society (AMS) and Bill Butterworth from Barat College of DePaul University. The goal of the show is to promote mathematics at all levels in an entertaining way. Students, teachers, and the general public can participate. The game has been played at math conferences and other special events.

When played by students at a local event, the creators can send teachers qualifying tests so that the top 2-4 students from a school can enter a more regional competition. Then a "Fastest Finger" round qualifies them for the actual play. At the grading, forty teachers volunteered to play and five names were drawn from a hat to get to play. There are fifteen prizes ranked in value commiserate with the difficulty of the question thatÍs been asked. The first prize is a "graphite calculator" all the way up to a $2000 grand prize. They are donated by The Mathematical Association of America, Maplesoft, Inc, Texas Instruments, and John Wiley & Sons.

As in the TV show, participants can receive assistance. Possible lifelines can be: Ask the Audience, 50:50, or Put Someone Else on the Spot. The multiple-choice questions cover Algebra, Trigonometry, Geometry, History of Math, and Discrete Math. Some typical questions are:

1. The ocean is like a sine graph becauseƒ
   1. both have waves
   2. both are all wet
   3. both can make you nauseous
   4. both have connections to tan gents
2. Two of the angles of a triangle measure 107 degrees and 61 degrees. What is the measure of the third angle in degrees? (Assume the triangle is in the Euclidean plane.)
   1. 12
   2. 22
   3. 73
   4. 119
3. What are the missing entries in the following magic square (in order of the subscripts)?

   10	x2	x4
   x1	7	x5
   6	x3	4

   1. 5, 2, 11, 8, 9
   2. 5, 4, 11, 7, 10
   3. 5, 3, 11, 8, 9
   4. It can't be determined from the given information.
4. What is the sum of the complex but not real, fifth roots of 1?
   1. -1
   2. 0
   3. 1
   4. i

In terms of enjoyment, this night ranked right up there with the ever popular talent night. You can check out past performances at http://www.ams.org/ams/wwtbam.html. If you have questions about the game or would like to schedule a game at a conference, school, or other special event, email Mike Breen at the AMS Public Awareness Office myb@ams.org.

REGROUPING THE ALTERNATING HARMONIC SERIES
Dan Teague - NC School of Science and Mathematics - Durham, NC

pp 35--37

Click here to view/download this article as a PDF document.

CALCULATOR ISSUE
Mark Howell - Gonzaga High School - Washington, DC

I do recall that numerical integration algorithms are especially vulnerable when the integrand involves an absolute value, or when there is a vertical tangent in the interval. At any rate, this issue brings up an important point for us and our students. Understanting what your calculator is doing is important. Try fnInt(e^(-X^2),X,0,10000). The TI-83 quicklly spits back 0 (which is clearly wrong!). That is, it is important for us to know when machines will stop trying to get a better numeric approximation using any algorithm... whether root finding, integrating, or whatever. The results are only trustworthy to the advertised accuracy, though the advertising is generally poor! Even then, you can't always trust 'em (see the e^(-X^2) example... what's happening there is athat the machine is evaluating the integrand only at places where X is so large that the integrand is 0... after making a few stabs at the value of the integral, it thinks it's getting convergence since it saw the same result, 0, after several attempts.

I remember a similar issue came up in 1995 when the Sharp 9300 used a lousy integration algorithm (I think it was just Simpson's Rule with N=100) that caused kids to get the wrong answer.

AP CALCULUS READING CONVENTIONS
(Handout from the AP Calclulus Reading, June 2003)

The purposes and methods of scoring the AP Calculus Exam are different from the purposes and methods we, as calculus teachers, use with our own students. Some of the conventions are used to ensure consistency and accuracy, as well as fairness to the student. We attempt to give each student credit when the student has shown knowledge and understanding of calculus. There are several accepted practices that pertain to reading the AP Calculus Exams. These include the following.

Copy errors

Typically a one-point deduction is taken for a copy error [see Terminology handout], and you should continue to read the student's work for correctness from that point forward. A student may need to meet eligibility requirements in order to receive further credit.

Saying too much

When a student has solved a problem or answered a question completely, but then goes on and does additional work, which may be incorrect, the student has said too much. Depending on the question, a deduction may or may not be taken for the error. The standard for an individual question will state the policy.

Parallel solutions

When a student presents two or more complete "solutions" to a problem, without choosing one to be graded, these are called parallel solutions. In such a case, you should read and score each solution. The student's score is then determined by truncating the average of the scores.

Crossed-out work

Do not read any work that a student has crossed-out or erased.

Three-decimal-place rule

Students are instructed to present answers accurate to three digits to the right of the decimal point. If those digits of the student's answer agree with the correct answer (rounded or truncated), then the student's answer is correct. For example, if the correct answer is π, then all of the following are correct: 3.141, 3.142, 3.14159, 3.1428. You should read only the first three digits to the right of the decimal point in the student's answer.

No simplification needed

The instructions for the exam stat that unless otherwise specified, an answer (numeric or algebraic) need not be simplified to be given full credit. For example, if the student's answer is e⁰ - 4 + 6, and the correct answer is 3, the student's answer is correct.

Immunity from further deductions

Some types of errors, typically errors in decimal presentation or in units, may receive only a one-point deduction in a problem. The student may repeatedly make the same type of error in a problem, but to be fair, a decision has been made to penalize the student only once.

We do not accept mere recipes or formulas

The student must apply the work to the specific problem at hand.

AP CALCULUS READING TERMINOLOGY
(Handout from the AP Calclulus Reading, June 2003)

"Our" problem

The problem as it is written on the exam.

Copy error

The student makes a minor error in copying a portion of the problem or in copying the student's own work from one line to another.

Re-start or false start

The student begins the problem,but then you see work unrelated to the first work. The student may have abandoned the first attempt at a solution without crossing it out and then begun a new solution.

Arithmetic and algebra errors

Errors that are non-calculus errors.

Eligible or eligibility requirements

In some cases, in order for a student to gain subsequent points in a problem, the solution at a particular point must meet certain requirements.

Recoup

A student may have lost a point, but a later part of the work corrects the error in some way, allowing the student to regain the lost point.

Bald answers

An answer without any supporting work is called a bald answer. The allocation of credit for bald answers may vary from question to question.

Reversal

A student's work may contain b - a rather than a - b, where a and b can refer to any type of mathematical object.

Read with the student

If the student has made an error, you should not quit reading the student's paper. If there are still points that may be earned, you should continue to read the student's work for full credit for the remaining points to be earned. A student may make an error at the beginning of a problem, but still earn most of the points in the problem because the student reasoned correctly form the point of the error forward.

0-2-0 or 0,2,0

This shows you which points have been earned in a sample paper. If you look a the right side of the scoring standard, pint values are listed vertically for a part of the problem. In this example, the student did not earn the first point(s), earned two points on the second portion, and then did not earn the last point(s).

0/3 or 3/4

These examples show that a student has earned no points out of the three possible points in the first case, and the student has earned three points out of a possible four in the second case.

CALCULUS AND FACTORIALS
Dan Teague - NC School of Science and Mathematics - Durham, NC

pp 46--49

Click here to view/download this article as a PDF document.

NOTES OF INTEREST FROM THE EDITOR
Deborah Britt - Asheville High School - Asheville, NC

1. College Board is putting together all of the Released Multiple Choice Questions in a PDF format that will be available for purchase this Fall. These will include 1969, 1973, 1985, 1988, 1997, 1998 and eventually 2003 released in the Fall of 2004.
2. The final copies of the MOES books with all of the essays (including an index of topics) are being sold until the supply runs out. Contact moes@I-2000.com.
3. College Board will be selling old essay and solutions or more recent ones can be obtained on AP Central.
4. The number one subject choice at AP Central for those logging on is Mathematics. Feature articles at AP Central change twice a week. There is now an AP Calculus electronic newsletter that you can receive if you register on AP Central. The newsletter highlights new updates on AP Central for Calculus teachers. The newest things on AP Central for Calculus are a Question of the Month (use link at top right of the Teachers' Corner Ð May, June and July questions), worksheets that go along with the explorations on the APCD, and a sign up to be notified about when the Multiple Choice Questions in PDF format will be available for purchase.
5. The Baron's review book for AP Calculus is being revised for the 8th edition and will be ready for 2004-2005 school year. If you have ideas for changes and improvements, please let David Bock know -- dbock@icsd.k12.ny.us.
6. Register at AP Central to be notified when the MC mentioned in #1 above will be available for purchase.
7. With all the Harry Potter Hype this week, thought some of you might enjoy this little site. I'm not sure of all the math formulas etc. but I got the pattern to make my nephew a scarf. http://www.girlfromauntie.com/patterns/clothing/yasp/yasp-theory.html
8. Math Tools has just opened its Calculus section. http://mathforum.org/mathtools/cell.html?&new_co=c.

   Math Tools is a new digital library created by the Math Forum with an NSF grant to assist teachers and students in finding, using, and fostering the development of software for the effective teaching of mathematics. Currently under development, the Math Tools site will include resources for pre-K through Calculus with computer, graphing calculator, PDA, and other platforms. Math Tools features:

   • user reviews and comments
   • stories of how others have used the software
   • problems which make use of the software
   • activities and lesson plans
   • discussions of all the above.

   FEATURED TOOL
   Surfing (Derivatives), International Education Software http://mathforum.org/mathtools/tool.html?&new_id=1002. A man surfs along a curve; the derivative is the slope of his surfboard.

   CHECK OUT THE MATH TOOLS SITE:
   Math Tools, http://mathforum.org/mathtools/
   Register, http://mathforum.org/mathtools/register.html
   Discussions, http://mathforum.org/mathtools/discuss.html
   Research Area, http://mathforum.org/mathtools/research
   Developers Area, http://mathforum.org/mathtools/developers/
   Newsletter Archive, http://mathforum.org/mathtools/newsletter/
   Susan Kornstein, Senior Content Editor, AP Central, http://apcentral.collegeboard.com/

9. I suggest you consider taking the Calculus with TI-89 on line class (http://education.ti.com) before you make a decision concerning which calculator to use with your calculus class. Lin McMullin has a posted review of the course posted at AP Central. It's on education.ti.com, but you can get there quickly: http://education.ti.com/us/t3/onlinecourses/ti89.html It says:

   Focus: The primary focus of this course is to use the TI-89 to enhance the teaching and learning of Calculus. The powerful techniques using the TI-89 are illustrated with standard calculus problems. This course contains 27 self-paced learning modules written by experienced teachers. Each module has 2-4 lessons as well as tips and hints on integrating the TI-89 into your lessons plans.

   There appear to be 26 modules--#27 is called Graduation and Evaluation. There are over 100 individual lessons/activities/topics.

   None of the topics are covered in very much depth, but they are not intended to be. This is not a course for learning calculus, but rather for learning how to use the TI-89 to teach calculus.... If you are new to the TI-89, you will get a good start on learning how to use its computer algebra system. All of the operations and features are carefully explained as they are being used. This course will not make you an expert TI-89 operator, but it will give you a good start.... The cost is U.S. $225.00 for each individual. Graduate and continuing education course credit is included in the purchase price. The $225 gets you Continuing Ed credit, but graduate credit, available at additional cost [ranging from $110 to $145], may, upon prior arrangements, be obtained from:

   French River Education Center/Worcester State College
   Portland State University
   University of San Diego
   University of Idaho

   There is a demo about limits, which only covers one unit on limits [asymptotes and holes], but has 4 lessons. To view the demo http://ti.blackboard.com/index.html Login as "demo" with password "demo1". (CasE MatTErs--lower case only!)
10. (Note primarily for those who teach AP Statistics... I have just returned from reading AP STATISTICS exams at the University of Nebraska, Lincoln. This was the fifth reading I have experienced. As has been true in the past, it was an enjoyable and educational experience. I enjoyed associating with AP Statistics colleagues and talking with many of the first-time readers.

    Bill Trill just sent a note relating to his Web site for AP Statistics. It is an excellent site. I recommend it to all, especially to those who are relatively new to the teaching of AP Statistics. In case you missed it, the address for Bill's site is... http://www.hw.com/academics/usmath/apstats/

    (a) My Web site is Herkimer's Hideaway ( http://www.cate.org/sms99/hmpsms.htm). It may be of some use to those who are new to the teaching of AP Statistics.
    (b) I have created 28 Excel spreadsheets (many interactive... allow user input, graphs adjust, etc.) that relate to statistics. These are not a substitute for the excellent commercial software that exists, but I do make great use of them in my teaching. Basically, I just send them (via. attachment) to my students at the appropriate time so that they can fiddle with them. I think students can learn a lot just be "fiddling around" on their own. I use them both in AP Statistics and in a one semester non-AP Statistics course that we offer.
    (c) After the one semester non-AP Statistics course, we offer a Mathematics of FINANCE course which is heavily spreadsheet-oriented. I have created 50 FINANCE spreadsheets. Many of these represent assignments that students do. Others are sent to the students so they can fiddle with them. For those who might be interested, I would be happy to send you (via attachment) the spreadsheets in (a) and (b). If you would like to take a look at them, let me know and I will send them. Please be aware that I am not a professional spreadsheet producer (if there is such a thing), but some folks have found these to be of some use. If you want the spreadsheets sent, please let me know if you want STATISTICS or FINANCE or BOTH. Also, indicate the e-mail address to which you want them sent.
    --- Sanderson M. Smith, Cate School, Carpinteria, California

11. Looking for slope field questions? (Lin McMullin)

    The Course Description http://apcentral.collegeboard.com/repository/ap03_cd_calculus_0405_4313.pdf and Calculus BC free-response questions posted on AP Central (1998-2003) provide some good examples. http://apcentral.collegeboard.com/members/article/1,3046,152-171-0-8031,00.html. The 1998 Released Exam, available in the College Board Store, has others. http://store.collegeboard.com/product_detail.asp?item=255113

    We were given the following on the slope field objectives at a recent workshop. The student should be able to:

    1. Sketch a slope field for a given differential equations (see old BC tests )
    2. Given a slope field, sketch a solution curve through a given point (see old BC tests)
    3. Match a slope field to a differential equation
    4. Match a slope field to a solution of a differential equation.
    Here's a slightly expanded list from my book Teaching AP Calculus (order from D&S Marketing Systems, Inc. http://www.dsmarketing.com) with references to past questions
    • Draw a slope field by hand at given points. 1998, BC 4(a), 2000 BC 6(a)
    • Given a slope field identify its differential equation (Multiple-choice) 1998 BC Multiple-choice 24.
    • Given a differential equation identify its slope field (Multiple-choice)
    • Given a differential equation draw a slope field. 1998 BC 4(a) and 2000 BC 6(a)
    • Interpret a slope field. 2000 BC 6(b), 2002 Form A: BC 5
    • Draw a solution curve on a given slope field 2002 Form A: BC 5
    • Given a solution curve, identify its slope field.
    • Given a slope field, identify its solution curve.
    NOTE: you can also download programs for slopefields, Euler's method and others for TI83+, TI89 and TI92 at the D&S website.

12. I don't claim that my materials are extraordinary but they are available for the next few weeks still. If you wish to go to my website you can see all of my assignment sheets and worksheets for the past year (both semesters) and you may find that t hey give you a feel for the flow of the course and the nature of the questioning that one calculus teacher uses in her courses. My students (AB) say after the test that with the exception of the occasional unfamiliar question, they feel quite prepared for what the AP test is like. I also have a number of "sheets" of sorted samples of previous years' questions that I make available to my students. Those are NOT on the website but a copy can be sent to anyone who wants them and contacts me privately.

    Susan Schwartz Wildstrom
    Walt Whitman High School
    Bethesda, MD
    http://www.wildstrom.com

13. Go to http://www.pfs.sytes.net/theatons/ Click on Calculator links, then go to a nice list of Calculus and other math program links. From there scroll down to slopefields Rodney Eaton, jrodneyeaton@yahoo.com.
14. Check out http://www.ticalc.org and search for slopefields.
15. The Voyage 200 is the new replacement for the TI92+.
16. TI now has a wireless network for handheld calculators. You hook up 4 calculators to a hub and this in turn goes to you computer where you receive instant student's work. You can also send notes, assignments etc. to the students calculators. This is called the TI-NAVIGATOR^(TM). A 32 student classroom set is $4000. A 16 student classroom sells for $2425. Each additional hub that supports 4 students is $450.
17. The solutions to AB and BC 2003 exams should now be at AP Central.
18. I cannot say enough good things about Audrey Week's Calculus in Motion^(TM). You can purchase a Free Response CD to be used with Version 4.0 of Geometer's SketchPad. The free response animations are from 1997 to 2003 AP exams. She now has Algebra in Motion^(TM). Visit her website http://www.calculusinmotion.com.
19. Make sure you try and go to one of the one-day workshops sponsored by College Board this Fall. Call the College Board office for your region or keep checking AP Central for a list of dates and places. The packets you have received in the past will be changed. They are now preparing a Professional Development Booklet that you will receive. It is now in a draft form. They are planning to do a new booklet each year with a new topic. The topic for this year is "Differential Equations and Slopefields." I have used the draft materials in a Summer Workshop I did at ECU. They are well written and include other information as well.
20. You can download a 3 page worksheet set on Slopefields by Nancy Stephenson at AP Central. It is a click at the very end of the page.

Concluding Remarks

Thanks to all of the contributors to this newsletter, especially Gloria Dupree who helped proof read all of this. Do not forget to come to Greensboro for the NCCTM meeting on October 9th and 10th. Our session to go over 2003 questions and have our business meeting is scheduled for Thursday. Check your program and we hope to see you there. Let us know how we are doing. We want to serve you better if we can. Please send in any information you have that might help another teacher. We have a lot of beginning teachers who need our help.