CAIS NORTHERN PROFESSIONAL SERVICES COMMITTEE



“Serving Our Strongest Students”

CAIS Math Day 2008

Please type your answers below and e-mail your completed form as an attachment to CAIS organizer Chris Davies at cdavies@.

Please try to be as expansive as possible. The more we share, the more we will take from this day!

(Teachers from the same school should feel free to collaborate on a single questionnaire.)

We hope to share all the completed questionnaires as soon as possible. Depending on how much data we receive, we might post answers online, burn answers to a CD, and/or transfer via flashdrive. Please bring a flashdrive (portable memory stick) to Math Day if possible.

|1) Please tell the group about YOURSELF. |

|Name: Naoko Akiyama, Ernie Chen, Chris Davies, Warren Fernandes, Steve Gregg, Shahana Sarkar, Molly Barrett, Scott Clark, Ciara Coleman, and Kenny Ewbank.|

|School: Head-Royce |

|Town: Oakland |

|Enrollment: 780 K-12, 340 in US |

|Grades you teach: 6 - 12 |

|Courses you teach: Math 6, Problem Solving 7, Algebra 1, Geometry, Alg 2, Precalculus, AP Calculus, AP Statistics, Statistics/Economics |

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|2) Does your school have TRACKING? (or courses offered at “honors” level, or some sort of structured differentiation in the courses?) Explain: |

|In K-8, all students take math with their agemates (a few strong MS students advance a grade). In 9-12, most courses are offered at 2 levels (regular and |

|honors). Students are given a recommendation but are allowed to make the final choice. |

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|If you offer advanced classes, briefly describe how they differ from the regular classes? |

|Honors moves at a faster pace, has a wider breadth of content, requires students to do more independent work, gives students less time to review/practice |

|new concepts, and gives students more challenge problems. Students are expected to have superior algebra/symbolic skills, high motivation, and high |

|interest in mathematics. |

|If you offer advanced classes, do you think they benefit the strongest students? What about the rest of the students? |

|We think the honors classes give our strongest students a broader exposure to various topics, and much more interaction with challenging problems. Our |

|strongest students benefit because they see more math, they are stimulated by more advanced topics/concepts, they are pushed to solve more difficult |

|problems, and they are asked to work independently (or with peers but without teacher) more often. |

|3) What types of CONTENT ENRICHMENT do you provide for the strongest students? Mention additional problems, projects, extra credit assignments, websites,|

|software, etc. by course (please include as many specifics as you can): |

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|Sixth Grade Math: |

|We provide additional amounts of problems from time to time or extensions. However, we do not add items often as we find our 6th graders are still |

|learning to manage their time and study skills. Problem of the Weeks offer extensions for all students. |

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|Pre-Algebra: |

|In the Problem Solving course, enrichment problems are provided for substitution. On projects, extra credit portions are provided for extension. |

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|Algebra: |

|In Algebra, packets are created with extra material students can choose from in place of regular homework. The material is related to the current topic but|

|is more in depth. Chapters that are not covered in the year, but are apart of the text provide a related source of extra material. |

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|Geometry: |

|There are numerous challenge sheets/problem sets. Students are usually required to attempt the problems and can earn extra credit if they do exceptionally|

|well. Some sheets are from math contests and are not focused on geometry. Problem sources include an old AMC test, the calendar from Mathematics |

|Magazine, and a book of middle school brain twisters. |

|Other sheets are extensions of geometry. They include the purple puzzles in the Discovering Geometry text, the area paradox sheet, the reflected line |

|sheet, the Euler Networks conjecture, the angles of a star, the hands of a clock sheet, the octagonal pizza box, the new soda can tray, and the spider and |

|fly problem. |

|Other challenges are for the Geometers Sketchpad. These include constructing a sextant, constructing a tangent, constructing a constant perimeter and |

|constant area rectangle, and trisecting a segment. |

|Finally, most of the chapter tests include an extra credit problem or two to stimulate students minds and give the strongest students another chance to |

|shine. |

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|Algebra 2: |

|In Algebra 2 Honors, problems selected from the text "The Art Of Problem Solving" are given throughout the year.  These problems come from AMC, AHME, and |

|Math Contests from years past.  Furthermore, problems from the AP Calculus curriculum involving algebraic concepts are introduced as well.  Lastly, I do |

|use some problems from Mr. Gregg's PreCalculus curriculum, as well as from the AP Statistics curriculum to show kids what's coming later on in their |

|mathematical career at HRS.  During the second semester I have the kids do an internet based data project that involves using Microsoft Excel and |

|Geometer's Sketchpad.  It is usually well received. |

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|Precalculus: |

|Most content enrichment takes the form of non-routine, math contest style problems.  These are typically taken directly from AMC tests, or found in |

|collected works of such problems.  By far the best source of non-routine problems is the "Art of Problem Solving" bookstore, which can be found online |

|at    |

|The original, classic problem solving textbooks that can be found on this site are "The Art of Problem Solving", Volumes 1 and 2, by Sandor Lehoczky and |

|Richard Rusczyk.  These two books cover the entire range of high school mathematics topics.  The other texts provide more in-depth coverage of specific |

|mathematical topics, such as counting and probability, and number theory.   |

|The strongest students are typically given these sorts of problems either in addition to or in place of the standard routine textbook problems for any |

|particular unit.     |

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|Calculus: AB Calculus exposes students to some BC Calculus problems when they get a chance. BC Calculus curriculum is challenging enough for our |

|strongest students! |

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|Statistics: Not much enrichment (the course is already AP). There is an extra credit sheet in the fall with a pair of calculus derivations. There are a |

|few links to articles containing more college level derivations. |

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|Other math courses: |

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|4) To what extent are CHALLENGE PROBLEMS (non-routine, math-contest, synthesis type problems that students have not been shown explicitly how to solve) |

|part of the standard curriculum (as opposed to extra credit)? |

|The MS classes offer challenge problems to everyone from time to time. In 6th Grade, Problem of the Weeks are regular assignments that are a mix of |

|previous and current material, but can often require a skill not formally taught. Our Problem Solving course definitely makes these part of the curriculum.|

|Often, these problems are during math lab or in side conversations and not graded for credit. Also, some challenge problems are just given to the |

|strongest students on the side. We also participate in AMC, SIGMA, CML and Math Counts. |

|The US uses challenge problems in the honors courses. They are common in Geometry Honors, Algebra 2 Honors, and Precalculus Honors. |

|Are students graded on their ability to solve such problems, and if so, how is that done? |

|Challenge problems are graded in 6th-YES, 7th-YES, 8th not graded, GeoH-YES (with potential for extra credit), A2H – just a bit, PCH – yes on tests we have|

|problems that really extend the current topic. |

|5) How do you modify your ASSESSMENT for strong students? Do you grade the strongest students differently or have different standards? |

|No, we don’t think it’s fair to grade using different schemes. Students are already separated into honors math classes in the upper school. |

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|Do you let strong students skip routine assignments in order to work on advanced assignments? 7th grade Problem Solving, Alg 1, AP Statistics - yes, they |

|can skip routine HW to do something else. In AP Calculus, the assignments encourage students to do what they need to do. A strong student will often |

|choose to skip a problem she already knows how to do. |

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|Do your strongest students have difficulty communicating their thinking in oral and/or written form (they can just DO the math in their head)? How do you |

|help them to improve? Sometimes they are worse at communicating their steps. We ask ALL students to show their reasoning. We constantly remind students |

|but some of them continue to withhold their steps! |

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|Do you deduct points if answers are correct but the reasoning is not sufficiently communicated? Almost all our teachers deduct points if an answer is |

|correct but there are no steps (or insufficient steps). All of our teachers deduct full points if there is an incorrect answer and no steps. |

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|6) What other types of PEDAGOGICAL ADJUSTMENTS do you make to serve strong students (Use of class time, differentiated learning, amount of collaborative |

|learning, modified teaching styles, etc.) In the Middle School, we tend to use heterogeneous grouping. We adjust class time for individual exploration |

|aside from class work if mastery is shown. We also entertain the natural conversations that happen with our strongest students and their desire to |

|understand more than the skill, but the next level in understanding or extension. In the second half of the 7th grade year, some warm up problems are |

|purposely designed with the strongest students in mind, while other students benefit from attempting the process as well. |

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|As for the Upper School: In BC Calculus, students are asked to give lectures in other math classes to younger students. In AB Calculus, students are |

|asked to teach concepts to each other in a formal way. Some teachers lecture much more in their honors classes than in their regular class. Other |

|teachers do not really differentiate their style, regardless of the level of the students. Most of our teachers commit some class time to collaborative |

|work among students (so students are required to help each other with the concepts.) Also, students in advanced classes are more likely to have a full |

|40-45 minutes of lecture on some days, followed by a day of practice. We almost never lecture for extended periods in regular classes. |

|7) Does your school allow 9th-12th graders to ACCELERATE in to math courses above their grade level? Yes. Some 9th graders are ready to take 10th grade |

|Algebra 2 Honors upon arrival. Others accelerate with summer work. |

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|Does your school schedule make this acceleration difficult? In the upper school, it has worked out. |

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|Does your school allow 5th-8th graders to accelerate above age level? How do you weigh the maturity/social issues? Almost never in 5th or 6th. We |

|occasionally have a 7th grader move up a year or two in math. Social/maturity issues are a factor, but have never resulted in a student not moving |

|forward. We state any concerns and watch students closely. We usually have 3 – 8 eighth graders who walk down the hill to take Geometry Honors with the |

|9th graders. |

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|How is this acceleration accomplished? Top 6th or 7th graders sort of learn the math outside on their own and with parents. We have Algebra 1 in the |

|summer for a top student going into 8th grade. We have Algebra 2 Honors in the summer for top students going into 10th grade. We try to have summer work |

|completed on our campus because we can’t really monitor the curriculum at other summer programs. (We have given credit for the CAL Summer Precalculus |

|course.) We evaluate candidates for acceleration by examining their current grade, ERB scores, Algebra Readiness Test, and teacher recommendation. |

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|Do you receive much parental pressure to allow students to accelerate beyond their age cohort? We have some families pushing to take honors when the |

|student should be in regular, some pushing to get credit for summer work, and some middle school students/parents pushing for greater challenge. |

|8) Do you have any SUMMER math offerings on your campus that serve to enrich strong students? As mentioned in question 7 above, we have Algebra 1 in the |

|summer for a top student going into 8th grade. We have Algebra 2 Honors in the summer for top students going into 10th grade. |

|Do you give credit to students who take acceleration/enrichment courses from outside programs? We try to have summer work completed on our campus because |

|we can’t really monitor the curriculum at other summer programs. (We have given credit for the CAL Summer Precalculus course.) Generally, we do NOT give |

|credit for courses taken off campus. |

|9) What math COURSES does your school offer for students who have completed Precalculus? At Head-Royce, we have AP Calculus AB, AP Calculus BC, AP |

|Statistics, Intro to Statistics/Economics, and Multivariable Calculus (which might run in a good year). |

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|Are there students who run out of math courses to take? What do they do? Rarely. We have many students taking calculus as juniors. They can take AP |

|Statistics as seniors. Occasionally, we have a sophomore in calculus. That is one reason we started offering Multivariable Calculus. A rare student |

|could “run out of math” if they did Calculus as a 10th grader, AP Statistics as a 11th grader, and then found that Multivariable was not going to run |

|during their 12th grade. A number of our students take a college math course in the late afternoon at CAL, because of its proximity to our campus. |

|10) Does your school have a MATH TEAM? Yes, Math Counts and ASMA in the MS. |

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|The HRS upper school has not had a competitive math team for many years. We have a Math Club that has waxed and waned in strength over the last decade. |

|This year, is has dwindled to just a few students. |

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|How much participation is there (in absolute and/or percentage terms)? In the Middle School, regular participation is approximately 7-8 students for Math |

|Counts and 10 students for ASMA. More students attend from time to time. |

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|Over the past 10 years, our US math club has had perhaps 0 – 15 members, which represent 0% - 5% of the student body. |

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|How often are math competitions held on campus? Twice a month in MS. |

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|In US, we have signed up for the CML contest regularly and also added the ASMA contest a few years ago. We are able to provide the Math Club with about a |

|dozen contests a year, lasting 30-35 minutes at a sitting. We also hold the AMC each February. |

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|How often does the team travel to compete? Perhaps twice a year in MS. We have not had a traveling team in many years in the US. |

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|Do you offer any incentives/extra credit for participating in math team events? No. We hope that students will participate out of their sheer enjoyment |

|and enthusiasm. We are brainstorming ways to increase participation. |

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|What other things do you do to get your strongest students to participate? In MS we make announcements, reminders and encouragement to the class and at |

|times, individually. |

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|In US we do little in terms of promotions or incentives. Perhaps we should do more. We want students to come out and participate voluntarily. |

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|Are your present day mathletes as strong as they were in the past? In MS, our mathletes are still strong. We acknowledge that there are the same amount |

|of students strong in skills and also the same amount of students that are strong in enthusiasm and participation. |

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|In the US, no. Objective measurements such as performance on AMC or CML is significantly lower today then it was 10 – 20 years ago. |

|11) Do you have a PEER TUTORING program where your strong students can work as math tutors? Describe: Yes. At Head-Royce, the upper school teachers |

|begin the fall by recruiting students to be tutors. We promote the program in our honors classes, especially. Students simply add their name to the list |

|if interested, and include their free periods. As the year goes on, struggling students make requests for a peer tutor and we match them up with someone |

|who has a common free period. We also try to match students with someone with whom they feel comfortable, if possible. Our high school tutors work with |

|other high schoolers, with middle schoolers, with lower schoolers, and even with students from other schools who live close to our campus. |

|We probably have 15%-20% of our math students sign up to be tutors, and about a fifth of them end up getting matched up with a tutee. |

|12) Do you track (or can you guess) what percent or numbers of your GRADUATES go on to major in mathematical fields? In science? We do have a Director |

|of Alumni Relations who keeps a data base on what our alums are up to. Of course, the further out our students go in time, the less complete is the |

|database. But we do know about some of our alums who major in math related fields and some who go on to work in math related fields. We have also started|

|keeping records of the college grades our alums earn. |

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|Do you know if any of your strongest math graduates went on to teach math? We have also been pleased to learn that some of our recent alums have gone on |

|to teach in math and science. On our own staff we have two science teachers and a history teacher who attended Head-Royce. |

|13) What other SUGGESTIONS do you have for serving our strongest students? We are wondering if we should more frequently ask our strongest students to |

|figure out the mathematics on their own. They are very good at practicing and regurgitating what we TELL them, but still weak at trying, investigating, |

|and working on their own. |

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|We continue to talk of the need to expose our strong students to math contest problems. |

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|We occasionally have special “Math Days” on campus and we like to invite our strongest students to participate. Last year, we had students exchange ideas |

|with our strongest math alumni. Later , they attended a talk by Professor Keith Devlin and participated in Q and A afterward. |

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