## Bard Math CAMP Day 5

8/31/2018

Today was the last day of CAMP!

In computer science, we wrapped up the week by learning more about the actual hardware of computers. In small groups, we each got a tower that we opened up and explored the computer guts inside. We had a small scavenger hunt for specific parts we had discussed during the week such as the CPU (Central Processing Unit), PSU (Power Supply Unit), and motherboard. Following our exploration of the towers, we came back together for a class discussion about more important computer vocabulary and misconceptions about things such as Wifi and servers.

In Math class, with Japheth, we finally got to uncover together the math behind liar’s bingo. After solving the mystery using all that we have learned about binary this week, we split up into pairs to work with different problems that we later found were extremely related. Some people worked with counting subsets, some with counting divisors, some with letter combinations, and more! Through these problems and a small tour around the classroom to discuss everyone’s sorted solutions, we realized that each of these problems were related to Pascal’s Triangle!

In art, students had a chance to continue working on their clay fractals from the day before. Students then utilized the idea from clay fractals and created cookies using this design. The cookie dough was kneaded and then combined to create a fractal pattern for the cookies. When students finished this, they had a chance to combine all of the things they worked on over the course of the week into one piece of art.

From 2:30-3:30, we had our CAMP open house for parents!

Blog by: Meagan Kenney, Elliott Goldstein, and Maya Schwartz.

## Bard Math CAMP Day 4

8/30/2018

Today was the fourth day of CAMP!

In art, students continued to expand on the fractal idea that they began to work on Wednesday. At the beginning of class, students were able to finish or improve upon their fractal paintings. After, students received clay (of either black, white or gray coloring) and kneaded them until they were thin enough to be put together, Students kneaded them to fit a triangular shape, then combined two of the kinds of clay and stretched them out. When the students cut the clay, a triangular fractal was visible. Students then used these triangular fractal cross-sections to spell out their names or create designs.

In computer science, students learned the properties of boolean logic relating to truth tables. Students learned about true/false statements that contained the boolean operators or/and. After working through more complex logical statements (i.e. true and (not true or not false)), students utilized these ideas to work with circuits. Students considered the properties of circuitry and the flow of electricity with boolean logic.

In math class, with Japheth, we learned about Hasse diagrams: a handy way to organize a number and all of its divisors to learn more about the divisors themselves. After learning two examples of these diagrams we all tackled creating the Hasse diagrams of the numbers one through thirty. We then sorted these interesting pictures and discussed our findings as a group. This helped us to solve one of our mysteries from Day 3 of how to characterize numbers with exactly four divisors. Through this exploration we showed that all numbers with exactly four divisors are either the product of two distinct primes or the cube of a prime!

After-lunch electives included Zome Tool, Open Studio, and Rubik’s Cube.

Blog by: Elliott Goldstein, Meagan Kenney, and Maya Schwartz.

## Bard Math CAMP Day 3

8/29/2018

Today was the third day of CAMP!

Today in Computer Science we got to practice our skills as drivers and navigators of our programs: one student would type the code out while the other kept watch for typos and helped guide the driver in writing the program. We mainly used Python to learn how to compare multiple compound logic operations by testing all possible inputs and comparing outcomes. Additionally we learned more about variables and functions and to utilize them to make our coding more efficient!

In math class we started with a fun trick. We had a huge collection of strips of papers with numbers colored black or red. When a student read out the colors of a random strip to Japheth, slipping in one lie about a color, Japheth was able to tell the exact number for which the color was lied about. Was he using magic? Binary logic? Who knows! Then we started an extensive exploration of the positive integers up to 30 and their divisors. We sorted the numbers by how many divisors they had and then began to analyze each group. Through this analysis we found that we could prove that a number has exactly two divisors if and only if it is prime. And also, we found that a number has exactly three divisors if and only if it is a square of a prime number! There’s so much more to learn from this exploration that we will continue to see in the remaining days of CAMP!

In Art, the students worked on creating fractals. Fractals are figures in which each part of the figure has the same structure as the whole. Fractals contain similar patterns that happen continuously on a progressively smaller scale. To make the fractals, students cut a piece of paper into 4 sections and then re-arranged the patterns after cutting. Students then were able to customize their fractal by coloring it.

After-lunch electives included juggling, creative writing and reading, and Rubik’s cube.

## Bard Math CAMP Day 1

8/27/2018

Today was the first day of CAMP!

The students started their day by collecting their t-shirts, making their name tags, and going into the auditorium for some morning activities.  Morning activities included working on a Rubik’s cube mosaic, playing cards, and juggling.

Starting with the warm-up activity, scavenger hunt, the kids hit off the art session with flaming conversation. The scavenger hunt was designed for them to get to know each other with prompt like: “find someone who has a dog with a fun fact” or “find someone whose favorite season is winter”.
The students then worked with beads to make necklaces that would “spell out” various binary spellings of words. The ASCII alphabet (American Standard Code for Information Interchange) is a binary system in which each letter is formed by a certain pattern of 1’s and 0’s. With two different colors of beads, students assigned each a value of 1 or 0, and then made words/initials out of these beads. Students also learned how to make “magic wooden blocks”, a structure of blocks that could be manipulated and moved in various ways.
In Computer Science, we learned how to develop the logical operation called XOR or “exclusive or.” We used our knowledge of other logical operations to extract the compound logic operators that would give us XOR, which is only true when the inputs differ (that is one is true and one is false). After forming the XOR using our Boolean operators we acted out how XOR would play out in a circuit. Some of us acted as different currents while others were gatekeepers who determined the output that would occur at each logic gate depending on how the two currents entered the gate as on or off. And then some of us used this new logical operation to further explore how one can use Boolean operators in Python, while other students built the XOR circuit using little bits!
In Math, we delved into symbolic logic through truth tables. The students learned about the binary operators “and” and “or”, as well as the unary operator negation.  After learning about truth tables, they worked on riddles about an island that has two types of people: liars and truth-tellers.  This relates to binary by considering the falses to be 0’s and the truths to be 1’s, thus linking the mathematics and computer science workshops.
The after-lunch electives today included recess games, Rubik’s cube, and hiking.
Blog by: Meagan Kenney, Leah Leiner, Elliott Goldstein, Shuang Cai, and Maya Schwartz.

# Senior Staff

## Frances Stern

Frances teaches math to teachers and students in New York City, working with struggling students and those eager for more and deeper math.  She has a master’s degree in mathematics and has written two books for parents and teachers, both titled Adding Math, Subtracting Tension, for grades pre-K to 2 and grades 3 to 5.  Drawing, painting, hiking, learning to juggle and folk dancing are favorite non-math activities.

## Matt Hughes

Matt works as a software developer at edX. He graduated from Bard College in 2013 as a Math Major, and went on to continue his studies at Georgia Institute of Technology for a degree in Computer Science. He’s taught various subjects including sight-singing, algebra, and a brief stint on basic technological literacy. He’s excited to expand his teaching experience in computer science at CAMP.

## Yulia Genkina

Yulia Genkina is a Curriculum Engineer at MongoDB, with several years of experience teaching Computer Science and Math at Stuyvesant High School in New York City. She volunteered with Math-M-Addicts for a year and has worked for a NYC non-profit called CSTUY (Computer Science and Technology for Urban Youth). Aside from teaching and programming she enjoys singing and playing music, volunteering for the circus, hiking and kickboxing.

## Sally Chakwin

I am an early educator currently teaching at Livingston Early Childhood Community in Kingston. I became connected to the world of education in 2013 when I began working as a student assistant at the Abigail Lundquist-Botstein Nursery School on campus. After graduating from Bard with an Art History degree, I began teaching full time at the Nursery School and Children’s Center on campus until summer 2018. I hope to bring attention to the interdisciplinary aspect of all learning, and its importance in the span of human development.

# Junior Staff

## Maya Schwartz, Program Coordinator

I am a senior Mathematics Major at Bard College.  This is my second summer as Program Coordinator of Bard Math CAMP, and this will be my second year being a coordinator for the Girls Math Club at Bard.  This will also be my second year working as a math tutor for Calculus.  Aside from doing and teaching math, I enjoy figure skating, horseback riding, playing violin, and traveling.

## Leah Leiner

My name is Leah and I am a senior Mathematics Major at Bard College. I have been working with students age 2-17 for the past 7 years, and have been tutoring math since high school. I appreciate getting the opportunity to teach a subject I love to middle school students.

## Meagan Kenney

Meagan is a senior and math major at Bard College. Meagan enjoys tutoring her peers in math as well as tutoring elementary and middle school students through the Bard Math Circle. One day she hopes to study number theory and be a professor! She loves to help people see the beauty in math that can be found by simply looking a little bit closer at any problem or formula. Aside from math, Meagan loves to make music, play frisbee, read, and go on adventures.

## Elliott Goldstein

I came to Bard for the opportunity to pursue a Computer Science degree in a very personalized, one-on-one setting. I will be a Sophomore and have really enjoyed my time working with professors from the Bard Math and Computer Science Department. I also play on the baseball team here. I look forward to supervising the students as they learn various Math, Computer Science and Art principles. Working with the kids allows me to instruct them and learn things from them as well.

## Shuang Cai

I am Shuang Cai. I am currently a sophomore at Bard. My major is potentially going to be Computer Science and Studio Art. I was a coding tutor for the Bard First Year Language and Thinking Program. This is my first year being part of CAMP. It’s my honor to explore the connection between art and math with the kids this summer.

# High School Volunteers

## Alex Warren

My name is Alex and this is my third year as a CAMP high school volunteer. I live in New York City and am going into my senior year at the Bronx High School of Science. I like all things math and I am really excited for this years CAMP. As a former camper in the program, I think that this year will really be a great one. Some of my hobbies are Computer Science and robotics. I enjoy learning about math which is why I think that this next week will be a great one.

## Sasha Fraser

Hi, my name is Sasha Fraser. I attended C.A.M.P. for three years, and I am returning this year as a high school volunteer. I’m homeschooled, and I am going into eleventh grade.  Some of the other things I enjoy are: reading, photography, and dancing ballet. I loved C.A.M.P. and am so excited to be returning as a high school volunteer!

## Keshav Ramji

Hi, I’m Keshav Ramji. I am very excited to be part of the CAMP staff! I am a rising junior at Arlington High School in Lagrangeville, New York. I have been involved with the Bard Math Circle since taking the AMC exams in 6th grade. I enjoy problem solving and teaching math as well. Some of my hobbies are playing tennis, badminton and traveling. I also like sports analytics, bracket challenges and logic puzzles.

# CAMP Director

## Program Director: Japheth Wood, PhD

Japheth is a math professor at Bard College who co-directs the Bard Math Circle, which he co-founded (with Lauren Rose) in 2007. Japheth is very excited that CAMP has grown by 50% from last summer. During the academic year, he teaches undergraduate math courses both in the undergraduate college at Annandale-on-Hudson, and with the Bard Prison Initiative at Eastern Correctional Facility. During the summer, Japheth teaches at the Hampshire College Summer Studies in Mathematics program. He has also worked extensively with pre-service math teachers through Bard’s Master of Arts in Teaching program, and was the executive director of the New York Math Circle for several years.

# Volunteer Coordinator and Cube Instructor

## Professor Lauren Rose

Lauren has been a math professor at Bard College for 20 years, and is co-founder (with Japheth Wood) of the Bard Math Circle.  She runs the Girls Math Club with female Bard Math majors, and is a coordinator of the Mid-Hudson Math Teacher’s Circle.  She is committed to math outreach and enrichment, and believes anyone can learn and enjoy mathematics, regardless of their background or experience.

## Bard Math CAMP Day 2

8/28/2018

Today was the second day of Bard Math CAMP!

Students came in, picked up their name tags, and signed up for an after-lunch activity.  Students then started playing warm-up activities such as cards, Rubik’s cube, and math puzzles.

We hit off with a classic “desert” question. Thinking about what book/movie/music would they bring to a desert to entertain themselves, the kids get to know their friends better. For the session and inspiration of art, we went through the “Pascal triangle” and found some interesting patterns for triangles. Using the patterns we found from “Pascal triangle”, the kids headed off to explore the amazing art land through water color and sketches.

In art, students continued to work on their magic blocks or binary beads. After, students learned about the mathematical principles of Pascal’s triangle and afterwords made their own. Students then were able to have a free draw time.

In Computer Science, boolean operators were expanded upon, were students learned upon true/false tables and the basis of Boolean logic in Python.

After-lunch electives included Rubik’s cube, Creative Writing and Reading, and Art.

Blog by: Shuang Cai, Elliott Goldstein, and Maya Schwartz

## AMC 10

The 2014 AMC 10/12 A will take place on Tuesday, February 4th
The AMC 10/12 B will take place on Wednesday, February 19th.

Strategy Essay of the Month
This month we’re focusing on Engage in Wishful Thinking. Videos and Bursts for this strategy are available here.

Edfinity
The MAA, in collaboration with Edfinity, is delighted to offer AMC Advantage, a short online course to help students prepare effectively for the AMC 10/12 contests. The course is carefully designed to help students of all levels prepare efficiently and at their own pace. AMC Advantage includes a diagnostic test, ‘skill building’ problem sets, and full-length contest simulations with performance analysis.  All AMC contestants are encouraged to explore AMC Advantage. Open student enrollment, for a modest fee, will commence in January 2014.  Additional details at http://amc-advantage.com
Videos and Slidecasts of Distinguished Lectures Available
Members who live too far from MAA headquarters to attend the public lectures MAA sponsors can watch video footage and slidecasts — presenters’ slides synced to audio from their talks and interspersed with still shots–online. Browse lectures.

## New: Rubik’s Cube Club

Hosted by the Bard Math Circle

Spring 2017 at Bard College
Location: RKC 111
Time:  4:00-5:30pm

February 17th,  March 10th,  April 14th ,  May 12th

All skill levels and ages welcome*
We will provide instruction for beginners!
Bring a cube if you have one, but not required.

NEW:  We will now have cubes for sale at the club!

This program is free of charge, but registration is required.
To register, go to: bardmathcircle.org

*Please note:  Students ages 10 and under must have adult supervision.

## 2017 AMC 8 Contest at Bard College

The Bard Math Circle is proud to offer the AMC 8 exam on November 14, 2017. This contest is intended to challenge middle school students with accessible mathematical concepts, but at a level that is above and beyond what is typically encountered in the school curriculum.

This activity is offered at no cost, but due to limited space, registration is required in advance. Parents or guardians must agree to a liability waiver and photo release for their child to participate.

Following the contest, participants will be treated to a talk by a Bard Mathematician. The entire program will run from 4:30pm – 6:30pm at Bard College in Annandale-on-Hudson, NY.

Please register as early as you can. We have limited space and you will be waitlisted if space fills up and we are unable to accommodate you.

## Prepare for the AMC 8 with us!

Before the contest, join us for AMC 8 prep sessions, led by Bard undergraduate math majors. The sessions will take place on the weekends leading up to the AMC 8 contest, and will be held on the Bard College campus. We will post further information about the sessions soon.

## About AMC 8

The AMC 8 is a 25-question, 40-minute, multiple choice examination in middle school mathematics designed to promote the development and enhancement of problem-solving skills. The contest is held in November every year.

## Purpose of the AMC 8

The AMC 8 provides an opportunity for middle school students to develop positive attitudes towards analytical thinking and mathematics that can assist in future careers by applying classroom learned skills to unique problem-solving challenges in a low-stress and friendly environment.

## SUPPORT THE BARD MATH CIRCLE

It costs approximately \$500 (and plenty of volunteer time) for us to run this event. Your donation will help the Bard Math Circle continue to offer this event free of charge.

1. Visit http://annandaleonline.org/bardgiving
2. Fill in the gift form. Be sure to select “Bard Math Circle” from the drop down list.
3. Send us an email at bardmathcircle@gmail.com to inform us of your donation.

Thanks for supporting math enrichment in the Mid-Hudson Valley!

## C.A.M.P.2017 Day 5

Greetings!

Today is the last day of C.A.M.P. 2017!  Our morning started out with a Rubik’s Cube mosaic, a game of SET, a game of NIM, and some AMC 8 problems.  We then had morning announcements and  split up into different classes at 9:30.

In math class, we started by analyzing The  Baffling Prediction, a trick that Frances performed at the end of class on Thursday. We used algebraic notation to figure out how/why the trick works. Then, we learned a quick method to figure out whether or not any number is divisible by 11. Finally, we ended class with a fun but frustrating trick. The students were paired up and attached by looping one rope through another and putting both ropes around both students’ wrists. The goal was to detach the ropes from one another without cutting the ropes or removing the ropes from their wrists. Frances did not  share the solution with the students so that they can continue working on the solution at home.

Today Matt began the class by setting a goal that all students were supposed to reach by the end of the class. the goal was to write a program implementing one of the  tricks learned int he Math class. Since the task was very complex, Matt encouraged students to divide it into smaller subtasks and solve them successfully. This exercise was supposed to show the students a very common approach to problem solving Computer Science. This assignment also required students to use all the knowledge and skills acquired throughout the past week.  Despite no one succeeding in implementing the  trick, everyone did really well, proving that this past week was indeed a very fruitful one!

Starting at 3 was the open house for parents!  The art projects that the students have been working on all week were on display in RKC 101, the Computer Science displays were in RKC 100, and the math lessons that the students studied throughout the week were in the RKC lobby where students could perform the magic tricks to their parents.

Blog by Maya Schwartz, Marysia Tran, and Kate Blaine.