Category: CAMP

The Creative and Analytical Math Program (CAMP) is a non-residential math enrichment summer program for middle school math students who are excited about learning. CAMP combines math, computer science, and art for a wonderful one-week academic experience at the end of each summer.

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C.A.M.P. 2017 Day 4

Greetings!

Our morning started off with AMC 8 prep questions, card games such as SET and tongues, a Rubik’s cube mosaic, and NIM.  The Rubik’s cube mosaic was pac man and four ghosts.  Students played these activities until 9:30, when it was time to go to class.

In math class, we started by analyzing the trick that Frances performed on the previous day using Fibonacci sequences. The students used algebraic notation to analyze the trick. We also learned a quick method to multiply any number by 11. The next trick we learned was the 3 Button Trick. In this trick, the spectator switches the positions of 3 buttons, telling the magician about each switch. Then the  spectator chooses a special button, and silently switches the  other 2. The spectator continues switching as before, until they decide to stop. Then the magician guesses which button was the chosen one. The students  analyzed this trick using diagrams in order to see how the trick works. Finally, Frances performed a trick called The Baffling Prediction to close out class.
The Computer Science class again started with a quick revision of all commands and terms learned so far. This is a necessary practice, as what students learn everyday builds upon the knowledge acquired in the previous days. After making sure everyone was ready to learn new things, Matt introduced students to fun commands such as mousePressed, mouseX, and mouseY. These commands allowed students to make their code more interactive and their animations more responsive. All students made sure to take advantage of this powerful tool.

In Art today, some students opted to use their color explorations from day 3 to construct interesting patterns, sequences, collages, and shapes. The idea was to exploit different gradients of color in order to establish an interesting visual effect. One of the nice things with this project is that since each student focused on only a few color tones, the project gave students the chance to share vastly different colors with each other, which was nice to see. On the other hand, many students painted and perfected their own clay models, crafting small boxes to carry them in. One of the most satisfying things for us to see was that even the creators of these geometric puzzles struggled to put them back together! We can’t wait to see how their friends and family react.

Afternoon activities were Rubik’s  cube, juggling, and Origami.

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C.A.M.P. 2017 Day 3

Greetings!

Today was our third day of Bard Math CAMP 2017!  Our day started off with distributing t-shirts at check-in because today was picture day!  We all gathered for a picture at 9:30 right outside the RKC.

In math class, we found a number pattern that allowed us to divide any whole number by 9 without using a calculator. After Frances performed a trick using only numbers at the end of yesterday’s class, everyone had a chance to think about how it works that evening at home. Then today, we used the number pattern and algebraic notation (a new concept!) to explain why the trick works for any multi-digit number. Later, we learned about  the Fibonacci sequence, and Frances performed a trick for the  class where the students made their own Fibonacci sequence and Frances guessed the sum knowing only one number of the sequence.

In Computer Science class students learned two powerful framework methods – setup and draw. These methods allow one to specify which commands should be executed once and which should be run repeatedly. In result students were able to play around with their code and create small animations. This was undeniabley the most exciting part of the class for the majority of the students!

During Art class, we gave the students a first introduction to color theory, describing different complementary colors and how artists use this idea to achieve colors they see in real life. After having them choose two tones with which to experiment, the kids created an assortment of squares that were all colored with their own various experiments. Outside of class, students have been building Rubik’s cube mosaics, but now they also have an assortment of small squares built out of colors they created for themselves. Hmm…

Afternoon activities were Rubik’s cube, juggling, and recess games.  Recess games included games such as freeze tag, dude, zip-zap-zop, 21, and what time is it mama bear.

Blog by Maya Schwartz, Kate Blaine, Marysia Tran, and Andres Mejia

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C.A.M.P. 2017 Day 2

Greetings!

Our day started off with activities such as SET, NIM, and a Rubik’s cube mosaic.  The design for the Rubik’s cube mosaic was the superman logo.  We then split into our  two groups and went to computer science class and math class.

We started our class by figuring out the magic tricks that we had learned on day one.  the class then proceeded to learn the penny trick.  The penny trick is where the magician puts at least 15 pennies on a table in the shape of a “9.”  the audience member has a tiny piece of paper and picks a number between 7 and however number of pennies there are.  They then start at the bottom of the 9 and count up first, up to the number they have chosen, and then around, again, counting up to the number they have chosen.  after they reach their destination penny, they place the piece of paper under the penny.  The magician, who has looked away the entire time, guesses the correct penny the piece of paper is under.

In the computer science class the students first reviewed all the Processing commands learned the day before. Then they learned more commands and got a little bit more familiar with the software. They were also introduced to the concept of variables in Computer Science. Finally, they modified the code that they were working on yesterday using variables to see how useful they are. Some of them got really creative with their drawings!

For art, the students continued to work on their clay pieces, which were in what Susie called the “leather-hard” stage of development. One difficulty in this stage was that when the clay dries, it shrinks slightly. Students rose to the challenge both mathematically and artistically, either using tools to smooth out the edges of their shapes so that they fit, or creating new shapes to place in the gaps created by the shrinkage.

After this, some students began using cardboard or wood to create small frames for their shapes to fit into, while others opted to try creating new puzzles. In either case, it was exciting to see that they were more familiar with how to work with the materials they were given and also thinking more carefully about how they wanted to craft their puzzles.

Afternoon activities today were a hike to Blithewood Gardens, Rubik’s Cube, and paper folding.

Blog by Maya Schwartz, Kate Blaine, Marysia Tran, and Andres Mejia

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C.A.M.P 2017 Day 1

Greetings!

We started our day ambitiously, playing a revised version of “set” where students all got the change to meet each other, after being assigned a “set” card and being sent out to meet two others who would complete a “set” trio. It’s the CAMP’s official opinion that the students were far better at achieving this goal than any of the staff.

Since the theme for this year is mathematics, magic, and mystery the  math class today focused on card tricks and the mathematics behind it.  The first thing they did was a card trick called the “27 card trick.”  The magician lays out 27 cards in three columns of nine cards each.  They ask the audience member to pick a card and only tell the magician which column it is in.  They shuffle up the cards in a very specific way and figure out which card it was.  Students then got into groups and tried to figure out how the trick works.  Frances then got the  class together and then explained it.

Frances then demonstrated the “missing card” trick where the  magician guesses which card is missing from the deck.  The  magician asks the audience member  to pick a card and keep it, and not show it.  The magician then starts setting individual cards on the table and eventually guesses the card in the audience members hand.

One Student Learns The Art Of Deception 
 
 
In the mathematical art section, students were asked to take the beginning steps in creating their own geometrical puzzles. At first, they were given some basic parameters about how to break a square into different pieces and after outlining the process, they began creating their own clay models, materializing these different their drawings. These pieces will be used to  draft various mental challenges they can pose to friends or family: the puzzle is to reconstruct an image from an assortment of small shapes.

The computer science class started with a small exercise demonstrating the differences between the natural language we use everyday and a programming language. The students were asked to write a list of commands that would make Matt (the instructor) draw a diamond shape on the board. To the frustration of all students, none of the attempts were successful. This showed how rigorous and specific a programming language is. Then the students were introduced to Processing, the software they’re going to learn and use in the next few days.

After lunch, students divided up into three groups for afternoon activities.  The three activities offered today were hiking to the Parliament of Reality, working on solving the Rubik’s Cube, and drawing portraits of each other.

Blog by Maya Schwartz, Kate Blaine, Marysia Tran, and Andres Mejia
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2017 CAMP Staff

Here is our 2017 CAMP staff!
 

 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 3-5.  Drawing, painting, hiking, learning to juggle and folk dancing are favorite non-math activities.






Matthew Hughes

Matt works as a software developer at Wayfair. 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.





 

 

Susan Tarnowicz


Susie is a visual artist and teacher living and working in the Hudson Valley.  She studied painting and visual perception at the Rhode Island School of Design and has taught art at both the middle and high school levels.  Susie loves drawing, growing food, the woods, and all ways that math and art co-create!






Junior Staff



Andres Mejia 

Andres is a rising Senior at Bard College and is a native New Yorker from Queens. In his free time, he enjoys listening to music, playing guitar, and of course doing math. He was junior staff at CAMP for the Summer of 2015, and is excited to get back!












Kate Blaine


Kate is a junior at Bard College, majoring in math and music. She is from Rochester, NY, and enjoys playing piano, reading mystery novels, and experimenting with Rubik’s Cubes. She is a co-head of the Bard Math Circle, and is very excited to be working at CAMP for the first time!


Marysia Tran

 

Marysia is a senior at Bard College majoring in Computer Science and Math. She is from Warsaw, Poland. She tutors for Bard Prison Initiative and is the head of the Asian Student Organization. She enjoys traveling, learning about other cultures and dancing. It is going to be her first time working at the Bard Math CAMP.

 

 

Maya Schwartz

Maya is a junior at Bard College majoring in math.  She is from Cincinnati, Ohio.  This is her first year working for Bard Math CAMP.  Aside from attending Bard, she enjoys figure skating, horseback riding, and traveling. 

 






High School Volunteers

 

Alex Warren

My name is Alex and this is my second year as a CAMP high school volunteer. I live in New York City and am going into my junior 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 and also doing magic tricks, which is why I think that this next week will be a great one.



Daniel Knop

 Hi, my name is Daniel Knop. I am so excited to be a part of the CAMP staff team! I am a rising senior at Arlington High School in Poughkeepsie, New York. I’ve been involved with the Bard Math Circle through their AMC exams since 8th grade. Aside from math, I like to spend my free time playing soccer, playing tennis, reading, and playing trombone. I can’t wait to start my first year of CAMP!

 

 Daniel Rose-Levine

Hi, I’m Daniel Rose-Levine. I attended CAMP for 3 years, and this is my first year as a high school volunteer. I have been doing the AMC 8 and AMC 10 exams for a few years. This year I will be starting my sophomore year at Red Hook High School. Some things I like to do include running in cross country and track, as well as playing violin in an orchestra and fiddle group. I also enjoy speedcubing, which is solving Rubik’s Cubes as fast as you can.


 

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 tenth 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!

 
 


Administration



 

Program Director: Japheth Wood, PhD 

Japheth is a math professor at Bard College who co-directs the Bard Math Circle, which he co-founded in 2007. Japheth envisions math circles as an effective way for mathematicians around the world to make a greater impact on math education at all levels, as well as opportunity to refresh and innovate their own teaching. He teaches undergraduate math courses both in the undergraduate college at Annandale-on-Hudson, and with the Bard Prison Initiative at Eastern Correctional. During the summer, he 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: Lauren Rose, PhD

I enjoy sharing my enthusiasm for mathematics with others and believe that mathematics can and should be made accessible to all. With this in mind, I co-founded the Bard Math Circle, an enrichment program for K-12 students, the Mid-Hudson Math Teachers Circle, an enrichment program middle school math teachers, the Mid-Hudson Mathematics Conference for Undergraduates, and the mathematics major in the Bard Prison Initiative. I particularly enjoy integrating Bard students into these programs, which expands their mathematical experience and creates a vibrant and inclusive mathematics community at Bard.

 

 

 
                                                    
 
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CAMP Day 5

Friday marked our final day of CAMP. Despite the sadness of the end of the Bard Math Circle CAMP quickly approaching, we were able to have an awesome and fun last day that began with our mathematicians working to solve a number of math problems and puzzles. Some of the problems were taken from the AMC, a competition that Bard Math Circle hosts at Bard every year, while others were found by our high school volunteers to let our mathematicians warm up their brains! These bright young students were able to whiz through many of these problems on their own and the more difficult ones they discussed with their peers to try to find a solution.



Our schedule was a little different for our last day. We had gotten far enough in our math class to combine the class with computer science! Side by side, we compared a list of how to create fractals geometrically, mirrored by the code that would be entered into the program in NetLogo to achieve the same transformation of a figure. Together, we learned the specific code that creates a scaling transformation and the code that translates our x-coordinates. Then, we split up in pairs to input this code and try to discover the specific commands that would program the proper translation of the y-coordinates. We all came up with the code that will generate the Sierpinski triangle in NetLogo and then some of us even went on to develop the code that would create other fractals from the Yale Fractal Lab worksheet that we had received in math class the day before. We were able to learn how to turn the rules we discovered the day before into code that would create these fractals!

 




 
After lunch we returned to the RKC to finish up what we needed to in art and to take a short break before returning to class. Some students who had been learning the algorithms of the Rubik’s cubes over the last few days, picked up a few of the cubes to practice and show their new skills to their friends. Some students even helped others who had not been to any of the Rubik’s cube activities to see how to start solving the Rubik’s cube.

In art class we finished designing and altering our fractal lamps in order to have them ready to present to our parents and friends at the open house that was happening at the end of the day. After finishing the creation of the lamps we discussed the installation of our art pieces and ventured out into the lobby of the RKC building (as well as some other rooms in the building) to install our art in beautiful and interesting ways. Some of the lamps were placed in a dark room with lights strategically placed within them. While others were attached to strings and then hung over the railings above the lobby. The lamps hung perfectly in front of the windows letting the light shine through them in just the right way to display the beautiful ways in which we had cut and sculpted the paper to make the lamps: finally now illuminated in the way they were meant to be.

 

After some final preparations of our computer programs and art pieces we were ready for our open house! Parents began to arrive and the students were able to showcase their accomplishments of the week. In one room the computer screens were filled with the wonderful and fascinating results of the code that the students had been writing to create fractals that we had learned about in math class. In the lobby one could see marbled paper and fractal lamps hanging from the second floor in front of the big windows and installed in tactical places to highlight the beauty and individuality of each piece of art. And in one room the lights were turned off to let the lamps really shine! The dark room showcased the amazing shadows that could be created by a light shining through the intricate lamps. After sharing with the parents, the staff was introduced and brief announcements were made before the Bard Math Circle CAMP of 2016 came to a close. Every student in the program this summer was absolutely brilliant and a joy to work with. Thank you to every student mathematician and staff member that made this amazing week the success that it was!
-Meagan (with the help of some amazing math CAMP friends!)
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CAMP Day 4

Thursday was our fourth day of CAMP and for our morning activity we played an observational game entitled “Find the Chief.” We sat in the auditorium in an ellipse, per the students’ request, and learned how to play this exciting game! A detective was picked and then asked to leave the room. While the detective was away we picked a chief who would serve as our leader. When the detective returned, the chief would begin performing a motion of their choice (a common favorite is to clap) and then the rest of the group would follow the chief. The chief’s job is to repeatedly change their motions while trying to make sure the whole group can follow them; the detective’s, to pick out the chief from the rest of the group. One of our student’s observantly pointed out that a great strategy would be to pick fake chiefs, who could watch the real chief, while the rest of the group could watch the fake chiefs to throw the detective off! After this fun game we started our classes of the day.

 

Our fractal lamp shades continued to be individualized as we accumulated our art projects from the week into our final art piece as we pleased. Alexis (one of our superb TAs) even taught us how to cut paper in simple ways resulting in intricate and gorgeous radial fractals! Some of us even added these radial fractals to our lamps!! Other students found more ways to incorporate the marbled paper they had created in the beginning of the week. In addition to working on our lamps we watched a video of a dancer who choreographed dances on sand that would result in geometric patterns drawn in the sand!

 
In math class we were able to apply our recently obtained knowledge of how we can use geometry to create and draw fractals! We experimented with applying planar transformations—specifically scaling and translating—onto the unit square to begin to make the Sierpinski triangle. We developed a set of rules that would transform the figure between stage 0 and stage 1, and then observed how the figure would change after multiple iterations of the rules we found together. Through this exercise, we were able to better understand how fractals are created using planar transformations. Frances, our lovely math instructor, then gave us a worksheet from the Yale Fractal Lab to work through in order to attempt to look at fractals, that had already gone through multiple iterations of a set of rules, and be able to discover these sets of rules on our own.

 


Our math class showed us the geometry behind making fractals, which connected fluidly to our computer science class where these brilliant mathematicians learned how to program our computers to make the fractals for us. We programmed commands that essentially perform the equivalent of scaling and translating, but instead of performing these planar transformations on points on a graph written on paper, the transformations were applied to our turtles in the world that we created in NetLogo. The students were able to see the program they created forming these fractals, and be grateful for the computers because they had personal experience with how complex and difficult it can become to compute and create fractals by hand!

Following lunch we held the much anticipated game of capture the flag: Team Team versus Team Mystic!!  Both teams defended their flags admirably, but Team Team was able to capture Team Mystic’s flag and return safely to their side without being caught!  The teams then united again to hear about options for their afternoon activities: finishing tessellation art, continuing work on their stunning lamp shades, or learning about the Physics of Chaos Theory from one of our excellent TAs Victoria!
 



And to end the day we hosted another game of Bard Math Circle CAMP Jeopardy! Today we achieved a new wonderful accomplishment: we were able to have a Jeopardy game that was not only filled with excitement, but also was filled with listening to other teams answer each question. We learned that, instead of planning an answer in case another group misses the questions, it actually is beneficial to listen as other teams guess because then it helps us understand the questions better and also makes it less likely to restate a wrong answer if the questions gets to your team! Another exciting part of this day’s Jeopardy was that during the game we all got our CAMP shirts to wear on the last day! So at the end of the fourth day of camp everyone left with more than they had when they came in that morning: a little extra knowledge and a fun shirt!

 

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CAMP Day 3

 

On Wednesday we began the journey of our third day of the Bard Math Circle CAMP of 2016 by experimenting with tooth picks to try to solve the many matchstick puzzles that one of our fantastic TA’s, Alexis, brought in for us to think over.  Some of us in pairs, and some individually, impressively worked through the sheet of puzzles solving many if not all of the matchstick problems!

 
We started our math class by learning more about planar transformations! We split up into groups of two or three to experiment and see if any pairs of planar transformations are commutative (meaning the resulting figure after both planar transformations were applied was not affected by the order in which the transformations occurred). Each group drew their findings on the board and presented their conclusions. After that, some students started drawing the Sierpinski triangle by beginning with an equilateral triangle as Stage 0, and then repeatedly “cutting” out a fourth of the previous stage’s triangles after each iteration. We then recorded the area and perimeter of our shape at each stage to observe what was happening to the triangle!
 
In art class our Sierpinski triangles, that we had made the day before, became three dimensional one of a kind sculptures! We noticed that the paper caught the light in really beautiful ways and so we began to design unique lamp shades using our marbled paper and the texture of the Sierpinski triangle.  So in order to add our own individual personalities to these fractal lamp shades everyone took their own steps to alter their designs: making constellational cut outs, layering, cutting out more shapes, attaching geometric solids, and more. And some of us simply spent time as designers, imagining and working through different ideas on our own as well as with our classmates.  
 
We learned about and started practicing our pair-programming techniques in computer science, where one of the students served as the driver and the other a navigator. This way we get to share ideas and come up with creative solutions together; when more of these brilliant computer scientist/artist/mathematicians are working together, the more amazing the solutions can become. Then we did a fun exercise where each person in the class said a line of code as we tried to write a program together. Additionally, we learned about creating functions in the code tab to make each button have only one function controlling it. This makes it easier to edit our program!

 


 
 
 
 
 
 
 
 
 

After a rousing game of blob tag, following lunch, these mathematicians split into three groups: some of us went to play a game entitled Staying Rational in the Infinite Hotel, some went to continue to explore the mysteries of the Rubik’s cube, and others went to learn about tessellations and create some beautiful and fascinating tessellation artwork.

 
We finished our day as we normally do with a rousing game of Bard Math Circle CAMP Jeopardy. Today the game was very similar to the day before, but we added the excitement of prizes! Origami paper was handed out as a prize that the students could use to create the intricate origami designs that we have learned during camp. Everyone went home happy: with a smile, some origami paper, and some new knowledge about math!
 
-Meagan (as normal with help from other lovely Math CAMP friends)
 
(Photo of Sierpinski’s triangle courtesy of zeuscat.com)
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CAMP Day 2

Welcome back! This Tuesday we started the day by getting excited about math through some competitive and fast-paced games of Set. Set is a game that uses cards that have four varying characteristics: the shape shown, the number of times that shape is pictured, the shading of the shape, and the color of the shape. The students attempted to discover sets of three cards for which each characteristic on the cards was either all the same or all different. These mathematicians caught onto the game so quickly that many soon had to start reusing cards from sets they had already discovered to keep the game going!

In math class we learned about scaling (by fractions) figures that were placed at the origin of a graph. We found out that after many iterations of this process we would only be able to perceive a tiny dot because the figure would become so minuscule. But if we magnified the picture we would be able to see that every figure is geometrically similar, meaning all of the angles remain the same and the lengths of the sides are proportional to the original shape though the area of the figures were changing. Because of this geometric similarity, you would not be able to tell which iteration of the scale you were looking at unless given additional information. This started to help us to understand the self-similarity of fractals!

 

In computer science we got to learn about local variables and creating functions in NetLogo. We explored producing geometric shapes using agent-based programming. Through what we learned we were able to create shapes within other shapes. We also learned about modifying different attributes of the turtles to create and experiment with individual effects. This was a fun way to customize our programs to our own original personalities and tastes!

 

For art class our mathematician/computer scientist/artists created our own fractal-like art projects! We created a three dimensional paper version of a famous fractal known as the Sierpinski Triangle. Students cut, folded, inverted, and repeated, to ‘infinity’!!!! We could clearly see that if we kept going with our cuts, that eventually the cuts would become too small for our scissors to cut and our eyes to see. This related to our math class because if you zoomed in on any of the triangles you would not be able to tell which part of the triangle you had magnified; similar to the affect that occurs after many iterations of scaling a figure by fractions.
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

In addition to our everyday classes, after some lunch and time outside, we split up for a few fun activities: a portion of us went to play cards and boardgames while other students ventured out to try to explore and learn the algorithms of a Rubik’s cube in order to solve the puzzle that has stumped many for years. A few of our mathematicians who were more experienced with Rubik’s cubes even helped out some of the novices of the group.

//www.youtube.com/get_player

 

At the end of the day we came back for another fun-filled round of Bard Math Circle CAMP Jeopardy. Today our Jeopardy was a little different than on our first day. The Jeopardy game was projected in the auditorium with organized categories containing five levels of questions each assigned a different point value based on difficulty. In four separate groups the students put their genius minds together to try to claim the title of Jeopardy Champions of Day 2 of the Bard Math Circle CAMP! In the end every student won as we were able to go home with a better understanding of art and math and computer science!
 
-Meagan (again with the help of some other Math CAMP friends)