For the first time in New Mexico

Mathematical Fun Puzzles Games Prizes

Friday February 24, 2017

9:30AM-1:30PM

Santa Fe Community College 6401 Richards Ave., Santa Fe, NM 87508

Presented by:

STEM Santa Fe

Santa Fe Community College Math Circles Collaborative of New Mexico

Summary Report Prepared by: Lina Germann

http://stemsantafe.org/news-events/julia-robinson-mathematics-Festival-santa-fe/

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Introduction The mission of the Julia Robinson Mathematics Festival (JRMF) is to inspire students to explore the richness and beauty of mathematics through activities that encourage collaborative, creative problem solving. Julia Robinson Mathematics Festivals have been held in 16 states and three countries. STEM Santa Fe, Santa Fe Community College, and Math Circles Collaborative of NM were excited to bring this Festival to New Mexico for the first time. So what actually happened in our Julia Robinson Math Festival? Seventh and eighth grade students flooded into a large room of tables—two tables per activity—and began to play with (explore or investigate) the mathematical puzzle or game. The table leaders engaged the students in the activities without solving the problems for them. Most of the activities had manipulatives or worksheets, and while the mathematics may not have been immediately clear to the students, it was often deep. The students gained a good intuition of the problem before the math became clear—but the math was very much present in the patterns being explored. Students might have found an activity not to their liking, but we had fifteen different activities for students to choose from during the two hours of the Festival. At the end of that time we served the students lunch and treated them to a large group exploration of yet another Math Circle activity led by one of the founder of the Julia Robinson Math Festivals. The schedule for our Festival was as follows: Friday February 24, 2017 JRMF-Santa Fe Schedule of Events 8AM Volunteer Check-in and Breakfast 8:30AM Table Leaders Program Led by special guest Josh Zucker 9:30AM Teacher and Student Check-in 10AM Student Mathematics Activities – Jemez Rooms Math Circle for Teachers and Chaperones Led by Josh Zucker – Room 414B 12 Noon Survey, Group Photo & Raffle 12:30 PM Lunch & Group Activity 1:30PM Wrap

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Student Mathematics Activities and their Table Leaders: We had 43 volunteers who served as Table Leaders (plus 2 more that were trained as Table Leaders but were unable to attend the Festival). Table Leaders ran the activities for the students. We drew volunteers from a wide variety of STEM professions as well as from K-12 and higher education. The volunteers were eager to guide students to practice mathematics using creativity and multiple approaches, while the students got to meet “real” people from STEM professions. For this Festival, students had a choice to circulate around 15 unique math activities choose which one they wanted to try. The descriptions of the activities follow: Space Chips Cook up some polyhedrons by following simple recipes. Invent your own recipes, too! Table Leaders: Bobby Kosowski, Lynn Heffron , Nikki Copeland Wolves and Sheep How many sheep can you place on a field, so that none can be attacked by the simpleminded wolf? Table Leaders: Daniel F Coope, Phyllis Baca, Tim Michael Cookie Monster How fast can the cookie monster eat all of the cookies, if he must follow some simple rules? Table Leaders: Esther Milnes, Melissa Carter, Toni Zupanc Switching Light Bulbs Can you see the light? That is, can you see the patterns in light bulbs that are left on, after following a series of simple rule to switch them on and off? Table Leaders: Aaron G. Tumulak, Nicholas Kunz, Tracy Sadler ConHex A simple game of strategy, where each player attempts to claim spaces to form an unbroken chain between opposite sides of the board. Table Leaders: Ed Barker, Reuben Hersh*, Robert Shankin Folding Fractals Fold a long strip of paper in half several times. Can you see a pattern in the creases formed along the length of the paper? What sorts of route do we trace if we use the creases to direct our turns along a path? Table Leaders: Paree Allu, Annette Hatch, Creighton Edington Hexaflexagons How can you fold a strip of paper into a shape that can be “flexed”, revealing several different faces than were visible at the start? Table Leaders: Carolyn Stupin, John Pantano, Nicole Berezin Mondrian’s Art Puzzle Let your inner artist out, to paint a canvas using colored rectangles. But there’s a catch: each rectangle must be a different shape or size. Table Leaders: Greg Malone, Michelle R Sherman, Thiago Brito

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Color Triangle Challenge Try to find patterns that allow you to predict colors that will appear in rows of dots. Each row is produced from the one above it, following simple rules. Table Leaders: Anna Romero, Dean Gerber, Sandra Bradley Difference Engine How long can you keep a simple subtraction process going, before running out of interesting differences? Table Leaders: Gordon McDonough, Heidi Henderson, Liz Martineau, Mark Bailey* Estimation Games Use simple calculations, and your intuition, to estimate some unexpected quantities. Table Leaders: Cody Smith, Emma Gould, Mary Lynn Collins Pillage and Profit A twist on the game of Dots and Boxes – but instead of capturing as many squares as possible, we’re after gold doubloons! Table Leaders: Allyson Holley, Elizabeth Kuehl, Laurel Stritzinger Primes in Evenland In Evenland, the citizens never managed to invent the number one; instead, they started with 2, and built up sums and products from that starting point. What can we say about prime numbers in Evenland? Table Leaders: Carla Romero, Leona Tsinnajinnie Star Polygons Under what conditions can you draw a star using all the vertices of a polygon, without lifting your pencil from the paper? Table Leaders: Aiyana Pendleton, Carrie Wood, Teri Roberts Stomping on Dots Use specially shaped blocks to “stomp out” dots on a grid of squares. But if you stomp on a square without a dot, a new one appears! Can you stomp out all the dots? Table Leaders: Blaine Collins, John Bogdan, Steven Rudnick * Attended training session but couldn’t make the Festival. All the above activities are described in more detail on the Math Circles Collaborative of New Mexico website, www.mathcirclesnm.org.

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Thank you! Many thanks to our volunteers listed above as Table Leaders. Thank you also to our volunteers who helped in other capacities: Steve Bradley, Sandy Frost, Tim Germann, Stephen Guerin, Pam Homer, Mary Jensen, and Ralph Milnes. Thank you to our dedicated photographer Vincent Harrild and to the energetic behind-the-scene volunteer Andie Manzanares. We couldn’t have done it without you all. We would like to especially thank AAUW of Santa Fe, NM for spreading the word and recruiting volunteers, as well as Santa Fe Preparatory School for all the color printing and copies, and Nambe for donating a precious gift to our special out-of-town guest. Also many thanks to the SFCC staff who went above and beyond: President Randy Grissom, John Pantano, Fran Nawrocki, Ben Lauer, Emily Drabanski, and the OIT department. Thank you Nick Telles, Vice President of Finance and Chief Financial Officer of SFCC, for welcoming the participating students to campus at the Festival.

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And finally, a big “Thank You” to our sponsors!

We couldn’t have done it without you!

Julia Robinson Mathematics Festival – Santa Fe Planning Committee:

Lina Germann, Chair Nick Bennett Vanessa Job

Jason Morgan James Taylor

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Festival Outcome

Number of participants: 7th-8th grade students: 148 (58% girls) Teachers and Chaperones: 14 Volunteers (STEM advocates): 59 Number of schools participating: 7 Out-of town special guests: 1 Schools represented: Gonzales Community School, Ortiz Middle School, Bernalillo Middle School, Santo Domingo Middle School, Cochiti Middle School, Las Lunas Middle School, San Felipe Pueblo Elementary School.

Special Guest: Josh Zucker, Julia Robinson Mathematics Festival Math Director

Joshua Zucker was our special guest for the Festival. Joshua Zucker is the co-founder and math director of the Julia Robinson Mathematics Festivals. In 2006, he helped begin the Math Teacher’s Circle project at the American Institute of Mathematics. Joshua’s work with math circles began in 1998 and he is now working with at least half a dozen different ones around the Bay area. He holds a Masters Degree in Mathematics from Stanford University. Joshua was also a member of the U.S. Sudoku Team at the World Sudoku Championships.

We conducted electronic surveys that were customized for each of the groups: Students, Teachers, and Volunteers. Students used either their phones or the available laptops at the Festival to take the survey. Teachers and Volunteers were emailed their surveys after the Festival.

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Out of 148 students who attended, we received 112 unique responses. The results were as follows:

The student population included about 38% Native Americans, and 47% Hispanic.

75 out of 112 students reported that the Festival activities were Awesome or close to Awesome.

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85 out of 112 students reported that the Festival overall was Awesome or close to Awesome.

Unedited student survey responses: “this Festival worked out my brain pretty good now its time for it to kick back and chill” “The art involve with math brought my artistic skills to enjoy math. I learned that math can be fun involving creativity! :)” “It was awesome” “I think everything was amazing” “i loved it here” “the way you gather up is amazing , and how you've decided to set this up , also the variety was amazing.” “This was an amazing experience!”

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Quotes from the table leaders who seemed to have enjoyed this Festival as much as the students: “The students who made it to the last question really felt rewarded for their efforts.” “Most of them stayed for at least 15-20 min. Some stayed more than an hour.” (This refers to one activity) “I liked how they could spend as long, or as little, as they wanted.” “I was surprised that we had groups come together to the table and after awhile even though some wanted to leave, others would stay.” “One student actually wrote down all the different scenarios and came up with different patterns.” “One group worked all the way through the 9 questions. They came up with patterns i hadn't noticed.” “Some got hooked and lost track of time.” “I was impressed with students that seemed frustrated with the activity but continued to work through it.” “Very surprised when a couple of students who were not engaged, became engaged after they fully understood how the wolves moved” “They were not afraid to play on a gameboard with triangles instead of squares.” “most kids, once they understood what to do, jumped right into it and started making rectangles.” “It was difficult to stand by and watch them struggle but it was interesting to see the outcomes from the different groups of students. I watched some students overcome and persevere with the activity and also watched some students take a look at the activity and decide it was not for them.” Quotes from teachers: “They (my students) told me it was difficult and challenging, but a lot of fun.” “(My students) Loved being able to think outside of the box.”

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Festival Summary This Festival was intended to expose the students to the fun of mathematics and to grow the interest of local math teachers in these types of activities. An additional benefit of such a Festival is to engage the community of STEM advocates, educators, and potential mentors directly with students in a productive environment for mentorship. Teachers and chaperones also got a chance to experience the joy of Math Circles activities as a special two-hour session with our special guest Josh Zucker. We hope that teachers will use Math Circle activities in their schools. Three training sessions were conducted in the week before the Festival to train volunteers on how to be table leaders and on how to run their assigned activity. Being a table leader does not presuppose mastery of the table’s activity, but rather having a sense of the struggles students will encounter. This involves the table leaders actually doing their table’s activity as a group during their pre-Festival training. Crucially, Table Leaders must learn how to be less helpful! This means learning when not to step in and explain what to do so that the students can experience “funstration” or productive struggle. Our Festival volunteers were affiliated with a variety of groups in Santa Fe and Northern NM including: AAUW of Santa Fe, Flow Science Inc. , IBM, LANL, Mathamuseum, Math Teacher Circle, New Mexico Environment Department , New Mexico Highlands University, New Mexico MESA, Q’tZ Animation , Santa Fe Community College, (students, faculty, and staff), Santa Fe Public Schools, Simtable, SMA, UNM Valencia, and many other retired and active STEM professionals. By giving those volunteers exposure to a Julia Robinson Math Festival and by association Math Circles, we hope to see more professionals of the Northern New Mexico community involved in STEM education.

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A Julia Robinson Mathematics Festival as an introduction to Math Circles A Julia Robinson Mathematics Festival (JRMF) can be a way of introducing large numbers of students, teachers, STEM educators and the larger education community to Math Circles.

“Math Circles bring K-12 students or K-12 mathematics teachers together with mathematically sophisticated leaders in an informal setting, after school or on weekends, to work on interesting problems or topics in mathematics. The Circles combine significant content with a setting that encourages a sense of discovery and excitement about mathematics through problem solving and interactive exploration. Ideal problems are low-threshold, high-ceiling; they offer a variety of entry points and can be approached with minimal mathematical background, but lead to deep mathematical concepts and can be connected to advanced mathematics.” (https://www.mathcircles.org/Wiki_WhatIsAMathCircle)

A math circle can be run at any level—from K-12 to adults (teachers, mathematicians, parents, etc.). This does not mean that the problems are easy, even for younger students. They are certainly not. In general, problems will start from an easily grasped place—perhaps involving some physical object or manipulative—and build to a more generalized understanding of the area of mathematics involved. For example, we might begin with a pile of candy, and distribute it in some way among five students (conference participants) at a table. Then we would have them share the candy in some regular pattern several different ways, with each new way helping them to discover something about the significance of the number of candies and candy sharers across the system. Or perhaps tables of students will be give strips of paper with numbers on them, then be told something as vague as “organize them.” The circle leader will do his or her best to not be too helpful. This math circle process is about discovery and invention—constructing mathematics from our innate (and teachable) ability to perceive patterns. Who is Julia Robinson? Julia Robinson, a pioneer among American women in mathematics, was the first woman elected to the mathematical section of the National Academy of Sciences and the first woman to become president of the American Mathematical Society. She was a mathematics professor at UC Berkeley for many years and is especially known for her work in solving Hi|bert’s Tenth Problem. The Julia Robinson Mathematics Festivals began in the San Francisco Bay Area in 2007 to honor her legacy and to encourage more students to pursue mathematics. The Festivals have since expanded to other cities around the world.

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Concluding Thoughts: When we opened the pre-registration for this Festival, within two weeks and with minimal advertising, 16 teachers from all over Northern NM signed up wanting to bring a total of over 700 students. Due to space restrictions, we had to limit ourselves to accepting around 165 students. The teachers, students and adult volunteers who participated in the Festival gave us very positive feedback and seem to enjoy this event and want to participate again. Clearly there is overwhelming demand for activities such as the Julia Robinson Mathematics Festival, and we hope to bring this Festival back next year - maybe even more than once a year.