Last week, The Atlantic published an excellent article questioning the trend toward requiring convoluted explanations of mathematical thinking in Common Core-aligned math classes. The authors rightly pointed out that verbal explanations are hardly the only way of determining whether a student understands a concept and that many of the brightest mathematical minds are verbally challenged.
The theory that if you cannot explain, you do not understand does logically lead to the conclusion that if you understand, you can explain. (IMACS Mathematical Logic students will recognize this as an example of contrapositive inference.) That theory, however, is completely false, yet it continues to drive the misguided practices of Common Core-aligned pedagogy to the detriment of another generation of students who, we worry, will be irreparably damaged in their understanding and appreciation of math.
Visual explanations are often a natural way to demonstrate mathematical understanding when designed thoughtfully and taught well, but even they can be gamed. There is another way, however, that is an effective measure of true understanding — demonstrating how well you can apply your knowledge to a novel situation. This approach does not call specifically for a verbal, visual or symbolic explanation, but it does require that teachers have the mathematical depth to recognize understanding when presented in a variety of explanatory modes, not just how a scoring rubric of model answers dictates.
Consider for a moment the art and science of cooking. Some people can only follow a recipe, and many have compared this to when students can only "plug 'n chug" math formulas and algorithms. Some people read cooking magazines or watch the Food Network and then impress with the right vocabulary at parties, the same way verbally skilled students will learn the right Common Core-friendly phrases to use in answering certain types of problems. Then there are the chefs, the ones who understand why certain ingredients and/or cooking methods work well together and what the fancy foodie talk actually means. What can they do with their genuine understanding?
If you've never watched the television show Chopped, take a moment. Competing against the clock and other chefs, each contestant must use everything in a basket of mystery ingredients to prepare an appetizer, entrée or dessert. When the ingredients are unveiled, it is not unusual for them to include such oddities as grasshoppers, gummy bears and leftover pizza. Talk about a novel situation!
It's hard to imagine a single traditional recipe that calls for such ingredients, or what erudite words you could utter about the culinary characteristics of a grasshopper. But leave it to the chefs on Chopped to shred the pizza crust, melt the gummy bears and use them with other ingredients to make breaded and glazed gourmet grasshoppers with a pepperoni pâté!
Mathematics is a lot like cooking. When you have a genuine understanding of mathematical concepts, you know what to do when faced with a problem that is unlike any you’ve seen before but that requires putting your knowledge together in a new way. Whether you can impress the Pulitzer Prize people as well is beside the point. Bon appétit!
You might recognize twin sisters Hadley and Delaney Robertson from their cooking show for kids, Twice as Good, that airs on PBS stations across the country. We at IMACS also have the pleasure of knowing them as two intelligent and delightful students who have been attending our Math Enrichment classes since they were in kindergarten. "IMACS has provided Hadley and Delaney with such an amazing mathematical foundation," their father, Johnathan, recently shared with us. And we are beyond thrilled to share that these talented girls were just named grand prize winners in the 2015 MOONBOTS Challenge!
The international MOONBOTS competition, also known as the "Google Lunar XPRIZE for Kids," is designed to encourage the next generation of space explorers and innovators. Kids ages 8-17 are invited to design, create and program their own lunar rover, based on a legend or theory that inspires them about the moon. This year 235 teams from 29 countries entered the competition, and the Linked Lunas team comprised of Hadley and Delaney won! As grand prize winners, they will travel to Japan to meet the Google Lunar XPRIZE teams that are competing to land a privately funded robot on the moon.
Hadley and Delaney have long been fascinated by the moon. When they were younger, their grandfather would regale them with a story of how the Earth once had two moons, which the sisters imagined were twins like themselves. They later discovered that planetary scientist Professor Erik Ausphaug theorized that the Earth, indeed, used to have two moons that eventually collided and merged to form the moon that we see today. This mythical tale and scientific theory inspired in Hadley and Delaney a deep interest in the moon and thoughts on how the same moon appears differently depending on one’s perspective. They share their inspiration in this clever entry video:
With a captivating presentation like that, it's no wonder that Linked Lunas was one of only 30 teams to move on to the technically challenging second phase of the competition. During the second round, Hadley and Delaney put their engineering, programming, and creative problem-solving skills to work in designing and building a lunar landscape, building and programming a sophisticated robot, and developing a game for their robot to rove the lunar landscape. Not bad for a pair of 9-year-olds! You can’t help but be impressed by their masterful moon mission in this next video:
The MOONBOTS Challenge, however, isn't only about individual achievement. An important component of the competition is how teams use their innovative projects to inspire members of their community through public outreach. Team Linked Lunas was able to secure donations of robotics kits and $5,000 for after-school robotics instruction at a local, underserved middle school. In this last video, Hadley and Delaney give a demonstration of their robot to students from that school and announce the exciting news of the donations to their school:
Everyone at IMACS is so proud of these remarkable girls. There is no doubt that Hadley and Delaney have a talent for math and science and love inspiring others to learn. The cooking show Twice as Good has produced 20 fun videos that explain how cooking can teach kids about nutrition as well as science, math, and geography. Share these with your children and maybe they, too, will be encouraged to shoot for the moon!
October 13, 2015 is Ada Lovelace Day, a day to honor the achievements of women in science, technology, engineering and math. IMACS asks that you join us in celebrating this day by encouraging a girl to pursue her interests in the STEM subjects.
She may be your daughter, sister, student or friend. She may be enthusiastically expressive about her love for STEM, or she may be the quiet type who will share deep thoughts if you ask. Or she may be especially in need of your encouragement because she’s not yet received that message or, worse yet, has been actively discouraged from pursuing her passion for STEM.
What can you do to encourage a girl in STEM today or any day? If you have the knowledge and time to share, become a mentor to her. If you don’t have the time to commit to mentoring, help her find appropriate enrichment activities such as local events at the science museum or after-school programming classes that will keep her engaged, especially when social pressure can push her off track. Even something as simple as sharing stories about talented women in STEM who can serve as role models can make a difference.
IMACS is honored to have been a meaningful part of the education of numerous high-achieving girls who have gone on to amazing college and professional careers. They now serve as inspirational role models for our younger students. Who knows? The girl you encourage today may one day be an IMACS alumna studying STEM at a top university!
This week, the IMACS Blog visits with eIMACS student Shuli Jones. Shuli is one of our star students, having excelled in our university-level computer science courses since the 6th grade. She recently attained the highest score possible on the AP Computer Science A test exam as a high school freshman. A multitalented young lady with a passion for programming, Shuli is well on her way to a bright future.
Please tell our readers a little bit about yourself and what you enjoy doing.
My name is Shuli Jones. I’m fifteen years old, and I’m currently a sophomore in high school. In my spare time, I like to participate in a variety of activities: I love to read, I do archery recreationally, I’m part of a trivia team and a classics society at my school, and, of course, I love programming. I’m also interested in learning new languages, coding and otherwise!
You’ve done some amazing things already at a young age. Tell us about the accomplishments and experiences of which you are most proud.
In recent memory, the thing I am the most proud of is scoring a 5 on the AP Computer Science A test. I took it while still a freshman, so it was my first AP test and I was very nervous beforehand. However, eIMACS had prepared me unbelievably well, and that, combined with my own hard studying, meant the test was nowhere near as hard as I expected. When the results came in, both my parents and I were really pleased.
Something else I’m proud of is my performance in my school’s classics society. Every year in May, we participate in the Ontario Student Classics Conference. This is a three-day competition with numerous other schools that tests knowledge of Latin grammar and vocabulary, as well as Roman life, mythology, and history. For me, this was my biggest commitment during the school year, and it’s something that I love to do. I put in many, many hours of hard work studying and working on projects with my team members, and it paid off.
My team won the Phyllis Morgan Trophy for Overall Excellence, which is typically regarded as the "top" trophy at the conference. I won several individual awards in the Intermediate category (for those having taken two years of Latin): First in Pentathlon, for having the best overall score on the five main events (notably with a first in Latin Derivatives), and first in Latin Oral Reading. I was also part of a group of four students who came second in Quaerite Summa ("Reach for the Top"), which is a quiz-bowl style competition based solely on Roman life. It felt great to get recognition for my work on something I love so much.
How did you become interested in computer science?
When I was in sixth grade, I spent Spring Break at a Girls Learning Code camp. They had partnered with eIMACS to give away a scholarship for the first eIMACS programming course, University Computer Science I. To apply for the scholarship, I took the eIMACS Aptitude Test. The test was interesting and challenging, so my parents said they would sign me up for the course. From there, my interest only increased. I’ve taken three eIMACS courses now, and each one has introduced me to new programming languages, topics, and ideas.
What do you enjoy most about the eIMACS computer science courses?
I have to say, the thing that appeals to me the most about these courses is their rigor. I can tell a lot of care was put into creating them: the information is always laid out in a logical sequence, and the learning curve is perfect. Assignments are usually just the right difficulty level to leave me challenged but not frustrated. At the same time, the programming that I’m learning is very in-depth; I feel that I’m being prepared very well to succeed in the rest of the coding world. I especially liked the variety of languages that eIMACS introduced me to (Scheme, Haskell, Python and Java), as well as the focus on "good" programming and not just on getting things done.
What are some ways in which your eIMACS experience has had a positive effect on your academic and non-academic pursuits?
Completely thanks to the knowledge I gained from my eIMACS courses, this past summer I was offered my very first paid programming internship. It was a great opportunity to learn more about the outside world of programming (and the endless debugging that real coders must carry out!). The courses I’ve taken through eIMACS have also greatly increased my capacity for logical analysis and thought; I often find myself applying the programming principles I’ve learned to my schoolwork and assignments. Additionally, eIMACS has had a positive effect on my life overall. I’ve been participating in their courses for three years now, and they have broadened my mind and introduced me to new things I might never have experienced otherwise. I’m so happy that I chose to learn computer science through eIMACS.
What kinds of things do you see yourself doing in the future?
I’m not sure yet. I know that I want to work in a STEM field, and right now my thinking is that I’d like to do something with engineering — perhaps be a mechanical engineer? I want my job to be something that lets me create new things and leave my mark on the world. Whatever that may be, I know eIMACS has helped to prepare me by giving me a solid grounding in programming and logical thought.
As a homeschooled student, Shakthi could learn computer science anywhere. She chose IMACS. From 10th grade to 12th grade, Shakthi completed IMACS’ Modern Computer Science track, which includes University Computer Science I, University Computer Science II and AP Computer Science: Java Programming. Shakthi directly credits IMACS for her ability to deftly switch between various programming languages.
Shakthi’s multiple talents have earned her numerous honors. Original research in Number Theory propelled her and her teammates to the finals of the 2014 Siemens Competition in Math, Science & Technology where they won a $20,000 scholarship. Shakthi shines as a writer as well, having been named a 2015 YoungArts Winner in Poetry by the National YoungArts Foundation. As a high school student, she earned an "A" in UT Austin’s graduate-level course in Abstract Algebra.
Shakthi was accepted at Princeton, Harvard, UC Berkeley and UCLA and will attend Princeton where she plans to study theoretical math, creative writing and philosophy. She hopes to do research in some capacity throughout her career, either in academia or in a think-tank.
“I chose IMACS because it was thorough — it combined my predilection for theory and concept with rigor and practicality, both of which are needed to learn computer science well.”
Jacob began homeschooling in 3rd grade. Because IMACS focuses on ability level, not age, Jacob was able to enroll in his first online IMACS course as a 4th grader. He went on to complete IMACS’ university-level courses in Computer Science and Logic for Mathematics. In 8th grade, Jacob was accepted at Stanford Online High School from which he graduated with scores of 35 on the ACT and 5′s on multiple AP exams.
Many teens have a passion for math, computers and gaming, but few can be a voice of expertise. In high school, Jacob spoke at the Games for Change conference and worked as a teaching assistant for AwesomeMath. He also authored three popular books on gaming, including Minecraft for Dummies: Portable Edition, which has been a best seller in the tech book market, at one point reaching #1 in its category on Amazon.com!
Jacob chose Harvey Mudd where he plans to double-major in Mathematics and Computer Science with an eye toward a career designing educational games.
“IMACS gave me a whole new toolbox for approaching problems and puzzles across many different subjects. I learned how to visualize information and algorithms, and I loved discovering new programming languages like Scheme.”
Sarah wanted to form a deep conceptual understanding of the algorithms and logic used in computer science. She started IMACS in the ninth grade and went on to complete IMACS’ University Computer Science sequence. Graduating as co-valedictorian of her high school class with a score of 1570 out of 1600 on the SAT, Sarah was also a National Merit Scholar Finalist, a National AP Scholar and winner of multiple awards in math, science and language arts.
Sarah credits IMACS with her exposure to functional programming and the powerful uses of data structures and algorithms therein, which are generally not taught in standard high school computer science courses.
Sarah was accepted at Stanford, UC Berkeley, Cornell, UVA, William & Mary, RPI and Virginia Tech. She chose Stanford where she will pursue coterminal bachelor’s and master’s degrees in Computer Science with a specialization in Human-Computer Interaction. During her academic and professional careers, Sarah plans to develop software and do research in natural language processing and computational linguistics and eventually share her knowledge in a teaching capacity.
“My IMACS experience gave me an appreciation for the fascinating and vast field of computer science and was integral to my decision to major in computer science. I learned many different methods for problem-solving, which will assist me in all my endeavors whether related to computer science or not.”
Rachel began attending IMACS as a first grader. Homeschooled since third grade, she has always made time for IMACS in a busy schedule that revolved around competitive chess. While rising to the rank of #1 player in the US and #15 player in the world among girls under 14 and later attaining the title of Woman FIDE Master at just 16 years old, Rachel completed IMACS’ Advanced Math Enrichment and university-level courses in Computer Science and Logic for Mathematics.
As a high school student, Rachel earned A’s in multiple undergraduate math, science and computer science courses taken at Carnegie Mellon. She also scored a perfect 2400 on the SAT on her first attempt and earned 5′s on all of her Advanced Placement exams, including Computer Science A, Calculus BC, Statistics and Physics C.
Rachel chose Harvard, where she plans to major in Computer Science and Mathematics. She credits IMACS for motivating her to choose Computer Science as a major.
“IMACS fostered precisely the clear, logical thought processes necessary to succeed in advanced math and computer science classes. It is very important, both in math and computer science, to be able to think in an abstract manner, and I am grateful that IMACS prepared me very well.”
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When it comes to providing their children with the lifelong benefits of genuine learning, South Florida parents know where to go — IMACS! For over 20 years, the Institute for Mathematics and Computer Science has been giving students an outlet for reaching their highest potential in math, computer science and logical reasoning. IMACS teaches its unique classes after-school at its own centers as well as at many of the top private schools in the tri-county area, including Pine Crest, American Heritage and University School. To meet the growing demand for its classes, IMACS is expanding to new locations in Delray Beach and Pembroke Pines this fall.
What sets IMACS apart from other academic programs? The serious answer is that all materials are developed in-house by a long-standing team of mathematicians, computer scientists, engineers and programmers who are unconstrained by the need to follow a standards-based curriculum. Furthermore, applicants for instructor positions must survive a highly-selective recruitment process and go through a year of rigorous training before being entrusted to lead an IMACS class by themselves. But if you ask the students, they'll simply tell you that IMACS is fun!
While IMACS may be well-known among the gifted and talented community, its program is truly beneficial for most children. "Our students are grouped by ability, not by age," explains IMACS President Terry Kaufman. "This allows us to take elementary school students of a wide variety of abilities and turn them into strong mathematical thinkers. At IMACS, every child is a 'math person'." IMACS challenges kids to think and work in ways that help them outperform the expectations of their parents, teachers and, eventually, their university professors. For the rest of their lives, IMACS graduates simply think better.
One of IMACS' new locations will be open to all students in the greater Delray Beach area; it is located on the campus of the American Heritage School on Linton Blvd. Since 2010, IMACS has offered classes to American Heritage students at the private school’s Plantation campus. AHS student Azzara Nincevic is a long-time IMACS student. "When I began IMACS in first grade, I immediately loved it," she said. "All of the problems were thought-provoking. The curriculum helped me to develop logical thinking skills and made me realize that I would like to pursue computer science in college and after."
The second new location will be at Greentree Preparatory Charter School in Pembroke Pines. "We've always had a lot of students from the Pembroke Pines community enrolled at our Weston center," said Kaufman, "So we're excited to be partnering with Greentree Prep to bring our program to where this population lives." The new Pembroke Pines location will also be convenient for families in Miramar, Cooper City, and northwest Miami-Dade.
At both locations, IMACS will initially offer the first three levels of its highly-acclaimed Mathematics Enrichment program for students in Grades 1-5. At Delray Beach, IMACS will also offer Computer Enrichment, University-Level Computer Science and University-Level Logic for Mathematics. With anticipated growth, additional classes will be added at both locations in the future.
Give your child an unfair advantage in life: enroll him or her at IMACS where students learn to think deeply and creatively. These skills will translate to all areas of your child’s academic and professional life. IMACS is offering FREE placement classes at Delray Beach and at Pembroke Pines during the months of August and September. Families may also register for a placement class at alternate IMACS locations in Boca Raton, Weston, Plantation, Fort Lauderdale and Aventura. To attend a class with your child, call 954.791.2333 or visit imacs.org.
The IMACS Blog is taking a short summer hiatus and will return next month. Have a safe and happy 4th of July!
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