Welcome to the Kids Page.
If you have a question that we have not answered
below, please email
it to us and we will add the question and answer to this list.
Q. Who develops the technology that
makes your smartphone thinner, faster and better?
A. Students at America’s top
colleges and universities conduct cutting edge research. Some schools like MIT allow you to conduct research during your first year of college.
In a
few short years, one such student could be you.
During my college years, I designed and fabricated
a special kind of chip. A friend helped to develop the LCD screen that you are
currently viewing as you read this document, while other classmates developed
antennas aimed at improving how cellphones send and receive signals.
Q. What did these college students
have in common?
A. We excelled at computational thinking; we were able to visualize (imagining or seeing something in your head) how the different parts of a system worked together; we used STEM in an interdisciplinary way. We were highly efficient problemsolvers who never gave up when the problems got tough.
Q.
When did you start thinking like engineers?
A.
Most of us started exploring math and science outside of the classroom by
age 9. We noticed patterns in numbers; were able to identify problems by type
and use appropriate problemsolving strategies; we built our own toys and games
using mathematical and scientific concepts learned in school. Building toys
allowed us to tackle hard problems by breaking them into smaller problems that
we could solve before fitting the solutions back together and coming up with a
toy we could use.
Q. Did you struggle with math as a
kid?
A. Briefly, yes; with Long Division. I needed to know WHY I was performing the steps because simply parroting my math teacher was frustrating to me. I did not want to "get the problem right", I wanted to know the "logic" behind the method. So, I was forced to teach myself because the answer to "why does it work that way?" was a shrug followed by "it just does!" I did finally happen upon the answer by observing the pattern in the numbers. I did originally include the answer here, but decided not to rob you of the joy of discovery.
Hint 1: write a Long Division problem and compare the numbers you "subtract off" with the dividend. Other math rules are revealed in this exercise, so the discovery is its own reward.
Email me if you think you've solved the mystery of why Long Division works the way it does.
Hint 2: I assign this particular problem in Computational Thinking in Mathematics.
Q. Did anybody teach you this?
A. No. I wanted an answer that
nobody could give me. Because I had done a certain simpler math topic before, I
eventually recognized a specific pattern in the numbers. After doing about three
or four Long Division problems to test my theory, I made my conclusion. This was
a defining moment in my life: it was at this point that I went from mediocre
math student to the top of my class. Once you learn to think this way, you can
solve any problem.
Q. Why should I care about
visualizing Long Division like this?
A. "You can solve any problem" when you learn to approach a math procedure in this way. I later learned that my Long Division exercise used Computational Thinking, a problemsolving technique that allows you to break apart and solve hard, unfamiliar, or large problems. In the case of Long Division, the steps are recursive
(hint 3), another term that relates to coding. Having done this when I was 9 helped me to better understand recursion when I took my first formal coding class in college. This is proof positive that mathematical thinking is transferable to Computer Science and to Coding. Once you solve the problem yourself, it becomes easy to see how to use the set of steps to instruct a computer to do Long Division. If you know how to program in SCRATCH you could easily write a script to solve a Long Division problem. Challenge yourself by having the program ask the user for the dividend and the divisor, perform the calculation as it displays the parts of the problem in an array, and return the answer.
Q.
Will the skill I gain from these classes help me to improve my grade?
A. Every so often a former student will return to show off his or her report card. We now have students that we tutored in 4th grade, return to let us know that they are still using our problemsolving techniques in high school, and are able to solve hard problems that stump their classmates. Here, students learn to think for themselves, they learn how to learn, how to interpret a problem statement, how to choose an appropriate problemsolving method, keep track of their thinking, and arrive at a solution. For them, math makes SENSE! Once you have opened to door to this kind of thinking, there is no going back. The short answer to your question is "YES!"
Q. I am not the top student in my
math class. Will I be able to handle the material?
A. All our classes are based on
gradelevel math. The difference is that you learn to see the concepts from
several different perspectives. We are not looking for "top students"
exclusively; we are seeking students who are interested in becoming mathematical
"thinkers". From my experience, not all students who are top performers in the
schoolroom are great mathematical thinkers. On the other hand, some students who
are not even in the top 5 in their class make excellent mathematical thinkers.
When I struggled with Long Division, I was not the top student in my math class.
I used to envy those boys and girls who could complete Long Division with speed
and accuracy. However, my presentation to my math teacher after I figured things
out ... well, IT became a teaching tool for the students in the grades below
mine as they moved into that math class. The topics taught from my model
included related areas of math reasoning that were made obvious in my
experiment. If a number is divisible by 5 and you add 25 to it, then the new
number will also be divisible by 5 (is this hint 4?). By trying to make sense of
Long Division, I discovered that Math was much more than just Arithmetic, and
that I was really good at mathematical thought. You have to be willing to
explore, and you must be willing to persevere. You also cannot be defeated by
perceived failure; mine was a teaching moment and a lifealtering one at that.
Q. What about Math Kangaroo and
MOEMS? Don't they help me to become a better problemsolver?
A. Math Kangaroo and MOEMS are
excellent places to start. In addition to the problems we design, we have been
selecting problems from their books and old exams for close to a decade. The
added reward, however, lies in HOW we make use of their material: when we use
these problems, our students take their own solutions to a higher level. By
applying Computational Thinking they are able to write stepbystep instructions
that can be used to solve similar problems, not only on paper but also via
SCRATCH code. So, one MOEMS or Kangaroo math problem sees three or four
different problemsolving methods, each producing a unique piece of SCRATCH code
that students present to their team mates for feedback and critique. Everybody
gets to view the problem from multiple perspectives; everybody learns to express
mathematical ideas.
Q. How else can I benefit from
these classes?
A. Based on mathematical maturity
and coacademic skills, top performers earn scholarship to Young Engineers Math
Circle. The cost of participation in the Math Circle is small but the benefits
are huge. Participants in the Young Engineers Math Circle will learn further
topics in problemsolving and will later participate in AMC,
AIME (by
invitation), USAJMO and (fingers crossed) USAMO. They attend presentations given
by guest speakers such as industry professionals and visiting professors. They
learn about cuttingedge technology and the role that mathematics play. The fee
per semester for students in the Math Circle is equal to the monthly fee for one
class outside of the Math Circle. Entry to the Young Engineers Math Circle is by
invitation, but starting in 2019, students will be able to test in.
Q. I want to sign up for classes;
where do I start?
A. Start with any class that has no prerequisites. If a class has prerequisites, you will be required to take another class (the prerequisite) before you can take that class. Different classes are offered in the Fall, Spring, Winter and Summer. If you plan on taking a class that has prerequisites, be sure to take those classes first, or come in and test out of the prerequisite. Testing out is free.
Q. How long does each class last? How frequently does each class meet?
A. It depends on whether you're taking the class during the school year or over the summer. During the school year, students meet less frequently  one 1.5 hr session per week. Schoolyear classes last for 3 consecutive months. Summer sessions are two 1.5 hr sessions per week and each class lasts 6 weeks, but you do more homework in a shorter time frame.
Q. Will these courses help me with the Mark Twain Math/Computer exam?
A. Yes. Our 5th grade students are accepted to Mark Twain and Bay Academy each year for Math/Computer and Science.
Q. What is your environment like?
A. We are very laidback, mostly because we want you to feel comfortable. Dress casually, work hard, complete your homework and show detailed work in ALL your answers, even if the questions are multiple choice. Use sound reasoning. To avoid damage to computers, no food or drink shall be consumed on the premises. We alternate between independent problemsolving and collaboration. We practice tournamentstyle problemsolving challenges to prepare students for exam stress. Students also learn testtaking strategies  how to take a multiplechoice test.
Q. Can a 3rdgrader enroll?
A. We have enrolled advanced 3rd graders in the past. If they are mathematically mature, they can outperform a struggling 4th or 5th grader  surprising, but true.
Q. Do 4th through 7th grade students sit in the same class?
A. No. For example: any student can
register for The Art of Thinking Mathematically, 7th graders will be using
gradelevel math, so would 4th graders. We open separate sessions where 4th and
5th graders meet (plus precocious 3rd graders), and sessions where 6th and 7th
graders meet. If there is overflow, there might be some sessions where 5th and
6th graders meet.
Q. Are all these classes offered at once?
A. No. Go to our
Classes page to see the classes that are currently being offered.
