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 how the different parts of a system worked
together; our STEM education was interdisciplinary. 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 outside of the classroom by age 9. We
noticed patterns in numbers, identified similar types of problems, and 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 an end product.
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 number 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 is 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. I later learned that my exercise is
known as Computational Thinking, a problemsolving technique that allows you to
break apart and solve hard problems, 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. 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 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. We have been using their books and old exams for
close to a decade. The added reward, however, lies in HOW we make use of these
two pillars of problemsolving: when we use these problem sets, we encourage 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 neighbors for feedback and critique. Everybody learns 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 nominal 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,
USAJMO and (we hope) 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 only.
Q. I want to sign up for classes;
where do I start?
A. Start with any class that has no
prerequisites. This means that you are not required to take another class before
it. 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.
The Art of
Thinking Mathematically: This class helps students to interpret math
statements, set up math problems, identify interrelationships between math
concepts, and to define realworld situations and events in mathematical terms.
It is packed powerful problemsolving tools.
Prerequisites: none
Technology: How
Computers Work 1: students explore the inner workings of the
computer as separate systems and as a foray into how systems work together. They
learn descriptively how computers store, retrieve, and process data. During the
course of the class, students create physical models of a computer memory cell.
For a final project, students create simplified physical model depicting of how
a microprocessor works.
Prerequisites:
none.
Basic Web Design:
students design and create a web site using HTML5, CSS and JavaScript. No
previous exposure to programming is necessary. If you can read and write a basic
sentence, you can learn basic coding in these three languages.
Prerequisites: none.
Computational
Thinking in Mathematics: Continuing from The Art of Thinking
Mathematically, this class finetunes mathematical thinking and
problemsolving skills. Students learn to solve complex or unfamiliar problems
by breaking the problem into smaller parts and identifying trends and patterns
between the parts. Problemsolving ends with each student writing a script (that
may or may not ask for user input) that allows the computer to solve the problem
by a specific mathematical method. The method will vary from student to student,
but each will use SCRATCH code and will learn various elements of programming as
the need arises. Participants also learn gradeappropriate Graph Theory
as yet another problemsolving tool. Problemsolving activities consist of both
independent and collaborative work and often include individual presentations
with peer feedback on problemsolving techniques.
Prerequisites: The
Art of Thinking Mathematically. You may register for Computational
Thinking in Mathematics if you successfully test out of The Art of
Thinking Mathematically.
Game Design in
SCRATCH: Students are given a basic game structure upon which to
build a game. The rules, levels and logistics of the game are up to the
individual student. Participants incorporate programming skills learned in
Computational Thinking in Mathematics. Creativity in design and in coding earns
design points. Please visit the
Game Design and play Blasteroids. Play
the game from the point of view of a game designer. Observe how the ship moves;
consider whether or not the asteroids' trajectories are random or specific; how
many asteroid Sprites would you make for this game? Think about the complexity
of the game and the function of the game.
Prerequisites:
Computational Thinking in Mathematics.
Summer Offerings:
Technology: How
Computers Work 2: Introduces the math and Boolean Logic related to
data transfer and data storage. Students learn the difference between HighLevel
Languages and Machine Code.
Prerequisites: The Art of Thinking Mathematically, and Technology:
How Computers Work 1
Computer Networks: teaches basic knowledge and terminology of
computer networks, including the internet. Students also learn about search
engines, browsers, and web pages. Select parts of Web Design 1 will also
be taught.
Prerequisite: The Art of Thinking Mathematically
Helpful, but not requisite: Basic Web Design
Graph Theory: for
Elementary School and beyond: A graph in this context is made up of
vertices, nodes, or points which are connected by edges, arcs, or lines. In
mathematics, graphs provide a way to formally represent a network, which is
basically just a collection of objects that are all interconnected. This class
teaches how Graph Theory is used in computer networks to choose the shortest
path for each data packet. Students also learn how Graph Theory is used in
network design.
Prerequisites: Computational Thinking in Mathematics
Prerequisite or corequisite: Computer Networks
Scientific Method
and Experimental Design: Students collect, organize,
and graph scientific and experimental data. Class covers Scientific Method:
experimental design; experimental variables; mathematical relationships;
mathematical models and unit conversion.
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
timeframe.
Q. Will these courses help me with
the Mark Twain Math/Computer exam?
A. Yes. At least 2 of our students
are accepted to Mark Twain Math/Computer Talent each year. At least 4 per year
are accepted to Bay Academy for Math/Computer or Science. This is a remarkably
high percentage, since we work with small groups of no more than four students
and many of our students are already in middle school.
Q. Do I need to know all the topics
on this page to pass the Math/Computer test for Mark Twain and Bay Academy?
A. No. We do not teach to an exam.
Some of the topics here go beyond what is expected for the Twain test.
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 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. While 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 and the schedule of sessions for each grade.
