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Mark Twain IS239 test prep, Bay Academy IS98 test prep
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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 problem-solvers 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 problem-solving 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 problem-solving 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 grade-level 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 life-altering one at that.

Q. What about Math Kangaroo and MOEMS? Don't they help me to become a better problem-solver?

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 problem-solving: 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 step-by-step 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 problem-solving 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 co-academic 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 problem-solving 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 cutting-edge 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 real-world situations and events in mathematical terms. It is packed powerful problem-solving 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 fine-tunes mathematical thinking and problem-solving skills. Students learn to solve complex or unfamiliar problems by breaking the problem into smaller parts and identifying trends and patterns between the parts. Problem-solving 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 grade-appropriate Graph Theory as yet another problem-solving tool. Problem-solving activities consist of both independent and collaborative work and often include individual presentations with peer feedback on problem-solving 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 High-Level 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. School-year 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 laid-back, 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 problem-solving and collaboration. We practice tournament-style problem-solving challenges to prepare students for exam stress. Students learn test-taking strategies -- how to take a multiple-choice test.

Q. Can a 3rd-grader enroll?

A. We have enrolled advanced 3rd graders in the past. If they are mathematically mature, they can out-perform 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 grade-level 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.


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