Why Squared School?
In a world full of choices, we work hard to make our program better than any of the alternatives. What makes us special are our teachers and our curriculum.
The teacher in our model plays a central role.
The teacher in our model plays a central role. You can learn by reading a book, but the power of having a fine teacher - a first rate coach - to guide you through the learning process, is enormous. This is true not only in math, but in music, sports, and many other disciplines and endeavors.
A fine coach will focus on what is essential. He or she will use their experience and expertise to optimize learning heuristics and to ensure that each student learns correctly and on his or her terms. This is done by providing a highly interactive and iterative experience where questions arise frequently and are answered quickly. A great coach will put things into context, paint a big picture, connect the dots, and inspire students to become self-motivated life-long learners.
Our teachers love teaching. They have a passion for working with children and helping them improve and grow. They have a strong command of the subject, know how to engage students and how to explain complex concepts in simple terms that are intuitively understood. We keep our classes small: they are capped at a maximum of 12 students, and our teachers ensure that everyone in the class is engaged.
We teach math in an engaging and fun way, with games and contests to make it enjoyable. We also maintain rigor and intensity of the program, with homework assignments and periodic quizzes and tests. As one parent noted, “It is amazing how much children learn, and yet they leave each class with a smile!” Our goal is to achieve this balance.
We emphasize abstract and conceptual thinking versus mechanical calculations and memorization.
We emphasize abstract and conceptual thinking versus mechanical calculations and memorization. Our students rarely touch a calculator. The “why” and the “how” are more important than the “what”. Our more senior students, when presented with new information, will often ask, “Can you show the proof?”. We want our students to prove things, as this is essential for deeper understanding. We also want them to develop strong problem-solving skills and learn how to deal effectively with complexity and ambiguity.
We want our students to be organized, disciplined, and meticulous, to: “solve the problem step-by-step and show each step.” “Have a paper trail of your work. That way if you make a mistake, you will be able to retrace your steps and find it.” “Keep good notes. They will be invaluable when you study for the test.” All of these are good habits to learn math, and critical study skills generally.
Along with meticulousness, we want our students to develop their intuition and acquire rapid math skills: to think on their feet, do mental math, and find shortcuts to solve seemingly difficult problems.
We deeply explore the concepts we teach from different angles. To master the material requires repetition, linking concepts, and careful practice: applying learned concepts to solve problems of increasing difficulty.
“In the mathematical field, a single notion precisely learned is worth a textbook of partially digested material… Understood ideas lead to understanding. Misunderstood ideas lead nowhere.”
A mathematics professor and author Jerry P. King in his book “Mathematics in 10 Lessons: The Grand Tour” correctly states: “In the mathematical field, a single notion precisely learned is worth a textbook of partially digested material. . . Understood ideas lead to understanding. Misunderstood ideas lead nowhere”. So, above all, we want to give our students a knowledge of mathematics that is deep and durable, and that becomes a foundation of a life skill.
To build a math curriculum of quality is an infinite process. To form our curriculum took years, and it is refined continuously. In considering a curriculum we realized there is no such thing as a “typical school curriculum”.
While the quality of math education varies widely depending where you are in the US, children tend to learn very little in the five years of elementary school. Yet this is the age when the ability to absorb new information is the highest. For instance, the age of 6 or even younger is ideal to begin learning chess or a foreign language, and math is a language! As we grow and age, learning becomes more difficult; see neuroplasticity.
Attempts to improve in middle school are often hampered by the need to address gaps created in elementary school. In high school the mathematical concepts quickly become complex and sophisticated, and many students lack a solid foundation to understand them.
There is far too little Geometry in the first 7 to 8 years of school. High school students are introduced to the full force of Euclidean Geometry, in all its demanding detail of axioms and theorems, but, unfortunately, very little problem-solving. The study of Algebra is needlessly delayed until late middle school, and includes a pointless buffer of so-called “Pre-Algebra”.
Our curriculum is a step ladder of carefully sequenced material, with concepts logically building on one another.
So, in developing a curriculum, we started from scratch. Our curriculum is comprehensive. We take students from simple arithmetic all the way to Calculus. While most of our students attend our Academy in addition to their regular school, we have had a number of home-schooled children learn from our curriculum exclusively, and effectively. We cover the learning objectives of a typical school curriculum plus many more topics typically not covered.
Our curriculum is a step ladder of carefully sequenced material, with concepts logically building on one another. There is a sharp trajectory for beginners, which prepares them well for increasingly more complex material down the road. We stress the fundamentals, the most critical/overarching concepts that serve as pillars that will support all future learning.
We cover a lot in Geometry early, beginning with younger classes. And Geometry runs as a continuous thread through most of our courses, gradually leading to development of powerful skills in our students. Likewise, Algebra — the language of math — is introduced early. Our students in Course 1200 have a lot of fun translating English sentences to “Math language” (Algebra), and vice versa.
There are certain topics that either get short shrift or are not covered in a typical school curriculum, although they appear frequently in major math competitions. They are essential building blocks of a strong foundation in math and a crucial link between the other main pillars of math. These topics include Number Theory, Logic, and Combinatorics/Probability; our curriculum covers these important subjects.
Our students understand the “why” and the “how” in addition to the “what.”
In covering new concepts, we extensively examine important proofs so that our students understand the “why” and the “how” in addition to the “what”, and learn to apply the concepts to solving difficult problems. We also cover applications of math in real life, such as in nature, or in fields of science or finance. Another unique feature of our curriculum is the attention to the history and culture of math. We need to know the giants on whose shoulders we are standing.
And all this, is what makes Squared School special.
