Friday, September 28, 2012

Introduction to Unizor Education

Unizor features a curriculum for advanced high school course of mathematics. The word "advanced" we mean in terms of depth of learning, rather than in terms of number of topics covered. We started with such topics as "Math Concepts", "Algebra", "Geometry", "Trigonometry" and "Vectors". In the future we plan to add more material to existing topics as well as include some new ones, like "Analysis".
Not everything is fully completed yet, but substantial part of the Web site is ready for use and new material is added daily.

Most important characteristic that distinguishes this course from many other on-line math courses is its emphasis on problem solving, rigorousness of presentation and proof of theorems as the main methodology, rather than memorization of formulas and properties, unfortunately typical in many cases. A short statement that encompasses this idea is "Knowledge vs. Skill" or "Why? vs. How?". Unizor emphasizes "Knowledge" and "Why?" rather than "Skill" and "How?". For instance, we don't just give a formula to solve some type of equations, we derive it. We don't just say that medians in a triangle intersect in one point, we prove it. And we offer hundreds of problems related to presented theoretical material because solving them is the main tool to develop intellectual power. Students forget formulas soon after completing their education, but ability to solve problems will be useful in all aspects of their future life, personal as well as professional.              

We would like our students to think about math for their intellectual development as they think about gym for physical development. Mathematical objects (equations, triangles, vectors etc.) are the language for problem solving inasmuch as weights are tools for lifting in a gym. The multitude of mathematical objects is used for balanced and harmonious intellectual development, same as many different tools in a gym are used for balanced and harmonious physical development of all groups of muscles. The time students usually spend on their physical development (gym, basketball, soccer etc.), in our opinion, should be comparable to time they spend on their intellectual development using the art of Mathematics. And what better develops the young mind than solving problems? Think about spending at least an hour a day learning theoretical material and solving problems presented on our site.

Unizor is designed for individualized learning, facilitated in the environment of homeschooling or "flipped" classroom, which allows different types of users: students as objects of education, their parents as a party interested in the results of education in homeschooling environment or teachers, delegated a supervisory role by parents, in a "flipped" classroom or group study environment.

In Unizor environment students will use lectures, problems, proofs and exams provided on the side. Homeschooling parents or teachers in their supervisory capacity will be more involved in a supervision of the educational process. They will have access to the results of all exams taken by students and will be able to enroll their students in different courses as well as to mark certain courses as completed, if the scores on exams taken by their students are satisfactory. In a "flipped" classroom or group study environment facilitated by Unizor teachers will be able to provide additional support for students requiring it.

Educational material on Unizor is provided in two forms: video presentation and notes for each one. Theoretical material is more or less identical in both forms. Most theorems are proven also in both forms, in lectures and in notes for them. Numerous problems are usually stated in notes without solutions, but solutions are presented in the corresponding lectures in an oral form. All material is controlled by a hierarchical menu and is intended to be studied in the order presented on the Web site, starting from "Math Concepts".

Unizor is free and has no advertizing. It is created just to spread the Knowledge and turn the mathematical education towards development of creativity and analytical thinking - qualities needed throughout an entire life, rather than memorization of formulas and properties, which are usually forgotten right after graduation.