Thinking and Problem Solving: A New Look at Mathematics

Level:
Open to students entering grade 9 or 10 in the fall
Session:
II - July 17–August 3, 2018
Days & Time:
Monday–Friday, 9:10 –11:00 a.m. and 1:10–3:00 p.m.
Teacher(s):
Lyubomir Detchkov
Prerequisites:

Algebra I and geometry.

“I have gained a greater understanding of mathematics and was exposed to challenging and interesting problems.”   — From a program course evaluation 

Course Description

Intended for students who enjoy math and logical reasoning, this course introduces participants to an inductive approach to mathematics, doing math as it is done by mathematicians. Instead of starting with a formula and applying it, students start with a real world or abstract mathematical problem and work together to discover the formula or the process that best solves that problem. Students work in groups to test creative solutions to these problems and then go on to analyze the diversity of approaches taken by the various groups.

The course takes three basic approaches:

  • Through analysis and the discussion of various rich mathematical problems, students reach a deeper understanding of concepts such as non-standard Euclidean geometric constructions and elementary and more advanced probability.
  • Participants use geometry software for hands-on activities illustrating concepts such as the Golden Ratio and Fibonacci numbers, conic sections, elements of non-Euclidean geometry, elements of graph theory, fractals, and chaos theory.
  • We engage with real world problems from fields such as applied finance (loans and investments), biology (bacteria growth), medicine (decrease of the concentration of a medication in the blood stream over time), and radioactive decay (its application for estimating the age of substances of biological origin).

The combination of subjects and methods in this course enables participants to experience math in a way traditional high schools are often unable to present it, approaching problems as open-ended opportunities for creativity, independent thinking, and intellectual excitement.

Teacher(s)

Lyubomir Detchkov

Lyubomir Detchkov holds a B.S. in physics and an M.S. in solid state and laser physics from the University of Sofia, Bulgaria, as well as an M.S. in medical physics from the Medical University of Sofia. From 1983 to 1996, he worked as the Chief Assistant Professor in the Department of Medical Physics and Biophysics of the School of Medicine in Stara Zagora, Bulgaria. Since 1996, he has worked as a mathematics teacher, a mathematics coach (coaching mathematics teachers), and an assistant principal for mathematics and science at various New York City public schools. He has also served as an Adjunct Professor at Fordham University, teaching an educational graduate geometry course to first-year New York City mathematics teachers. Since 2010, Lyubomir has been the Mathematics Department Chair at Hunter College High School. 

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Specific course detail such as hours and instructors are subject to change at the discretion of the University. Not all instructors listed for a course teach all sections of that course.