Offering serious and challenging mathematics to intellectually gifted students

1200 Kensington Road
McLean, Virginia 22101
(703) 855-0948


Vern Williams


Based in McLean, Virginia, we provide a challenging mathematics curriculum for gifted upper elementary and middle school students in the metropolitan Washington DC area. I have taught math in The Fairfax County Public School system for over thirty-five years and I have taught in the gifted and talented program for over thirty years. I have received awards from Fairfax County Public Schools and the Mathematical Association of America. I’ve coached many successful Mathcounts teams and taught Math Reasoning for The Johns Hopkins Center for Talented youth. In 2007, I was appointed to the National Mathematics Advisory Panel by President George W. Bush. I am proud to have managed to teach Real math for over thirty years without lowering my standards and have no intention of changing my methods.


I had junior high school teachers who were intellectual and had a passion for their subject. Those great teachers helped me to develop a passion for learning and a respect for hard work that remains with me to this day. At Paul Junior High School in Washington DC, intellectual excellence was the norm and it was celebrated. There was no cooperative learning, fake self esteem, differentiated instruction or ten pound textbooks loaded with pictures and useless content. I decided to become a math teacher during my last year of junior high school because I knew that I wanted to return some day to continue the fun, the learning, and the celebration of excellence that I experienced in seventh, eighth, and ninth grades.

After attending the University of Maryland in the early nineteen seventies, I accepted a math teaching position at Hayfield Secondary School in Fairfax County, Virginia. That experience helped to shape my attitude towards teaching math for the next thirty years. Teachers were forced to individualize 150 students using math booklets written for non-readers. Seventh and eighth grade students were put into the same math classes and teachers were told that this program was "cutting edge". I would hear that phrase many times over the next thirty years. I quickly decided to find a school where I was allowed to "teach". After seven great years teaching math at Ellen Glasgow School in Fairfax County, I transferred to H.W. Longfellow Middle School where I remained for over thirty years. At Longfellow, I developed and taught the original Honors Math course to students in the Gifted Talented Center program. I also taught Algebra/Geometry which was a one year course that I developed in which two high school credits were awarded. I also taught an enriched version of Honors Algebra 7 and a special proof based Honors Geometry course enriched with AMC/AIME/USAMO level problem solving.

At present I teach Algebra 1, Algebra 2, and Precalculus at BASIS Independent Mclean located in the Tysons Corner area. I am thrilled to be part of a school where academic excellence and personal responsibility are celebrated.


Classes will remain open until filled by qualified students.

Session I : July 13 – July 24 (9 AM - 11:30 AM) 
Session II : July 27 – August 7 (9 AM – 11:30 AM)

Vern Williams  Sessions I & II

Class Size:
12-15 students




This course is for rising seventh and eighth graders who are able to grasp abstract and complicated mathematical concepts at a very fast pace. Younger students with exceptional mathematical ability and backgrounds may enroll with special permission. Material covered will include topics from number theory, Euclidian and non-Euclidian geometries, Picks Theorem, Herons Formula, Mathematical proof, transcendental real numbers such as "e" and "pi" , derivation and use of the square root algorithm, unitary divisors, permutations and combinations, derivation and use of summation formulas, and RSA coding. In addition, students will develop new techniques and short cuts for solving both routine and difficult math problems taken from Mathcounts, AMC8, and other middle and high school contests.

Students who qualify for programs such as CTY (Johns Hopkins Center for Talented Youth) or EPGY (Stanford’s Education Program for Gifted Youth) should have an excellent experience taking this course. An AMC 8 score of 15 or higher should also serve as an excellent predictor of success in the course. If a student has not taken the AMC 8 contest (40 minutes for 25 problems, no calculator), previously given ones can be found on the Art of Problem Solving website at: ( Of course if a student is a strong member of his/her school Mathcounts team, this indeed serves as an excellent predictor of success in the Math Reasoning course.

July 27 - August 7 (1 PM – 4 PM)

Vern Williams and Dr. Ryan Grove

Class Size:
We will have two levels and will assign a maximum of 12 students to each class.




This course is mainly for rising eighth, ninth, and tenth graders who would like to prepare for high school math contests such as the AMC10, AMC12, ARML, the American invitational Mathematics Exam and USAMO. Problems will be selected from a variety of sources and problem solving techniques will be developed and applied. Other topics of interest, such as advanced number theory, combinatorics, and advanced topics from geometry will be discussed. The student should have the ability to reason abstractly and the desire to solve challenging problems in order to be successful in this course. We are planning to have two levels of APS. Adam Barth who attends Virginia Tech and was a USAJMO qualifer as an eighth grader will instruct the more experienced students. He was also a member of the four person 2010 Virginia State Mathcounts team.

Students who were very successful in the Math Reasoning course and/or advanced math courses from CTY (Johns Hopkins Center for Talented Youth) or Stanford’s Education Program for Gifted Youth (EPGY) should be prepared for this course. Acceptance to programs such as MathPath as well as a score of 90 or above on the AMC10/12 also serve as excellent predictors of success in this course. Even though we will have two levels of APS, the entry level section will be quite rigorous. Students will be assigned to their respective section based on their mathematics course backgrounds and problem solving experience.


I provide a limited amount of mentoring/enrichment during the school year for small groups. I currently meet with two small groups on Saturday mornings at 9 AM and 10:15 AM. There are currently no openings in the 9 AM class and two openings in the 10:15 (advanced) class. 

For information regarding content and fees, please contact me.

I have advised educational establishments such as The College Board ( and Achieve, Inc.( on various issues involving curriculum and testing. I also advise parents on dealing with school and classroom issues involving curriculum for gifted students. Fees are generally $100 - $130 per hour.



Offering serious and challenging mathmatics to
intellectually gifted students

Last update: 5/26/2020