Online Intensive AMC 10/12/ARML Prep (for 6th to 11th Graders) Spring Weekend Course (Geometry) Starting Feb. 12

It’s time to prepare for the 2023 AMC 10/12 contests!  “Chance favors only the prepared mind.” Success is doing ordinary things EXTRAordinarily well!

Purpose: To prepare for the AMC 10/12A —Friday, November 10, 2023 and AMC 10/12B — Thursday, November 16, 2023.

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Course Outline

Class Handout Sample

Spring Session I (Triangle and Polygon Geometry)
9 Weekends (EASTERN Time: 6:00 – 8:00 pm), Total: 18 Hours
2/12,  2/19,  2/28,  3/5,  3/12,  3/19,  3/26,  4/2,  4/9

Spring Session II (Circles and Advanced Geometry)
9 Weekends (EASTERN Time: 6:00 – 8:00 pm), Total: 18 Hours
4/16,  4/23,  4/30,  5/7,  5/14,  5/21, 5/28, 6/4,  6/11 (Final Mock Exam/Review)

Online Registration is now open! Click HERE to register and pay.

  • This is a live class, not a pre-recorded one. Instructors will ask students questions, and students can also ask questions during the class or email their questions to instructors after class.
  • We record all of our lessons as a big bonus so that our students can watch class videos after class for review and self-study.
Tuition (including all materials)
Session I:  New Student: $810   Buy Now Button
Returning Student: $790 Buy Now Button
Session II:  New Student: $810   Buy Now Button
Returning Student: $790   Buy Now Button
Sessions I & II:  New Student: $1,595  Buy Now Button
Returning Student: $1,560   Buy Now Button
Click HERE to see payment and refund policy.

You are very welcome to sign up for our online course which offers a quick, efficient way for students to interact with teachers over long distance. We use Google Meet to video chat and easily connect with students to teach them our tricks and shortcuts to getting an amazing score on their contests, as well as offer them our guidance and support. Students can ask questions face-to-face, and can complete problems with the supervision of our teachers/coaches. Click HERE to see detailed instruction.

A commitment to the whole course can maximize the benefit of learning all the math ideas, methods, strategies, tactics, skills, and techniques.

  • We will help students gain a deeper understanding of the fundamental math concepts, build a solid foundation in math, and develop the critical thinking and problem-solving skills different from those in the school classes, motivation, and perseverance for reaching their full potential.
  • We will focus on efficient tricks, shortcuts, and strategies to solve competitive math problems, especially those hard problems on the AMC 10/12 and easy problems on the AIME, as well as test-taking tactics.
  • The emphasis of this class will be on systematic, comprehensive, and in-depth problem-solving in contest geometry, which is extremely common in competitive math, but is not included in school curriculum.
  • We will utilize a highly effective teaching model as described in the article: Small-sized Class Instruction-focused Model.

Instructors:

Contact Information:
Ivy League Education Center
Tel:  301-922-9508     or        240-406-3402
Email:  chiefmathtutor@gmail.com

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Specific Goal: 

To earn a score of 120 or more out of 150 on the American Mathematics Contest 10 (AMC 10), or a score of 100 or more out of 150 on the American Mathematics Contest 12 (AMC 12), and then qualify for the American Invitational Mathematics Examination (AIME), which is used to determine qualification for the United States of America Mathematical Olympiad (USAMO).

AMC-General

There are many math competitions in the United States. Of those, only

AMC → AIME → USAMO sequence

would take you to the IMO (International Math Olympiad), the highest level math competition for high school students in the world!

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Click here to read more!

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Who should take this class: 

This class is very appropriate for 6th-11th grade students who are hoping to qualify for the AIME.

Benefits:

  • 18 tutorial handouts (>760 pages) developed by Dr. Henry Wan and 500 new problems similar to AMC 10/12 level from the licensed AMC Database. Click HERE to see a typical class handout sample we developed.
  • 2 FREE mock tests that are intended to mimic an actual math competition exam, each of which has 25 questions similar to AMC 10/12 level taken from the licensed AMC Database. These simulated tests help students assess their level of preparation for the Math Competitions. After attempting the test, students get answers, explanations, and a detailed score report and wise performance summary.
  • FREE registration for the AMC 10/12A — Friday, November 10, 2023 and AMC 10/12B — Thursday, November 16, 2023. Please see: The 2023 AMC 10/12 Contests at the Ivy League Center on Nov. 10, 2023, and Nov. 16, 2022

Weekly Homework:

At least 3 hours per week. Problem sets include all problems from 92 past real AMC 10/12 test booklets from 2000-2022, and 500 brand new problems having similar difficulty and style as the real AMC 10/12 problems, extracted from the licensed AMC Database.

The focus will on the final 15 problems on the AMC 10/12, and the first 5 problems on the AIME, as well as those hard problems on the ARML. Note that some hard problems on the recent AMC 10 and 12 are exactly the same as previous ARML Problems.

Read More at:

Each week, we will carefully review and check 2 students’ homework, and correct any mistakes. The next week, we will check another 2 students’ homework, and this will continue on a rotational basis until all students have had their homework checked at least once and the cycle will start again. Based on the work of the 2 students that week, we will provide the those 2 students with individualized proposal and support.

Qualifying AIME

Class Outline:
In the final sprint of AMC 10/12 preparation, we will focus on efficient tricks, shortcuts, and strategies to solve AMC problems as well as test-taking tactics. The emphasis of this class will be on systematic, comprehensive, in-depth problem-solving in advanced geometry, which is very common in competitive math. We will also help students develop quick problem solving strategies and effective time management skills. We reserve the right to adjust the teaching content and method according to students’ understanding and comprehension of new knowledge.

Spring Session I

Class Date Topic
1 2/12, Sun Using the Pythagorean theorem and sophisticated algebra to solve hard geometry problems on the AMC/ARML
2 2/19, Sun Triangle geometry: common base theorem of triangles, and angle bisector theorem
3 2/26, Sun Special triangles I (30o-60o-90o triangles, equilateral triangles, and 45o-45o-90o triangles) and hexagon/octagon geometry
4 3/5, Sun Special triangles II (15o-75o-90o triangles) and dodecagon geometry
5 3/12, Sun Golden triangle, golden gnomon, and special right triangles
6 3/19, Sun Comparing the areas of triangles
7 3/26, Sun Mass point geometry and barycentric coordinates
8 4/2, Sun Polygon geometry
9 4/9, Sun Cyclic quadrilaterals, Ptolemy’s theorem and Brahmagupta’s formula

Spring Session II (Continuation of Session I)

Class Date Topic
1 4/16, Sun Circle geometry
2 4/23, Sun Power of a point, intersecting chords theorem
3 4/30, Sun Circles and triangles: circumcircles and incircles
4 5/7, Sun Circles and regular polygons, efficient strategy to construct auxiliary lines in circles
5 5/14, Sun Fundamental Trigonometry
6 5/21, Sun More on Trigonometry
7 5/28, Sun 3-D geometry
8 6/4, Sun Analytic geometry
9 6/11, Sun Constructing auxiliary lines and applying the ruler, protractor, and compass to solve hard AMC geometry problems (See more at: Optimal Strategies to Solve Hard AMC Geometry Problems

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Small-sized Class Teaching Model: 

We utilize the highly effective small-sized class teaching model. Smaller classes lead to pupils receiving more individual attention from teachers, and having more active interactions with them. We focus on every individual, not the whole class. Students will thrive from the smaller class sizes that allow them to reach their full potential. Particularly, students can benefit tremendously from high-frequent individualized student-teacher interactions leading to establishment of a stronger foundation for lifelong learning.

Our main purpose is to help our students gain deeper understanding of the fundamental math concepts, build a solid foundation in math, and develop the critical thinking and problem-solving skills that are so valuable to success in any career. We are big believers in the FUNDAMENTALS! Our students will receive the LIFELONG BENEFITS from learning math.

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Regardless of his/her math level, each student will have the opportunity to learn math in a fun, friendly, cooperative, supportive learning environment. The most important thing is to have fun.

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Our Students

In 2022, we had 3 students qualified for the Math Olympiad Summer ProgramRead more at: Brendon J., Kyle S., and Isabella Z. Qualified for the 2022 Math Olympiad Summer Program

In 2022, we had 1 student competed in International Girls’ Math OlympiadRead more at: sabella Z. Competes in International Girls’ Math Olympiad

In 2022, we had 7 students qualified for the USAMO andstudents for the USAJMO. Read more at: 2022 USAMO and USAJMO Qualifiers Announced — Seven Students Qualified for the USAMO and Seven Students for the USAJMO.

In 2022, we had 88 students who obtained top scores on the AMC 8 contest!

  • 10 of our students were among the top 131 worldwide winners (Perfect Scorers), as shown in Table 1. Click Here see a full list of the 131 worldwide winners.
  • 52 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers. They were among the 1,010 worldwide winners. Click Here see a full list.
  • 26 students received National Honor Roll Certificates awarded to top 5% test takers. They were among the 2,449 worldwide winners. Click Here see a full list.
  • 88 out of our 91 students (96.7%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 022 AMC 8 Results Just Announced — Ten Students Received Perfect Scores

In Fall 2021, we had 93 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 5 Perfect Scorers worldwide on the AMC 10A: Nina L. and one of our students was among the 2 Perfect Scorers worldwide on the AMC 10B: Ming Y. Read more at: 93 Students Qualified for the 2021 Fall AIME and 2 Students Received Perfect Scores on the 2021 Fall AMC 10/12

In 2021, we had 6 students qualified for the USAMO and 6 students for the USAJMO. Read more at: 2021 USAMO and USAJMO Qualifiers Announced — Six Students Qualified for the USAMO and Six Students for the USAJMO

In Spring 2021, we had 91 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. Two of our students was among the 17 Perfect Scorers worldwide on the AMC 12A: Evan L. and Suraj O. and one of our students was among the 27 Perfect Scorers worldwide on the AMC 10A: Xinchen L. Read more at: 91 Students Qualified for the 2021 AIME and 3 Students Received Perfect Scores on the 2021 AMC 10/12

In 2021, we had 8 students who got into the MathCounts state-level top 10. Yunyi L. won 9th Place in the 2021 MathCounts National Competition!

In 2020, we had 79 students who obtained top scores on the AMC 8 contest!

  • 5 of our students were among the top 57 worldwide winners (Perfect Scorers).
  • 49 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 25 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 79 out of our 81 students (97.5%) received National Awards for the AMC 8 from the Mathematical Association of America.

Read more at: 2020 AMC 8 Results Just Announced — Five Students Received Perfect Scores

In 2020, we have 2 students, Isabella Z. and Sameer P., who were among the 61 students selected nationwide to attend. Read more at: Warmest congratulations to Isabella Z. and Sameer P. for being accepted into the Math Olympiad Program!

In 2020, we had 82 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 11 Perfect Scorers worldwide on the AMC 12A: Yiyang X, and one of our students was among the 13 Perfect Scorers worldwide on the AMC 10A: Jason W.. 43 middle schoolers and 9 elementary schoolers qualified for the AIME! Read more at: 2020 AIME Qualifiers Announced — 82 Students Qualified for the AIME

In 2019, we had 71 students who obtained top scores on the AMC 8 contest!

  • 8 of our students were among the top 151 National Winners (Perfect Scorers), including 2 sixth graders.
  • 36 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 27 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 71 out of our 73 students (97.3%) received National Awards for the AMC 8 from the Mathematical Association of America.

Read more at: 2019 AMC 8 Results Just Announced — Eight Students Received Perfect Scores

In 2019, we had 4 Students Qualified for the USAMO and 4 Students for the USJMO.

  • Of the 280 USA Math Olympiad national qualifiers, 4 are our students: Luke C., Zipeng L., Sameer P., and Peter P.
  • Of the 235 USA Junior Math Olympiad national qualifiers, 4 are our students: Michael H., Noah W., Holden W., and Isabella Z.

Read more at: 2019 USAMO and USAJMO Qualifiers Announced — Four Students Qualified for the USAMO and Four Students for the USAJMO

In 2019, we had 76 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 22 Perfect Scorers worldwide on the AMC 10A: Noah W. and one of our students were among the 10 Perfect Scorers worldwide on the AMC 12B: Kenneth WVery impressively, 32 middle schoolers and 7 elementary schoolers qualified for the AIME!

In 2018, we had 64 students who obtained top scores on the AMC 8 contest!

  • of our students were among the top 44 National Winners (Perfect Scorers): Eric B., Kevin Y., and Isabella Z.
  • 40 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 21 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 64 out of our 66 students (96.5%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2018 AMC 8 Results Just Announced — Three Students Received Perfect Scores

In 2018, we had 73 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. Two of our students were among the 35 Perfect Scorers worldwide on the AMC 10A: Austen M. and Jason W.  and two of our students were among the 21 Perfect Scorers worldwide on the AMC 12B: Kaan D. and Edward W. Remarkably, 11 middle schoolers and 2 elementary schoolers qualified for the AIME!

In 2017, we had 63 students who earned top scores on the AMC 8 contest!

  • of our students were among the top 75 National Winners (Perfect Scorers).
  • 34 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 22 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 63 out of our 65 students (97%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2017 AMC 8 Results Just Announced — Seven Students Received Perfect Scores

In 2017, we had 61 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 28 Perfect Scorers worldwide on the AMC 10A: Austen M., and two of our students were among the 65 Perfect Scorers worldwide on the AMC 10B: Ashwin A. and Brad Z. Remarkably, eight middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Very impressively, Bryan Z., a 6th grader, gained a score of 132 out of 150 on the AMC 10B.Read more at: 2017 AIME Qualifiers Announced — 61 Students Qualified for the AIME

In 2016, we had 36 students who are qualified to take AIME either through AMC 10A/12A or AMC 10B/12B. One of our students was among the 23 Perfect Scorers worldwide on the AMC 10A: Joel (Junyao) T. Particularly, seven middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Pravalika P., a 6th grader, got a 115.5 out of 150 on the AMC10B, which is very impressive. Read more at: 2016 AIME Qualifiers Announced — 36 Students Qualified for AIME

2011 – 2015: In total, 37 students scored above 120 on the American Mathematics Contest 10 (AMC 10) and qualified for the American Invitational Mathematics Examination (AIME); 26 students scored above 100 on the American Mathematics Contest 12 (AMC 12) and qualified for the American Invitational Mathematics Examination (AIME); 3 students qualified for the USA Mathematical Olympiad (USAMO), the highest level of math competition for high school students in the USA

2011 – 2015: In total, 23 students achieved perfect scores of 28 on the AMC 8

Read more at: Notable Achievements of Our Students

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Our Uniqueness

We have a long history of close collaboration with the MAA’American Mathematics Competitions (AMC), which are dedicated to strengthening the mathematical capabilities of our nation’s youth, and are the first of a series of competitions in high school mathematics that determine the United States team for the International Mathematical Olympiad (IMO).

We are only one in the Washington DC metropolitan area to offer elementary, middle, and high-school level competition math courses. Our students have received top scores and awards at prestigious national and math competitions.

Great Benefits of Math Competitions

In an increasingly competitive college application pool, the process of mastering math skills through our courses and participating in the American Math Competitions will help students strengthen and diversify their extracurricular activities. These contests can motivate students’ interest and passion in math, and they can discover their talent through solving challenging problems different from those in the school classes. Many top colleges also request AMC scores as part of the college application process. Both MIT and Caltech have entry blanks on their official admission application forms for the applicant to enter their best AMC and AIME scores. Ivy League Colleges and Stanford ask for to the AMC and AIME scores in their Supplement to the Common Application Forms. Your children deserve the chance to list these scores on their applications! Good AMC scores will greatly enhance admission opportunities for students to elite colleges.

Read more at::

education priceless treasure

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Click HERE find out more about Math Competitions!sat-logo-3

Click HERE to find out more about SAT Prep!

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2022 Winter – Competitive Math Courses

Winter is the crucial time to develop students’ math skills and to prepare for the American Mathematics Competitions!

Only undertake what you can do in an excellence fashion. There are no prizes for average performance.

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Competitive Math Program — Winter 2022 Schedule

Class Day/Time Grade
Online Intensive AMC 10/12/ARML Prep Winter Session Winter Session (Algebra) 
Total: 20 Hours
10 Classes (Eastern Time: 6:00 – 8:00 pm)
11/20, 11/27, 12/4, 12/11, 12/18, 1/8, 1/15, 1/22, 1/29, 2/5
View Course Outline
6-12
Online Intensive AMC 8/Mathcounts Prep Winter Session Winter  Session (Comprehensive Problem-Solving)
Total: 18 Hours
9 Classes (Eastern Time: 6:00 – 8:00 pm)
11/19, 11/26, 12/3, 12/10, 12/17, 12/24, 12/31, 1/7, 1/14
View Course Outline
4-8
Online Intensive AIME Prep Winter Weekend Course Winter Session I (Contest Geometry)
Total: 12 Hours
6 Classes (EASTERN Time: 3:00 – 5:00 pm)
11/20, 11/27, 12/4, 12/11, 12/18, 12/24

Winter Session II (Comprehensive Problem Solving)
Total: 12 Hours
6 Classes (EASTERN Time: 3:00 – 5:00 pm)
12/31, 1/8, 1/15, 1/22, 1/29, 2/5

View Course Outline

6-12

We record all of our lessons as a big bonus so that our students can watch class videos after class for review and self-study.

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There are many math competitions in the United States. Of those, only

AMC → AIME → USAMO sequence

would take you to the IMO (International Math Olympiad), the highest level math competition for high school students in the world!

AMC-AIME-USAMO-IMO

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Featured Math Instructors

All of our sessions are taught by highly qualified instructors who are excellent experts on preparing students for the exam. We distinguish ourselves by the high quality of our instructors. Finding top-quality instructors is no easy task. We’ve hand-picked some of the best, including graduates of Ivy League institutions.

Our instructors are dedicated to teaching and student success. They are very knowledgeable, patient, available, and willing to help our students. Our students receive a quality education that goes beyond the classroom.

Meet some of them here:

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Our Students

In 2022, we had 3 students qualified for the Math Olympiad Summer ProgramRead more at: Brendon J., Kyle S., and Isabella Z. Qualified for the 2022 Math Olympiad Summer Program

In 2022, we had 1 student Competes in International Girls’ Math OlympiadRead more at: Isabella Z. Competes in International Girls’ Math Olympiad

In 2022, we had 7 students qualified for the USAMO andstudents for the USAJMO. Read more at: 2022 USAMO and USAJMO Qualifiers Announced — Seven Students Qualified for the USAMO and Seven Students for the USAJMO.

In 2022, we had 88 students who obtained top scores on the AMC 8 contest!

  • 10 of our students were among the top 131 worldwide winners (Perfect Scorers), as shown in Table 1. Click Here see a full list of the 131 worldwide winners.
  • 52 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers. They were among the 1,010 worldwide winners. Click Here see a full list.
  • 26 students received National Honor Roll Certificates awarded to top 5% test takers. They were among the 2,449 worldwide winners. Click Here see a full list.
  • 88 out of our 91 students (96.7%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 022 AMC 8 Results Just Announced — Ten Students Received Perfect Scores

In Fall 2021, we had 93 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 5 Perfect Scorers worldwide on the AMC 10A: Nina L. and one of our students was among the 2 Perfect Scorers worldwide on the AMC 10B: Ming Y. Read more at: 93 Students Qualified for the 2021 Fall AIME and 2 Students Received Perfect Scores on the 2021 Fall AMC 10/12

In 2021, we had 6 students qualified for the USAMO and 6 students for the USAJMO. Read more at: 2021 USAMO and USAJMO Qualifiers Announced — Six Students Qualified for the USAMO and Six Students for the USAJMO

In 2021, we had 8 students who got into the MathCounts state-level top 10. Yunyi L. won 9th Place in the 2021 MathCounts National Competition!

In Spring 2021, we had 91 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. Two of our students was among the 17 Perfect Scorers worldwide on the AMC 12A: Evan L. and Suraj O. and one of our students was among the 27 Perfect Scorers worldwide on the AMC 10A: Xinchen L. Read more at: 91 Students Qualified for the 2021 AIME and 3 Students Received Perfect Scores on the 2021 AMC 10/12

In 2020, we had 79 students who obtained top scores on the AMC 8 contest!

  • 5 of our students were among the top 57 worldwide winners (Perfect Scorers).
  • 49 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 25 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 79 out of our 81 students (97.5%) received National Awards for the AMC 8 from the Mathematical Association of America.

Read more at: 2020 AMC 8 Results Just Announced — Five Students Received Perfect Scores

In 2020, we had 2 students, Isabella Z. and Sameer P., who were among the 61 students selected nationwide to attend. Read more at: Warmest congratulations to Isabella Z. and Sameer P. for being accepted into the Math Olympiad Program!

In 2020, we had 82 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 11 Perfect Scorers worldwide on the AMC 12A: Yiyang X, and one of our students was among the 13 Perfect Scorers worldwide on the AMC 10A: Jason W.. 43 middle schoolers and 9 elementary schoolers qualified for the AIME!

Read more at: 2020 AIME Qualifiers Announced — 82 Students Qualified for the AIME

In 2019, we had 71 students who obtained top scores on the AMC 8 contest!

  • 8 of our students were among the top 151 National Winners (Perfect Scorers), including 2 sixth graders.
  • 36 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers, as shown in Table 2.
  • 27 students received National Honor Roll Certificates awarded to top 5% test takers, as shown in Table 3.
  • 71 out of our 73 students (97.3%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2019 AMC 8 Results Just Announced — Eight Students Received Perfect Scores

In 2019, we had 4 students qualified for the USAMO and 4 Students for the USAJMO.

  • Of the 280 USA Math Olympiad national qualifiers, 4 are our students: Luke C., Zipeng L., Sameer P., and Peter P.
  • Of the 235 USA Junior Math Olympiad national qualifiers, 4 are our students: Michael H., Noah W., Holden W., and Isabella Z.

Read more at: 2019 USAMO and USAJMO Qualifiers Announced — Four Students Qualified for the USAMO and Four Students for the USAJMO

In 2019, we had 76 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 22 Perfect Scorers worldwide on the AMC 10A: Noah W.and one of our students were among the 10 Perfect Scorers worldwide on the AMC 12B: Kenneth WVery impressively, 32 middle schoolers and 7 elementary schoolers qualified for the AIME!

In 2018, we had 64 students who obtained top scores on the AMC 8 contest!

  • of our students were among the top 44 National Winners (Perfect Scorers): Eric B., Kevin Y., and Isabella Z.
  • 40 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 21 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 64 out of our 66 students (96.5%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2018 AMC 8 Results Just Announced — Three Students Received Perfect Scores

In 2018, we had 73 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. Two of our students were among the 35 Perfect Scorers worldwide on the AMC 10A: Austen M. and Jason W.  and two of our students were among the 21 Perfect Scorers worldwide on the AMC 12B: Kaan D. and Edward W. Remarkably, 11 middle schoolers and 2 elementary schoolers qualified for the AIME!

In 2017, we had 63 students who earned top scores on the AMC 8 contest!

  • of our students were among the top 75 National Winners (Perfect Scorers).
  • 34 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 22 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 63 out of our 65 students (97%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2017 AMC 8 Results Just Announced — Seven Students Received Perfect Scores

In 2017, we had 61 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 28 Perfect Scorers worldwide on the AMC 10A: Austen M., and two of our students were among the 65 Perfect Scorers worldwide on the AMC 10B: Ashwin A. and Brad Z. Remarkably, eight middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Very impressively, Bryan Z., a 6th grader, gained a score of 132 out of 150 on the AMC 10B.Read more at: 2017 AIME Qualifiers Announced — 61 Students Qualified for the AIME

In 2016, we had 36 students who are qualified to take AIME either through AMC 10A/12A or AMC 10B/12B. One of our students was among the 23 Perfect Scorers worldwide on the AMC 10A: Joel (Junyao) T. Particularly, seven middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Pravalika P., a 6th grader, got a 115.5 out of 150 on the AMC10B, which is very impressive. Read more at: 2016 AIME Qualifiers Announced — 36 Students Qualified for AIME

2011 – 2015: In total, 37 students scored above 120 on the American Mathematics Contest 10 (AMC 10) and qualified for the American Invitational Mathematics Examination (AIME); 26 students scored above 100 on the American Mathematics Contest 12 (AMC 12) and qualified for the American Invitational Mathematics Examination (AIME); 3 students qualified for the USA Mathematical Olympiad (USAMO), the highest level of math competition for high school students in the USA

2011 – 2015: In total, 23 students achieved perfect scores of 28 on the AMC 8

Read more at: Notable Achievements of Our Students

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Our Uniqueness

We have a long history of close collaboration with the MAA‘s American Mathematics Competitions (AMC), which are dedicated to strengthening the mathematical capabilities of our nation’s youth, and are the first of a series of competitions in high school mathematics that determine the United States team for the International Mathematical Olympiad (IMO).

We are only one in the Washington DC metropolitan area to offer elementary, middle, and high-school level competition math courses. Our students have received top scores and awards at prestigious national math competitions.

Great Benefits of Math Competitions

In an increasingly competitive college application pool, the process of mastering math skills through our courses and participating in the American Math Competitions will help students strengthen and diversify their extracurricular activities. These contests can motivate students’ interest and passion in math, and they can discover their talent through solving challenging problems different from those in the school classes. Many top colleges also request AMC scores as part of the college application process. Both MIT and Caltech have entry blanks on their official admission application forms for the applicant to enter their best AMC and AIME scores. Ivy League Colleges, Caltech, and Stanford ask for to the AMC and AIME scores in their Supplement to the Common Application Forms. Your children deserve the chance to list these scores on their applications! Good AMC scores will greatly enhance admission opportunities for students to elite colleges.

Read more:

Contact Information:

Ivy League Education Center
Tel:  301-922-9508     or        240-780-8828
Email:  chiefmathtutor@gmail.com

education priceless treasure

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Click HERE find out more about Math Competitions!sat-logo-3

Click HERE to find out more about SAT Prep!

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education priceless treasure

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2022 AMC 10B/12B Problems and Answers

The 2022 AMC 10B/12B contest will be held on Wednesday, November 16, 2022. We posted the 2022 AMC 10B Problems and Answers, and 2022 AMC 12B Problems and Answers at 8:00 a.m. on November 17, 2022. Your attention would be very much grateful.

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2022 AMC 10A/12A Problems and Answers

The 2022 AMC 10A/12A will be held on Thursday, November 10, 2022. We posted the 2022 AMC 10A Problems and Answers, and 2022 AMC 12A Problems and Answers at 8:00 a.m. on November 11, 2022. Your attention would be very much appreciated.

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Online Intensive AMC 10/12/ARML Prep (for 6th to 12th Graders) Winter Weekend Course (Algebra) Starting Nov. 20

It’s time to prepare for the 2022 AMC contests!  “Chance favors only the prepared mind.” Success is doing ordinary things EXTRAordinarily well!

Purpose: To prepare for the AMC 10/12A —Friday, November 10, 2023 and AMC 10/12B — Thursday, November 16, 2023.

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Course Outline

Winter Session (Algebra)
10 Classes (Eastern Time: 6:00 – 8:00 pm), Total: 20 Hours
11/20, 11/27, 12/4, 12/11, 12/18, 1/8, 1/15, 1/22, 1/29, 2/5

Online Registration is now open! Click HERE to register and pay.

  • This is a live class, not a pre-recorded one. Instructors will ask students questions, and students can also ask questions during the class or email their questions to instructors after class.
  • We record all of our lessons as a big bonus so that our students can watch class videos after class for review and self-study
Tuition (including all materials)
New Student: $900   Buy Now Button
Returning Student: $880   Buy Now Button

Although the last round of this year’s AMC 10/12 will be coming at a close on November 16, 2022, we must prepare in advance for the 2023 AMC 10/12 contests. As the great scientist Louis Pasteur said, “Chance favors only the prepared mind.” Those who strive to prepare early, and work hard are the ones who achieve the best results. The AMC is a complex math competition that requires dedication and focus. Therefore, the earlier our students start preparing, the better their scores will be.

AMC 10-12-New

You are very welcome to sign up for our online course which offers a quick, efficient way for students to interact with teachers over long distance. We use Google Meet to video chat and easily connect with students to teach them our tricks and shortcuts to getting an amazing score on their contests, as well as offer them our guidance and support. Students can ask questions face-to-face, and can complete problems with the supervision of our teachers/coaches. Click HERE to see detailed instruction.

A commitment to the whole course can maximize the benefit of learning all the math ideas, methods, strategies, tactics, skills, and techniques.

  • We will help students gain a deeper understanding of the fundamental math concepts, build a solid foundation in math, and develop the critical thinking and problem-solving skills different from those in the school classes, motivation, and perseverance for reaching their full potential.
  • We will focus on efficient tricks, shortcuts, and strategies to solve competitive math problems, especially those hard problems on the AMC 10/12 and easy problems on the AIME, as well as test-taking tactics.
  • The emphasis of this class will be on systematic, comprehensive, and in-depth problem-solving in algebra, which is extremely common in competitive math, but is not included in school curriculum.
  • We will utilize a highly effective teaching model as described in the article: Small-sized Class Instruction-focused Model.

Instructors:

Contact Information:
Ivy League Education Center
Tel:  301-922-9508     or        240-406-3402
Email:  chiefmathtutor@gmail.com

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Specific Goal: 

To earn a score of 120 or more out of 150 on the American Mathematics Contest 10 (AMC 10), or a score of 100 or more out of 150 on the American Mathematics Contest 12 (AMC 12), and then qualify for the American Invitational Mathematics Examination (AIME), which is used to determine qualification for the United States of America Mathematical Olympiad (USAMO). See for more details: Optimal Strategies to Solve Hard AMC Problems

AMC-General

There are many math competitions in the United States. Of those, only

AMC → AIME → USAMO sequence

would take you to the IMO (International Math Olympiad), the highest level math competition for high school students in the world!

AMC 10-12-New

Click here to read more!

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Who should take this class: 

This class is very appropriate for 7th-12th grade students who are hoping to qualify for the AIME.

Benefits:

  • 10 tutorial handouts (>500 pages) developed by Dr. Henry Wan and 500 new problems similar to AMC 10/12 level from the licensed AMC Database.
  • 2 FREE mock tests that are intended to mimic an actual math competition exam, each of which has 25 questions similar to AMC 10/12 level taken from the licensed AMC Database. These simulated tests help students assess their level of preparation for the Math Competitions. After attempting the test, students get answers, explanations, and a detailed score report and wise performance summary.
  • FREE registration for the AMC 10/12A — Friday, November 10, 2023 and AMC 10/12B — Thursday, November 16, 2023. Please see: The 2023 AMC 10/12 Contests at the Ivy League Center on Nov. 10, 2023, and Nov. 16, 2022

Weekly Homework:

At least 3 hours per week. Problem sets include all problems from 92 past real AMC 10/12 test booklets from 2000-2022, and 500 brand new problems having similar difficulty and style as the real AMC 10/12 problems, extracted from the licensed AMC Database.

The focus will on the final 15 problems on the AMC 10/12, and the first 5 problems on the AIME, as well as those hard problems on the ARML. Note that some hard problems on the recent AMC 10 and 12 are exactly the same as previous ARML Problems.

Read More at:

Each week, we will carefully review and check 2 students’ homework, and correct any mistakes. The next week, we will check another 2 students’ homework, and this will continue on a rotational basis until all students have had their homework checked at least once and the cycle will start again. Based on the work of the 2 students that week, we will provide the those 2 students with individualized proposal and support.

Qualifying AIME

Class Outline:
We will focus on efficient tricks, shortcuts, and strategies to solve AMC problems as well as test-taking tactics. The emphasis of this class will be on systematic, comprehensive, in-depth problem-solving in algebra, which is very common in competitive math. We will also help students develop quick problem solving strategies and effective time management skills.

Class Date Topic
1 11/20, Sun Arithmetic Ratios
2 11/27, Sun Exponentials and Radicals
3 12/4, Sun Algebraic Manipulations
4 12/11, Sun Newly-Defined Functions and Operations
5 12/18 Sun Quadratic Functions
6 1/8, Sun Polynomials
7 1/15, Sun Arithmetic and Geometric Sequences and Series
8 1/22, Sun Recursive Sequences and Telescoping Series
9 1/29, Sun Floor and Ceiling Functions
10 2/5, Sun Binomial and Multinomial Theorems, and Algebraic Methods in Counting and Probability

AMC Logo

Small-sized Class Teaching Model: 

We utilize the highly effective small-sized class teaching model. Smaller classes lead to pupils receiving more individual attention from teachers, and having more active interactions with them. We focus on every individual, not the whole class. Students will thrive from the smaller class sizes that allow them to reach their full potential. Particularly, students can benefit tremendously from high-frequent individualized student-teacher interactions leading to establishment of a stronger foundation for lifelong learning.

Our main purpose is to help our students gain deeper understanding of the fundamental math concepts, build a solid foundation in math, and develop the critical thinking and problem-solving skills that are so valuable to success in any career. We are big believers in the FUNDAMENTALS! Our students will receive the LIFELONG BENEFITS from learning math.

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Regardless of his/her math level, each student will have the opportunity to learn math in a fun, friendly, cooperative, supportive learning environment. The most important thing is to have fun.

Bronze_medal

Our Students

In 2022, we had 3 students qualified for the Math Olympiad Summer ProgramRead more at: Brendon J., Kyle S., and Isabella Z. Qualified for the 2022 Math Olympiad Summer Program

In 2022, we had 1 student competed in International Girls’ Math OlympiadRead more at: sabella Z. Competes in International Girls’ Math Olympiad

In 2022, we had 7 students qualified for the USAMO andstudents for the USAJMO. Read more at: 2022 USAMO and USAJMO Qualifiers Announced — Seven Students Qualified for the USAMO and Seven Students for the USAJMO.

In 2022, we had 88 students who obtained top scores on the AMC 8 contest!

  • 10 of our students were among the top 131 worldwide winners (Perfect Scorers), as shown in Table 1. Click Here see a full list of the 131 worldwide winners.
  • 52 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers. They were among the 1,010 worldwide winners. Click Here see a full list.
  • 26 students received National Honor Roll Certificates awarded to top 5% test takers. They were among the 2,449 worldwide winners. Click Here see a full list.
  • 88 out of our 91 students (96.7%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 022 AMC 8 Results Just Announced — Ten Students Received Perfect Scores

In Fall 2021, we had 93 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 5 Perfect Scorers worldwide on the AMC 10A: Nina L. and one of our students was among the 2 Perfect Scorers worldwide on the AMC 10B: Ming Y. Read more at: 93 Students Qualified for the 2021 Fall AIME and 2 Students Received Perfect Scores on the 2021 Fall AMC 10/12

In 2021, we had 6 students qualified for the USAMO and 6 students for the USAJMO. Read more at: 2021 USAMO and USAJMO Qualifiers Announced — Six Students Qualified for the USAMO and Six Students for the USAJMO

In Spring 2021, we had 91 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. Two of our students was among the 17 Perfect Scorers worldwide on the AMC 12A: Evan L. and Suraj O. and one of our students was among the 27 Perfect Scorers worldwide on the AMC 10A: Xinchen L. Read more at: 91 Students Qualified for the 2021 AIME and 3 Students Received Perfect Scores on the 2021 AMC 10/12

In 2021, we had 8 students who got into the MathCounts state-level top 10. Yunyi L. won 9th Place in the 2021 MathCounts National Competition!

In 2020, we had 79 students who obtained top scores on the AMC 8 contest!

  • 5 of our students were among the top 57 worldwide winners (Perfect Scorers).
  • 49 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 25 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 79 out of our 81 students (97.5%) received National Awards for the AMC 8 from the Mathematical Association of America.

Read more at: 2020 AMC 8 Results Just Announced — Five Students Received Perfect Scores

In 2020, we had 82 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 11 Perfect Scorers worldwide on the AMC 12A: Yiyang X, and one of our students was among the 13 Perfect Scorers worldwide on the AMC 10A: Jason W.. 43 middle schoolers and 9 elementary schoolers qualified for the AIME! Read more at: 2020 AIME Qualifiers Announced — 82 Students Qualified for the AIME

In 2019, we had 71 students who obtained top scores on the AMC 8 contest!

  • 8 of our students were among the top 151 National Winners (Perfect Scorers), including 2 sixth graders.
  • 36 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 27 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 71 out of our 73 students (97.3%) received National Awards for the AMC 8 from the Mathematical Association of America.

Read more at: 2019 AMC 8 Results Just Announced — Eight Students Received Perfect Scores

In 2019, we had 4 Students Qualified for the USAMO and 4 Students for the USJMO.

  • Of the 280 USA Math Olympiad national qualifiers, 4 are our students: Luke C., Zipeng L., Sameer P., and Peter P.
  • Of the 235 USA Junior Math Olympiad national qualifiers, 4 are our students: Michael H., Noah W., Holden W., and Isabella Z.

Read more at: 2019 USAMO and USAJMO Qualifiers Announced — Four Students Qualified for the USAMO and Four Students for the USAJMO

In 2019, we had 76 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 22 Perfect Scorers worldwide on the AMC 10A: Noah W. and one of our students were among the 10 Perfect Scorers worldwide on the AMC 12B: Kenneth WVery impressively, 32 middle schoolers and 7 elementary schoolers qualified for the AIME!

In 2018, we had 64 students who obtained top scores on the AMC 8 contest!

  • of our students were among the top 44 National Winners (Perfect Scorers): Eric B., Kevin Y., and Isabella Z.
  • 40 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 21 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 64 out of our 66 students (96.5%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2018 AMC 8 Results Just Announced — Three Students Received Perfect Scores

In 2018, we had 73 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. Two of our students were among the 35 Perfect Scorers worldwide on the AMC 10A: Austen M. and Jason W.  and two of our students were among the 21 Perfect Scorers worldwide on the AMC 12B: Kaan D. and Edward W. Remarkably, 11 middle schoolers and 2 elementary schoolers qualified for the AIME!

In 2017, we had 63 students who earned top scores on the AMC 8 contest!

  • of our students were among the top 75 National Winners (Perfect Scorers).
  • 34 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 22 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 63 out of our 65 students (97%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2017 AMC 8 Results Just Announced — Seven Students Received Perfect Scores

In 2017, we had 61 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 28 Perfect Scorers worldwide on the AMC 10A: Austen M., and two of our students were among the 65 Perfect Scorers worldwide on the AMC 10B: Ashwin A. and Brad Z. Remarkably, eight middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Very impressively, Bryan Z., a 6th grader, gained a score of 132 out of 150 on the AMC 10B.Read more at: 2017 AIME Qualifiers Announced — 61 Students Qualified for the AIME

In 2016, we had 36 students who are qualified to take AIME either through AMC 10A/12A or AMC 10B/12B. One of our students was among the 23 Perfect Scorers worldwide on the AMC 10A: Joel (Junyao) T. Particularly, seven middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Pravalika P., a 6th grader, got a 115.5 out of 150 on the AMC10B, which is very impressive. Read more at: 2016 AIME Qualifiers Announced — 36 Students Qualified for AIME

2011 – 2015: In total, 37 students scored above 120 on the American Mathematics Contest 10 (AMC 10) and qualified for the American Invitational Mathematics Examination (AIME); 26 students scored above 100 on the American Mathematics Contest 12 (AMC 12) and qualified for the American Invitational Mathematics Examination (AIME); 3 students qualified for the USA Mathematical Olympiad (USAMO), the highest level of math competition for high school students in the USA

2011 – 2015: In total, 23 students achieved perfect scores of 28 on the AMC 8

Read more at: Notable Achievements of Our Students

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Our Uniqueness

We have a long history of close collaboration with the MAA’American Mathematics Competitions (AMC), which are dedicated to strengthening the mathematical capabilities of our nation’s youth, and are the first of a series of competitions in high school mathematics that determine the United States team for the International Mathematical Olympiad (IMO).

We are only one in the Washington DC metropolitan area to offer elementary, middle, and high-school level competition math courses. Our students have received top scores and awards at prestigious national and math competitions.

Great Benefits of Math Competitions

In an increasingly competitive college application pool, the process of mastering math skills through our courses and participating in the American Math Competitions will help students strengthen and diversify their extracurricular activities. These contests can motivate students’ interest and passion in math, and they can discover their talent through solving challenging problems different from those in the school classes. Many top colleges also request AMC scores as part of the college application process. Both MIT and Caltech have entry blanks on their official admission application forms for the applicant to enter their best AMC and AIME scores. Ivy League Colleges and Stanford ask for to the AMC and AIME scores in their Supplement to the Common Application Forms. Your children deserve the chance to list these scores on their applications! Good AMC scores will greatly enhance admission opportunities for students to elite colleges.

Read more at::

education priceless treasure

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Click HERE find out more about Math Competitions!sat-logo-3

Click HERE to find out more about SAT Prep!

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education priceless treasure

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Online Intensive AMC 8/Mathcounts Prep (for 4th to 8th Graders) Winter Weekend Course Starting Nov. 19

Winter is the BEST time to prepare for the AMC 8 and Mathcounts!

The period of time between 4th-8th grade is most critical to the development of students’ mathematical fascinations, interests, and skills!

Winter  Session (Comprehensive Problem-Solving)
9 Classes (Eastern Time: 6:00 – 8:00 pm), Total: 18 Hours
11/19, 11/26, 12/3, 12/10, 12/17, 12/24, 12/31, 1/7, 1/14

Course Outline

Online Registration is now open! Click HERE to register and pay.

Tuition (including all materials)

New Student:    $630   Buy Now Button  

Returning Student:   $620   Buy Now Button  

Click HERE to see payment and refund policy.

You are very welcome to sign up for our online course which offers a quick, efficient way for students to interact with teachers over long distance. We use the Google Meet to video chat and easily connect with students to teach them our tricks and shortcuts to getting an amazing score on their contests, as well as offer them our guidance and support. Students can ask questions face-to-face, and can complete problems with the supervision of our teachers/coaches. Click HERE to see detailed instruction.

commitment to the whole course can maximize the benefit of learning all the math ideas, methods, strategies, tactics, skills, and techniques.

  • This is a live class, not a pre-recorded one. Instructors will ask students questions, and students can also ask questions during the class or email their questions to instructors after class.
  • We record all of our lessons so that our students can watch them after class for review and self-study.

Instructors: Dr. Henry Wan

mathequalsawesomelogo

Purpose: To prepare for math competitions, such as

Contact Information:
Ivy League Education Center
Tel:  301-922-9508
Email:  chiefmathtutor@gmail.com

Math-Competitions

Specific Goal of the 2023 AMC 8:

To become part of the top 5% of scorers on the AMC 8, and then receive National Honor Roll Certificates.

Specific Goal of the 2023 AMC 10:

To earn a score of 90 or more out of 150 on the AMC 10, and then receive National Achievement Honor Roll Certificates.

Specific Goal of the MathCounts:

To become one of the top winners in the individual competition at the chapter level and then advance to the state competition.

AMC-General

There are many math competitions in the United States. Of those, only

AMC → AIME → USAMO sequence

would take you to the IMO (International Math Olympiad), the highest level math competition for high school students in the world!

amc8

Click here to read more!

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Description:
Our curriculum focuses on advancing the mathematical skills of 4th-8th graders to prepare them for math competitions, such as AMC 8, AMC 10, Mathcounts, Math Olympiads for Elementary and Middle Schools (MOEMS), Math Kangaroo, and Math League. A variety of contest questions, including all past official AMC 8 problems, the first 15 problems on each old AMC 10 tests, and MathCounts Competition problems at the school, chapter, state, and national level, are used to teach students strategies to solve problems and help students prepare for the competitions. These problems stimulate their interest and enthusiasm for critical thinking and problem solving, broaden their mathematical intuition, and develop their brainpower. The topics taught in this class are not covered in regular school math classes, allowing our students to stay one step ahead.

Benefits:

Grade Levels: Grades 4-8

AMC Logo

Class Outline:

This class focuses on efficient tricks, shortcuts, and strategies to solve competitive math problems as well as test-taking tactics. The emphasis of this class will be on comprehensively problem-solving, which is the most important to competitive math. In particular, we will help students use mental math for accurately and quickly solving contest questions in their heads. 

Class

Date

Topic

1

11/19, Sat

Plane Geometry

2

11/26, Sat

Solid Geometry

3

12/3, Sat

Sequences and Patterns

4

11/10, Sat

Number Theory

5

11/17, Sat

Counting and Combinatorics

6

12/24, Sat

Probability

7

12/31, Sat

Statistics and Data Analysis

8

1/7, Sat

Arithmetic Ratio and Proportional Reasoning

9

1/14, Sat

Equations and Algebraic Methods

We reserve the right to adjust the teaching content and pace according to the actual performance of students.

Homework:

The focus will be on the final 15 problems on the AMC 8, and the first 15 problems on the AMC 10, as well as those Those medium and hard-level difficulty questions on the MathCounts. We will provide students with 500 brand new problems, extracted from the licensed AMC Database, having similar difficulty and style as the hard real AMC 8 problems.

On average, at least 6 hours per week, as described in the article: Homework assignments are a fundamental part of our courses. Click HERE to see a typical homework sample we developed. Each week, we will carefully review and check 3 students’ homework, and correct any mistakes. The next week, we will check another 3 students’ homework, and this will continue on a rotational basis until all students have had their homework checked at least once and the cycle will start again. Based on the work of the 3 students that week, we will provide the those 3 students with individualized proposal and support. More details can be found in the article: Homework Correction is very Important — We Give an Extensive Correction of the Incorrect Answers of All Homework.

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We have to face the simple truth that to do well on these grueling contests, we will need to practice. Just like it is for sports and music, the key to success is repetition and practice. We strongly believe in effort and the malleability of intelligence. Intelligence can be enhanced through effort. People can develop impressive levels of expertise through hard work and practice. Effort and persistence are the keys to success. Hard work always pays off: practice makes perfect!

All problems from past AMC 8 exams (1985-2022),  AMC 10 exams (2000-2022), and MathCounts (1990–2022) form our “big data” system. Based on artificial intelligence (AI), machine learning, and deep learning, we devised a data mining and predictive analytics tool for math problem similarity searching. Using this powerful tool, we examined the types, styles, frequencies, characteristics, and traits of questions in all these materials, and then completely “decoded” the AMC, and MathCounts. We always completely show all the “secret code” cracked from the above big data to our students, and teach them to totally grasp and “control” the AMC and MathCounts. For all questions on the recent AMC/MathCounts contests, we can find their “ancestors” and “roots” from the old AMC/MathCounts problems. Therefore, the best way to prepare for the contest is to practice by solving old AMC/MathCounts problems.

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Main Purpose:

Our main purpose is to help our students gain deeper understanding of the fundamental math concepts, build a solid foundation in math, and develop the critical thinking and problem-solving skills that are so valuable to success in any career. We are big believers in the FUNDAMENTALS! Our students will receive the LIFELONG BENEFITS from learning math.

Regardless of his/her math level, each student will have the opportunity to learn math in a fun, friendly, cooperative, supportive learning environment. The most important thing is to have fun.

Bronze_medal

Our Students

In 2022, we had 3 students qualified for the Math Olympiad Summer ProgramRead more at: Brendon J., Kyle S., and Isabella Z. Qualified for the 2022 Math Olympiad Summer Program

In 2022, we had 1 student Competes in International Girls’ Math OlympiadRead more at: sabella Z. Competes in International Girls’ Math Olympiad

In 2022, we had 7 students qualified for the USAMO andstudents for the USAJMO. Read more at: 2022 USAMO and USAJMO Qualifiers Announced — Seven Students Qualified for the USAMO and Seven Students for the USAJMO.

In 2022, we had 88 students who obtained top scores on the AMC 8 contest!

  • 10 of our students were among the top 131 worldwide winners (Perfect Scorers), as shown in Table 1. Click Here see a full list of the 131 worldwide winners.
  • 52 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers. They were among the 1,010 worldwide winners. Click Here see a full list.
  • 26 students received National Honor Roll Certificates awarded to top 5% test takers. They were among the 2,449 worldwide winners. Click Here see a full list.
  • 88 out of our 91 students (96.7%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 022 AMC 8 Results Just Announced — Ten Students Received Perfect Scores

In Fall 2021, we had 93 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 5 Perfect Scorers worldwide on the AMC 10A: Nina L. and one of our students was among the 2 Perfect Scorers worldwide on the AMC 10B: Ming Y. Read more at: 93 Students Qualified for the 2021 Fall AIME and 2 Students Received Perfect Scores on the 2021 Fall AMC 10/12

In 2021, we had 6 students qualified for the USAMO and 6 students for the USAJMO. Read more at: 2021 USAMO and USAJMO Qualifiers Announced — Six Students Qualified for the USAMO and Six Students for the USAJMO

In 2021, we had 8 students who got into the MathCounts state-level top 10. Yunyi L. won 9th Place in the 2021 MathCounts National Competition!

In Spring 2021, we had 91 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. Two of our students was among the 17 Perfect Scorers worldwide on the AMC 12A: Evan L. and Suraj O. and one of our students was among the 27 Perfect Scorers worldwide on the AMC 10A: Xinchen L. Read more at: 91 Students Qualified for the 2021 AIME and 3 Students Received Perfect Scores on the 2021 AMC 10/12

In 2020, we had 79 students who obtained top scores on the AMC 8 contest!

  • 5 of our students were among the top 57 worldwide winners (Perfect Scorers).
  • 49 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 25 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 79 out of our 81 students (97.5%) received National Awards for the AMC 8 from the Mathematical Association of America.

Read more at: 2020 AMC 8 Results Just Announced — Five Students Received Perfect Scores

In 2020, we had 82 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 11 Perfect Scorers worldwide on the AMC 12A: Yiyang X, and one of our students was among the 13 Perfect Scorers worldwide on the AMC 10A: Jason W.. 43 middle schoolers and 9 elementary schoolers qualified for the AIME!

In 2019, we had 71 students who obtained top scores on the AMC 8 contest!

  • 8 of our students were among the top 151 National Winners (Perfect Scorers), including 2 sixth graders.
  • 36 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers, as shown in Table 2.
  • 27 students received National Honor Roll Certificates awarded to top 5% test takers, as shown in Table 3.
  • 71 out of our 73 students (97.3%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2019 AMC 8 Results Just Announced — Eight Students Received Perfect Scores

In 2019, we had 4 Students Qualified for the USAMO and 4 Students for the USJMO.

  • Of the 280 USA Math Olympiad national qualifiers, 4 are our students: Luke C., Zipeng L., Sameer P., and Peter P.
  • Of the 235 USA Junior Math Olympiad national qualifiers, 4 are our students: Michael H., Noah W., Holden W., and Isabella Z.

Read more at: 2019 USAMO and USAJMO Qualifiers Announced — Four Students Qualified for the USAMO and Four Students for the USAJMO

In 2019, we had 76 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 22 Perfect Scorers worldwide on the AMC 10A: Noah W. and one of our students were among the 10 Perfect Scorers worldwide on the AMC 12B: Kenneth WVery impressively, 32 middle schoolers and 7 elementary schoolers qualified for the AIME!

In 2018, we had 64 students who obtained top scores on the AMC 8 contest!

  • of our students were among the top 44 National Winners (Perfect Scorers): Eric B., Kevin Y., and Isabella Z.
  • 40 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 21 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 64 out of our 66 students (96.5%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2018 AMC 8 Results Just Announced — Three Students Received Perfect Scores

In 2018, we had 73 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. Two of our students were among the 35 Perfect Scorers worldwide on the AMC 10A: Austen M. and Jason W.  and two of our students were among the 21 Perfect Scorers worldwide on the AMC 12B: Kaan D. and Edward W. Remarkably, 11 middle schoolers and 2 elementary schoolers qualified for the AIME!

In 2017, we had 63 students who earned top scores on the AMC 8 contest!

  • of our students were among the top 75 National Winners (Perfect Scorers).
  • 34 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 22 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 63 out of our 65 students (97%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2017 AMC 8 Results Just Announced — Seven Students Received Perfect Scores

In 2017, we had 61 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 28 Perfect Scorers worldwide on the AMC 10A: Austen M., and two of our students were among the 65 Perfect Scorers worldwide on the AMC 10B: Ashwin A. and Brad Z. Remarkably, eight middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Very impressively, Bryan Z., a 6th grader, gained a score of 132 out of 150 on the AMC 10B.Read more at: 2017 AIME Qualifiers Announced — 61 Students Qualified for the AIME

In 2016, we had 36 students who are qualified to take AIME either through AMC 10A/12A or AMC 10B/12B. One of our students was among the 23 Perfect Scorers worldwide on the AMC 10A: Joel (Junyao) T. Particularly, seven middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Pravalika P., a 6th grader, got a 115.5 out of 150 on the AMC10B, which is very impressive. Read more at: 2016 AIME Qualifiers Announced — 36 Students Qualified for AIME

2011 – 2015: In total, 37 students scored above 120 on the American Mathematics Contest 10 (AMC 10) and qualified for the American Invitational Mathematics Examination (AIME); 26 students scored above 100 on the American Mathematics Contest 12 (AMC 12) and qualified for the American Invitational Mathematics Examination (AIME); 3 students qualified for the USA Mathematical Olympiad (USAMO), the highest level of math competition for high school students in the USA

2011 – 2015: In total, 23 students achieved perfect scores of 28 on the AMC 8

Read more at: Notable Achievements of Our Students

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Our Uniqueness

We have a long history of close collaboration with the MAA’American Mathematics Competitions (AMC), which are dedicated to strengthening the mathematical capabilities of our nation’s youth, and are the first of a series of competitions in high school mathematics that determine the United States team for the International Mathematical Olympiad (IMO).

We are only one in the Washington DC metropolitan area to offer elementary, middle, and high-school level competition math courses. Our students have received top scores and awards at prestigious national and math competitions.

Great Benefits of Math Competitions

In an increasingly competitive college application pool, the process of mastering math skills through our courses and participating in the American Math Competitions will help students strengthen and diversify their extracurricular activities. These contests can motivate students’ interest and passion in math, and they can discover their talent through solving challenging problems different from those in the school classes. Many top colleges also request AMC scores as part of the college application process. Both MIT and Caltech have entry blanks on their official admission application forms for the applicant to enter their best AMC and AIME scores. Ivy League Colleges and Stanford ask for to the AMC and AIME scores in their Supplement to the Common Application Forms. Your children deserve the chance to list these scores on their applications! Good AMC scores will greatly enhance admission opportunities for students to elite colleges.

Read more at:

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Click HERE find out more about Math Competitions!sat-logo-3

Click HERE to find out more about SAT Prep!

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Online Intensive AIME Prep Winter Weekend Course Starting Nov. 20

Winter is the crucial time to develop students’ math skills and prepare for the American Invitational Mathematics Examination!

Winter Session I (Contest Geometry)
6 Classes (EASTERN Time: 3:00 – 5:00 pm),  Total: 12 Hours 
11/20, 11/27, 12/4, 12/11, 12/18, 12/24

Winter Session II (Comprehensive Problem Solving)
6 Classes (EASTERN Time: 3:00 – 5:00 pm),  Total: 12 Hours 
12/31, 1/8, 1/15, 1/22, 1/29, 2/5

Course Outline
Online Registration is now open! Click HERE to register and pay.

  • This is a live class, not a pre-recorded one. Instructors will ask students questions, and students can also ask questions during the class or email their questions to instructors after class.
  • We record all of our lessons as a big bonus so that our students can watch class videos after class for review and self-study.
Tuition (including all materials)
Session I: New Student: $600 Buy Now Button
Returning Student: $590 Buy Now Button
Session II: New Student: $600  Buy Now Button
Returning Student: $590 Buy Now Button
Sessions I & II: New Student: $1,185 Buy Now Button
Returning Student: $1,165 Buy Now Button
Click HERE to see payment and refund policy.

commitment to the whole course can maximize the benefit of learning all the math ideas, methods, strategies, tactics, skills, and techniques.

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This program has been carefully designed for the students who have higher expectation for their American Invitational Mathematics Examination (AIME) scores. While enriching their resume through exciting math competition experience, honing the test skill for AIME becomes even more critical.

AMC-General

The AIME is used to determine qualification for the United States of America Mathematical Olympiad (USAMO). There are many math competitions in the United States. Of those, only

AMC → AIME → USAMO sequence

would take you to the IMO (International Math Olympiad), the highest level math competition for high school students in the world!

You are very welcome to sign up for our online course which offers a quick, efficient way for students to interact with teachers over long distance. We use the Google Meet to video chat and easily connect with students to teach them our tricks and shortcuts to getting an amazing score on their contests, as well as offer them our guidance and support. Students can ask questions face-to-face, and can complete problems with the supervision of our teachers/coaches. Click HERE to see detailed instruction.

Instructors:

Contact Information:
Ivy League Education Center
Tel:  301-922-9508     or        240-780-8828
Email:  chiefmathtutor@gmail.com

Purpose: To prepare for AIME I (Tuesday, February 7, 2023) and AIME II (Wednesday, February 15, 2023)AIME-Logo

  • Improve student scores by working on both fundamental theorems and ideas
  • Develop and foster creative problem solving strategies
  • Make the USA(J)MO!!!

For Whom?
This AIME course is aimed at those students with AMC 10/12 scores of 100+ to students who have scored around 4 on the AIME.

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What?
This class will focus mostly on building strong basics in the five main pillars of Combinatorics, Number Theory, Geometry, Algebra, and Probability. The goal is for students to obtain the mental agility required to tackle these complex problems and hopefully get them within and past range of qualification for the USAMO and USAJMO, or around 9 problems.

How?
Focus on basic concepts and essential knowledge before moving on developing the skills and intuition to find and pursue good lines of attack for complex problems.

Class Outline:
This class focuses on efficient tricks, shortcuts, and strategies to solve AIME problems as well as test-taking tactics. We reserve the right to adjust the teaching content and pace according to the actual performance of students.

Session I (Geometry)

Class Date Topic
1 11/20, Sun Triangle Geometry
2 11/27, Sun Circle Geometry
3 12/4, Sun  Polygon Geometry
4 12/11, Sun Analytical Geometry
5 12/18, Sun Trigonometry Bashing
6 12/24, Sun Spatial Geometry

Session II (Comprehensive Problem Solving)

7 12/31, Sun Using the Advanced Algebra Toolkit to Solve the AIME Problems
8 1/8, Sun Logarithmic and Exponential Functions, Trigonometric Functions, and Complex Numbers
9 1/15, Sun The Art and Craft for Solving AIME Number Theory Problems
10 1/22, Sun  Advanced Topics in Number Theory
11 1/29, Sun Tricks and Shortcuts for Solving AIME Combinatorics Problems
12 2/5, Sun Advanced Topics in Combinatorics

Benefits:

  • 12 tutorial handouts (>480 pages) developed by Dr. Henry Wan and 500 new problems at the AIME level from the licensed AMC Database
  • 2 FREE mock tests that are intended to mimic an actual math competition exam, each of which has 15 questions similar to the AIME level taken from the licensed AMC Database. These simulated tests help students assess their level of preparation for the Math Competitions. After attempting the test, students get answers, explanations, and a detailed score report and wise performance summary.

Homework: At least 2 hour of homework per class. Students are expected to complete all of the previous AIME contests in the past 10 years, which is over 60 hours of practice. Our instructors are open to questions on any previous AIMEs.
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All problems from all of the previous 63 AIME contests (1983-2022) form our “big data” system. We have used data mining and predictive analytics to examine the types and the frequencies of questions in all these materials, and then completely “decoded” the AIME. We will show all the “secret code” cracked from the above big data to students, and teach them to totally grasp and “control” the AIME. For all questions on the recent AIME contests, we can find their “ancestors” and “roots” from the old AIME problems. Therefore, the best way to prepare for the contest is to practice by solving old AIME problems.

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Our Students

In 2022, we had 3 students qualified for the Math Olympiad Summer ProgramRead more at: Brendon J., Kyle S., and Isabella Z. Qualified for the 2022 Math Olympiad Summer Program

In 2022, we had 1 student Competes in International Girls’ Math OlympiadRead more at: sabella Z. Competes in International Girls’ Math Olympiad

In 2022, we had 7 students qualified for the USAMO andstudents for the USAJMO. Read more at: 2022 USAMO and USAJMO Qualifiers Announced — Seven Students Qualified for the USAMO and Seven Students for the USAJMO.

In 2022, we had 88 students who obtained top scores on the AMC 8 contest!

  • 10 of our students were among the top 131 worldwide winners (Perfect Scorers), as shown in Table 1. Click Here see a full list of the 131 worldwide winners.
  • 52 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers. They were among the 1,010 worldwide winners. Click Here see a full list.
  • 26 students received National Honor Roll Certificates awarded to top 5% test takers. They were among the 2,449 worldwide winners. Click Here see a full list.
  • 88 out of our 91 students (96.7%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 022 AMC 8 Results Just Announced — Ten Students Received Perfect Scores

In Fall 2021, we had 93 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 5 Perfect Scorers worldwide on the AMC 10A: Nina L. and one of our students was among the 2 Perfect Scorers worldwide on the AMC 10B: Ming Y. Read more at: 93 Students Qualified for the 2021 Fall AIME and 2 Students Received Perfect Scores on the 2021 Fall AMC 10/12

In 2021, we had 6 students qualified for the USAMO and 6 students for the USAJMO. Read more at: 2021 USAMO and USAJMO Qualifiers Announced — Six Students Qualified for the USAMO and Six Students for the USAJMO

In 2021, we had 8 students who got into the MathCounts state-level top 10. Yunyi L. won 9th Place in the 2021 MathCounts National Competition!

In Spring 2021, we had 91 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. Two of our students was among the 17 Perfect Scorers worldwide on the AMC 12A: Evan L. and Suraj O. and one of our students was among the 27 Perfect Scorers worldwide on the AMC 10A: Xinchen L. Read more at: 91 Students Qualified for the 2021 AIME and 3 Students Received Perfect Scores on the 2021 AMC 10/12

In 2020, we had 79 students who obtained top scores on the AMC 8 contest!

  • 5 of our students were among the top 57 worldwide winners (Perfect Scorers).
  • 49 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 25 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 79 out of our 81 students (97.5%) received National Awards for the AMC 8 from the Mathematical Association of America.

Read more at: 2020 AMC 8 Results Just Announced — Five Students Received Perfect Scores

In 2020, we had 82 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 11 Perfect Scorers worldwide on the AMC 12A: Yiyang X, and one of our students was among the 13 Perfect Scorers worldwide on the AMC 10A: Jason W.. 43 middle schoolers and 9 elementary schoolers qualified for the AIME!

Read more at: 2020 AIME Qualifiers Announced — 82 Students Qualified for the AIME

In 2019, we had 4 Students Qualified for the USAMO and 4 Students for the USAJMO.

  • Of the 280 USA Math Olympiad national qualifiers, 4 are our students: Luke C., Zipeng L., Sameer P., and Peter P.
  • Of the 235 USA Junior Math Olympiad national qualifiers, 4 are our students: Michael H., Noah W., Holden W., and Isabella Z.

Read more at: 2019 USAMO and USAJMO Qualifiers Announced — Four Students Qualified for the USAMO and Four Students for the USAJMO

In 2019, we had 76 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 22 Perfect Scorers worldwide on the AMC 10A: Noah W.and one of our students were among the 10 Perfect Scorers worldwide on the AMC 12B: Kenneth WVery impressively, 32 middle schoolers and 7 elementary schoolers qualified for the AIME!

In 2018, we had 64 students who obtained top scores on the AMC 8 contest!

  • of our students were among the top 44 National Winners (Perfect Scorers): Eric B., Kevin Y., and Isabella Z.
  • 40 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 21 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 64 out of our 66 students (96.5%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2018 AMC 8 Results Just Announced — Three Students Received Perfect Scores

In 2018, we had 73 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. Two of our students were among the 35 Perfect Scorers worldwide on the AMC 10A: Austen M. and Jason W.  and two of our students were among the 21 Perfect Scorers worldwide on the AMC 12B: Kaan D. and Edward W. Remarkably, 11 middle schoolers and 2 elementary schoolers qualified for the AIME!

In 2017, we had 63 students who earned top scores on the AMC 8 contest!

  • of our students were among the top 75 National Winners (Perfect Scorers).
  • 34 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
  • 22 students received National Honor Roll Certificates awarded to top 5% test takers.
  • 63 out of our 65 students (97%) received National Awards for the AMC 8 from the Mathematical Association of America

Read more at: 2017 AMC 8 Results Just Announced — Seven Students Received Perfect Scores

In 2017, we had 61 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 28 Perfect Scorers worldwide on the AMC 10A: Austen M., and two of our students were among the 65 Perfect Scorers worldwide on the AMC 10B: Ashwin A. and Brad Z. Remarkably, eight middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Very impressively, Bryan Z., a 6th grader, gained a score of 132 out of 150 on the AMC 10B.Read more at: 2017 AIME Qualifiers Announced — 61 Students Qualified for the AIME

In 2016, we had 36 students who are qualified to take AIME either through AMC 10A/12A or AMC 10B/12B. One of our students was among the 23 Perfect Scorers worldwide on the AMC 10A: Joel (Junyao) T. Particularly, seven middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Pravalika P., a 6th grader, got a 115.5 out of 150 on the AMC10B, which is very impressive. Read more at: 2016 AIME Qualifiers Announced — 36 Students Qualified for AIME

2011 – 2015: In total, 37 students scored above 120 on the American Mathematics Contest 10 (AMC 10) and qualified for the American Invitational Mathematics Examination (AIME); 26 students scored above 100 on the American Mathematics Contest 12 (AMC 12) and qualified for the American Invitational Mathematics Examination (AIME); 3 students qualified for the USA Mathematical Olympiad (USAMO), the highest level of math competition for high school students in the USA

2011 – 2015: In total, 23 students achieved perfect scores of 28 on the AMC 8

Read more at: Notable Achievements of Our Students

AAEAAQAAAAAAAAKeAAAAJDkzYTk2ZjE5LTk1YWQtNDBkNy1hZDhjLTVjOTA2YWQ2NmQ2Mw

Our Uniqueness

We have a long history of close collaboration with the MAA‘s American Mathematics Competitions (AMC), which are dedicated to strengthening the mathematical capabilities of our nation’s youth, and are the first of a series of competitions in high school mathematics that determine the United States team for the International Mathematical Olympiad (IMO).

We are only one in the Washington DC metropolitan area to offer elementary, middle, and high-school level competition math courses. Our students have received top scores and awards at prestigious national and math competitions.

We have extracted 5,000 brand new problems at the level of the AIME from the licensed AMC Database. In addition, we have also collected all AMC8/10/12 and AIME Official Solutions as shown in the article “American Mathematics Competitions (AMC) Materials.” All these materials have formed a golden resource for our students, who are the ultimate beneficiaries.

2014124135627709

Click HERE find out more about Math Competitions!sat-logo-3

Click HERE to find out more about SAT Prep!

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education priceless treasure

How to Learn Math

You can learn math both inside and outside of the classroom, and it doesn’t have to be stressful or overwhelming! Once you have a good grasp of the basics, learning the more complex stuff will feel a lot easier. This article will teach you those basics (addition, subtraction, multiplication, and division) and also give you strategies you can use in and out of the classroom to help you better learn math.

Part 1

Keys to Being a Good Math Student

Step 1 Show up for class.
  • Come to class on time. In fact, come a little early and open your notebook to the right place, open your textbook and take out your calculator so that you’re ready to start when your teacher is ready to start.
  • Only skip class if you are sick. When you do miss class, talk to a classmate to find out what the teacher talked about and what homework was assigned.
Step 2 Work along with your teacher.
 
 
If your teacher works problems at the front of your class, then work along with the teacher in your notebook.
  • Make sure that your notes are clear, easy to read and cover all of the steps you need to solve the problems.[2] Don’t just write down the problems. Also write down anything that the teacher says that increases your understanding of the concepts.
  • Work any sample problems that your teacher posts for you to do. When the teacher walks around the classroom as you work, answer questions.
  • Participate while the teacher is working a problem. Don’t wait for your teacher to call on you. Volunteer to answer when you know the answer, and raise your hand to ask questions when you’re unsure of what’s being taught.
Step 3 Do your homework the same day as it's assigned.
 
 
When you do the homework the same day, the concepts are fresh on your mind. Sometimes, finishing your homework the same day isn’t possible. Just make sure that your homework is complete before you go to class.[3]
 
 
Step 4 Make an effort outside of class if you need help.
[4] 
 
Go to your teacher during his or her free period or during office hours.
  • If you have a Math Center at your school, then find out the hours that it’s open and go get some help.
  • Join a study group.[5] Good study groups usually contain 4 or 5 people at a good mix of ability levels. If you’re a “C” student in math, then join a group that has 2 or 3 “A” or “B” students so that you can raise your level. Avoid joining a group full of students whose grades are lower than yours.
  • If you’re still struggling, consider hiring a tutor. They’ll address the areas you’re having trouble with and help you build a solid foundation in math.[6]

Part 2

Learning Math in School

Step 1 Start with arithmetic.
 
 
In most schools, students work on arithmetic during the elementary grades. Arithmetic includes the fundamentals of addition, subtraction, multiplication and division.[7]
  • Work on drills. Doing a lot of arithmetic problems again and again is the best way to get the fundamentals down pat. Look for software that will give you lots of different math problems to work on. Also, look for timed drills to increase your speed.
  • Repetition is the basis of math. The concept has to be not only learned, but put to work for you to remember it!
  • You can also find arithmetic drills online, and you can download arithmetic apps onto your mobile device.
Step 2 Progress to pre-algebra.
 
 
This course will provide the building blocks that you’ll need to solve algebra problems later on.[8]
  • Learn about fractions and decimals. You’ll learn to add, subtract, multiply and divide both fractions and decimals. Regarding fractions, you’ll learn how to reduce fractions and interpret mixed numbers. Regarding decimals, you’ll understand place value, and you’ll be able to use decimals in word problems.
  • Study ratios, proportions and percentages. These concepts will help you to learn about making comparisons.
  • Solve squares and square roots. When you’ve mastered this topic, you’ll have perfect squares of many numbers memorized. You’ll also be able to work with equations containing square roots.
  • Introduce yourself to basic geometry. You’ll learn all of the shapes as well as 3D concepts. You’ll also learn concepts like area, perimeter, volume and surface area, as well as information about parallel and perpendicular lines and angles.
  • Understand some basic statistics. In pre-algebra, your introduction to statistics mostly includes visuals like graphs, scatter plots, stem-and-leaf plots and histograms.
  • Learn algebra basics. These will include concepts like solving simple equations containing variables, learning about properties like the distributive property, graphing simple equations and solving inequalities.

Step 3 Advance to Algebra I.
 
 
In your first year of algebra, you will learn about the basic symbols involved in algebra. You’ll also learn to:[9]
  • Solve linear equations and inequalities that contain 1-2 variables. You’ll learn how to solve these problems not only on paper, but sometimes on a calculator as well.
  • Tackle word problems. You’ll be surprised how many everyday problems that you’ll face in your future involve the ability to solve algebraic word problems. For example, you’ll use algebra to figure out the interest rate that you earn on your bank account or on your investments. You can also use algebra to figure out how long you’ll have to travel based on the speed of your car.
  • Work with exponents. When you start solving equations with polynomials (expressions containing both numbers and variables), you’ll have to understand how to use exponents. This may also include working with scientific notation. Once you have exponents down, you can learn to add, subtract, multiply and divide polynomial expressions.
  • Understand functions and graphs. In algebra, you’ll really get into graphic equations. You’ll learn how to calculate the slope of a line, how to put equations into point-slope form, and how to calculate the x- and y-intercepts of a line using slope-intercept form.
  • Figure out systems of equations. Sometimes, you’re given 2 separate equations with both x and y variables, and you have to solve for x or y for both equations. Fortunately, you’ll learn many tricks for solving these equation including graphing, substitution and addition.

Step 4 Get into geometry.
 
 
In geometry, you’ll learn about the properties of lines, segments, angles and shapes.[10]
  • You’ll memorize a number of theorems and corollaries that will help you to understand the rules of geometry.
  • You’ll learn how to calculate the area of a circle, how to use the Pythagorean theorem and how to figure out relationships between angles and sides of special triangles.
  • You’ll see a lot of geometry on future standardized tests like the SAT, the ACT and the GRE.
Step 5 Take on Algebra II.
 
 
Algebra II builds on the concepts that you learned in Algebra I but adds more complex topics involving more complex non-linear functions and matrices.[11]
 
Step 6 Tackle trigonometry.
 You know the words of trig: sine, cosine, tangent, etc. Trigonometry will teach you many practical ways to calculate angles and lengths of lines, and these skills will be invaluable for people who go into construction, architecture, engineering or surveying.[12]
 
Step 7 Count on some calculus.
 Calculus may sound intimidating, but it’s an amazing tool chest for understanding both the behavior of numbers and the world around you.[13]
  • Calculus will teach you about functions and about limits. You’ll see the behavior or a number of useful functions including e^x and logarithmic functions.
  • You’ll also learn how to calculate and work with derivatives. A first derivative gives you information based on the slope of a tangent line to an equation. For instance, a derivative tells you the rate at which something is changing in a non-linear situation. A second derivative will tell you whether a function is increasing or decreasing along a certain interval so that you can determine the concavity of a function.
  • Integrals will teach you how to calculate the area beneath a curve as well as volume.
  • High school calculus usually ends with sequences and series. Although students won’t see many applications for series, they are important to people who go on to study differential equations.
  • Calculus is still only the beginning for some. If you are considering a career with a high involvement of math and science, like an engineer, try going a bit farther![14]
 

The Heart of Mathematics: Beauty, Exactness, Simplicity, and Crazy Ideas

Israel Gelfand

The Unity of Mathematics

“The Unity of Mathematics” was an International Conference in honor of the 90th Birthday of Israel M. Gelfand. It was held in Cambridge, MA on August 31st to September 4th, 2003.

Below are his conference talk and his dinner talk (given at the conference dinner at Royal East Restaurant).

MATHEMATICS AS AN ADEQUATE LANGUAGE

(a few remarks)

PDF of the full talkINTRODUCTION

This conference is called The Unity of Mathematics. I would like to make a few remarks on this wonderful theme.

I do not consider myself a prophet. I am simply a student. All my life I have been learning from great mathematicians such as Euler and Gauss, from my older and younger colleagues, from my friends and collaborators, and most importantly from my students. This is my way to continue working.

Many people consider mathematics to be a boring and formal science. However, any really good work in mathematics always has in it: beauty, simplicity, exactness, and crazy ideas. This is a strange combination. I understood earlier that this combination is essential on the example of classical music and poetry. But it is also typical in mathematics. Perhaps it is not by chance that many mathematicians enjoy serious music.

This combination of beauty, simplicity, exactness, and crazy ideas is, I think, common to both mathematics and music. When we think about music we do not divide it into specific areas as we often do in mathematics. If we ask a composer what is his profession, he will answer, “I am a composer.” He is unlikely to answer, “I am a composer of quartets.” Maybe this is the reason why when I am asked what kind of mathematics I do, I just answer, “I am a mathematician.”

I was lucky to meet the great Paul Dirac, with whom I spent a few days in Hungary. I learned a lot from him.

In the 1930’s, a young physicist, Pauli, wrote one of the best books on quantum mechanics. In the last chapter of this book, Pauli discusses the Dirac equations. He writes the Dirac equations have weak points because they yield improbable and even crazy conclusions:

  1. These equations assume that, besides an electron, there exists a positively charged particle, the positron, which no one ever observed.
  2. Moreover, the electron behaves strangely upon meeting the positron. The two annihilate each other and form two photons.
    And what is completely crazy:
  3. Two photons can turn into an electron-positron pair.

Pauli writes that despite this, the Dirac equations are quite interesting and especially the Dirac matrices deserve attention.

I asked Dirac,
“Paul, why, in spite of these comments, did you not abandon your equations and continue to pursue your results?”

“Because they are beautiful.”

Now there is a radical perestroika of the fundamental language of mathematics. I will talk about this later. During this time, it is especially important to remember the unity of mathematics, to remember its beauty, simplicity, exactness and crazy ideas. I want to remind you that when the style of music changed in the 20th century many people said that the modern music lacked harmony, did not follow standard rules, had dissonances, and so on. However, Shoenberg, Stravinsky, Shostakovich and Schnitke were as exact in their music as Bach, Mozart and Beethoven.

read the full talk

DINNER TALK OF ISRAEL GELFAND

(given at the conference dinner at Royal East Restaurant on September 3, 2003)

It is a real pleasure to see all of you. I was asked many questions. I will try to answer some of them.

  • The first question is: Why at my age I can work in mathematics?
  • The second: What we must do in mathematics?
  • And the third: What is the future of mathematics?

I think these questions are too specific. I will instead try to answer my own question:

  • What is mathematics? (Laughter)

Let us begin with the last question: What is mathematics?

From my point of view, mathematics is a part of our culture like music, poetry and philosophy. I talked about this in my lecture at the conference.

There, I have mentioned the closeness between the style of mathematics and the style of classical music or poetry. I was happy to find the following four common features: first — beauty, second — simplicity, third — exactness, fourth — crazy ideas. The combination of these four things: beauty, exactness, simplicity and crazy ideas is just the heart of mathematics, the heart of classical music. Classical music is not only the music of Mozart, or Bach, or Beethoven. It is also the music of Shostakovich, Schnitke, Shoenberg (the last one I understand less). All this is classical music. And I think, that all these four features are always present in it. For this reason, as I explained in my talk, it is not by chance that mathematicians like classical music. They like it because it has the same style of psychological organization.

There is also another side of the similarity between mathematics and classical music, poetry, and so on. These are languages to understand many things. For example, in my lecture I discussed a question which I will not answer now, but I have the answer: Why did great Greek philosophers study geometry? They were philosophers. They learned geometry as philosophy. Great geometers followed and follow the same tradition — to narrow the gap between vision and reasoning. For example, the works of Euclid summed up this direction in his time. But this is another topic.

An important side of mathematics is that it is an adequate language for different areas: physics, engineering, biology. Here, the most important word is adequate language. We have adequate and nonadequate languages. I can give you examples of adequate and nonadequate languages. For example, to use quantum mechanics in biology is not an adequate language, but to use mathematics in studying gene sequences is an adequate language. Mathematical language helps to organize a lot of things. But this is a serious issue, and I will not go into details.

Why this issue is important now? It is important because we have a “perestroika” in our time. We have computers which can do everything. We are not obliged to be bound by two operations — addition and multiplication. We also have a lot of other tools. I am sure that in 10 to 15 years mathematics will be absolutely different from what it was before.

The next question was: How can I work at my age? The answer is very simple. I am not a great mathematician. I speak seriously. I am just a student all my life. From the very beginning of my life I was trying to learn. And for example now, when listening to the talks and reading notes of this conference, I discover how much I still do not know and have to learn. Therefore, I am always learning. In this sense I am a student. Never a “Fuhrer”.

I would like to mention my teachers. I cannot explain who all my teachers were because there were too many of them. When I was young, approximately 15-16 years old, I began tutoring in mathematics. I did not have the formal education, I never finished any university, I “jumped” through this. At the age of 19, I became a graduate student, and I learned from my older colleagues.

At that time one of the most important teachers for me was Schnirelman, a genius mathematician, who died young. Then there were Kolmogorov, Lavrentiev, Plesner, Petrovsky, Pontriagin, Vinogradov, Lusternik. All of them were different. Some of them I liked, some of them — I understood how good they were but I did not agree with their, let us say softly, point of view. (Laughter) But they were great mathematicians. I am very grateful to all of them, and I learned a lot from them.

At the end, I want to give you an example of a short statement, not in mathematics, which combines simplicity, exactness, and other features I mentioned. This is a statement of a Nobel Prize winner, Isaac Bashevis Singer: “There will be no justice as long as man will stand with a knife or with a gun and destroy those who are weaker than he is.”

Text written by Tatiana V. Gelfand.

taken from the Unity of Mathematics website.

数学大师华罗庚的数学教育思想

我虽然从学生时代起就多次见过华罗庚先生,但并无机会当面聆听他的谈话。这里提到的华先生的数学教育思想,都已经公开发表。这些耳熟能详的名言,已经深刻刻印在中国数学教育的历史上。我只是千千万万受益者中的普通一员。

20世纪中国数学教育深受两位数学大家的影响。一位是苏步青先生,他亲临中小学第一线,主编教材,为中学数学教师授课,设立苏步青数学教育奖,嘉惠后人。另一位便是华罗庚先生,他并没有关于中小学数学教育的直接论述,而是通过本人的传奇故事,怎样学习数学的谈话,以及倡导数学竞赛、撰写科普文章、使用杨辉三角等民族化数学命名等途径,深刻地影响了中国数学教育的进程。

我觉得在他的许多论述中,有四句话最有代表性,就是“熟能生巧”、“厚薄读书法”、“数形结合”以及“弄斧到班门”。这四句话, 科学地、辩证地处理了“基础与创新”新关系。时至今日,重温华先生的这些名言,仍然具有巨大的现实意义。

从熟能生巧说起

“熟能生巧”是中国的教育古训。不过,时下的教育理念,却完全摒弃了这一观点。这句话翻译成英是“Practice  make  perfect”,国外的教育家大多不赞成。国内的教育家也认为“熟能生巧”几近于“死记硬背”,将它丢在一边不予理睬。

那么我们看看华先生是怎么说的。华先生在“聪明在于学习,天才由于积累” [1]一文中认为:向科学进军必须“脚踏实地,循序前进,打好基础”。接着,有一段非常精辟的论述:

“我想顺便和大家谈谈两个方法问题。我认为,方法中最主要的一个问题,就是‘熟能生巧’。 搞任何东西都要熟,熟了才能有所发明和发现。但是我这里所说的熟,并不是要大家死背定律和公式,或死记人家现成的结论。不,熟的不一定会背,背不一定就熟。如果有人拿过去读过的书来念十遍、二十遍,却不能深刻地理解和运用,那我说这不叫熟,这是念经,熟就是要掌握你所研究的学科的主要环节,要懂得前人是怎样思考和发明这些东西的。”

古老的教育箴言“熟能生巧”,经过华先生一解释,将它和死记硬背区分开来,就可以成为数学教育的一个基本出发点。我们在中小学教学中, 对一些基本的内容,必须做到“熟能生巧”。

一个有意思的事情是,数学大师陈省身,同样在数学教育中倡导“熟能生巧”。2004年12 月7日,中央电视台《东方之子》播出对陈省身“几何人生”的采访,记者李小萌评论说:“面对成功, 陈省身说他只是熟能生巧而已。”接着,陈先生说:“ 所有这些东西一定要做得多了,比较熟练了,对于它的奥妙有了解,就有意思。所以比方说在厨房里头炒菜,你做个菜,炒个木须肉,这个菜炒了几十年以后,是了解得比较多,很清楚,数学也这样子,有些工作一定要重复,才能够精,才能够创新,才能做新的东西。”

两位大师的见解如此相同,我们当知“熟能生巧”对创新的重要性了。现如今,讲创新的言论遍地皆是,却对“熟能生巧”讳莫如深,实在不是一种好的倾向。

读书要“从薄到厚”,然后“从厚到薄”

如果说“熟能生巧”,还是借用古人的话来谈打好基础的重要性,那么华先生关于“厚薄读书法”则是关于“基础与创新”的全新创见。1962年,华先生在《中国青年》发表《学与识》的文章,根据他多年积累的治学经验,明确地提出了“由薄到厚”和“由厚到薄”的 两阶段读书法。这一充满个性的语言,立即传遍大江南北,现已成为中国数学教育理论的宝贵遗产,至今我还清楚地记得当初读到这篇文章时的心灵震撼。

做研究要打好基础,人所共知;做学问要弄懂弄通,人所共求。但究竟怎样算打好基础了?什么是把知识“弄懂”了?却难以说得清楚,心理学上有种种界定,也是云里雾里。华先生的这一“厚薄读书法”,就把这层窗户纸捅破了。华先生说:

“有人说,基础、基础,何时是了?天天打基础,何时是够?据我看来,要真正打好基础,有两个必经的过程:即‘由薄到厚’和‘由厚到薄的过程。‘由薄到厚’是学习、接受的过程,‘由厚到薄’是消化、提炼的过程。

经过‘由薄到厚”和‘由厚到薄’的过程,对所学的东西做到懂,彻底懂,经过消化的懂,我们的基础就算是真正的打好了,有了这个基础,以后学习就可以大大加快,这个过程也体现了学习和科学研究上循序渐进的规律。”

打基础与创新的关系,是当前数学教育一个十分重大的课题。国家需要创新人才,但是中小学教育是基础教育。基础教育要打基础,天经地义。在基础教育阶段,学生还没有能力做到真正的“创新”。那么,基础教育应该怎么做呢?按照华先生的意见,就应该是按照“厚薄读书法”的含义去做。第一步是让学生吸取知识,反复练习,广泛涉猎,加进自己的理解,把书读“厚”,然后是第二步,帮助学生通过反复咀嚼,消化吸收,自己总结经验,包括数学问题解决的经验,能够提纲挈领,如数家珍似的把知识融会贯通。

这样做,既是打基础,又是创新。中小学生能够做到这样,将来的发展前途必然广阔,创新的机会大大增多。这对当前的某些假“创新”之名,行功利之实的浮躁风气,实在是一剂令人清醒的良药。

这里,我们也不妨引用吴文俊先生的话加以佐证。吴先生说[2]:

“关于创新的含义,牛顿曾说,他之所以能够获得众多成就,是因为他站在过去巨人的肩膀上,得以居高而望远。我国也有类似的说法,叫推陈出新。我非常赞成和推崇‘推陈出新’这句话。有了陈才有新,不能都讲新,没有陈哪来新!创新是要有基础的,只有了解得透,有较宽的知识面,才会有洞见,才有底气,才可能创新!其实新和旧之间是有辩证的内在联系的。所谓陈,包括国内外古往今来科技方面所积累的许多先进成果。我们应该认真学习,有分析有批判地充分吸收。”

基础教育的创新,不能强求学生去做一些他们不喜欢的所谓“探究”工作。学生的创新,主要在于把“陈”了解得透,把“厚”书读“薄”。

数学见识之一:“数形结合百般好”

华先生的数学教育名言中,以“数形结合”一词流传最广。你走到任何一所学校,问任何一位数学老师,没有不知道“数形结合”的。我没有考证,在华先生之前,是否有人提出过“数形结合”,但是可以肯定,“数形结合”能够走进中国每一位数学教师的心田,是从华罗庚先生的一首教学诗开始的:

数与形,本是相倚依,焉能分作两边飞。
数缺形时少直觉,形少数时难入微。
数形结合百般好,隔裂分家万事非。
切莫忘,几何代数统一体,永远联系切莫离。

华先生在谈到“知识、学识、见识”[3]时说道:“知了,学了,见了,这还不够,还要有个提高过程,即识的过程。因为我们要认识事物的本质,达到灵活运用,变为自己的东西,就必须知而识之,学而识之,见而识之,不断提高。”什么是“识”?我想“数形结合”就是一个范例。

清代袁枚说过“学如箭簇,才如弓弩,识以领之,方能中鹊”。说得很对。我们的数学教育理论中,强调不能只学知识,还要培养能力。这当然对。但是,你有能力却没有见识,把箭乱放一通,怎能打中目标?

华先生提倡“识”,对数学教育的启示是,需要培养数学意识,用你的能力,把箭发向那个需要射中的目标。如何培养学生的“识”,是一个值得研究的课题。

“弄斧班门”

最后,我们要提到华先生关于“弄斧必到班门”的名言。真正的“弄斧班门”,需要勇气、自信、胆量和能力,不是每个人都能达到的。但是作为期望的目标,还是要有一点精神,正如“不想做元帅的士兵不是好士兵”的说法那样。值得提到的是,华罗庚先生在1980年应邀在国际数学教育大会上作大会发言,题目是“在中华人民共和国普及数学方法的若干个人体会”[4]。这几乎是一个数学教育工作者能够得到的最高荣誉。

华先生离开我们30多年了。但是他的传奇故事,奋斗精神,爱国情怀,以及有关数学教育的思想等,一定会在未来岁月发挥更大影响。

作者:张奠宙
来源:《数学教学》