
## Overview

The latest generation of web technologies have made it possible for us to offer real-time online classes that are similar to our <a href="/localclasses">local classes</a>. Students anywhere in the world can now sign up for our classes and receive the same personalized attention that they would receive if they lived near us. Our <a href="/methodology">teaching methodology and curriculum</a> are the same online and offline, but to ensure that they run smoothly, our online classes have a maximum enrollment of 5 students. We make exceptions to this rule in special circumstances, like when we run online enrichment activities and training sessions. If you would like to enroll more than 5 students in a class please <a href="/contact">contact us</a>.

Just like in our offline <a href="/localclasses">local classes</a>, our small class size enables us to address students’ individual concerns. In particular, we carefully prepare for every session, which is customized to meet the needs of each student. In addition we help each of our students create a custom online portfolio, which showcases the student&#8217;s math and computer science projects.

## How it Works

The logistics of online classes are similar to those of regular classes. The instructor writes on a shared virtual whiteboard where students can also show their work that everyone else in the class can see. This is analogous to students coming up to a whiteboard in a regular class and presenting their ideas and problem solutions to the whole class. All classes use audio so that students and instructors can hear each other and many classes use video as well, but no special equipment is required besides a computer (or tablet) and a high speed internet connection. Just as in our in-person classes, one instructor is assigned per class and teaches it for its entire duration. If the instructor’s schedule permits, classes can be rescheduled to accommodate students’ needs and we don’t require a long-term commitment or up-front payment for multiple classes.

## Registration

After you sign up for a class, you will receive an email from the instructor of the class explaining the logistics in more detail and how payments should be made. If the the type of class you request is not currently available, you will be given other options and can discuss them with the instructor. To sign up or learn more about online classes, please <a href="/contact">contact us</a>.

## Tuition

After the first session of a class (which is free), payment should be made either for the following two or four classes depending on the particular type of class. Payment details will be provided in the instructor’s introductory email, and a payment schedule can be set up that is convenient for everyone in the class.
<div class="note"><strong>Note:</strong> The first session of any new class is free. If a student drops or joins a class, the rate per student increases or decreases based on the new total number of students in the class.</div>

<div class="responsive-table">
<table id="lessontypes">
<thead>
<tr>
<th>Number of Students</th>
<th>Hours per Class</th>
<th>Hourly Rate per Student</th>
</tr>
</thead>
<tbody>
<tr>
<td>5 or more</td>
<td>2</td>
<td>$40</td>
</tr>
<tr>
<td>4</td>
<td>2</td>
<td>$45</td>
</tr>
<tr>
<td>3</td>
<td>2</td>
<td>$50</td>
</tr>
<tr>
<td>2</td>
<td>2</td>
<td>$65</td>
</tr>
<tr>
<td>1</td>
<td>2</td>
<td>$120</td>
</tr>
</tbody>
</table>
</div>

## Scheduling

Scheduling is flexible but depends on instructor and student availability. If a third or more of the students in a class cannot attend a session, it must be rescheduled so that the class stays on track.


Online Classes


We appreciate contributions of any size. Any funds that we raise help us keep the <a href="/mathcircle">math circle</a> running and help create new low-cost or free math and computer science programs.

To donate, make your check payable to **Gentle Knowledge** and mail it to:

**Gentle Knowledge**

65 Beecher Place

Newton, MA 02459

If you are interested in volunteering or partnering with us please <a href="/contact">contact us</a>.


Donations


#### What is Gentle Knowledge?

Gentle Knowledge is a mathematics program for school-aged kids. We provide a complete mathematics education for homeschooled kids, as well as for kids who attend school. For students who want to go beyond a standard mathematics curriculum, we provide various enrichment opportunities. In addition to mathematics, we offer computer science and programming classes.

#### How is Gentle Knowledge different from other math programs?

The single biggest differences between what we do and what most other programs do is our focus on problem solving. The standard mathematics curriculum is devoted almost exclusively to an ad hoc collection of mechanical procedures that students need to memorize in order to solve standard exercises. Most textbooks and math programs teach students by presenting a step-by-step solution to a prototypical exercise and then asking students to repeat those steps in dozens of similar exercises. This type of rote learning has some short-term benefits, but it does not teach students how to think. In contrast, our approach puts thought-provoking problems center stage. These problems are nonstandard because they don’t follow a predefined template, and because they require students to uncover and explore new mathematical topics by thinking, not by mindlessly plugging numbers into formulas. Beyond covering all of the same topics covered in the standard mathematics curriculum, we introduce interesting and nonstandard concepts that are usually left out, all while students are thinking, not simply following directions.

#### Can you give an example that illustrates the difference between problems and exercises?

A typical textbook exercise involving averages is: 

>Find the average of the numbers 12, 35, 67, 80, and 95.

This exercises requires nothing except the straightforward application of the textbook definition of the average of a set of numbers (adding the 5 numbers and then dividing the sum by 5). In contrast, a sample Gentle Knowledge problem involving averages is: 

>Some number of scientists moved from country A to country B. As a result of this move, could the average IQ have increased in both countries?

At first glance, it seems that the answer is no. Students’ everyday experience with conservation laws (e.g. if water is poured from one glass into another, one glass gains water and the other loses water) tells them that the same principle should apply to averages. After some thought, students see that if the average IQ in country A (call it AIQ) is greater than the average IQ in country B (call it BIQ), then, if the IQs of the scientists who move from A to B are between BIQ and AIQ, the average IQs of both countries will increase. This careful analysis not only reveals a lot more about averages than the textbook exercise, it makes students feel a lot more accomplished because they have to think, not just do trivial arithmetic.

#### How will my child learn basic math skills if you focus so much on problem solving?

We do not believe that achieving computational fluency (the ability to do basic arithmetic and algebra) and learning how to solve difficult problems are mutually exclusive goals. Fundamental math skills are a vital first step, and students need to practice them even while working on interesting and challenging problems. For this reason, we assign practice exercises as part of every homework assignment.

#### I am worried about college admissions and standardized tests like the SATs and AP exams. Will you prepare my child for these future challenges?

The short answer is yes. We are not a test preparation service, in that we do not “teach to the test,” but we do something better. In our experience the most difficult part of a test like the SAT is the set of problems that do not exactly follow a standard template. By focusing on nonstandard problems that require thinking, we prepare students for the hardest problems on any standardized tests. Beyond classwork and homework, we offer students opportunities to work on independent projects that can play a major role in the college admissions process. We help motivated students find projects that interest them, and we either supervise them directly, or we connect them with mentors working at top universities and high tech companies. We also write recommendation letters and provide college counseling services.

#### What can you offer children who are ahead of their peers, and how are you different from other advanced math programs?

Unlike math programs that specialize in working with only the most mathematically mature students, we are open to everyone. Most students will find something that is challenging in what we do. For extra ambitious students who want to prepare for math olympiads, or who have math backgrounds that are exceptionally advanced, we offer specialized classes and private tutoring.

#### What does computer science/programming have to do with math?

Many computer science concepts are part of mathematics, and programming is, in many ways, the new literacy. Writing computer programs requires serious problem solving, gives students their first real taste of engineering, and most importantly, provides endless opportunities for rewarding mathematical exploration in a new medium.

#### Do you assign homework and give tests, and do you have any other requirements?

We don’t give tests, but we do assign homework after every class. Although we don’t expect students to solve all of the problems, we expect them to devote some serious thought to each problem and to do all of the exercises. Even partial solutions or rough ideas are an important part of the learning process. Our goal is to gently nudge students to the limits of their abilities, and we would rather challenge them, than give them a false sense of accomplishment.

#### Who are the people behind Gentle Knowledge?

Gentle Knowledge instructors are mathematicians and educators, all of whom have graduate degrees in mathematics and years of experience teaching students at all levels. Several of our team members are celebrities in the world of math education and have made major contributions to both mathematics and education. Learn more about them <a href="/team">here</a>.


Frequently Asked Questions

Students rarely experience the elegance and power of mathematics because they have few opportunities to do <a href="https://www.maa.org/external_archive/devlin/devlin_03_08.html" target="_blank">real mathematics</a>, which requires solving nonstandard and open-ended problems, not just mindlessly memorizing and repeating a series of steps for solving uninspiring cookie-cutter exercises. Our students realize their mathematical potential by solving deep problems that come out of a one-hundred-year-old <a href="https://en.wikipedia.org/wiki/Math_circle" target="_blank">math circles</a> tradition. They also study computer science and learn how to program, applying their newly gained knowledge and skills to <a href="/student-projects/congress-treaties" target="_blank">projects</a> that <a href="https://labs.loc.gov/work/experiments/congressionalchallenge/" target="_blank">win competitions</a>. All of this is made possible by our team of world-class educators and mathematicians.


An Ambitious Math and Computer Science Program that Challenges and Inspires

If you don't live near us, you can join one of our real-time online class. Our small class size ensures that students can effectively engage with each other and the instructor.


/onlineclasses

We offer private, semi-private, and small group classes at a location and time that is convenient for you.


Local Classes

/localclasses

We partner with schools and organizations to conduct professional development workshops, consult on education issues, and bring STEM activities to a wide range of students.


Outreach

/partnering

Home


To accommodate parents and students who would like to minimize their commute or who would like scheduling flexibility, we offer in-home classes and lessons. Parents who are interested in this option and who can put together a group of students in their home should <a href="/contact">contact us</a> for more details. Although we offer one-on-one instruction, we believe that the kind of collaborative learning that happens in a group is highly beneficial to each student, and we encourage parents to put together a class if possible.

Our small class size enables us to address students’ individual concerns. In particular, we carefully prepare for every session, which is customized to meet the needs of each student. In addition we help each of our students create a custom online portfolio, which showcases the student’s math and computer science projects.

<div class="note"><strong>Note:</strong> The first session of any new class is <strong>free</strong>. If a student drops or joins a class, the rate per student increases or decreases based on the new total number of students in the class.</div>

<div class="responsive-table">
<table id="lessontypes">
<thead>
<tr>
<th>Number of Students</th>
<th>Hours per Class</th>
<th>Hourly Rate per Student</th>
</tr>
</thead>
<tbody>
<tr>
<td>5 or more</td>
<td>2</td>
<td>$40</td>
</tr>
<tr>
<td>4</td>
<td>2</td>
<td>$45</td>
</tr>
<tr>
<td>3</td>
<td>2</td>
<td>$50</td>
</tr>
<tr>
<td>2</td>
<td>2</td>
<td>$65</td>
</tr>
<tr>
<td>1</td>
<td>2</td>
<td>$120</td>
</tr>
</tbody>
</table>
</div>

## Scheduling

Scheduling is flexible but depends on instructor and student availability. If a third or more of the students in a class cannot attend a session, it must be rescheduled so that the class stays on track.




## Math Circle

#### Information and Registration

As part of its community outreach, Gentle Knowledge is offering weekly math enrichment for students in grades 5 through 8. These weekly one hour sessions are based on the same principles as Eastern European math circles, where collaborative learning around a set of interesting extracurricular problems and ideas replaces lectures. Each session involves a set of &#8220;non-standard&#8221; problems from an area of mathematics, like number theory and combinatorics, that does not usually appear in the standard school curriculum. The goal of the math circle is to introduce students to the beauty of real mathematics (as opposed to &#8220;school mathematics&#8221;) while both exposing them to useful problem solving methods and inspiring them to further pursue mathematical studies. Occasionally, sessions may feature guest speakers who are practicing mathematicians.

The math circle enriches but does not replace the regular mathematics curriculum. Parents who want instruction that includes elements of the math circles approach but that also covers the standard curriculum should consider our <a href="/localclasses">local</a> or <a href="/onlineclasses">online</a> classes.

#### Cost

The math circle is **free**. We want to share our contagious love of mathematics with as many students as possible, including those from low-income families. If you would like to help us, you can make a <a href="/donations">donation</a> to support this and other community outreach efforts.

#### Late Enrollment

Students are welcome to join the math circle at any point. Our sessions are mostly self-contained, although some problems and topics will span two or three sessions. Please register before attending.

#### Schedule

The math circle meets on Sundays between 12:30 PM and 1:30 PM. The following is the schedule for the full academic year.

<div class="responsive-table">

<table id="yearscheduletable">
<thead>
<tr>
<th></th>
<th></th>
</tr>
</thead>
<tbody>
<tr>
<td>October 16, 23, 30</td>
<td>November 6, 13, 20, 27</td>
</tr>
<tr>
<td>December 4, 11, 18, January 8</td>
<td>January 15, 22, 29, February 5</td>
</tr>
<tr>
<td>February 12, 19, 26, March 4</td>
<td>March 11, 18, 25, April 1</td>
</tr>
<tr>
<td>April 22, 29, May 6, 13</td>
<td>May 20, June 3, 10, 17</td>
</tr>
</tbody>
</table>
</div>

#### Location

Math circle sessions are held at Center Makor which is in the school building of Temple Bnai Moshe, located at 1845 Commonwealth Avenue, Brighton, MA 02135. The entrance is at ground level, to the right of the steps leading to the main entrance. The nearest T station is Chiswick on the B branch of the Green Line. Also nearby are the Cleveland Circle (C branch of the Green Line) and Reservoir (D branch of the Green Line) T stations. Limited free parking is available in the small parking lot that is to the left of the main steps or on Commonwealth Ave.

<iframe width="600" height="550" frameborder="0" scrolling="no" marginheight="0" marginwidth="0" src="https://maps.google.com/maps?hl=en&amp;client=firefox-a&amp;q=1845+commonwealth+ave+brighton+ma&amp;ie=UTF8&amp;hq=&amp;hnear=1845+Commonwealth+Ave,+Boston,+Massachusetts+02135&amp;gl=us&amp;t=m&amp;vpsrc=6&amp;ll=42.341607,-71.160936&amp;spn=0.034893,0.051498&amp;z=14&amp;iwloc=A&amp;output=embed"></iframe>


Math and Computer Science Circle

## How We Teach

Our most important guiding principle is that, on the one hand, no student is inherently incapable of succeeding in mathematics and, on the other hand, no student should be bored and unchallenged. We make it a priority to accommodate students with widely varying levels of preparation by placing students in an appropriate level class based on their motivation and personal preference. Of course, even within a particular class, students learn at different paces, and we prepare for that by incorporating problems of varying difficulty into our classes so that all students get a sense of accomplishment and improvement. We strive to make sure that no students feel intimidated either by the subject or by their classmates.

Our experience shows that an informal and friendly classroom setting helps reduce fear of mathematics while encouraging collaboration among students to solve the most difficult problems. Below is the structure of a typical class:

1.  A warm-up session where students solve logic puzzles and other problems that do not require any mathematics beyond what students already know.

2.  Short session devoted to practicing basic computational skills. Students work by themselves and receive help from the teacher. During this time students can individually discuss the computational part of their homework. Advanced students who finish their work early receive more difficult problems.

3.  A 10 minute break.

4.  A reinforcement session where students discuss challenging homework problems and solve problems using ideas and techniques that they have already developed in previous classes and homework assignments.

5.  A session devoted to the main topic of the day which can include both an in-depth discussion of standard school topics beyond what schools and textbooks cover as well as nonstandard topics and problems.

We assign students homework that includes both computational practice exercises as well as more challenging problems usually based on the main topic of a class. Although we do not give out grades, we expect that students will complete at least the practice exercises and will make a serious effort to solve as many of the remaining problems as possible. Even partial solutions or rough ideas are an important part of the learning process. Our goal is to gently nudge students to the limits of their abilities, and we would rather challenge them than give them a false sense of accomplishment. As a result, we do not expect all of our problems to be solved, and we know that the new ideas and problem solutions that students generate will be their most powerful source of encouragement.

## Math Topics

Beyond the standard school topics that we cover in-depth here is a sample of some others topics that students are likely to encounter:

<div class="responsive-table">
<table>
<thead>
<tr>
<th>Grade</th>
<th>Topics</th>
</tr>
</thead>
<tbody>
<tr>
<td>3-5</td>
<td>logic puzzles, original word problems (involving constructions, weighings, lateral thinking, and spatial reasoning), basic counting principles (combinations and permutations), number bases, mathematical games</td>
</tr>
<tr>
<td>6-8</td>
<td>logic puzzles (involving disjunctions, conjunctions, and negations), word problems (involving unusual applications of ratios and rates), coloring and parity problems, divisibility and arithmetic with remainders, infinitude of primes, basic graph theory, invariants, pigeon hole principle, basic combinatorics</td>
</tr>
<tr>
<td>9-12</td>
<td>logic puzzles (more involved than in earlier grades), basic number theory (modular arithmetic, Fermat&#8217;s little theorem, applications to cryptography), proof by induction, proof by contradiction, inequalities (triangle, A.M.-G.M.), Pascal&#8217;s triangle, extreme principle, semi-invariants, straight edge and compass constructions, geometry from a dynamical view point, geometric inequalities</td>
</tr>
<tbody></table>
</div>

## Standardized Tests

For a variety of legitimate reasons, including college and private school admissions and scholarships, parents and students often worry about standardized tests like the SAT. Students usually take their first practice test in high school and when faced with mediocre or poor results turn to expensive tutoring and test preparation services in an attempt to quickly raise their scores. Although a large investment of time and money can improve scores to a limited extent, the process of studying for these tests has few educational benefits. The most difficult problems on standardized tests, those that are responsible for low scores, are problems that require unconventional thinking. Our experience has shown that instead of last minute cramming in high school, students are much better served by becoming used to, and even enjoying, a regular diet of nonstandard problems from an early age. Students who become comfortable solving problems for which there is no obvious solution method that can be memorized are much better equipped to perform well on standardized tests with minimal or no special preparation. Of course, the main benefit of this long-term approach is that students receive a real-problem solving education that will be much more useful throughout their lives than an extremely limited set of test taking skills that has little educational value.

## Computer Science Component

Our computer science curriculum pursues three goals:


+ Enriching the mathematics curriculum. By implementing classic mathematical algorithms (such as finding the greatest common divisor of two numbers) in a programming language, students develop their intuition about those fundamental algorithms. Additionally, programming allows students to explore computation-intensive areas of mathematics that are otherwise inaccessible to them.
+ Learning a practical skill. As the economy becomes more information-based and data-driven, programming is becoming increasingly more useful even to non-programmers. Without following a particular industry fad that is likely to become outdated within a few years, we wish to leave students with the knowledge and skills that allow them to learn any new technology on their own.
+ Giving students their first taste of engineering. Programming opens the door to engineering at an early age and gives students an opportunity to be creative in a new medium while sharpening their problem solving skills.

Some of the topics we cover include functions, function composition, variables, recursion, basic data structures, searching, sorting, and algorithm efficiency. In addition to core computer science curriculum topics, we leave room for fun and even artistic programming projects.


Methodology and Curriculum

## What We Do

Gentle Knowledge is a unique collaboration between mathematicians and educators, with experience both in the US and abroad, who have identified the main reasons behind the widening gap between what schools teach and what global competition demands.

Unlike other programs that focus exclusively on computational fluency (basic arithmetic and algebra skills) and test preparation to the detriment of a real problem-solving education, we teach students to solve the kinds of problems that best prepare them for the real world outside of standardized tests. Success on standard metrics like the SAT and regular school work is a natural byproduct of this approach because students who learn to tackle nonstandard problems, become logical thinkers, and lose their fear of the unexpected can easily handle simple exercises that constitute the latest trend in test-based assessment.

Instead of preparing students only for short-term results and nearsighted goals, we look ahead at what they need to know to succeed in science, technology, engineering, and mathematics (STEM) professions and incorporate the necessary prerequisites into our methodology. The single most important such prerequisite is the ability to think abstractly, to generalize problem solving methods in novel situations.

As part of our commitment to teaching problem solving, we teach other vital 21st century skills like computer programming. Our goal is to leave our students with a toolset that they can use throughout their education and later in their careers regardless of whether or not they ultimately pursue STEM professions.

## Our History

Gentle Knowledge has its roots in an old Eastern European problem-solving tradition that values creativity and critical and lateral thinking above mindless pattern memorization. It is in part a descendant of the Gelfand Correspondence Program in Mathematics, which at its height in the 1970s reached over 40,000 students all over the former USSR and, among other achievements, helped improve the quality of mathematics education in the most remote regions and in the weakest schools in the country.

Our mission remains to gently elevate the level of mathematical competence of students and teachers without undermining the role of schools. Among the changes we have made is adopting our methodology to the specific needs of an American audience and embracing the role of technology without violating our core principles (outlined below).

## Key Principles of Our Approach

*   Changing the “either you get it or you don’t” culture and breaking down the negative stereotypes surrounding school mathematics to reduce fear among students who perceive themselves as weak and to challenge those who want to progress beyond the standard school curriculum.
*   Achieving computational fluency as soon as possible and practicing it alongside more advanced and exciting topics.
*   Leading students to discover mathematical ideas and problem-solving techniques on their own through an inquiry-based or Socratic approach.
*   Enriching the standard school mathematics topics and making sure that students understand the origins of concepts as well as their connections to each other, especially when textbooks and schools fail to emphasize this.
*   Exploring the beautiful world of mathematics and science that lies within reach of students &#151; but just beyond the standard school curriculum &#151; through problems, hands-on activities, games, and guest lectures.
*   Helping students become technology creators, not just technology users, by teaching the basics of computer programming, algorithms, and rudimentary engineering principles.
*   Conveying the importance of precise communication skills and giving students the opportunity to practice those skills while making logical  arguments and catching and correcting flawed ones.
*   Opening the doors to mathematical competitions and accessible research and engineering projects for the most ambitious and motivated students.


Our Approach

## After School Enrichment Services

After school programs provide a unique opportunity for schools to provide their students with an education that extends beyond ordinary classroom instruction. Gentle Knowledge opens up new learning opportunities for children by running fun and educational classes that involve elements of math, programming, and brain games. For more details about our teaching methodology refer to our <a href="/methodology">methodology and curriculum page</a>. For more information on how we can best suit your school&#8217;s needs please <a href="/contact">contact us</a>.

## Professional Development Services

Gentle Knowledge provides various professional development services to schools and schools districts guided by the belief that 	dramatic improvements to any education institution can be achieved through cost-effective in-service teacher training. Our ultimate goal is to ensure that, at minimum, there is no gap between what schools teach and what institutions of higher learning and the workplace expect from incoming school graduates.

You can learn more about our approach in our professional development white paper: <a href="/images/ProfessionalDevelopment.pdf">A Gentle and Cost-Effective Approach to Dramatically Improving Mathematics Education</a> [PDF].

**Key Principles**

+ Teachers are at the heart of the solution to the problems of education and need all the support they can get. We recognize that teaching is difficult and provide materials and techniques that significantly decrease teachers’ workload while improving the quality of the work they do.
+ Insufficient teacher preparation in mathematics is best addressed by the topics that are immediately relevant in the classroom, not by submitting teachers to grueling reeducation involving topics that are best suited for graduate or advanced undergraduate work
+ Teacher accomplishment depends on the accomplishments of their students. Our teaching materials and training classes allow teachers to give their students opportunities to do work that is recognized as far above and beyond the requirements of education standards. We are in the business of bringing prestige back to the teaching profession.

**What We Offer**

+ **Teaching Material**: Gentle Knowledge has access to a wealth of original teaching materials, including problems, articles, and interactive activities, some of which have appeared in books and other publications written by team members, and some of which have never appeared in print before. After taking into account the particular sequence of topics in a school or school district, we incorporate the relevant material at our disposal into custom teaching kits that become the basis for professional development workshops and which are subsequently used by teachers in their classes. These teaching kits, which are in effect detailed lesson plans, include class discussion manuals, homework assignments, assessment tools, enrichment activities, and detailed solutions to all problems.
+ **Training Courses**: Teacher training is a critically important component in the successful use of the teaching kits described above. Because no assumptions are made about teachers’ mathematics backgrounds, these professional development classes allow us to go over the material before it is presented by teachers to their students, discussing both the requisite mathematics and common pedagogical scenarios that may arise in the classroom. As an additional advantage of these classes, teachers can earn Professional Development Points (PDPs) for attendance and written work. Throughout the duration of training classes, we incorporate feedback from teachers to continually improve what we offer, and we put special emphasis on a stress-free environment.
+ **Technology Support**: Password-protected teaching kits are available online for all teachers in a client school without regard to whether they participate in professional development classes. In addition, we host an online forum to facilitate collaboration between teachers and to allow us to answer any questions that may arise. This is a major cost-cutting measure that seeks to reduce the number of actual classes and workshops that need to be run, while significantly increasing the distribution of materials and best practices across multiple schools. Several other web-based solutions are currently under development.

Long-term teacher training classes can also focus on working with advanced students or introducing basic computer science into the STEM curriculum. We also run short-term workshops and consult on curriculum development and other education issues. For more information please <a href="/contact">contact us</a>.




Partnering


## Core Members

#### Victor Gutenmacher

Victor Gutenmacher is a distinguished mathematician and educator. He was a Professor of Mathematics at Moscow State University for almost twenty years and has extensive teaching experience at all levels, from secondary school to graduate school. He served as a member of the Editorial Board of <a href="https://www.nsta.org/quantum-magazine-math-and-science#tab-about">Quantum</a> (a top educational mathematics and science magazine in Russia that was, for over a decade, published in English by the National Science Teachers Association in conjunction with the National Council of Teachers of Mathematics) where he also organized and directed the &#8220;Teacher&#8217;s Corner,&#8221; a section of the magazine devoted to creating instructional materials for teachers. In addition, he served as the Chairman of the Methodology Committee for the Gelfand Correspondence School, a member of the Methodology Committee of the USSR Mathematics Olympics, a member of the Advisory Panel on the Committee for American Mathematics Competitions, and as the coach of the Soviet Team at the International Mathematical Olympiad. Dr. Gutenmacher is the author of more than 80 publications in mathematics and mathematics education, most notably the classic text <a href="http://www.amazon.com/Lines-Curves-Practical-Geometry-Handbook/dp/0817641610">Lines and Curves</a> which has been translated into several languages including English.

#### Ilya Bronshtein

Ilya Bronshtein holds an M.A. in mathematics and a B.A. in computer science from Brandeis University. As a student he published research but decided to leave academia and devote himself to fixing the education problems that he encountered when he was in school. Over the years, he has taught classes and led math and computer science circles for adults and K-12 students in public and private schools, and in the homeschooling community. He has also developed software that students use to discover ideas in mathematics, computer science, physics, and biology while learning how to code. Ilya attended the Newton and Brookline public schools and is intimately aware of the challenges and opportunities that they and other American schools present.

#### Tatyana Finkelstein

Tatyana Finkelstein is an award-winning mathematics teacher who has taught for over a decade in the Lexington Public School system after teaching mathematics for a decade in St. Petersburg, Russia. She is a 2006 recipient of the <a href="http://www.maa.org/awards/sliffe.html">Distinguished High School Mathematics Teaching Edyth May Sliffe Award</a>. Ms. Finkelstein has years of experience in teacher professional development, as a counselor in the <a href="http://www.promys.org/pft/">PROMYS for Teachers program at Boston University</a>, an intensive 6 week summer mathematics program for teachers, and as a participant in the Park City Mathematics Institute Secondary School Teachers Program. She has also run a summer mathematics program for middle school students in Lexploration, a Lexington-based initiative that serves surrounding communities.

#### Boris Klebanov

Boris Klebanov holds a PhD degree in mathematics from Moscow State University. He has taught mathematics at levels ranging from postgraduate studies to high school classes and summer camps for gifted elementary school students. Dr. Klebanov has also authored many publications on the topic of problem solving and olympiad-style mathematics. He was the Director of the Math Circle for school students run under the auspices of the Israeli Weizmann Institute of Science and was Chairman of the Moscow Organizing Committee of the <a href="http://www.mathkangaroo.org/">Kangaroo Mathematics Contest</a>. Together with his students he participated in the International Junior Mathematical Congress. He has taught at the Math Circle in Boston and several of his students achieved high scores in the American Mathematics Contest and American Invitational Mathematics Examination. Dr. Klebanov has also edited several mathematics textbooks for leading US educational publishers.

#### Tanya Khovanova

Tanya Khovanova holds a PhD degree in mathematics from Moscow State University and was a gold medalist at the International Mathematical Olympiad. She is an educator, a blogger, and a popularizer of mathematics who has a keen interest in the subject of women in mathematics. Besides coaching the math team at the Advanced Math and Science Academy Charter School in Marlborough, MA she has been an organizer of the Women and Mathematics program at the Institute for Advanced Study in Princeton, NJ. Dr. Khovanova helped design the Math Alive course at Princeton University which seeks to expose those who have not had college mathematics to the concepts behind important modern applications. As a research scientist at the Council on Cybernetics under the Presidium of the Academy of Sciences of the USSR, she designed innovative educational programs in computer science for children.

## Advisers

#### Wallace Feurzeig

Wallace Feurzeig is a Principal Scientist at BBN Technologies with extensive experience in mathematics education. The central focus of his work is in research, design, and application of advanced technology to improve learning and teaching. He conducted the first teaching experiments involving children&#8217;s use of an interactive programming language. This work led directly to the development of the <a href="http://el.media.mit.edu/Logo-foundation/logo/index.html">LOGO programming language</a> in 1966 by Feurzeig and collaborators. He has authored and edited numerous books including <a href="http://www.amazon.com/Modeling-Simulation-Precollege-Science-Mathematics/dp/0387983163">Modeling and Simulation in Precollege Science and Mathematics</a>. He has been Principal Investigator on several NSF mathematics education research projects including Programming Languages as a Conceptual Framework for Teaching Mathematics and Advanced Mathematics from an Elementary Viewpoint. These projects have produced widely disseminated educational software tools including Logo, the Algebra Workbench, MultiMap, and Function Machines.

#### Deborah Belle

Deborah Belle is a Professor of Psychology and the Director of the Human Development Program at Boston University. She has been a chair of the Women in Science and Engineering (WISE) network and has worked to encourage girls to pursue science and mathematics careers. Professor Belle has also focused her attention on the issues surrounding poverty and inequality and the ways in which they affect children and their education. She is the author of several publications on the subject including the book The After-school Lives of Children: Alone and With Others While Parents Work.


Number of Students	Hours per Class	Hourly Rate per Student
5 or more	2	$40
4	2	$45
3	2	$50
2	2	$65
1	2	$120