FINAL PAPER

Success in Reach

In our society, I have observed and taken part in something I like to call, "The Quick

Fix." What is the quick fix? It is exactly what one probably thinks it is- a fast and easy

solution. We want these every day. I like to just heat up a Trader Joe's dinner. Others

like asking Siri for a good fro-yo shop. Some look everything up on Google. In the most

popular TV series, such as Two and a Half Men or Modern Family, we see an easy

solution in the end of each episode (Meyer). Society today is constantly seeking fast and

easy answers.

That has turned us into what I have labeled as, "A Compromised Mathematical Mind."

We are always looking for the easiest solution to each equation, looking for the shortcut

method. This practice has seeped into our school systems, creating a student demand

for simple answers. No one is angry when a formula is given to them in math class. All

one has to do is just keep plugging numbers in, straight through to the test. Then, when

the final exam rolls around, students receive a blank note card. Students are allowed to

write all the formulas they couldn't memorize onto this note card in order to continue to

plug in numbers on the exam.

Through my experience, I do not have the time or the chance to even consider the

formula. I do not understand why this formula is important. I have no idea what the

variables even mean or where they came from. This is all because, my class and I did not

derive the formula. Deriving formulas, from experience, is a torturous and malicious

time in the classroom for everyone involved. Students are confused and frustrated, and

the teacher grows frustrated in return.

After the class gets the formula written on the board, just as a meal on a silver platter,

I plug-n-chug. Through this straightforward, robotic process, it is difficult to figure out

what each variable means and what it stands for. If anyone gave me a sheet of paper

with any algebra or geometry problem from the past four years, I would only be able

to solve the computation problems, or the factoring and quadratics. This type of math

as Dan Meyer said in his TED talk is, "really easy to relearn, provided you have a really

strong grounding in reasoning (Meyer)."

In my experience, when the teacher starts a new unit, the teacher shows us one sample

problem. We go through the problem step-by-step, and then, we reach a solution. After

that, we are given a problem to try on our own. Half the class’ hands shoot up and the

teacher is left with a long waiting list of students to attend to, bouncing from student

to student answering questions. This system does not meet the needs of each student

because students have to wait for the teacher, and when this happened to me, I got

frustrated with the teacher, and then frustrated with the topic as a whole. Then, the

teacher goes over the problem with a student reciting the steps, and the cycle continues

on until the final exam review.

The big missing ingredient is the process of reaching a solution. The method used in

Public School for problem solving gives a notion of simplicity and that we can always

reach a nice convenient number, just as an audience would expect a simple resolution

at the end of sitcoms like Two and a Half Men or Modern Family. As Albert Einstein

said, “The formulation of a problem is far more often more essential than its solution,

which may be merely a matter of mathematical or experimental skill” (Einstein). In

classrooms that I have been in, the class and I are not thinking about the formulation of

a problem, we are just thinking about two things: the problem and its solution. To really

understand a problem, reasoning is required.

Reasoning requires thinking and analyzing. It is the part of mathematics that is crucial

to the understanding of the world around us. A common complaint coming from

students is, "How will I use this in my life?" Reasoning is the answer. Reasoning gives

students practice in analytical thinking. As young minds, and the future generation, if

we continue to hold ourselves in the realm of simplicity and one road answers, we are

training our minds to expect a shortcut or a simple solution to each problem.

Our job market is changing. As Ilya Rifkin stated in an online interview, "There is a

stark demand for someone that can genuinely think" (Rifkin, Ilya). We need reasoning

more than ever. We are outdated. This is not the Industrial Revolution and all you need

is a good pair of hands trained for the factory. We need minds that are trained to be

constantly reasoning and thinking, preparing us for the exceedingly difficult job market.

I hope this is no surprise to anyone, but the world is a big place full of problems that we

take on as our job to solve. Our math education is essential for preparing us to be better

equipped for the world that we will emerge into.

So if I go to the 12th best public school in Massachusetts, why is there a math

enrichment program down the street that has 2,362 kids enrolled in the Newton branch,

and has seven other locations in Massachusetts and two others in California? What do

these programs have that the best public school systems do not have to offer?

Math from Two Different Worlds

When juxtaposing the curriculum outlines of the National Council of Teachers in

Mathematics the Russian School of Math (RSM) they are not as different as I expected

them to be. There was logical sequencing of topics and the only main distinction

was that algebra is introduced much earlier in RSM. But what is different, is the

methodology behind the curriculum and expectations. This paper, due to its limited

scope, is unable to conduct a deep analysis of curriculum development. However,

this paper can take a significant look at the prospective of an institutional model that

genuinely brings about undeniable success in each student.

To place the origin of the school in a suitable context, it is worthwhile to start with the

immigrant experience of those involved with the foundation of the school. I start right

from the name of the school- The Russian School of Mathematics. Why Russian? In

1989, Inessa Rifkin, the founder of the school, and her family arrived in America as part

of an enormous immigrant group fleeing from the former Soviet Union. “Between 1989

and 2003, 1.6 million Jews and their non-Jewish relatives left the former Soviet Union.”

Approximately 315,000 (or 20%) of this group came to settle in America (Chiswick and

Wenz, 3). Life was less than ideal and opportunities were limited. America was a place

for children to achieve the dreams that would not be possible behind the iron curtain.

Rifkin’s move to America was for the success of her children; it was a sacrifice, and the

majority of families immigrated for those exact reasons.

In Russia, both Rifkin and her husband had been highly trained as mechanical

engineers. In Russia, Rifkin was entered in a specialized track for mathematically

inclined students and had been trained as a mechanical engineer at the Polytechnic

Institute of Minsk. They were able to attain professional jobs and bought a house in the

suburbs of Newton for “the best educational system possible” (Rifkin, Inessa) As her

eldest son entered high school, Rifkin’s view of the Newton educational system began

to tarnish as she noticed what was happening in his math classes. There was a great gap

between the material and her standards and expectations. With the growing gap, Rifkin

became more concerned as it threatened the model of success that had been the reason

for her to move her family and to come to this country.

When Rifkin was faced with the reality of an educational track that did not deem fit

for her standards, she didn’t just complain, she took action. Her new awareness of

a potential failure in America was the driving force for Rifkin to leave her full time

position in order to tutor her son. Her son, Ilya Rifkin, attributes his admission to

Cornell to the tutoring that his mother started. He stated in an interview, “It totally

changed how I thought about math, from a subject, to a way of thinking about a

problem…It opened up subjects like Debate, Physics classes, as a way of thinking about

the problems I saw in that class. When asked “What does RSM’s mission mean to you?”

Ilya replied, “It is the idea that if you give kids a solid mathematical foundation- it gives

them the advantage to become anything they want to be in this life” (Rifkin, Ilya). At

that time, the Russian immigrant community in the Boston area was coming to the

same realizations. They shared the frustrations of a lagging math education which

was considered weak compared to the training they had in the USSR. From the shared

frustrations and worries of the community, blossomed the beginnings of RSM. Rifkin

started to help her son with his math in the kitchen, but by the end of that year, she was

tutoring 67 other Russian children.

Math Matters

The school was created due to the shared belief that there is value in studying

mathematics. As many of the Russian immigrants are engineers and computer

programmers, there is an undeviating association with math skills in their perspective

careers. But the school’s and the community’s stress on math goes farther than numbers

and computation, but into the realm of reasoning, analyzing, and mental development

as a whole. Rifkin states, “we believe mathematics is the foundation…this is where the

child develops their analytical abilities” (Rifkin, Inessa).

Math is not and should not be viewed as numbers and variables; it is a mode of

reasoning. The Russian community truly values math, especially with a great percentage

of the community consisting of computer programmers and engineers, there is a direct

connection as to why the Russian community holds focus on math skills. Due to their

career paths, they were able to attain professional level jobs, not because of math

skill alone, but because of the way they approached problems and how they thought

of solving them. It is a mode of mental development that you cannot get in any other

subject matter. Rifkin attributes her comfortable assimilation into a country to her

mathematical education. Clearly, math is not the golden key. The transition to American

life was due to a collection of economic and other education achievements. But, what

is important to retract is that the value of math is unquestionable in the Russian

community, and it is a true component of their almost immediate success in a new

country.

The Fundamentals

As Rifkin began tutoring her son, she was drawn towards analyzing the fundamental

differences between the education she received, and the one her son was receiving.

In her research, she found that a key element in her educational background can be

attributed to Lev Vygotsky.

Vygotsky was a 20th century Russian scholar who worked with philosophy, literature,

and culture, and was a theorist in social learning (Newman and Holzman, 5). He was

deeply interested in the maturation of abilities and potential for future advancement,

rather than in realized capabilities, or what he came to be labeled as the zone of

proximal development (ZPD). He was believed intellectual potential is connected to

his belief that development is shaped due to genetic, environmental, and socio cultural

influences.

In focusing upon the student, Vygotsky focuses on the pathways of learning instead

of the outcomes. Vygotsky highlights the need “to concentrate not on the product of

development but on the very process by which higher forms are established” (Tappan,

24). The process is a means to analytical efficiency and increasing their capacity to

produce knowledge (Edwards, 171). Then, learning becomes a matter of reading the

landscape in increasingly informed ways and knowing how best to use the resources

available (Edwards, 161-186). Then math problems don’t just appear to be a plug-n-

chug straight answer, but a potential solution with many facets as methods to solving

them. There is more than one way of looking at any speed-distance-time word problem

or quadratic equations. Then, learning grows beyond the horizon of knowledge building,

but it becomes a “socially useful enterprise that enhances each individual’s capacity

to develop” (Edwards, 170). The value of math education is not in derivatives or

trigonometry applications, but in the ways in which a student comes to understand the

relationship that the material holds to other bodies of knowledge.

In addition to the theoretical approach to learning, Vygotsky also stresses the reciprocity

of pupil and instructor. The teacher is an enabler, using dialogue to bring the theoretical

understanding to the world into contact with the child’s own experience, thus not

cast in the role of forcing information into passive students’ minds (Tappan, 24).

In my experience, the math teachers have had difficulty engaging the entire class,

and only the passionate students become successful. By the Vygotskyian model,

when a child is interacting with other people and internally processing the new

information, there is more significant intellectual development “which gives birth to

the purely human forms of practical and abstract intelligence, occurs when speech and

practical activity…converge” (Tappan, 30). In the RSM classroom, there is a constant

conversation in the classroom, whether it is as a class, on the board, in a game, or with

the teacher, there is always a way to continue internalizing information. That practical

intelligence is impossible to reach with silent busy work that is handed out in the public

school classrooms. The reciprocity of students and teacher is an element that allows for

the students to achieve the abstract intelligence.

In order for a teacher to engage the classroom in a way that is successful, with a

consistent flow of solving, discussing, and continuing to find new ways of solving

complex problems, the teacher should not only have a high level of mathematical

competency, but equally should hold a degree of comfort and enjoyment of the subject

matter. This comfort is so essential because it sets a tone for the students. If there

is apprehension, the students will then be apprehensive. But more importantly, the

teacher is a facilitator, not a speaker or an answer sheet. A valued trait in Rifkin’s eyes is

the invitation to challenge. “Teachers must challenge students but also be willing to be

challenged in return” (Green, 14).

In my senior calculus class, we were beginning a unit on integrals. After a few days of

working with it, I raised my hand and suggested a more complicated problem that I was

seeking an answer to. In return, I got a “we are just going over the basics.” Not only was

I ignored as a curious student, but challenge was not part of the class. I wanted to go

further than the confines of what was in the textbook, and in return, I was completely

dismissed. This is not only detrimental to a student-teacher relationship, but it

discouraged me from pursuing more from the topic. After the incident, I was frustrated

and lost my drive for the topic.

If I was not exposed to a welcoming environment that encouraged questions and

pressing curiosity, I would have never thought to wonder about more complicated

matter. Humans are curious by nature (Willingham, 3). And as Daniel Pink believes, we

seek Mastery, Autonomy, and Purpose. If this curiosity and challenge is not encouraged

and welcomed, I find it difficult to see how teachers expect students to expand their

knowledge base and expand their analytical efficiency. I am not completely ruling out

American teachers as teachers who discourage questions. But I have had discouraging

experiences in a considerable amount of my classes throughout middle and high school,

where a teacher doesn’t know what to do with my questions, and as a result, I was

dismissed and ignored. With that, I grew some level of discomfort with math. RSM has

changed my outlook on math as a subject, but even greater, has morphed me into the

student that I continue to be. I feel the direct impact of math and reasoning, and due

to the passionate classroom environment, I am never afraid to ask questions and be an

intellectually curious student. Intellectual curiosity is a universal factor, as it applies to

all subject areas.

Why U.S?

While looking at the success of Russian Math, I had to look closely at why there is failure

in U.S. Math as well. With one glance at a U.S. textbook, one can clearly see that things

are broken down into simple, easy steps. With that, the teacher holds a different role.

The teacher becomes the speaker for the textbook, following the steps. The student has

no room to experiment, grapple with, or form their own realizations about the concepts.

We are given too many details. In Dan Meyer’s TED talk, he believes that because of the

explicit break down in textbooks, students do not become patient problem solvers. In

Figure A, one can see that four separate questions are given in order to reach the final

question of, “which section is the steepest?” (Meyer). Rifkin states, “I don’t like [it] when

for every kind of problem you have examples with step one, two, three, and then after

that you have exercises with ten [or] fifteen world problems exactly like those three

steps in the example. This repetitive format Rifkin says flatly, “[doesn’t] teach anything”

(Rifkin).

Anyone can learn a sequence and follow it. By learning doing a step-by-step process,

there is no thinking involved. If a student knows the steps, they continue to follow

them with any problem. But if they are stuck or confused, they have nothing to fall back

on to get through the problem. Students need to think about how to get to the final

answer. If for example, a student in was asked, “How long will it take to get to New

York City?” the student will start thinking about modes of transportation being a car,

bus, train, or a plane. Then, the student will need to think about how fast each mode of

transportation moves at. And then distance is needed to figure out speed. This way, a

student concretely can understand the relationship of speed, distance, and time, instead

of being given the formula and plugging number in. If the student can experiment with

a new topic and create their own connections, they can rely on those to apply to any

problem, instead of a simple series of steps.

In addition, the math curriculum, in Rifkin’s opinion, lacks continuity and purpose.

There is no connection between topics, which takes away the ability for students to

build a foundation based on a network of things they learn. Rifkin gives a great analogy

to such a flaw; “You will remember [a] movie very well because it has one plot.” But

without the plot, it is nearly impossible to remember all the scenes individually and

draw a connection between them. Rifkin believes that “Our brain cannot remember

so many isolated facts” (Green, 11). Also, without purpose, students are left without

a sense of accomplishment. I can guarantee that there is at least one student in every

math classroom that I have been in that has asked, “Why are we learning this?” If I

were posed that question, I would respond with, “to practice reasoning and analytical

efficiency.” But truthfully, it is very difficult to stay motivated and curious in an

environment where the connections are not easily made.

As a student, I have adapted to the format or weekly quizzes and chapter tests, and so

have other students in U.S. schools. We are given one topic at the beginning of the week.

We have the weekly quiz, and move on. There is almost no way of truly grounding the

material that you cover. This system is exactly why computation-style problems stay

retained. This not only contributes to the disappointing math ability in our children, but

it truly gives math a bad reputation among students.

Math is viewed as unimportant, frustrating, and difficult. Rifkin labels this as a

general “fear of mathematics.” Christopher Green, a former RSM student experienced

this first hand. “Two years on my high school math team only reinforced my awareness

[of] what was already a blatant social norm in my hometown; “math is not cool, it is

difficult, and something no one should want to do for fun.” The students of RSM could

not disagree more with this social norm.

Quite recently, RSM created a math Olympiad class for students after much popular

demand. The Olympiad classes are for those “who enjoy intellectual challenge or wish to

prepare for Olympiads and challenging math competitions” (Russianschool.com). There

is no homework in the class and kids truly just work with problems that their regular

classes do not have the time to work with. The most important thing to take away is

that, kids were the driving force behind these classes. They wanted the challenge, they

wanted more. If someone were to walk into an RSM classroom, you would see kids with

their arms eagerly up, all hoping to get called on. Or, students coming up to the board

to publically grapple with a challenge problem. If the RSM way was adopted on a bigger

scale, I can only image the removal of the stigma related to math, and more importantly,

that kids would be more intellectually curious. Intellectual curiosity is not only with

math, but can carry over to more subjects, building more knowledgeable and driven

students. With this method, math’s personality in America can be flipped upside down,

finally.

Who gets it right?

At RSM, the concepts in the curriculum are mapped in such a way that they are always

connected to each other, building on one another. To do this successfully, algebra

is introduced in the second grade. By having the basics of arithmetic and algebra

understood early, “everything that you ever learned is just one layer more…you repeat it

constantly, you go deeper and deeper” (Rifkin).

With the understanding that younger minds are more flexible and receptive to new

concepts, it can also be understood that with maturation, it becomes more difficult.

From an observational point of view, Rifkin found that “it was much easier to explain

arithmetic sequence[s] to a group of 4th graders than to a group of 11th graders.” From

the outlined curriculum for 11th graders at North, that is exactly when sequences and

series are introduced. With the Vygotskyian model, and the more recent understanding

of the cognitive and linguistic development, RSM has allowed kids to truly understand

math concepts and continue with their learning at higher levels.

Concepts are introduced earlier to allow for the principles to be grounded and built

upon later on. For that reason, “Rifkin does something that American public schools

are hesitant to do; namely introduce algebraic and geometric material to elementary

students” (Green, 13). In the first and second grade, word problems begin framing

questions in terms of variables. Introductions are typically done by showing a scale.

The goal of having a scale is to keep it balanced and equal. See Figure B. Equations with

variables were introduced in 5th grade in public school. By this time, Rifkin believes

there is already a fear and apprehension to mathematics and with earlier introduction

and success, the fear is nonexistent. Just because the concepts are introduced at an

early age, does not mean that calculus is also given to 6th graders. But the distinct

introductions allows for continuity and more complex topics to be understood later,

instead of memorized for the upcoming quiz.

The Teacher

As an RSM student, I was not afraid to do so and ask the questions that I needed to.

But, as revealed earlier, I was constantly rejected in the classroom and tossed to the side

because I was not moving at the speed of the class. In essence, that is my motivation

for this paper. I feel deserving of a place where I can prosper academically and

intellectually. And if I attend a highly ranked high school, why can’t I prosper, especially

if I am motivated to be?

The classroom environment is part of the mission at RSM. In Rifkin’s experience in

hiring teachers, she has found it nearly impossible to find an American teacher worth

the position. She tests their mathematical ability. But more interestingly, she “finds

that the aspiring teachers often trivialize the importance of such a test by asking why

they need to know this information if they have an answer sheet” (Green, 15). It is

important to note that the teacher is not expected to be able to derive every piece of

information about a concept for the class, but even if they forget a formula, they should

have a background solid enough that they can work through what they remember to

reformulate their own.

Furthermore, the teachers are held accountable for their mathematical competency

as well as their teaching methods. Teacher workshops are held regularly to refine

mathematical capabilities and teaching methods. Rifkin, being the founder of RSM, and

continuously opening branches across the U.S, holds the same standard for herself as

she still holds a teaching position to see how the material is digested by kids in order

to see where improvements can be made either in the curriculum or the facilitation.

Through the mentioned methods, the teacher never loses touch with the classroom, and

holds a consistent motivation.

Conclusion

In recognizing the extent of the school’s success, student achievement at RSM goes

beyond the standardized test scores. Although the SAT scores are extremely impressive,

with a 7th and 8th grade average of 672/800 whereas the national average for 11th graders

is 518, Rifkin believes “her student’s mathematical abilities go on a broader scale than

the test” (Green, 15). It is an ability to think. As stated earlier, the teacher exhausts every

single approach to solving a problem. This is a skill that is applicable in any field that

has a problem to solve or to analyze.

In my vision of a utopian math classroom, I see kids squirming out of their seats, raising

their hands in attempt to show their knowledge and share their knowledge with the

class. As I have observed and bore witnessed to the infectious passion and engagement

that the children within the walls of RSM, it brings me hope that someday, I can see that

in classrooms everywhere.

The Russian School of Math is one of many models that challenge the public school

mode. There are distinct elements that would spark a broad and widespread

improvement in mathematical ability as well as analytical efficiency. It is not possible

due to the framework of public school to mimic the RSM model, but introducing

algebraic and geometric concepts earlier is possible and should be done. The entire front

of elementary schooling would change in regards to materials and teacher capabilities.

But it is frustrating to see undeniable success at RSM, and then see the majority of kids

go to public school where they are at a disadvantage. By developing young minds to be

able to grapple with math concepts at an early age, and also having teachers expected to

continually improve their own math abilities, math in America can move up in rankings

and we can be a more successful nation.

Appendix

Figure A

Figure B

Bibliography

AmericasBestTV. "Russian School of Mathematics on Best of the Northeast." YouTube. YouTube,

07 Nov. 2011. Web. 22 Feb. 2012.

Anderson, Jenny. "Making Education Brain Science." New York Times. 13 Apr. 2012. Web. 15

Apr. 2012.

Chiswick, Barry, and Michael Wenz. The Linguistic and Economic Adjustment of Soviet Jewish

Immigrants in the United States 1980-2000. Aug. 2005. Web. 15 Apr. 2012.

Edwards, Anne. Researching Pedagogy: A Sociocultural Agenda. Vol. 2. 2001. Web. 23 Apr.

2012.

Lev Vygotsky Revolutionary Scientist. London, 2003. 5. Print.

Newman, Fred, and Lois Holzman. "Lev Vygotsky: Revolutionary Scientist." Google Books. 2003.

Web. 17 Apr. 2012.

Ojose, Bobby. Applying Piaget’s Theory of Cognitive Development to Mathematics Instruction.

Thesis. NCTM, 2005. 2008. Web. 8 Apr. 2012.

Pink, Daniel H. "Type I and Type X." Drive: The Surprising Truth About What Motivates Us. New

York, NY: Riverhead, 2009. Print.

Ravitch, Diane. The Death and Life of the Great American School System: How Testing and

Choice Are Undermining Education. New York: Basic, 2010. Print.

RussianMathSchool. "A Glimpse into Our Younger Classes." YouTube. YouTube, 04 Feb. 2011.

Web. 27 Jan. 2012. <http://www.youtube.com/watch?v=T8lbGhEBbbQ>.

RussianMathSchool. "An Interview with Ilya Rifkin." YouTube. YouTube, 19 Oct. 2010. Web. 16

Feb. 2012.

Steen, Lynn Arthur. "Connecting Math with Reason." Mathematics and Democracy: The Case for

Quantitative Literacy. [Princeton, N.J.]: NCED, 2001. 31-60. Print.

Tappan, Mark B. "Sociocultural Approaches to Learning and Development." Sociocultural

Approaches to Learning and Development. Educational Psychologist. Web. 25 Apr. 2012.

"TEDxNYED - Dan Meyer - 03/06/10." YouTube. YouTube, 06 Mar. 2010. Web. 10 Feb. 2012.

Torgesen, Joseph K. "Recommendations for the Use of Diagnostic Tests in Reading First

Schools." Web. 26 Jan. 2011.

Wiggins, Grant P., and Jay McTighe. "The Six Facets of Understanding." Understanding by

Design. Alexandria, VA: Association for Supervision and Curriculum Development, 1998.

Print.

Willingham, Daniel T. Why Don't Students Like School?: A Cognitive Scientist Answers Questions

about How the Mind Works and What It Means for the Classroom. San Francisco, CA:

Jossey-Bass, 2009. Print.