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's exactly what you
probably think 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. We are seeking fast and easy answers.
That has turned us into what I have labeled as, "A Compromised Society." We are always looking for the easiest solution. This practice has seemed into our school systems, creating more students that want simple answers. No one is angry when a formula is given to them in math class. All you have 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 their final.
Through my experience, I do not have the time or the chance to even ponder 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. My solution was to not even bother thinking about it, not even fight with the teacher on dragging out this tedious time, but I just shut up. I kept my mouth shut and waited until someone arbitrarily guessed the right formula.
I would get my formula and then as I am told to, I plug-n-chug, I am figuring out what each variable means and what it stands for. That is how I stayed afloat through my lovely thirteen years in the Newton Public Schools. 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. The factoring and quadratics. This type of math as Dan Meyer put is, "really easy to relearn provided you have a really strong grounding in reasoning..."
That has turned us into what I have labeled as, "A Compromised Society." We are always looking for the easiest solution. This practice has seemed into our school systems, creating more students that want simple answers. No one is angry when a formula is given to them in math class. All you have 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 their final.
Through my experience, I do not have the time or the chance to even ponder 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. My solution was to not even bother thinking about it, not even fight with the teacher on dragging out this tedious time, but I just shut up. I kept my mouth shut and waited until someone arbitrarily guessed the right formula.
I would get my formula and then as I am told to, I plug-n-chug, I am figuring out what each variable means and what it stands for. That is how I stayed afloat through my lovely thirteen years in the Newton Public Schools. 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. The factoring and quadratics. This type of math as Dan Meyer put is, "really easy to relearn provided you have a really strong grounding in reasoning..."
In my experience, when I start 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. 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. This method of problem solving gives a notion of
simplicity and that we can always reach a nice convenient number. 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.” In
classrooms that I have been in, we are not thinking about the formulation of a
problem, we are just thinking about the problem and its solution. To really
understand a problem, reasoning is required.
Reasoning requires thinking. 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 answers that question very simply because it is giving us practice in analytical thinking. If we are not trained for analytical thinking, we end up using Siri for everything.
Our job market is changing. As Ilya Rifkin states, "there is a stark demand for someone that can genuinely think." 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 close 2,000 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 curriculums of the National Council of Teachers in Mathematics’
the Russian School of Math, it is not too astray. But what is different, is the
methodology behind the curriculum and expectations. This paper, due to its
limited scope, is unable to conduct deep analysis of curriculum development;
however, it can take an apparent look at the prospective of an institutional
model that genuinely brings about success in every aspect that is undeniable.
When
looking at the beginnings of 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.” [1]Approximately
315,000 (or 20%) of this group came to settle in America.[2]
Rifkin’s move to America was for the vision of success for 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. They were able to attain professional jobs and bought a house in the
suburbs of Newton for “the best educational system possible”. 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 from the material
and her high standards. 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. This awareness of a
potential failure due to her move to America was the drive for Rifkin to leave
her full time position in order to tutor her son. At that time, the Russian
immigrant community in the Boston area was coming to the same realizations.
They shared the frustrations of a lacking mathematical education. From the
shared frustrations and worries 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.
*Insert
American adult opinions on math here.
Math Matters
The school was created due to the acknowledgment of the
value of mathematics. As many of the Russian immigrants are engineers and
computer programmers, there is a 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.”
Analytical ability is a fancy term for problem solving.
Problem solving is the basics of the world we live in- the jobs that we need to
be qualified in, require problem solving at the most basic level. The best
problem solvers will get the best jobs. Because it doesn’t matter if you know
the formula, it matters if you can reason.
Math is not and should not be viewed as numbers and variables;
it is a mode of reasoning. And the Russian community truly values that, as I
believe any one should. 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
When Rifkin began her tutoring,
she had to look at the many differences in educational systems. 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.[3] He
believed in the maturation of abilities and potential for future advancement
instead of realized capabilities. He stressed on the process by which higher
forms are established bringing about some level of analytical efficiency.
Analytical efficiency is the ability to “comprehend and utilize existing
knowledge, and also enables them to more readily connect and adapt to further
knowledge.”[4] With higher analytical
efficiency, Vygotsky believed there is better human development for the
society. He believed the advancement of
the abilities occurred in the zone of proximal development.
In the zone of proximal
development, Vygotsky focuses on the pathways of learning instead of the
outcomes. ZPD had been defined as “the distance between the actual developmental level as determined by
independent problem solving and the level of potential development as
determined through problem solving under adult guidance, or in collaboration
with more capable peers."[5] More
simply, this means focusing on the process of learning instead of the product.
By doing so, individuals are gaining analytical efficiency and increasing their
capacity to produce knowledge.[6]
With this thinking in mind, the value of education moves from the test scores
and other such facts, to how an individual comes to seeing and understanding
the material and the relationship that their new knowledge has to other bodies
of information.
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.[7] By
being an enabler, the teacher avoids becoming a figure that forces information.
From experience, the math
teachers that I have had had difficulty engaging the entire class, and only the
passionate ones were successful. By the Vygotskyian model, both passive and
passionate students are engaged and are successful because they are all making
distinctions and connections with the dialogue of the class. In order for
students to learn within the zone of proximal development, students must be
learning in social-communicative interactions. Vygotsky believes that is
incredibly important. 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.”[8]
What I believe is truly unique
and important is scale of reciprocity between pupil and instructor. The teacher
provides a framework in which the students work and experiment with, and the
teacher then has the opportunity to work with active and engaged students that
are making connections to their previous base of knowledge, thus building a
stronger foundation. Rifkin is a firm believer in the significant relationship
between a teacher and a student.
Not only should a teacher 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.”[9]
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 turns away students from wanted to know more,
and expanding their curiosity, which is extremely dangerous and destructive.
At RSM, the reciprocity is
indispensable. 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. I believe that humans are curious by nature. As Daniel
Pink believes, we seek Mastery, Autonomy, and Purpose. If this curiosity and
challenge is not encouraged and welcomed, then how can we expect our students
to expand their knowledge base and expand their analytical efficiency? Now I am
not completely ruling out American teachers as teachers who discourage
questions. But I have had that experience in considerable amount of my classes,
and then a teacher doesn’t know what to do with me, so I get dismissed and
ignored. With that I grew some level of discomfort with math, because that
happened so often. 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 am never
afraid to ask questions and to seek more information, which I believe is an
invaluable quality to have as a student of any subject.
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. 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.”
Anyone can learn a sequence and
follow it. By learning through a 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. 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.”[10]
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 I looked at the math
curriculum for Juniors at Newton North, I saw that the requirements were:
series and sequences, exponents, intro to functions, exponential functions,
logarithms, circular trigonometry, and trigonometry laws. Not only is this
curriculum far behind the curriculum of RSM, but due to the step process that
it was taught in, and the unwelcoming environment of the classroom, I saw
little connection between the topics. If I were given a logarithms quiz right
now, I can guarantee I will not pass. This is due to compartmentalization. The compartments
that most students hold onto are the computation problems. But the math
reasoning, or the application of math processes to the world around us, is not
there.[11] Since
there is no “plot,” I could only put pockets of information away at a time. So
I only hold onto a small percentage of what I learned earlier. The topics are
heavily segmented and doesn’t allow for much retention or understanding.
As a student, I have adapted to
the format, 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 one. There is
almost no way of truly grounding the material that you cover. I would not call
this system as a place where I can learn. 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.”
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 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 show exactly how this is
done, Rifkin explains how she teaches the concepts of percents. When
introducing percents, she gives the students a word problem. She then would
allow the students to grapple with the concept and discuss it as a class. In the
discussion, a student mentioned what they learned about fractions since
fractions and percents are all parts of a whole. By using this method, “everything
that you ever learned is just one layer more…you repeat it constantly, you go
deeper and deeper.
Also,
at RSM, algebra is introduced at a very early stage. 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 in higher levels.
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. 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.”[12]
In the first and second grade, word problems begin framing questions in terms
of variables. 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
mentioned earlier, the teacher does play an integral role in the environment
for learning. If the teacher is not comfortable with the material, neither will
the students. Throughout high school, the teacher completely orchestrated if I
had a successful year or not. As a student, it is frightening to know that your
success lies in the hands of a teacher. I did not like that, so I had to
develop my own ways of translating what the teacher says. Not all students can
do that or even have the particular will to do that, since math is such an
undesirable topic. 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. With 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.”[13] 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.
Rifkin
is also resolute about how a teacher should explain a topic. She states, “Teachers
should never use the same explanation twice,” but instead look at every single
angle to approaching a problem. If explaining a concept that only about 20% of
the class understands, then there is no use in using the same explanation,
because the focus should be on the remaining 80%. She does not expect the teacher
to have every approach to a problem at their disposal, but students are
encouraged to show their own explanations to the class. The reciprocity builds
a unique and successful environment where everyone grows off of one another,
something that I have failed to find in any American classroom.
Furthermore,
the teachers are held accountable for maintaining their grip on mathematics. 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 has consistent
motivation.
[RSM
not only works with math, but also breaking down the biases held by American
students. Increasingly over the years, RSM has had a decrease in students of
Russian background, but an influx of students of American dissent. With the
Americanization, there are kids that have strongly grounded beliefs about
mathematics, and the school works to battle against those beliefs.]
Conclusion
As
part of recognizing the extent of the school’s success is found in measurement
of student achievement that go 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.”[14]
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.
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.
[1]
Barry Chiswick and Michael Wenz. The
Linguistic and Economic Adjustment of Soviet Jewish Immigrants in the United
States 1980-2000. IZA Discussion Paper No. 1726 (Auguist 2005) : 3.
[2]
Ibid
[3] Fred
Newman and Lois Holzman. Lev VygotskyL
Revolutionary Scientist (London: Routledge, 2003): 5.
[4]
Christopher Green (2008): 7.
[5]
Vygotsky (1978): 6.
[6]
Anne Edwards. “Researching Pedagogy: a Sociocultural Agenda” Pedagogy, Culture and Society 9 no.2 (2001):
171.
[7]
Mark B. Tappan. “Sociocultural Psychology and Caring Pedagogy: Exploring
Vygotsky’s ‘Hidden Curriculum.’” Educational
Psychologist 33 no. 1 (1998): 24.
[8]
Tappan, 30.
[9]
Christopher Green (2008): 14.
[10]
Christopher Green (2008): 11.
[11]
Dan Meyer
[12] Christopher
Green (2008): 13.
[13]
Christopher Green (2008). 15.
[14]
Christopher Green (2008). 22.
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