Draft #2

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.

[Charlene 1] 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 seemed into our school systems, creating more students that want simple answers. [Charlene 2] No one[LKam3]  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. [Charlene 4] This type of math as Dan Meyer put is, "really easy to relearn provided you have a really strong grounding in reasoning (Meyer[LKam5] )."

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. [Charlene 6] 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. This method of problem solving gives a notion of simplicity and that we can always reach a nice convenient number. [Charlene 7] 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, 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" (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(Kamenetsky).

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

[Charlene 8] [Charlene 9] 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 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.

[Charlene 10] 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” (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 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. 

[Charlene 11] [LKam12] 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. Illya 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). [LKam13] 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.

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” (Rifkin, Inessa).

[Charlene 14] Analytical ability is a the basic ability potential employers need in 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 and come up with a viable solution

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. [Charlene 15] 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.[LKam16] 

The Fundamentals

[Charlene 17] When Rifkin began her tutoring, she had to look her own education, and see why she and her peers were successful now. In her research, she found that a key element in her educational background can be attributed to Lev Vygotsky.

Vygotsky was a 20^th 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. [Charlene 18] [LKam19] Analytical efficiency is the ability to apply knowledge by connecting to previous knowledge (Green, 7). “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 [Charlene 20] zone of proximal development or more commonly known as, ZPD.

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] [Charlene 21] 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. [Charlene 22] 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. [Charlene 23] 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]

[Charlene 24] 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.

[Charlene 25]  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, [Charlene 26] which is extremely dangerous and destructive.

[Charlene 27] 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.[Charlene 28]  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. [Charlene 29] 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.

[Charlene 30] 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. [Charlene 31] 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.

[Charlene 32] 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.

[Charlene 33] 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. [Charlene 34] 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.

[Charlene 35] 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 4^th graders than to a group of 11^th graders.” From the outlined curriculum for 11^th 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. [Charlene 36] 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 5^th 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 6^th 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

[Charlene 37] 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?

[Charlene 38] 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.

[Charlene 39] 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.

[Charlene 40] [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 7^th and 8^th grade average of 672/800 whereas the national average for 11^th 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.

[Charlene 41] 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.

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[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.