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Common Ground

Thoughts & Reflections

There’s a lot of buzz in the media about common core standards. Not only what it means for students, but also how it effects teachers. In this article, we thought we would take the opportunity to try to further examine what underlies this change, how it relates to Montessori, and learn more about how we can work together to achieve common ground.

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With the state-by-state implementation of common core standards, we have witnessed a shift in educational emphasis. Some might call it a cultural modification of our widely accepted assumptions and values. From a focus on rote memorization to the acquisition of critical-thinking skills, a concerted effort has been made to change the conversation. “Problem-solving”, has taken center stage.

What it means to think, as opposed to just recite short-term stored information, has become the focal point of these new, long-term measures. While this may sound like an oversimplification of the problem, the move towards evaluating the role thinking should play, remains the same. Namely, if we are to adequately prepare the next generation, to not only meet, but ultimately anticipate the challenges of the twenty-first century, thinking, it is said, is what will be required. Yet, how can we teach “thought”?

“ These standards are rigorous enough to prepare students for the real world. – Arne Duncan ”

In the Montessori community, many have applauded the transition to common core. They see it, and the move towards more concrete, substantiative explanations, rather than just abstract ideations of concepts, as a clear sign of the effectiveness of Montessori.

The success of Montessori, they articulate, is based on its ability to lay the practical framework for academic necessities, but also, and just as important, to inspire the confidence that thought demands. Alongside experience, Montessori has always promoted thinking as the cardinal point of what it means to learn.

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Thinking, it is agreed by both advocates of common core and Montessori traditionalists alike, must play a more decisive role in the education of our students. It is the bedrock of what it means to learn and to challenge oneself. Eventually, if we are to make an impact, and if we are lucky enough to develop an appreciation of the world, maybe, just maybe, we will leave it better off than we found it.

“ Memorization might have been a necessary skill needed to get us to the moon, but it didn’t provide the mechanical blueprints for the rocket ship, nor the impetus for the dream. ”

Of course, there are many details to common core standards, which extend beyond the scope of this post, but we thought it might be helpful if we concentrate on a specific set of problematics, or more broadly, the approach to mathematics, and how it directly corresponds to how Montessori treats math.

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As many of you have heard us say, for Montessori, the only way to truly understand abstract concepts, is to first develop a concrete appreciation. It’s kind of become a refrain for us in trying to best articulate the novelty of the academics that underlies Montessori:

“to get the pie-in-the-sky, you must first have a taste of the pie.”

With Montessori, then, we can describe the process as slowly working towards abstraction. Incrementally, we transition away from the physical, always keeping the end in mind. For instance, and to provide an example with the photo above, you’ll notice the tangible assistance the materials provide, as the student progressively works towards using only paper and pencil to solve their math problem.

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How does this approach resonant with the way “common core” addresses math? Well, as we will come to learn with the following example, posted below, it shares much of the common ground, not only with an emphasis on trying to form a concrete representation of the problem, but also in encouraging children how to think on their own.

Here’s an example of how most of us learned:

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This problem seems pretty clear. It’s simple subtraction. If you will, however, please take a moment and think about how you would solve this equation. Personally, we would first look at the column on the right, focusing our attention on the top. We would notice that 2-2 is 0, and place a 0 below, to reflect the operation. We would then proceed to the next column, to subtract 3-1, which would yield 2. When we put these together, the answer we arrive at is 20. This seems pretty straightforward.

Now, here’s an example of the same problem in common core:

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For many of us, we might be puzzled by this formulation. What’s at work here? Let’s take a closer look. When you glance at the column highlighted in green, you’ll notice that when you add those numbers together, you come up with the answer, 20. Yet, how exactly do we arrive at this solution? Isn’t it easier to do it the way we learned? Is common core just making things too complicated?

Let’s examine the problem, and try to unpack things. Let’s start from 12. If we take 12 + 3 that gets us to 15. We then take that 15 and add 5, to reach 20. With the 20, then, we add 10, to arrive at 30. We will require only 2 more units, which helps us reach 32, to complete our problem. What was added, therefore, (in the green column) is the answer to the equation.

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Taking things one step further, we thought we would offer one more example, to highlight the nature of the process, which can feel so foreign, especially to those of us with a different mathematical background. With the exact same equation, you could also start by adding 8 + 12 to reach 20. From there, the method would require that we add 10, to reach 30. This means that we would only need to add 2 more units to complete the equation. Once more, when you add up the green column, you arrive at the answer.

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This process, which is similarly aligned to the way children learn in Montessori, is trying to empower children to think on their own. It’s helping them break things down, to fully understand what they’re going to be building back up. Children do subtraction, by using addition.

“ The goal is to help children think on their own, having a firm grasp of exactly what they are trying to compute. ”

If we look back at how most of us learned, keeping in mind what we know of the decimal system, we can start to make sense of the logic behind this approach. With the first graph, the traditional approach, many of us simply do not think about what we are subtracting. We merely look at the numbers, make the calculations, and find the answer. Of course, this process is largely based on our foundations in memorization.

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Math, and the way it was taught, became too abstract. Math lost its relevance, because there was nothing to hold on to, nothing to firmly grasp. The common core, which essentially follows the one-hundred-year old approach by Montessori, is out to change this.

“ Common Core wants to make mathematics more concrete. ”

The common core wants the joy of understanding to come front-and-center. Yet, the question which we alluded to from the start remains. Will adults who were trained to think otherwise, by adopting the approach to math that doesn’t require thinking per say, be able to fully help children, students who have yet to know what it means to think on their own?

We’re optimistic.

It’s important to note, in the final instance, that while this new approach is starting to pick up steam, and the attention of the media is largely focused on academic relevance, it would serve us well to remember the other side: confidence, persistence, understanding, happiness and a willingness to thoughtfully engage in the world.

Written by:

Bobby George

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