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The following article is by Robert M. Berkman who has worked in mathematics and science education since 1984. He publishes educational materials under the name SamizdatMath, which can be found on

**Teachers Pay Teachers**. His also has a blog is entitled Better Living Through Mathematics. He currently lives in Brooklyn, New York.
I've always found Robert's forum posts and blog articles interesting because they contain a great deal of depth along with a bit of humor. He was kind enough to agree to write an article as a guest blogger for my blog. I think you will find the following article (it's part of a full day workshop called “Wiring the Brain for Mathematics Neuroscience and Numeracy") very thought provoking.

__Thinking About Skills, Context and Neuroscience__Many years ago I was hired to coordinate a mathematics program at a private school in Manhattan: I had been a classroom teacher for the previous 15 years, and my views definitely tilted towards the “progressive” end of the educational philosophical spectrum. I had no choice: I had seen the results of both “traditional” and “progressive” educational practices, and while neither was perfect, I definitely saw that progressive practices aligned better with what I wanted to see happen in the classroom. I remember the “sage on the stage” practices from my own school years, and while I responded to well to them (I was that kind of learner), many of my classmates were left in the dust. At the same time, I was familiar with the criticisms of progressive math practices, and was ready to modify practices in the classroom to address them.

Of course, although I had a thorough understanding of what progressive math looked like, this did not mean that everyone with whom I worked shared that same comprehension. I had two “bosses” at this school: the first was the head of my division, which spanned from kindergarten through 4th grade; she was impressed by both my philosophy and how I intended to translate it into practice.

My other “boss” was the chair of the math department, who was ten years my junior and lacked any kind of experience or understanding of what a K - 4 mathematics program looked like. She held some very ignorant views of progressive education, including the idea that using these methods, students would not be required to learn “basic facts.”

This came to a head during a meeting where “Jen” (I changed her name to protect those with similar names) described a situation where a 7th grade student she was tutoring for several months had forgotten the answer to 6 x 8. She recounted how she prompted the student to figure out the answer for himself and then watched in dismay as the student made 6 rows of 8 dots per row, and counted them one by one. Initially, I wanted to say the following: “Jen, you must be a pretty cruddy tutor if the parents are paying you all this money to help their son, and you wasted 10 minutes watching him draw and count out all these dots. Why didn't you just tell him that 6 x 8 is 48?”

However, Jen was my boss, so I activated my internal editor and I sadly shook my head and agreed that this was a sad state of affairs. But I also understood that this colleague was inadequately informed about many aspects of educational philosophy, especially the difference between “practice” and “outcomes.” Unfortunately, engaging her in discussions to tease out the difference inevitably led her to recount yet another story of a “progressive education failure.”

So let’s begin at the beginning: progressive education, in which I firmly believe, has nothing to do with the outcomes of that practice. There is nothing in the practice of progressive education that states that students don’t have to learn how to add, subtract, multiply or divide. This is because progressive education has nothing to do with outcomes: it has to do with methodology. As a progressive educator, my goals are fairly anodyne: I want my students to master mathematics with a balance of conceptual understanding factual knowledge (like computational facts) as well as the application of the latter to problem solving. This doesn’t sound particularly “radical” to me, and I would expect that it probably sounds reasonable to even the most traditional mathematics educator.

I’ll repeat this again:

**progressive and traditional mathematics educators seek exactly the same outcomes**. Where we part ways is in the methodology: when I think of “progressive,” I don’t long for some long-lost 60’s era where students wrestled with “new math” or counted on their fingers in 5th grade. As a “progressive,” I’m sensible enough to understand that the “good old days” never really existed, and that students of today struggle with the same learning issues that they did in bygone years. I also don’t buy into the fact that students today are “different” from those of 10, 20 or even 100 years ago: students are students, and except for the fact that they’re more likely to come from economically impoverished households, I haven’t really seen much of a change in my three decades of teaching.

As a progressive educator, I do believe in one thing: scientific research. As a progressive, I’m interested in what advancements have been made in understanding how the brain comprehends the world and how it learns new things. My particular interest is in the neuroscience of numeracy, which has led to great insights into the learning of mathematics during the last two decades.

One of the best books on the subject is Brian Butterworth’s book,

**What Counts: How Every Brain****is Hardwired for Math****.**Although this book is 15 years old, it presents the basics of how the brain works with numbers quite clearly and with a minimum of jargon. My favorite chapter is where Butterworth demolishes “neuromyths” like the idea that the ability to work with numbers is localized to the left side of the brain. How this pernicious piece of factual idiocy got indoctrinated into our educational culture is beyond me, but it still remains pervasive, perhaps because some people make a living perpetuating it as a “fact.”In the course of his book, Butterworth describes a finding which would have helped Jen’s student who had forgotten the solution to 6 x 8. As it happens, multiplication facts are stored in a particular part of the brain that works with language, particularly words that are remembered as associations. This would include things like song lyrics, nursery rhymes and prayers. In essence, they are linguistic phrases that we repeat over and over again with little thought. The remedy was not to ask the student to “figure it out,” but to teach him the fact and help him create a “linguistic hook” that would help remind him of the answer when it appeared again (such as “6 x 8 is really great because the answer is 48....”) To me, this is what progressive education is about: I too want that student to have factual knowledge, but I want to use what science has shown me to help troubleshoot and correct the student’s deficit.

Of course, this brief treatise does not begin to cover the complete belief system of the progressive educator, but it should give you a better understanding of its depth and complexity. In fact, you may be using the technique I described in the previous paragraph, in which case, congratulations and welcome to our ranks!

*-Robert Berkman*
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