Friday, February 12, 2010

Math duh!

Using the golden beads to represent four-digit numbers.
Hi All,
 I found this great article on Montessori Matters blog at
Word Press...she's great!

News Flash: Pre-Schoolers Can Understand Math Concepts (no duh)

December 22, 2009 in following the child, math, on being a guide, parent education, social issues
Tags: children, early childhood education, education, mathematics, montessori, neurocognitive research, new york times, school, schools, science, teaching

Yesterday, the most popular article on the New York Times website discussed a recent finding in the field of cognitive neuroscience.

Brace yourselves Montessorians!!! Contrary to long-held beliefs in the highest echelons of scientific research, the cognitive neuroscience community has discovered that children as young as four can grasp fundamental math concepts.

*pause for effect*

Uh, we could’ve told them that.

So, maybe we should!

Dear cognitive neuroscientists,

Congratulations on your ground-breaking discoveries in the field of pedagogy. You must have been quite pleased when you found out that young children can understand basic math concepts before the age of six. I’m so glad you finally put your expensive Harvard Ph.Ds to good use!

I hate to burst your bubble (actually, I quite enjoy it), but I thought you might want to know that a woman named Maria Montessori figured this out 100 years ago. Talk about arriving late to the party!

It is my pleasure to introduce you to the Primary Montessori classroom, where pre-schoolers have been actively working with math concepts – from numbers and quantities to long division and fractions – for over a century.

Maria Montessori believed that children have a natural curiosity for mathematical concepts, and look for order and patterns in the world around them. She called it the “mathematical mind”. However, because the concepts of math (the value of numbers, arithmetical operations, geometry, etc.) are not instantly recognizable to the untrained eye, Dr. Montessori deemed it necessary to create a curriculum where children could use concrete representations to discover these mathematical abstractions.

In other words, for children to understand what a number represents, what addition is about, or why we need to borrow during subtraction, they need to involve their senses, and we need to isolate the concept being introduced. These are two of the (many) reasons why traditional math education has never worked, and why so-called experts thought that young children were incapable of learning math.
Traditional approaches to teaching math have been truly uninspired and frankly insulting to a child’s intelligence. Using a pizza slice to illustrate the concept of a triangle is one of the dumbest things I’ve ever read about, and yet according to the NYT article, this technique is used in many children’s books (among many other equally idiotic tactics). And speaking of dumb techniques, why should pre-schoolers be using books to learn math, in the first place???

In Montessori, children start working with mathematical concepts around the age of three, when they are exposed to fractions, geometry, algebra, equivalences, and base-ten from a sensorial perspective (this means they’re using their senses to explore mathematically-precise materials without knowing they’re learning about math). By the time they’re 3 1/2, if they’ve been in the Montessori environment for at least six months, many are ready to begin their formal math education.

Yes, 3 1/2. I’ll give you a moment to pick yourself off the floor and climb back into your ergonomically-correct office chair. Ready? Let’s continue.

Associating symbols and quantities through the use of the number rods.

Montessori students move at their own pace through the math curriculum, first exploring quantities through the use of the number rods, then learning to identify symbols (aka, numbers 0-9), and then associating the symbol with the quantity.

Guide a child through this process, and voila! She can clearly understand that “5″ is not just a hard-to-write squiggle named “five”, but is an actual quantity she has carried, counted, and compared to other quantities. Deny a child the right to understand this concept clearly, and you’re setting her up for a lifetime of struggle and confusion.

Within a few weeks of commencing their formal math education, Montessori children will have learned about quantities, odds & evens, and the concept of zero as an empty space. Then it’s on to the decimal system, where – hold on to your lab coats! – children who just turned four learn how to work with four-digit numbers.

I bet you’ve never witnessed a four-year old who sees the number 8,657, says “eight thousand, six hundred, and fifty-seven”, AND represents the quantity accurately using golden beads. I know you’ve never seen this because, in the article, you were excited about children who could touch their nose seven times. You guys sure do have low standards for what children are capable of.

At the same time our students are discovering the joys of arithmetic, they’re also developing a clear understanding of what the numbers 11-99 represent, through the use of several beautiful, precise, and engaging materials. Skip-counting is also introduced, and the concepts of carrying and borrowing are practiced extensively.

As before, we follow a specific method of presenting the information to the children: first the quantity, then the symbol, and finally the association of the quantity and the symbol.

Yes, you mention this ground-breaking process in your article… Guess it’s not so ground-breaking after all.

Throughout this entire time, the children are free to move at their own pace, revisiting concepts as they see fit and staying with a particular material as long as necessary. If we, as guides, see that a particular concept has not been clearly understood by a child, we have the ability to bring him back to the appropriate material. We’ll gladly spend quality time re-presenting the concept and encouraging repetition through one-on-one games and small group activities.

Only when the above-mentioned concepts are clearly established in the child’s mind, will we guide her towards the memorization of tables. After all, what good is it to regurgitate 3+4=7, 3+5=8, etc. if there’s no understanding of what the concept means, and thus no way of applying it to daily life?

Oh, wait, I forgot. Traditional schools educate children to succeed on tests, so regurgitation is not only sufficient, it is required.

Well, here’s the thing: we, as Montessorians, would rather prepare children to succeed in life.

And speaking about preparing a child for life… If a child is fortunate enough to remain in the Montessori environment for her Kindergarten year, she will continue learning the arithmetic tables (always through the use of materials she can manipulate). Little by little, she will wean herself off the materials, as her brain matures and she learns to apply the knowledge she acquired in the first two years in the classroom. Upon solving an arithmetic problem without the use of the materials, it is not unusual for a five-year old Montessori child to remark: “I don’t know why I know, but I know.” If that doesn’t build self-esteem, I don’t know what does!

After reading the NYT article, it sounds to me like you guys are just re-inventing the wheel. Fortunately, you are starting to discover that you under-estimated children’s abilities (and over-estimated your own). Stop wasting time pretending your theories are ground-breaking, do some real research, and use your soapbox to give children the type of education they really deserve and are desperate for.

Welcome to Montessori. It matters more than you think.

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