Monday, November 26, 2012

Delayed Math and Reading: Not as radical/scary as it sounds

From Trivium Pursuit: Delayed Formal Math Approach:

Depending upon the child, upon the method, and upon the subject matter covered, there exists the potential for developmental harm from the formal teaching of arithmetic before age ten. Small children cannot understand many arithmetic concepts at an early age. We can teach them to perform the process, but we cannot make them understand the concepts. The child “learns” to hate “learning.” The child’s understanding develops along the wrong lines. He may actually develop mental “blocks” to arithmetic – actual physiological blocks in the brain.

I find this idea of delaying formal math interesting, especially since it is based on a historical perspective and education research. My own take is that math is a language and therefore its vocabulary should be taught every single day, just like we use letters and simple words every single day with our very young children. Further, I think math should be a game, always. When it is considered a game, it's less likely to cause the physiological brain blocks referenced in the quote above.

With math-as-games, I think it's okay to challenge children before age ten.

We are using Singapore math 1A/1B this year, but more often Gilgamesh's math learning is coming from his own independent play with manipulatives, refrigerator magnets, and technology (flash card app on my phone, exercises).

He's getting a much broader base in math than I ever had, especially for his age, because we aren't obsessing over a "spiral method" or a "linear method." To label it, I guess it would be a Pyramid Method: broad foundation leading up to finer math later on. He's played with:

  • cardinal and ordinal numbers
  • sets
  • addition
  • subtraction 
  • multiplication
  • division
  • charting
  • graphing 
  • tallying 
  • skip counting 
  • time-telling
  • money-counting 
  • scales
  • measurement
  • estimation
  • geometric building 
  • fitting shapes into each other (tangrams, pattern blocks)
  • spotting and creating patterns
  • symmetry
  • sorting
  • three-dimensional and two-dimensional shapes
  • geometry terms
  • story problems
  • dot-to-dot 
...and probably some things I'm not even aware of, as he's sponging up anything he sees, hears, or reads even when I'm not around to make sure he does.

I've read many opinions about delayed math and delayed reading, and even delayed potty training. I see the wisdom in it with a child who is struggling. But I think the terminology is wrong. It isn't really delayed -- just channeled differently.

Instead of forcing a young child through a traditional reading program, we take a step back and read copiously to the child, help him notice traffic signs, cereal boxes, help him memorize sight words through word games: give the reading context and fun.

Not delaying math, you're really just giving them room to learn some of the intuitive principles on their own, making them come to you when they want to know how to carry the one, how to multiply big numbers, etc.

Through extensive read-aloud time with my oldest child, he began asking about apostrophes at the age of 4 and understood the basics of the contraction at that age. Now, at age 5, he's learning that it can also mean possession and that that's different for plural possessive. I didn't miss an opportunity by waiting to explain the intricacies of apostrophe usage. Rather, I introduced it as he became interested, and he understood it because he wanted to understand it. At 4 1/2, he was reading at a first grade level. Now, at 5 3/4, he's reading on the cusp of a fourth grade level. We didn't delay reading training. But we didn't force it on an arbitrary schedule either.

Through math play, he's come to addition of double-digit numbers because of his own interest. Story problems are more of a natural thing as he looks to math to solve questions in his own play: how many blocks can I stack up, how many should make the base of the pyramid so I can end with one on top and use all of them, etc.

So, to ease the troubled minds of parents who read "delayed" and think "problem" and "stunted," think of it in these terms: You're not delaying crucial life skills. You're only delaying the formal, rigid structure of the way you were taught reading or math. What you're really doing is channeling your child's focus into the basic vocabulary, letting her play with the basic tools to see how the pieces fit together and what it means to her personally.

If a child knows enough Latin words, it will be a piece of cake for him to learn the language when he is developmentally ready. That's the principle here, as well.

Give a child a fish and you've fed him for one meal. Teach a child to fish and you've fed him for a lifetime. Hand a child the tool, the fishing rod and the fishy lake, and give him a few hours to himself... and he'll teach himself.

Photo source: Great Lakes Echo

As parents and teachers, sometimes all we need to do is provide the tools, be accessible for questions, and then get out of the way.

p.s. This fits into classical education's trivium stages of grammar, logic, rhetoric, believe it or not. This research only claims that a child's logical faculties aren't ready to absorb complex math principles until 8-10 years of age. That doesn't mean we should delay memorization of math (and reading) facts. Just as students memorize the states and capitals without necessarily understanding that Phoenix is hot and Juneau is cold, they can memorize that 8 x 6 = 48 without understanding that it means six hours of work at $8 an hour earns them $48. The understanding and depth can come later, during the logic stage. But those building blocks can and should be put into place now.

Friday, November 23, 2012

Purpose and Priorities in Education

I just read this teen's open letter about standardized testing. He's making a documentary about education and how standardized testing has affected the education of many young people. 

I think this is important. 

Students absolutely should be engaging in the global and national conversations about education. Of course, this would have been a lot easier had education been returned to local control (under a President Mitt Romney). Unforunately, that's not in the cards. Our current POTUS, President Barack Obama, is only a reformer insofar as it means making America like all the other nations of the world and increasing globalization. He doesn't care about the quality of education; he's more interested in its quantity -- that is, making sure all students fit under the umbrella of government schooling

While I agree all children should have access to learning tools, I disagree that all students deserve and need the same education. The difference? 

Learning tools tend to be universal: letters, numbers, blocks, books, videos, internet access. They are tools which can be used to present information in a beautiful variety of ways. 

It's not the same thing as providing "education" which to the government generally means a standard curriculum which all children are taught and must be proved to have accepted by means of standardized testing. 

But how is this resolved? How do we ensure we are providing top-notch tools and making sure those tools are used wisely for continued learning? How do we ensure students are prepared to become productive citizens who are also independent thinkers?

It's so tricky, really. I mean, there's a reason we haven't gotten it all sorted. 

The way I see it, there are two legitimate purposes for education, and a third more cynical purpose: 

1) To expand the mind and allow continued learning, 
2) To provide preparation, life skills, and job training, 
3) To manipulate the culture to fit a government ideal.

For that first purpose, you really don't need any kind of testing at all. Teachers can tell if a child is learning or not, and with such a broad goal as "continued learning" there's ample room for creative encouragement. In the past, before this round of standardized testing, American schools embraced the fuzzy math, creative spelling, e-for-effort ideal. The result of ignoring life preparedness and job training has been pretty glaring: America has fallen behind.

For that second purpose alone, you get China. No wiggle room for different types of learners. The sole purpose of education is to produce educated, useful citizens. You test into your caste system, as it were. Even before NCLB, we had this obsession with standardized testing. The results are no more desirable than previously. You get squashed spirits, kids who do fall behind a standardized norm, and tremendous burnout so that by the time kids get to college, they just want a break.

The third purpose needs no help. Those wheels have been in motion a long time, stretching into higher education and ensuring all teachers value the same government-sanctioned cultural ideals.

Going forward, we really need to figure out what our priorities are as a society. Personally, I value both 1 and 2, and am wary of 3. I'd rather see parents take care of cultural training. Nobody is an island, and we couldn't keep our kids from popular culture if we tried, but that doesn't mean we have to give up our traditions to favor a whitewashed, government model of culture. I know many immigrants have lamented that their children are abandoning their language and heritage because of this cultural immersion in government schools.

But where is the balance between 1 and 2? Is education for learning or job training? 

And who gets to decide?

My own view is that the decision should be left to individuals. Some schools (college prep, etc.) could specialize in life preparation and job training while others (charter schools with a fine arts focus) could specialize in the virtue of learning, separate from its job applications. 

The only way this works, though, is for school choice to become the norm. And that rubs the wrong way anybody who believes all kids should be learning exactly the same things (standardized education proponents). 

So the battle continues.