Tuesday, September 23, 2014

Math Education: It Ain't 1975

It's been 4 months since I last posted on this blog.

4 months. A long time.

But it's been even longer since the 70s. In 1975, I was an elementary student, as were many of today's parents (...or, perhaps, grandparents!) In the past several months I've been doing a lot of thinking about the way the teaching of math has changed and how to communicate with families who were raised with a very, very different math education.

So today I reflect on how math education has changed since I was a schoolchild.

Second Grade, 1975
Yes, that is a poncho!
Might even be wearing culottes/gauchos.

When I was a child...
I thought only some people had math smarts. And then there were the rest of us. Except for a fraction blip in 4th grade, I thought I was one of the smart people. Then I hit high school and it didn't make sense anymore. But I still got an A because our teacher wore 2 hearing aids, didn't take questions, and only required us to turn in one paper as a whole class.

Today's children...
benefit from researchers like Carol Dweck. Children learn that growth mindset means they can become better at math if they work hard and persevere.

When I was a child...
I thought that the correct answer was the only thing that mattered in math.

Today's children...
know that while the correct answer is important, it is also essential for them to be able to communicate the answer and the mathematical thinking behind it; communication skills are essential for twenty-first century work places.

When I was a child...
From Math Vocabulary Cards app
I didn't really use--or even consider--mathematical vocabulary.

Today's children...
use precise mathematical language, symbols, and labeling to create tools for understanding. We've learned that neglectful use of language can lead to misconceptions as students move into upper grades and more complex math topics.

When I was a child...
I thought there was only one way--the standard algorithm--to do a problem. It worked...most of the time...if you could remember the steps. A lot of my peers could not. And we wonder why two-thirds of American adults are math phobic.

Today's children...
learn a variety of mathematical strategies that help them make sense of math. Over time, they are able to select the strategy that is the most efficient for a given situation.

When I was a child...
numbers were the only option. And then, only if you could memorize the steps using the numbers.

Today's children...
use a wide variety of manipulatives (sometimes on an app!), tools, sketches, pictures and models to represent their thinking visually, using concrete items to make sense of the abstract. Math means something because they can model the mathematics behind a problem. They see it and understand it.  3 x 4 is more than a math fact. It's the dimensions on an array that show the area as a product in the number of square units.

When I was a child...
math was a solitary endeavor. Each of us hunkered down to answer our own problems--odd or even or, gulp (!), both--out of the textbook. No talking!

Today's children...
talk about their strategies and solutions. They learn about efficient ways to solve problems as they listen to one another. They prove their thinking and critique the thinking of others, deepening skills in communication while increasing conceptual understanding.

When I was a child...
math didn't necessarily make sense. Math was just math: plug numbers into a standard algorithm and arrive at an answer...hopefully the right one.

Today's children...
know that math makes sense. They look for patterns and structures. They might make sense of 4 x 6 by knowing that it's made up of 2 sets of 2 x 6...  2 x (2 x 6).  (See right.) They know that if you "make 10" a problem is easier to solve. So they might see 9 + 4 as 10 + 3. They can reason that 15 x 13 is (15 x 10) + (15 x 3). Math makes sense.

When I was a child...
math with any complexity whatsoever was done with paper/pencil.

Today's children...
can do a problem like 16 x 12 in their heads. In seconds. Because they can picture it. (See left.)

When I was a child...
it felt as if math was isolated to math class.

Today's children...
know that math is everywhere.




It's not 1975 anymore. And my students (who laugh after hearing that I was taught problems could only be solved one way) would say that it's a good thing, mathematically speaking.



8 comments:

  1. Welcome back to blogging, Cynthia. I have a lot farther back to reach for my elementary school math ed, but I loved wearing gauchos in the 70's. Glad to know that math has become more conceptual and visual. I would have liked that.

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    1. Thanks, Shirley. I wish my math education had been far more conceptual & visual. But then, OTOH, I might have never become an English major. ;)

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  2. I love this post and the childhood photo! There's been wonderful changes in teaching of math which is a relief. But curious to know how children are tested in mathematics these days. Do they require them to how work (written explanation or visuals)? Also, I just read recently that they don't use the term "improper" fraction anymore.

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    1. Hi Min! Good to hear from you! I think the new testing will require a lot more of students than it did in the past. You can find PARCC and SmarterBalance samples online. I just read an article that said that the SAT is also being changed to reflect current practices. Since this is the first year of implementation of testing, it will be interesting to see if it's succeeds in the intent... Didn't know that improper fraction isn't used anymore. Will have to check into that! ;)

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    2. p.s. do you have a link that talks about the term "improper?"

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  3. I just looked it up. It was in the Beast Academy 3D Guide. It must have been a personal preference of the writers because they believe there isn't anything "improper" about them so they choose to call them just fractions. Lol.

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  4. Love your post! I'm a huge fan of Carol Dweck.

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