Get in the math car with a list of destinations and no map. Take whatever route you want, and marvel at the things you discover along the way.
— Nick Harris
CREDITS: Today’s quote is from @Mr_Harris_Math, via Twitter. Background photo courtesy of Forrest Cavale (CC0 1.0) via Unsplash.
The January math education blog carnival is now posted for your browsing pleasure, featuring 23 playful ways to explore mathematics from preschool to high school:
Highlights include:
Young children making bar graphs.
A wide variety of math games.
Fractions on a clothesline.
Quadrilaterals on social media.
Non-transitive dice.
Writing in math class.
Negative number calculations made physical.
Inverse trig graphing.
Function operations.
And much more!
There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else — but persistent.
— Raoul Bott
CREDITS: Today’s quote is from Raoul Bott, via The MacTutor History of Mathematics archive. Background photo courtesy of Swedish National Heritage Board (CC BY 2.0) via Flickr.
[Feature photo above by Samuel Mann (CC BY 2.0) via Flickr.]
Here’s one more quote from homeschooling guru Ruth Beechick. It applies to classroom teachers, too!
Everyone thinks it goes smoothly in everyone else’s house, and theirs is the only place that has problems.
I’ll let you in on a secret about teaching: there is no place in the world where it rolls along smoothly without problems. Only in articles and books can that happen.
— Ruth Beechick
You Can Teach Your Child Successfully (Grades 4-8)
[Feature photo above by Samuel Mann, Analytical Engine photo below by Roͬͬ͠͠͡͠͠͠͠͠͠͠͠sͬͬ͠͠͠͠͠͠͠͠͠aͬͬ͠͠͠͠͠͠͠ Menkman, both (CC BY 2.0) via Flickr.]
An algorithm is a set of steps to follow that produce a certain result. Follow the rules carefully, and you will automatically get the correct answer. No thinking required — even a machine can do it.
This photo shows one section of the first true computer, Charles Babbage’s Analytical Engine. Using a clever arrangement of gears, levers, and switches, the machine could crank out the answer to almost any arithmetic problem. Rather, it would have been able to do so, if Babbage had ever finished building the monster.
One of the biggest arguments surrounding the Common Core State Standards in math is when and how to teach the standard algorithms. But this argument is not new. It goes back at least to the late 19th century.
Here is a passage from a book that helped shape my teaching style, way back when I began homeschooling in the 1980s…
“Understanding this item is the key to choosing your strategy for the early years of arithmetic teaching. The question is: Should you teach abstract notation as early as the child can learn it, or should you use the time, instead, to teach in greater depth in the mental image mode?
“Abstract notation includes writing out a column of numbers to add, and writing one number under another before subtracting it. The digits and signs used are symbols. The position of the numbers is an arbitrary decision of society. They are conventions that adult, abstract thinkers use as a kind of shorthand to speed up our thinking.
“When we teach these to children, we must realize that we simply are introducing them to our abstract tools. We are not suddenly turning children into abstract thinkers. And the danger of starting too early and pushing this kind of work is that we will spend an inordinate amount of time with it. We will be teaching the importance of making straight columns, writing numbers in certain places, and other trivial matters. By calling them trivial, we don’t mean that they are unnecessary. But they are small matters compared to real arithmetic thinking.
“If you stay with meaningful mental arithmetic longer, you will find that your child, if she is average, can do problems much more advanced than the level listed for her grade. You will find that she likes arithmetic more. And when she does get to abstractions, she will understand them better. She will not need two or three years of work in primary grades to learn how to write out something like a subtraction problem with two-digit numbers. She can learn that in a few moments of time, if you just wait.”
— Ruth Beechick
An Easy Start in Arithmetic (Grades K-3)
(emphasis mine)
I just sent out my first newsletter to everyone who signed up for math updates. If you’re not on the mailing list, you can still join in the fun:
[Feature photo above by Scott Lewis and title background (right) by Carol VanHook, both (CC BY 2.0) via Flickr.]
Did you know that playing games is one of the Top 10 Ways To Improve Your Brain Fitness? So slip into your workout clothes and pump up those mental muscles with the Annual Mathematics Year Game Extravaganza!
For many years mathematicians, scientists, engineers and others interested in math have played “year games” via e-mail. We don’t always know whether it’s possible to write all the numbers from 1 to 100 using only the digits in the current year, but it’s fun to see how many you can find.
Use the digits in the year 2015 to write mathematical expressions for the counting numbers 1 through 100. The goal is adjustable: Young children can start with looking for 1-10, middle grades with 1-25.
Denise Gaskins' Let's Play Math 