Showing posts with label math. Show all posts
Showing posts with label math. Show all posts

May 14 - Happy Birthday, John C. Fields

    Posted on May 14, 2022


This is an update of my post published on May 14, 2011:



As a college professor and math researcher in the late 1800s, John C. Fields was disappointed in the state of math research in North America (he was Canadian and was teaching in the U.S.). So he went to Europe to hang out with some math greats and to make some math discoveries.


When he returned to Canada in 1902, Fields worked hard to raise the reputation of mathematicians in North America. One way that society honors people is to award prizes and especially to award prize money. So Fields started an award for younger mathematicians to give recognition of their contributions to mathematics, and also to help support their work with a monetary prize of $15,000.


The Fields Medal is very prestigious and is considered the Nobel Prize of Mathematics. (But Nobel Prize winners get a million dollars!!) One thing that makes this award different from most is that it has to be awarded to a person who is less than forty years old.



Wonder about math...

When I read about mathematicians, I often see words like research and discovery – and for a while there, that surprised me. In my world of helping little kids with arithmetic, math has been something to be learned and used—something very, very practical as we deal with counting things, money, time, measuring lengths and weights and volumes... Math seemed like something to be used in professional research or scientific inquiry--rather than to be the subject of it. And using a word like discovery made me feel like there must be some magical math land that mathematicians visit—and that they come back and tell the rest of us about their latest findings...

But as I read and heard more about all the fascinating areas of math research and exploration - even in popular TV shows, like the 2000's series NUMB3RS - I realized more and more that "higher math" could seem esoteric, but mathematical discoveries can be used in practical fields such as detective work and robotics and architecture and and and....


What would Mathematics Land look like?




Enjoy math!

If you like the idea of Mathematics Land, be sure to check out The Phantom Tollbooth, by Norton Juster, and A Gebra Named Al, by Wendy Isdell.


If you like the idea of math being all around us and very useful, check out the book Math Curse, by Jon Scieszka.


And of course, there's always that wonderful old Disney film Donald in Mathmagic Land! Love it!



Also on this date:


































Birthday of botanist and chromatography pioneer Mikhail Tsvett 




(Second Saturday in May)




(Second Saturday in May)



(Second Saturday in May)





(Second Saturday in May)










Plan ahead:



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January 31 - Happy Birthday, Sam Loyd

  Posted on January 31, 2022


This is an update of my post published on January 31, 2011:


Take a great game like chess and cross it with the fun of puzzles—and you might just get what is called a chess composer.

I didn't know such a job title existed, either, but apparently there are people who create chess problems for others to solve. Sam Loyd, who was born on this day in 1841, was a popular and witty chess composer. He can also be said to be a recreational mathematician.


Sam Loyd was obviously pretty good at chess. At one time he was one of the best chess players in the United States and #15 in the world. But he could never be truly great because he would go for complicated and fantastic layouts on the board rather than just going for the win.

Loyd was known for self-promotion—even to the point of lying about his accomplishments. For example, he claimed that he had created the 14-15 puzzle in which players slide number tiles within a frame in order to put them in numeric order—but he had nothing to do with the invention or popularization of the puzzle.
However, Loyd did create a number of popular chess problems, Tangram designs, and other sorts of puzzles or problems. One of the most famous chess problems ever is his Steinitz Gambit problem. Loyd's chess puzzles were so popular that he was inducted into the U.S. Chess Hall of Fame.


Learn chess online, for free, at Chess Kid.


Here is Kid Chess's Puzzle Jam. 


Try Tangrams and other math puzzles. (I love the puzzles in Simon Tatham's pack!)





(Last Monday in January)



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November 27 - Happy Birthday, New-Math Guy!

 Posted on November 27, 2021


This is an update of my post published on November 27, 2010:



Edward Begle, who was born on this day in 1914 in Michigan, became a mathematician—a topologist, to be exact. (Topology is the study of shapes and spatial properties of things, even when those things are deformed—say, bent or curved around or stretched.) 

When the Soviet Union surprised the world by successfully launching a man into outer space (the 1957 Sputnik 1 launch), many people in the U.S. became upset. Americans had thought of themselves as leaders in space technology. Some people called for better education, especially in math and science. Because of these calls for newer, better math instruction, a group called the School Mathematics Study Group was launched, and Begle was chosen to be the director.

In the 1960s the group released educational materials for all levels of school (K-12), and the these materials and the philosophy behind them were dubbed “The New Math.”

Begle thought that traditional math relied too heavily on memorization and drill of algorithmic processes. (An algorithm is a set of steps designed to solve a problem. For example, when doing long division - say, 425 divided by 25 - you might say to yourself, “25 goes into 42 one time, 1 times 25 is 25; 42 take away 25 is 17; bring down the 5; 25 goes into 175 seven times, 7 times 25 is 175; 175 take away 175 is zero. So 425 divided by 25 is 17.” These repeated steps of dividing, multiplying, subtracting, and “bringing down” make up the algorithm of long division.)


Many kids successfully memorized “math facts” but then later forgot them, and many kids didn't know which algorithm to use to solve particular math problems.


My brain on "old math" - a whole bunch of memorized
algorithms mixed up, misunderstood, and mis-remembered.


Begle thought it was more important that kids develop understanding of the fundamentals of mathematics.

Begle was right about all of that, and yet “New Math” has been considered a giant flop. By and large, students, parents, and even teachers didn't like it, and it was abandoned rather quickly. It is still sometimes referred to, even today—but almost always with scorn.

New Math and Me


I went to school while New Math was being taught, and I actually liked it! We learned lots of stuff about sets, Venn diagrams, and number bases. I understood it, and I still remember it pretty well—although how much I've actually USED it is another thing altogether.





I was also taught traditional math algorithms with traditional drills and timed tests—and I hated that stuff! I obediently memorized algorithms but didn't understand most of it, and eventually things I supposedly knew how to do mushed into one big glom of half-remembered muck. I would get the steps to adding fractions mixed up with the steps to reducing fractions, say, or forget when and how to cross multiply. I became more and more sure that I was terrible at math.

Years later, I learned the “why” of all those steps and all those processes—and I got a lot better at math. If I can't remember an algorithm, my understanding of what I'm actually doing helps to me re-invent it. My own experience, plus tons of research findings, show that Begle was correct when he said that understanding is more important than memorization.



If he was right, what went wrong with New Math?

Some of the topics introduced with the New Math materials were far outside of kids' experiences, and when stuff is completely irrelevant, it's usually hard to learn. Also, some of the abstract concepts were taught too early, when kids should be using real things that they can count and sort and measure. Finally, most teachers and parents felt uncomfortable with the new-ish concepts and wondered why on earth anyone needed to know that stuff, so the lessons were undercut by their attitudes.

There was a lot of coverage of the whole backlash: "New Math"?
Why do we need NEW math? What's wrong with the math I
learned as a kid?


If you've never learned about Number Bases...


...give the topic a whirl with Cut the Knot lessons.






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