Wednesday, 9 September 2009
Maths Lament and Dice Games
One of the home ed lists I'm on pointed me at this wonderful maths essay:
http://www.maa.org/devlin/LockhartsLament.pdf
It is the sort of thing that makes you (ok, makes *me*) yearn to be a mathematitican. A passage half-way through got me thinking:
"SIMPLICIO: Then what should we do with young children in math class?
SALVIATI: Play games! Teach them Chess and Go, Hex and Backgammon,
Sprouts and Nim, whatever. Make up a game. Do puzzles. Expose
them to situations where deductive reasoning is necessary. Don’t
worry about notation and technique, help them to become active and
creative mathematical thinkers."
That struck a chord. Our eldest is now seven and although very good at mental addition and subtraction, we're struggling to get him interested in multiplications or any writing. (I know I shouldn't worry, but that's easier said than done.) Then I had an idea. He loves cricket, could I make up a game that would need multiplication and involved cricket. What I came up with was to throw three six-sided die and multiply the resulting numbers to get each batsman's score. E.g {2, 4, 3} results in a score of 24. You then of course need to add up the scores to get the team result. This game in hand #1 son wrote down all of the names of the English and Australian cricket teams (I helped with spelling) and did lots of multiplication. Past experience says this game will stick for a week or two then we'll be on to the next thing.
Has anyone got any pointers to other games that need multiplication as part of the game play? Any suggestions for other simple dice-based sports simulations?
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Having posted this blog I received the following forwarded on to me:
How Can Parents Help Challenge Young Math Students?
Too many bright elementary school math students spend their time sitting through lessons aimed at struggling classmates, and completing problem after problem on concepts they already mastered. These students quickly conclude that math is boring.
Parents need to take the initiative and find appropriately challenging substitute assignments for their child to work on in class.
Students who can learn independently would enjoy working through the book, The Ten Things All Future Mathematicians and Scientists Must Know (But are Rarely Taught). Written by former teacher Ed Zaccaro, Ten Things illustrates the connection between math, science and the real world through analyzing events such as the Three Mile Island nuclear accident.
Number Sense and Nonsense, by Claudia Zaslavsky, presents challenging problems, puzzles and activities on interesting number concepts such as "Zero - Is It Something? Is It Nothing?"
Students may also be intrigued by It's Alive, by Asa Kleiman and David Washington. Promising "math that makes you squirm," this book offers problems to "challenge, motivate and gross-out math students who like the unusual."
If Internet connections are available in the classroom, the Web also offers a wealth of playgrounds for inquiring young math minds.
For open-ended math exploration, students can go to http://www.mathcats.com. Younger students in particular might be intrigued by the math cats balance section, where they can try to virtually balance objects ranging from electrons to galaxies.
The wonderful University of Cambridge site, http://nrich.maths.org/public, offers intriguing problems (with solutions) on a variety of challenge levels, math games, and interesting articles on issues such as math palindromes.
As for homework, if students can get four or five problems of an assignment completed correctly, that should be the end of the exercise. Parents then need to provide options that offer more challenging and thought-provoking opportunities for math exploration.
All the books and Web sites mentioned above for use in the classroom can be used at home as well.
Parents can also explore math concepts together with their child at Web sites such as http://figurethis.org. This site offers math challenge problems for families, including guidance about how to get started thinking about the problem, solutions and follow-up problems.
Parents and students are also encouraged to think together about "unusual and important" math ideas at http://www.ccs3.lanl.gov/mega-math.
While fully meeting the needs of advanced math students can be difficult, these approaches offer a simple start for for parents and schools to keep talented young mathematicians challenged and intrigued.
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