I wandered over to see how one of my best students was performing. This student, I was confident, would do well in the test, and indeed get an A for the subject. I was right. But what I saw as I looked over her shoulder will stick in my mind until the end of my career.
The student had almost completed a difficult problem. All that remained to get the right answer was to multiply one and a half by two. A piece of cake, for that student's ability and academic level. Then, to my horror, the student reached for the calculator, and punched in the keys :
Calculators : A Blessing Or A Curse?
There's no question that calculators are a useful tool. Kids should be familiar with them before leaving school, if they are to function effectively in modern society. A calculator makes arithmetic faster and more accurate, by transferring part of the brainwork to electronic circuitry. What is the effect of all this on a student learning math? In one way, a calculator is like a crutch. A student struggling with arithmetic might use a calculator to confirm the results of their own efforts. In this way, the student will gain confidence, until they no longer need the calculator for that level of problem. On the other hand, a student might become dependent on the crutch, unwilling to try to walk without it, and eventually losing the ability to walk correctly as his or her mental math muscles atrophy.
Calculator games!
Below I give a couple of games involving the use of a calculator. The goal with these games is to put kids in a situation where using the calculator helps them with their math, in a fun and interesting way. They use calculators in these games to explore numbers, and so gain some kind of intuition for the relationships between them as they manipulate them to achieve the goal set for them.
This free "fours" contest closed on the 20th of October, 2009. The idea was to make as many numbers as possible using the digit '4' (as many times as you like) and the operations plus, minus, divide and times. Soon I'll upload the contest results, and ideas for how you can run a contest like this one in your own classroom.
In the Magical Calculator Birthday Trick and the "Threes" Math Trick, one child gives a sequence of arithmetic instructions to another, then performs a few simple mental steps on the result. Almost like magic, the other's birthday (or another secret number) appears as the result of the sum! Good for fourth grade kids and up.
There is a famous story about the inventor of chess, who was offered a reward by the emperor of India. He chose a reward that seemed to the emperor very cheap - just a few sacks of rice - but in reality came to more rice than India could produce in a million years. This site has worksheets to help kids work through a Modern Rice-And-Chessboard Story and see for themselves how rich the reward was.
This is one of two math tricks on this site that let you guess someone's birthday after a sequence of mathematical operations.
The Upside-Down Calculator Word Game is recommended for kids in fifth grade and fourth grade, and maybe also third grade. Younger children may find it too challenging - although my son's grade one teacher recently gave an exercise like this one to her class! The aim is to find numbers that make words when keyed into an upside-down calculator. See the game's page for more details.
The Easter Date Worksheets allow a child to compute the date of Easter Sunday in any year at all, with no math more complex than long division. Alternatively, try younger kids on the simpler versions of the worksheets - fewer calculations, smaller numbers, but they only work in certain centuries.
MathGolf is a simple game to play, and a very hard game to master. The high scores for each month are recorded on the website. The tips for parents and teachers explains how to help your kids get the most out of the game.In one famous puzzle, you must make as many numbers as you can using only the given four digits and the basic arithmetic operations. I've worked out which sets of four digits make this puzzle the most interesting, and provided worksheets on this page. Good for grades four and up.
This Angle Geometry Quiz tests your knowledge of a few facts relating to angles. Race against the clock as you prove your skills! Topics covered include the interior angles of triangles and quadrilaterals, angles near parallel lines, lines meeting at a point and others.
This Power Puzzle is an exercise to get kids exploring numbers with their calculator, and observe patterns in the numbers they explore.
In the Math Architect Online Game the goal is to design an apartment with the given area. The catch? Each room is a square, and you must have as few rooms as possible! This makes the game challenging enough to keep kids occupied, and deep enough to keep them learning as they play. There is also a high scores table showing the best players each month, year and for all time, and some ideas for playing math architect as a paper and pencil game.