Thought for the Day

"There is a great danger in the present day lest science-teaching [and mathematics education] should degenerate into the accumulation of disconnected facts and unexplained formulae, which burden the memory without cultivating the understanding."

--J. D. Everett [In the preface to his 1873 English translation of Elementary Treatise on Natural Philosophy by A Privat Deschanel. (D. Appleton and Co.)]

Pop Quiz: Petals Around the Rose

Thanks to Chicky for this fun logic game called "Petals Around the Rose."

http://crux.baker.edu/cdavis09/roses.html

The computer will generate a random roll for 5 dice. See if you can figure out how many petals there are around the rose for that particular roll. Enter your answer and check with the computer. You may repeat the simulation as many times as you wish.

What is the logic behind the question? Can you accurately answer how many petals are around the rose in any given roll?

If this was too easy for you, answer the following questions:

• What is the greatest number of petals around the rose for this game.
• Which dice will be displayed when there are 11 petals around the rose?
• Can the game be played with only 2 dice? If so, what is the greatest number of petals around the rose.
• Can the game be played with 6 dice? If so, what is the greatest number of petals around the rose.

Thought for the Day

"It is little short of a miracle that modern methods of instruction have not already completely strangled the holy curiosity of inquiry…. I believe that one could even deprive a healthy beast of prey of its voraciousness if one could force it with a whip to eat continuously whether it were hungry or not…"

--Albert Einstein

Pop Quiz

Is the following possible:

11+ 2 = 1 ?

If yes, please give an example. If no, please explain why not.

Thought for the Day

"I am beginning to suspect all elaborate and special systems of education. They seem to me to be built upon the supposition that every child is a kind of idiot who must be taught to think. Whereas, if the child is left to himself, he will think more and better, if less showily. Let him go and come freely, let him touch real things and combine his impressions for himself, instead of sitting indoors at a little round table, while a sweet-voiced teacher suggests that he build a stone wall with his wooden blocks, or make a rainbow out of strips of coloured paper, or plant straw trees in bead flower-pots. Such teaching fills the mind with artificial associations that must be got rid of, before the child can develop independent ideas out of actual experience."

-- Anne Sullivan

Philosophy of Mathematics Education

Philosophy of Mathematics Education

Three things are essential in a good math classroom:

Counter Intuitive Thinking
Students need experience with counter-intuitive problems to develop logical thinking skills.

Manipulatives
Manipulatives not only help students understand concepts more clearly, they also give concrete examples of how mathematics surrounds us. For instance, baby toys can teach integral calculus, a Slinky demonstrates geometry formulas, sewing patterns are derived from statistics, M&Ms follow patterns of probability, applesauce teaches about similar figures, fingerprints coincide with the binary system used by computers.... Fun examples are everywhere.

Technology
Calculators and computers allow students the freedom to explore the beauty of mathematics without the time consuming calculations. Children can understand complicated mathematical ideas even though they cannot yet perform the cumbersome arithmetic that makes those concepts possible.

Good Morning Class

Welcome to Ask the Math Teacher.

This blog is an eclectic grouping of tips for concerned parents, critiques on educational legislature, personal rantings on mathematics education, bits of wit and wisdom and mind bending math problems sprinkled with a little Q&A from my visitors.

Enjoy!