A Computer Algorithm for Randomization

Back in the early days of computers, one of the more popular methods of generating a sequence of random numbers was to employ the following scheme: 1. Choose a starting number between 0 and 1. 2. Multiply the starting number by 4 ("stretch" it). Subtract 4 times the square of the starting number from the quantity obtained in step 2 ("fold" the interval back on itself in order to keep the final result in the same range). 3.Given a starting number between 0 and 1, we can use the proce-dure—o...

 Pattern-Building When Learning a New Word

Words are fundamentally conceptual—although they are physical objects, they represent something ideational. Just giving students definitions of words or having them evaluate the context of word use does not fully use the brain’s patterning style of identifying information. Th e value of word pattern sorting extends beyond their defi nition to relating words to the pattern of categorization where they fi t. Students attend to how words relate to other words through a number of types of categor...

 Use a Big Opening for Class

In your planning, consider what you most want students to know and then work backward to develop an opening that promotes sustained interest toward that goal. If possible, represent the unit in several different ways that appeal to different learning strengths and levels of achievable challenge so you can continually engage all students. Here are some fascinating facts you can use as “big openings” with your students to help them with number sense, specifi cally with understanding large numb...

 The Plural of Thrips

Much the same can be said of the Thrips, those tiny plant insects that haven't so much as a decent singular to their name, one wished to specify an individual Thrips. You may speak many Thrips, or of one Thrips, but never of one Thrip, how strongly you may feel that such a ruling is in restraint of 'our personal liberties. Nor may you employ the word Thripses to mean one or more Thrips, convenient as it might be in a pinch. The New English Dictionary states, with what end in view I don't know...

 The Meaning of "We" in Science and Mathematical Texts

I request a last indulgence from the reader. The introductory material, thus far, has been written in the friendly and confiding first person singular voice. Starting in the next paragraph, I will inhabit the first person plural for the duration of the mathematical expositions. This should not be construed as a “royal we.” It has been a construct of the community of mathematicians for centuries and it traditionally signifies two ideas: that “we” are all in consultation with each other through...

 The Word Explosion in Infants

Babies first bridge the gap between sounds and meaning as early as nine or ten months of age. They learn the names of family members and pets, the meaning of no! and perhaps a few general labels like shoe and cookie. By his first birthday, the average child understands around seventy words, mostly nouns like people's names and terms for objects, but also certain social expressions, like hi and bye-bye. Of course, he cannot say nearly that many. The median number of words spoken by a one-year-...