Growing up, I remember listening to and watching "The Lone Ranger." The opening of each show began with the announcer saying something like, "Return with us to those thrilling days of yesteryear." During the past several weeks, I have been reminded of that experience when I hear the call to return to "traditional" mathematics in Columbia Public Schools. This call was reported in the Tribune Sept. 25 under the headline "Schools return to traditional mathematics. I have a question: What is "traditional" mathematics? Does "traditional" mathematics mean being able to execute computational algorithms to add, subtract, multiply and divide large numbers by hand? If so, how large? Should students be able to divide by hand the national debt ($9,896,842,816,000) by the current number of U.S. cit...
...They also learned names for properties such as associative and commutative and explored a...
With the No Child Left Behind federal mandate, teachers and school administrators are challenged to provide the best instruction possible in mathematics and reading. Students are required to take the state mandated tests in grades three through eight and in grade ten. The stakes are high in that students may not be passed on to the next higher grade level if a test is not passed in the required grades of testing, If the exit test for graduation is not passed, a student may not receive a high school diploma. The punishments for not passing a test then are indeed very stringent. The best curriculum possible needs to be aligned with the state mandated objectives so that each student may achieve optimally. Mathematics is one of two curriculum areas mandated for testing under No Child Left B...
...* place value of whole numbers. * properties of the four basic operations, number one above, inncluding the commutative, associative, and distributive laws. * fractions, ...
...Throughout R will represent an associative ring with Z(R). R is said to be 2-torsion free if ...The properties of this type of mapping were discussed in many pap.... Theorem 3.1. If R is a commutative 2-torsion free ring and (f, [partial derivative]) ...
... and with the same multiplicative properties, i.e., . (x + x', [gamma]) = (x, [gamma])(x', [gam... of addition denoted by + that is commutative, i.e., for each a,b in G, a + b = b + a, lies in GG and is associative ((a+b) + c = a + (b+c), i.e., it does not matter i...
...Thus, D is a commutative ring with a unit element [11] . Clifford introduce...Properties of these operators are used to find some mathemati.... Moreover, using the associative property of dual quaternion's multiplication it is...
.... We wish to note that stability properties of different functional equations can have applica... on [0,1] is defined as an increasing, commutative, associative mapping T : [[0,1].sup.2] [right arro...
... Algebraic Structures mainly with associative binary operation. Since then the subject has been ... Groupoids exhibit simultaneously the properties of a semigroup and a groupoid. . In [11], most of ..., G is said to be a Smarandache commutative groupoid if there is a proper subset, which is a s...
... y, z [member of] X, satisfies the four properties: . 1. ((x * y) * (x * z)) * (z * y) = 0; . 2. (x *...
... Algebraic Structures mainly with associative binary operation. . In [11], [12], [13], [14], W. ... are an excellent means to study local properties in Rings. The definitions of two levels of Smarand...(x) > 1 such that [x.sup.n(x)] = x is commutative and [x.sup.n(x)-1] is an idempotent element of R, ...
... is a complete lattice Q with an associative binary operation "&" satisfying: . a&([??][b.sub.[...Then we can prove that Q is a commutative Girard quantale. And we can prove that a, b and c ...
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