ADVANTAGES OF LEARNING MATHEMATICS

DIFFERENCE BETWEEN INTEGRATION AND DIFFERENTIATION

MATHEMATICAL POEM

Met-a-Four

“Met-a-Four”


I “met a four”
when I was three
and oh the things
it did to me
and fingers counting
one-two- three.
When the four
brought in a five
all my counting fingers
came alive.
Reaching for the
other hand
said “times two”
is oh so grand.
They ran through
six, then seven – eight
danced with the nine
to celebrate.
Then the quantum leap
to ten
and shouts of 
let’s do it again.
Somehow the
ones and two and threes
increase in size
exponentially.
Still, my fingers are
mathematically smitten
seeking warmth
within a mitten.


John G. Lawless

HISTORY OF PROTRACTOR

Protractors are mathematical drawing instruments used to draw and to measure angles. Americans typically encounter them in elementary or middle school, when they are learning to produce reasonably accurate geometrical figures in order to explore mathematical relationships between those figures. Perhaps many people then never have reason to consider these objects again. However, protractors are not merely tools for enhancing learning but rather have a lengthy history of application in a variety of fields. The protractors in the mathematics collections of the National Museum of American History (NMAH) illustrate stories of technical work and innovation in navigation, surveying, engineering, and war.

The protractor is over 500 years old. Although there were earlier instruments that were used for angle measurement in addition to other mathematical tasks, Thomas Blundeville described a tool specifically for drawing and measuring angles in his 1589 Briefe Description of Universal Mappes & Cardes. As the title indicates, he used the protractor in the preparation of maps, particularly navigational charts for use at high latitudes. It is not clear that Blundeville invented the protractor, for other European mathematical practitioners wrote about similar objects around the same time period. Regardless of who was first to describe the instrument, protractors entered the standard practices of navigators at sea and surveyors on land by the early 17th century. By the 18th century, the makers of mathematical instruments were explaining the manufacturing process for protractors, while the objects were beginning to appear in surveying textbooks and in introductions to geometry.

By the 19th century, machinists were devising a variety of specialized forms of protractors.

Draftsman’s Protractor By Brown & Sharpe, 1887

By the 20th century, protractors had become commonplace in school mathematics.

TYPES OF GRAPH

TIMELINE OF CALCULATORS

Traditional Views of Mathematics

Most adults will acknowledge that mathematics is an important subject, but few understand what the discipline is about. For many, mathematics is a collection of rules to be mastered, arithmetic computations, mysterious algebraic equations, and geometric proofs. This perception is in stark contrast to a view of mathematics that involves making sense of mathematical objects such as data, form, change, or patterns. A substantial number of adults are almost proud to proclaim, "I was never any good at mathematics." How has this debilitating perspective of mathematics as a collection of arcane procedures and rules become so prevalent in our society? The best answer can be found in the traditional approaches to teaching mathematics. Traditional teaching, still the predominant instructional pattern, typically begins with an explanation of whatever idea is on the current page of the text followed by showing children how to do the assigned exercises. Even with a hands-on activity, the traditional teacher is guiding students, telling them exactly how to use the materials in a prescribed manner. The focus of the lesson is primarily on getting answers. Students rely on the teacher to determine if their answers are correct. Children emerge from these experiences with a view that mathematics is a series of arbitrary rules, handed down by the teacher, who in turn got them from some very smart source.