Math Exercise: Multiple Approaches to Problem-Solving

For example, if the problem was to fi nd the answer to 8 × 6, students may suggest three options: memorizing the multiplication table for 6, knowing that 8 × 5 = 40 and adding another 8 to equal 48, or adding a column of six 8s. Allowing students to personally choose among approaches all confi rmed as correct and to support their choice will increase their comfort levels. Th is process also builds math logic, intuition, and reasoning skills that extend into other academic subjects and real-...

 Physics Delves into More and More Abstract Mathematics

The steady progress of physics requires for its theoretical formulation a mathematics which get continually more advanced. ... it was expected that mathematics would get more and more complicated, but would rest on a permanent basis of axioms and definitions, while actually the modern physical developments have required a mathematics that continually shifts its foundation and gets more abstract. Non-euclidean geometry and noncommutative algebra, which were at one time were considered to be pu...

 Elementary Teachers Misrepresent Mathematics

All the modern higher mathematics is based on a calculus of operations, on laws of thought. All mathematics, from the first, was so in reality; but the evolvers of the modern higher calculus have known that it is so. Therefore elementary teachers who, at the present day, persist in thinking about algebra and arithmetic as dealing with laws of number, and about geometry as dealing with laws of surface and solid content, are doing the best that in them lies to put their pupils on the wrong trac...

 The Thrill of Landing on a New Planet

To ANYONE who has been in space and experienced its changelessness, the real excitement of space flight comes when it is time to land on a new planet. The ground speeds backward under you as you catch glimpses of land and water, of geometrical areas and lines that might represent fields and roads. You become aware of the green of growing things, the gray of concrete, the brown of bare ground, the white of snow. Most of all, there is the excitement of populated conglomerates; cities which, on ...