**ERIC Number:**ED437109

**Record Type:**RIE

**Publication Date:**1999-Jul

**Pages:**17

**Abstractor:**N/A

**Reference Count:**N/A

**ISBN:**N/A

**ISSN:**N/A

Two Modes of Mathematics Instruction.

Aloff, Simon

There is a popular view that arithmetic is only a collection of dull algorithms containing no interesting ideas. However, if one goes a little below the surface, it will become apparent that there are many fascinating ideas waiting to be discovered. The paper tries to show that mathematical ideas can be recognized and understood without the use of "high tech," graphing calculators. Calculators are fast and accurate, and when properly used they allow students to bypass tedious arithmetic and get to the important concepts in a problem. However, educators must be careful not to let the new technology become the driving force in the curriculum. The focus must always be on conceptual mathematical understanding. This paper presents some key "mini-lessons" from arithmetic, algebra, and geometry that will illustrate that elementary mathematics rests on a set of key ideas that are best illustrated using simple calculations. Lesson 1 explores fractions and factor trees. Lesson 2 teaches repeating decimals. Lesson 3 looks at infinite sums. Lesson 4 discusses Gauss's early discovery in finding the sum of the first 100 integers. Lesson 5 explores solutions to the mixture problem, or what students dread--word problems. Lesson 6 explores Pythagorean triples. (VWC)

**Publication Type:**Guides - Non-Classroom; Opinion Papers

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Note:**In: Issues of Education at Community Colleges: Essays by Fellows in the Mid-Career Fellowship Program at Princeton University, 1998-1999; see JC 000 068.