# Multicultural Mathematics and Alternative Algorithms

By Philipp, Randolph A. | Teaching Children Mathematics, November 1996 | Go to article overview

# Multicultural Mathematics and Alternative Algorithms

Philipp, Randolph A., Teaching Children Mathematics

Up until recently I wasn't even aware that other people in the world did things [arithmetic algorithms] differently. I thought God sent these. That's the way of the world. The first day you [to another teacher] were talking about some way you did things differently in Ireland. It never occurred to me. I thought there was a world standard.

- A sixth-grade teacher reflecting on alternative-mathematical algorithms

A teacher's beliefs about mathematics significantly affect the manner in which he or she teaches (Thompson 1992). Teachers, from school experience, often believe that there is one right way to solve a particular mathematics problem or to apply a computational algorithm for adding, subtracting, multiplying, and dividing. In turn, these beliefs become the beliefs of their students. The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) has called for decreasing the attention paid to isolated treatment of paper-and-pencil computations and the memorization of rules and algorithms and suggests instead that we increase the attention paid to students' creating algorithms and procedures. Implicit in this suggestion is that the algorithms we have come to learn and to use are not the only way, and may not even be the best way, to compute.

Although teachers are usually aware that various cultures have historically used algorithms that are different from those currently taught in United States schools, these teachers may not be aware that, various algorithms are being used currently in the United States. Many of these algorithms are culturally based and are used by people with common ethnic and cultural backgrounds. This article describes how preservice elementary school teachers developed an awareness that the algorithms we teach in school are not the only algorithms for operating on numbers and that if they look, they may find alternative algorithms in their community and school.

An Invented Algorithm

Dictionaries define an algorithm as a rule. or procedure for solving a problem. Computational algorithms are invented by people to streamline the process by which we compute. The fact that algorithms are a convention is often lost on our students, who come to think of a particular algorithm as the way, instead of as a way, to compute. The following example illustrates the role that algorithms play in school mathematics.

Although Michelle's dad suggested that she write down only what she needed, Michelle said that it helped her to write "How many 3s are in 579?" so she could remember what she was doing. Notice the unconventional approach that Michelle invented for this problem. This "algorithm," although nonroutine, was based on Michelle's understanding of the meaning of division and her sense for numeration. …

• Questia's entire collection
• Automatic bibliography creation
• More helpful research tools like notes, citations, and highlights

If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

Highlights (0)
Some of your highlights are legacy items.
Citations (0)
Some of your citations are legacy items.
Notes (0)
Bookmarks (0)

Project items include:
• Saved book/article
• Highlights
• Quotes/citations
• Notes
• Bookmarks
Notes

#### Cited article

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

#### Cited article

Multicultural Mathematics and Alternative Algorithms
Settings

#### Settings

Typeface
Text size Reset View mode
Search within

Look up

#### Look up a word

• Dictionary
• Thesaurus
Please submit a word or phrase above.

Why can't I print more than one page at a time?

Full screen

## Cited passage

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

## Welcome to the new Questia Reader

The Questia Reader has been updated to provide you with an even better online reading experience.  It is now 100% Responsive, which means you can read our books and articles on any sized device you wish.  All of your favorite tools like notes, highlights, and citations are still here, but the way you select text has been updated to be easier to use, especially on touchscreen devices.  Here's how:

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select.

## Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.