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Reflections on Chinese Numeration Systems: Teaching and Learning the Numeration System of Counting Rods

Frank J. Swetz (The Pennsylvania State University)

Now that we have some historical background on the development and use of Chinese rod numerals, how can this knowledge be used in the training of preservice elementary teachers? While they may have learned about Roman numerals in school and encountered Egyptian (hieroglyphic) or Babylonian (cuneiform) numeration systems as undergraduates, they may not have heard of rod numerals. However, Chinese rod numerals are easier to understand and simpler to work with than these other ancient numeration systems. Introducing the concept of Chinese rod numerals, even anecdotally, fosters not only awareness, but also a cross-cultural appreciation for mathematics and a broader historical mathematical orientation. Holding an examination and discussion of rod numerals in the classroom can impart several historically-relevant facts, namely:

  1. The Chinese were the first people to use a decimal place value numeral system.
  2. They were also the first to employ a system of decimal fractions.
  3. Their arithmetic is recognized as the first in the world to accommodate negative numbers.

Instructors could also show preservice teachers how to devise activities employing rod numerals for young students. In particular, the rods lend themselves to number recognition exercises and exploration. For example, a set of rods can be made from match sticks that have a square cross section or cut from a flattened paper soda straw. (Remember the rods should not roll.) Of course, a set of rods could also be cut out of stiff paper or cardboard.

The demonstration rods then could be manipulated on a document camera (i.e., the instructor could place rod number configurations on the screen of the projector to form images for the class to identify). A video by Jeff Suzuki [2020] could assist instructors with demonstrating the basic properties without having to write their own lectures:

Students of all ages also enjoy manipulating rods to form their own numerals and challenging their friends to correctly identify the number represented. Any flat surface—such as a table or floor—can be made into a computing board. Masking tape, applied to designate decimal columns, reinforces place value and encourages renaming. Able students can build on their experience with rod numerals to further explore the arithmetic of computing rods. Instructors might ask: How do you think subtraction was performed using rods? Multiplication? Root extraction? Indeed, many questions can be asked and fruitful learning experiences constructed around the Chinese rod numerals.

​If deeper or more extended study is desired, Primary Source Project modules such as [Beery et al. 2004] and [Flagg 2017] are available for secondary school students and undergraduates.

Frank J. Swetz (The Pennsylvania State University), "Reflections on Chinese Numeration Systems: Teaching and Learning the Numeration System of Counting Rods," Convergence (February 2022)