With regard to elementary schooling, the different numbering systems of the various cultures that have succeeded each other over time, and the counting tools used by them, are considered among the materials of the “MaMa-mathematics for elementary school” project commissioned by the Department of Education, Culture and Sports to the Mathematics Teaching Competence Center of the Department of Formation and Learning/High Pedagogical School in Locarno, Switzerland. These materials can be downloaded free of charge at this link: https://mama.edu.ti.ch/.

In particular, it is suggested to consult:

• the Guidelines for having mathematical, educational and historical insights related to the various number systems of the ancients. This document also presents some historical tools, including those presented here, used by various cultures. This document may also be useful for later school levels;
• the Context of Meaning “Mathematics Traveling in Space and Time,” a document in which insights are provided for designing meaningful learning situations related to mathematics from different cultures, used in different historical periods;
• the Teaching Practice “The Number Systems of the Ancients“, a document in which are collected teaching proposals relating to, among others, the number systems of primitive men, the Sumerians, the Incas, the Egyptians, the Mayans, the Babylonians and the Romans the teaching practice “Different Algorithms of Calculus“, where different algorithms are proposed, some of which have followed each other throughout history and have characterized different places;
• the teaching practice “Figures and the Positional System“, where there are many ideas related to the Indo-Arabic numeral system, including the construction of a small abacus.
• the Teaching Sheets designed for learners, which can be found by setting the filter “Other Number Systems” in the teaching materials search engine. In particular, we highlight: “The Speed Race,” “Ten Notches,” “Sumerian Numbers 1,” “Sumerian Numbers 2,” “Sumerian Numbers 3,” “Sumerian Numbers 4,” “Inca Numbers 1,” “Inca Numbers 2,” “Roman Numbers 1,” “Roman Numbers 2,” “Roman Numbers 3,” “Roman Numbers 4,” “Maya Numbers 1,” “Maya Numbers 2, “The Mayan Numbers 3“, “The Mayan Numbers 4,” “The Egyptian Numbers 1,” “The Egyptian Numbers 2,” “The Egyptian Numbers 3,” “The Egyptian Numbers 4,” “Race Between Systems,” “Comparing Systems,” “Ancient Calculations,” “The Use of the Abacus,” “Let’s Know the Abacus,” “Decimals What a Passion,” “Laura Don’t Get Distracted.“

In addition, there are 22 comics related to important mathematicians throughout history in the collection “Mathematicians in Comics“, which can be downloaded free online or purchased in hard copy published by Daedalus Publishing House. In particular, for an in-depth look at the birth of our numbering system see the comic strip by mathematician Al-Khwārizm (9th cent).

Also available for active middle school teachers are teaching materials called “Mathematics in History“, supplemented by student worksheets that can be downloaded from the ScuolaLab portal (where you must register to download the documents).

DIDACTIC DOSSIER “Counting system” (ENG) – download