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History of Math and Culturally Responsive Math Instruction

From KNILT


Author: Daniel Alfeo

Navigation Links: Daniel Alfeo's Portfolio Page | ETAP 623 Spring 2025 (Byrne) - Systematic Design of Instruction.

Overview and Purpose

Throughout the history of mathematics, culture has had a profound impact on the development of various counting systems and problem solving techniques. This mini-course will explore the origins of the Hindu-Arabic, Egyptian, and Babylonian numeral systems and examine the prevalence of magic squares across various cultures. From these considerations, math educators can be culturally conscious and begin to find ways of implementing culturally responsive activities into their mathematics instruction, leveraging cultural knowledge and lived experiences as assets.

The purpose of this course is to allow the reader to make connections between some mathematical techniques or strategies they may have learned about, and the cultural context from which it came to be.

Needs Assessment

Many students may feel a disconnect between themselves and the relevance of mathematics in their every day experiences. In order to foster students' positive mathematical identities, the intersection of culture and mathematics needs to be addressed and reflected upon.

This course will be designed for math teachers who are looking for some ways to authentically address diverse cultures and identities in their mathematics instruction. Participants who may already be familiar with properties of the number systems or techniques discussed can gain insight into the historical contexts and cultural backgrounds from which they came to be.

The National Council of Teachers of Mathematics (NCTM) supports fostering students' mathematical identities and implementing equitable and purposeful mathematics instruction, but they state that even so, traditional mathematics instruction often results in students feeling a disconnect from the relevance of math to their daily lives. Many people may view mathematics as an independent abstract system with no connection to culture, but just like any other discipline it has evolved within diverse cultural contexts worldwide. Many students may be able to perform mathematical operations or be familiar with techniques, but may not have the historical context from which they arose. Ideally, students' understanding of various mathematics concepts could be enhanced by providing insight into the diverse cultural contexts and needs which influenced their creation.

NCTM addresses the disconnect students face when seeing the relevance of math to their daily lives, and they suggest that we need to move beyond surface-level activities for cultural explorations within mathematics experiences. In their position regarding The Intersection of Culture and Mathematics, they make four declarations that serve as guidance for mathematics educators to mitigate this disconnect:

  1. Mathematics is not culture neutral.
  2. Effective mathematics instruction leverages cultural knowledge and lived experiences as assets.
  3. Effective mathematics teachers are culturally conscious.
  4. Effective schools develop systemic approaches that embrace culturally relevant mathematics instruction.

This course is intended to provide insight on some of the ways culture is embedded in the history of mathematics through examining the contexts surrounding the origins of various counting systems and magic squares. This will offer some ways for current and aspiring math teachers to implement authentic, culturally responsive mathematics instruction.

Performance Objectives

  • Reflect on the historical origins and spread of the commonly used Hindu-Arabic Numeral System (Decimal)
  • Reflect on the cultural contexts and unique needs from which the Egyptian and Babylonian number systems arose.
  • Utilize various techniques to solve magic squares and reflect on their cultural roots
  • Implement culturally responsive activities or discussions into mathematics instruction

Prerequisites

Before starting this course, please review the prerequisites listed below. These skills are essential for successfully navigating and understanding the material in this mini-course:

  • Have basic familiarity with numbers and arithmetic operations
  • Have an understanding of the concept of place value
  • Be aware of the benefits of culturally responsive instruction

Course Units

This mini-course includes the following units. Click the title of a unit to go to its page.

Unit 1: Counting Origins – The Hindu-Arabic Numeral System

  • Describe the historical origins of the Hindu-Arabic numeral system.
  • Explain the importance of the place-value concept and the invention of zero.
  • Identify key stages in the spread of the numeral system across cultures.
  • Reflect on how this system compares to earlier non-place-value systems.

Unit 2: Alternative Counting Systems – Egyptian & Babylonian

  • Explain the structure of the Egyptian and Babylonian counting systems.
  • Convert numbers between base-10 and base-60 representations.
  • Analyze the cultural factors that shaped the development of each system.
  • Compare the advantages and limitations of the Egyptian and Babylonian number systems.

Unit 3: Problem Solving Across Cultures – Magic Squares

  • Define a magic square and describe its mathematical properties.
  • Identify examples of magic squares from at least two different cultural traditions.
  • Explain the symbolic or cultural significance of magic squares in various historical contexts.

Unit 4: Culturally Responsive Math Instruction

  • Explain how understanding cultural roots of mathematics can enhance student engagement.
  • Identify strategies for incorporating culturally diverse mathematical examples into instruction.
  • Reflect on how their own perception of mathematics has evolved.

References & Resources

  • Daniels, M. (2014). The magic, myth and math of magic squares | Michael Daniels | TEDxDouglas. YouTube. https://www.youtube.com/watch?v=-Tbd3dzlRnY
  • Eves, A. (2022). The Fascination of Magic Squares. Royal Institution. https://www.rigb.org/explore-science/explore/blog/fascination-magic-squares
  • History Matters. (2020). Why does the west use Arabic Numerals? (Short Animated Documentary). YouTube. https://www.youtube.com/watch?v=j9WV2T7Y_E4
  • Jones, S. (2016). Culturally Relevant Pedagogy in Mathematics: A Critical Need | Shelly Jones | TEDxCCSU. YouTube. https://www.youtube.com/watch?v=EjLOuUhN6xY
  • Larson, M. B., Lockee, B. B., Erlewine, M., & Fuchs, M. L. (2020). Streamlined ID: A Practical Guide to Instructional Design. Routledge.
  • Lippman, D. (2022). Math in Society. LibreTexts.
  • Made In History. (2023). Ancient Mathematics in the Babylonian Empire and Egypt | Ancient Science Documentary. YouTube. https://www.youtube.com/watch?v=PXvyG40cCq4
  • Mawhinney, T. (2016). Culturally Relevant Math. YouTube. https://www.youtube.com/watch?v=uY21YWeDBKY
  • National Academies of Sciences, Engineering, & Medicine. (2018). How people learn II: Learners, contexts, and cultures. The National Academies Press.
  • National Council of Teachers of Mathematics. The Intersection of Culture and Mathematics (2024). https://www.nctm.org/Standards-and-Positions/Position-Statements/The-Intersection-of-Culture-and-Mathematics/
  • Project Shivoham. (2021). The History of Hindu Numerals || A film on the heritage of Hindu Numerals || Project SHIVOHAM. YouTube. https://www.youtube.com/watch?v=iVAOGx8NgJ0
  • Suzuki, J. (2002). A History of Mathematics. Prentice Hall.
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