Daniel Alfeo's Portfolio Page

About Me

A picture of me when I was a TA at Glencliff Elementary School in Niskayuna, NY.

My name is Daniel Alfeo and I am pursuing a MSSE from UAlbany in order to become a high school physics teacher. I finished undergrad at Utica College with a BS-Physics in May 2019 and I am looking forward to learning how to become an effective science teacher so that I can help my students succeed. I’ve spent a good amount of time working as a camp counselor at the Schenectady JCC summer camp and have been spending recent summers there teaching archery to campers as the archery specialist, and it has been a blast! I also got to spend some time working as a teaching assistant at Glencliff Elementary School in Niskayuna, and my time there showed me the impact teachers can have when it comes to helping students succeed. My experience working as a camp counselor and a teaching assistant has led me to decide to pursue a career in education so that I too can help students achieve their goals. In my free time I enjoy playing basketball, football, and video games.

My Topic and Purpose

This course aims to introduce the learner to some of the ways in which culture is embedded in the history of mathematics. This course will identify some of the different systems of counting, measurement, and problem-solving techniques developed by various civilizations across the globe, and examine how they are influenced by their unique needs, environments, and social practices. Some examples which will be analyzed in this course are the Egyptian tally number system, the Babylonian base-60 number system, the origins of the commonly used base-10 decimal system (also referred to as the Hindu-Arabic numeral system), as well as the prevalence of magic squares in various cultures across the globe. 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.

Scope of Learning Outcomes and Content

By the end of this course, participants will be able to:

Understand how different number systems can be used to represent values
Recall various techniques or strategies used for counting, measuring, or problem-solving
Identify the advantages of these various counting systems and problem-solving techniques and the cultural values which led to their use
Have an appreciation for the various ways in which culture is embedded in the history of mathematics
Implement activities into mathematics instruction which provides students insight to these connections

Course Outline:

Lesson 1: Counting Origins - The Hindu-Arabic Numeral System (Decimal)

Lesson 2: Alternative Counting Systems - Egyptian & Babylonian

Lesson 3: Problem Solving Across Cultures - Magic Squares

Lesson 4: Culturally Responsive Math Instruction

Needs Assessment

The educational problem or opportunity: 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. In doing this, students can begin to value community members' cultures as assets to teaching and learning mathematics. Having an awareness of some of the cultural impacts throughout the history of mathematics can be beneﬁcial when implementing culturally responsive mathematics instruction.

The learners/participants involved: 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. By the end of this course, learners should be able form some connections between mathematics and culture.

Analysis of gaps: 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.

Existing efforts: 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.

Intent statement: 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.

Analysis of the Learner and Context

Learners: Participants in this mini-course will be current or aspiring teachers. This course is intended for math teachers, but could be beneficial for any teacher who wishes to view some of the cultural relevance in mathematics and possibly share it with their students. Participants will likely have familiarity with various mathematical concepts and techniques, but may not be as familiar with historical contexts or events. Teaching experience may vary among participants, but they should have an awareness of the benefits of culturally responsive instruction.

Instructional Context: This course will be taken fully online using the KNILT website. Participants will need internet access and a device with web-browsing capabilities. Learners are free to progress through the course at whatever speed they wish, and they will be able to access previous units again after completion. Participants should be able to use lessons from the mini-course to enhance their instruction by implementing various culturally responsive activities or discussions for their students. This course will offer ideas to teachers regarding some ways they can help students form connections to see the intersection of culture and mathematics.

Performance-Based Objectives

After completing this mini-course, learners will be able to:

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

Task and Content Analysis

Prerequisites: Before taking this course, the learner should:

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

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.

Curriculum Map

References and Resources

Larson, M. B., Lockee, B. B., Erlewine, M., & Fuchs, M. L. (2020). Streamlined ID: A Practical Guide to Instructional Design. Routledge. 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/

Suzuki, J. (2002). A History of Mathematics. Prentice Hall.