, ACI2605 Assignment 3 (COMPLETE ANSWERS)
Semester 1 2025 - DUE 3 July 2025; 100% TRUSTED
Complete, trusted solutions and explanations.
QUESTION 1: The History of Numbers
1.1 Provide a critical analysis of the Steen’s (1988) definition of
mathematics in relation to:
Steen (1988) views mathematics as the "science of patterns" and
emphasizes that mathematical structures are built through recognizing,
formalizing, and manipulating these patterns. This conceptualization of
mathematics provides a rich framework to understand how different
number systems—such as binary and decimal—function within
mathematical thinking and education. The analysis below considers
how Steen’s idea applies specifically to the binary and decimal number
systems, especially in light of how these systems are understood and
taught in primary education.
1.1.1 The binary number system (10)
The binary number system, which uses only two digits (0 and 1), is a
clear example of a mathematical structure built from a simple, yet
powerful, pattern. According to Steen's definition, mathematics involves
seeking patterns and applying functions or mappings to interpret them.
Binary aligns with this definition in several ways:
Pattern Recognition: Binary numbers form repeating patterns that
are predictable (e.g., 1, 10, 11, 100, 101, ...), demonstrating Steen’s
idea of pattern-seeking. These patterns relate closely to place
value, doubling, and powers of 2.
Semester 1 2025 - DUE 3 July 2025; 100% TRUSTED
Complete, trusted solutions and explanations.
QUESTION 1: The History of Numbers
1.1 Provide a critical analysis of the Steen’s (1988) definition of
mathematics in relation to:
Steen (1988) views mathematics as the "science of patterns" and
emphasizes that mathematical structures are built through recognizing,
formalizing, and manipulating these patterns. This conceptualization of
mathematics provides a rich framework to understand how different
number systems—such as binary and decimal—function within
mathematical thinking and education. The analysis below considers
how Steen’s idea applies specifically to the binary and decimal number
systems, especially in light of how these systems are understood and
taught in primary education.
1.1.1 The binary number system (10)
The binary number system, which uses only two digits (0 and 1), is a
clear example of a mathematical structure built from a simple, yet
powerful, pattern. According to Steen's definition, mathematics involves
seeking patterns and applying functions or mappings to interpret them.
Binary aligns with this definition in several ways:
Pattern Recognition: Binary numbers form repeating patterns that
are predictable (e.g., 1, 10, 11, 100, 101, ...), demonstrating Steen’s
idea of pattern-seeking. These patterns relate closely to place
value, doubling, and powers of 2.
