FMT3701
Assignment 2
(Exceptional Answers)
Due 26 July 2025
,FMT3701
Assignment 2: Exceptional Answers
Due 26 July 2025
QUESTION 1
1.1 Explain the Concept “Number Sense” and Its Development
Definition of Number Sense Number sense refers to an intuitive understanding of
numbers, their magnitude, relationships, and how they are affected by operations. It
encompasses the ability to estimate, compare, and manipulate numbers flexibly in
various contexts, forming the foundation for mathematical proficiency (Berch, 2005).
Number sense is not merely rote memorization but a conceptual grasp of numerical
properties.
Development of Number Sense The development of number sense begins in early
childhood and progresses through stages:
• Infancy (0–2 years): Infants demonstrate subitizing (recognizing small quantities
without counting) and an innate sense of magnitude, such as distinguishing
between larger and smaller sets (Wynn, 1992).
• Preschool (3–5 years): Children develop verbal counting skills, recognize
numerals, and begin to understand one-to-one correspondence. They also start
comparing quantities (e.g., “more” or “less”).
• Foundation Phase (6–9 years): Learners refine their ability to estimate, perform
mental calculations, and understand place value, which supports arithmetic
operations.
This development is influenced by both biological predispositions and environmental
factors, such as exposure to counting games and real-world applications (Jordan et al.,
2009).
, References:
• Berch, D. B. (2005). Making sense of number sense: Implications for children
with mathematical disabilities. Journal of Learning Disabilities, 38(4), 333–339.
• Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358(6389),
749–750.
• Jordan, N. C., Kaplan, D., Ramineni, C., & Locuniak, M. N. (2009). Early math
matters: Kindergarten number competence and later mathematics outcomes.
Developmental Psychology, 45(3), 850–867.
1.2 Distinguish Between Verbal and Object Counting, Giving Two Examples for
Each (10 Marks)
Verbal Counting Verbal counting involves reciting the number sequence orally without
necessarily associating numbers with physical objects. It focuses on memorizing the
numerical order and is a foundational skill for developing number sense (Gelman &
Gallistel, 1978). Verbal counting is abstract and does not require physical referents.
• Examples of Verbal Counting:
1. A child reciting the numbers from 1 to 10 in sequence during a counting
song (e.g., “One, two, three, four, five…”).
2. A learner counting backwards from 20 to 1 as part of a classroom activity.
Object Counting Object counting requires assigning numbers to physical objects in a
one-to-one correspondence, ensuring each object is counted once. This process
reinforces the cardinality principle (the last number counted represents the total
quantity) and connects numerical symbols to real-world quantities (Fuson, 1988).
• Examples of Object Counting:
1. A child counting five apples by pointing to each one and saying, “One, two,
three, four, five.”
Assignment 2
(Exceptional Answers)
Due 26 July 2025
,FMT3701
Assignment 2: Exceptional Answers
Due 26 July 2025
QUESTION 1
1.1 Explain the Concept “Number Sense” and Its Development
Definition of Number Sense Number sense refers to an intuitive understanding of
numbers, their magnitude, relationships, and how they are affected by operations. It
encompasses the ability to estimate, compare, and manipulate numbers flexibly in
various contexts, forming the foundation for mathematical proficiency (Berch, 2005).
Number sense is not merely rote memorization but a conceptual grasp of numerical
properties.
Development of Number Sense The development of number sense begins in early
childhood and progresses through stages:
• Infancy (0–2 years): Infants demonstrate subitizing (recognizing small quantities
without counting) and an innate sense of magnitude, such as distinguishing
between larger and smaller sets (Wynn, 1992).
• Preschool (3–5 years): Children develop verbal counting skills, recognize
numerals, and begin to understand one-to-one correspondence. They also start
comparing quantities (e.g., “more” or “less”).
• Foundation Phase (6–9 years): Learners refine their ability to estimate, perform
mental calculations, and understand place value, which supports arithmetic
operations.
This development is influenced by both biological predispositions and environmental
factors, such as exposure to counting games and real-world applications (Jordan et al.,
2009).
, References:
• Berch, D. B. (2005). Making sense of number sense: Implications for children
with mathematical disabilities. Journal of Learning Disabilities, 38(4), 333–339.
• Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358(6389),
749–750.
• Jordan, N. C., Kaplan, D., Ramineni, C., & Locuniak, M. N. (2009). Early math
matters: Kindergarten number competence and later mathematics outcomes.
Developmental Psychology, 45(3), 850–867.
1.2 Distinguish Between Verbal and Object Counting, Giving Two Examples for
Each (10 Marks)
Verbal Counting Verbal counting involves reciting the number sequence orally without
necessarily associating numbers with physical objects. It focuses on memorizing the
numerical order and is a foundational skill for developing number sense (Gelman &
Gallistel, 1978). Verbal counting is abstract and does not require physical referents.
• Examples of Verbal Counting:
1. A child reciting the numbers from 1 to 10 in sequence during a counting
song (e.g., “One, two, three, four, five…”).
2. A learner counting backwards from 20 to 1 as part of a classroom activity.
Object Counting Object counting requires assigning numbers to physical objects in a
one-to-one correspondence, ensuring each object is counted once. This process
reinforces the cardinality principle (the last number counted represents the total
quantity) and connects numerical symbols to real-world quantities (Fuson, 1988).
• Examples of Object Counting:
1. A child counting five apples by pointing to each one and saying, “One, two,
three, four, five.”
