Author: Ms Ruoyu Wen,
Lecturer at Yew Chung College of Early Childhood Education
The Erikson Institute, a child development research institute in the United States, has proposed four foundational mathematical concepts for infants and toddlers aged 0–3: attributes, comparison, change, and pattern. In this discussion, let’s focus on “change.”
The Pre-Mathematical Concept of "Change"
“Change” is everywhere. Infants and toddlers experience various types of changes in their daily lives, some of which are actively initiated while others occur passively. Some changes spark curiosity, some lead to frustration, and others hold mathematical significance. If the mathematical concept of “comparison” involves comparing similarities and differences, “change” emphasizes the process of “becoming different.” For infants and toddlers, perceiving the concept of “change” involves the following aspects:
- Change can involve changes in quantity (e.g., eating up all the cookies) or changes in attributes (e.g., a caterpillar transforming into a butterfly).
- Combining, separating, and altering objects can bring about change.
- The difference between the original state of an object and its changed state should be perceptible.
Stages of Development in Infants and Toddlers' Pre-Mathematical Concepts
Infants and toddlers’ development of pre-mathematical concepts follows a specific process and stages, progressing from broad, sensory-based, non-mathematical perception to increasingly accurate and language-related mathematical understanding. Infants and toddlers’ understanding of “change” also follows the following developmental patterns:
- Emerging Stage (0–14 months)
During this stage, infants and toddlers understand mathematical concepts based on sensory perception. They play with their hands and toys hanging in their cribs, gradually realizing that it’s not the objects themselves but their perspective that causes the change. - Developing Stage (12–24 months)
In this stage, infants and toddlers engage in purposeful exploration of objects. They want to know, “What is this?” and “How does this thing work?” It’s common to see two-year-olds enjoying activities like pouring and filling, continuously exploring the “changes” in object states. - Transition Stage (22–36 months)
By this stage, infants and toddlers can express their understanding of things using language, and they begin to grasp more mathematical meanings in their surroundings. For example, they start considering the cause and effect of changes and attempt to explain why things undergo certain changes based on their own experiences. They also develop a clearer perception of changes in quantity, which lays the foundation for later learning about counting and calculations.
Strengthening Infants and Toddlers' Perception of "Change" in Daily Life and Play
Adults can reinforce infants and toddlers’ understanding of “change” in their daily lives and play through various methods, such as:
- Using comparative words in everyday life to draw attention to changes between objects: “Did you notice that the car was going ‘fast’ earlier and now it’s’slow’?”
- Describing changes that occur when infants and toddlers manipulate and pour objects: “The box was full earlier, but now it’s empty.”
- Guiding infants and toddlers to notice changes in nature, such as weather changes, seasonal changes, day and night transitions, and the growth of plants and animals.
- Pointing out changes in familiar environments helps develop infants’ ability to observe details, such as the construction of a new park or the planting of new plants in the community.
- Laying the foundation for learning calculations by highlighting changes in quantity, such as emphasizing that some toy cars were given to friends, so there are fewer toy cars now, or mentioning that new stuffed toys were purchased, so there are more stuffed toys now.
- Cultivating the ability to observe changes through picture books. For example, in the book “Goodnight Moon,” infants and toddlers may notice the gradual darkening of the pages.
- Playing games like “Who’s Missing” together, where infants and toddlers observe a group of objects, then close their eyes while parents remove some objects, and finally, they identify which objects are missing.
References:
- Hynes-Berry, M., Chen, J. Q., & Abel, B. (2021). Precursor Math Concepts: The Wonder of Mathematical Worlds with Infants and Toddlers. Teachers College Press.
