Importance of Informal Mathematics Knowledge
Baroody and Ginsburg (1986) termed the knowledge that children develop in everyday settings prior to attending formal schooling “informal knowledge.” Most preschoolers arrive at school with important mathematical competencies, such as a sense for numbers and counting that are foundational for formal mathematics learning if understood by educators. Even with older children, the everyday, informal knowledge that is developed through experience can be tapped for enhancing formal mathematics learning.
Seo and Ginsburg conducted an interesting study of the types of informal mathematical activities in which four- and five-year-old children were engaged in natural settings (2004). The researchers classified observable activities by their mathematics characteristics:
- Classification activities involved sorting, grouping, or categorizing objects.
- Magnitude activities were statements made about global magnitude of objects, direct or side-by-side comparisons, or judgments without quantification.
- Enumeration activities involved saying number words, counting, subitizing, and even reading and writing numbers.
- Dynamics involved putting things together, taking them apart, or making other transformations such as turning and flipping.
- Pattern and shape activities included identifying or creating patterns or shapes and exploring the properties and relationships of shapes. (Seo & Ginsburg, 2004, pp. 93–94)
After coding 15-minute videotaped segments of ninety children, the researchers concluded that most children (88%) engaged in mathematical activities naturally and that about forty-three percent of the time observed was spent in math-like activities. Very significant in their findings was the conclusion that there were no income level or gender differences in these activity levels. In general, children engaged in pattern and shape activities the most, and classification the least, and were capable of achieving quite complex levels of performance. For example, some children demonstrated estimating the number in a set without counting and transforming a rhombus shape into a trapezoid.
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