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Young children with limited knowledge of formal mathematics can intuitively perform basic arithmetic‐like operations over nonsymbolic, approximate representations of quantity. However, the algorithmic rules that guide such nonsymbolic operations are not entirely clear. We asked whether nonsymbolic arithmetic operations have a function‐like structure, like symbolic arithmetic. Children (
- Award ID(s):
- 1844155
- NSF-PAR ID:
- 10442947
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Cognitive Science
- Volume:
- 47
- Issue:
- 6
- ISSN:
- 0364-0213
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Active learning—
doing —supports learning.Collaborative learning—doing
together —supports learning.Classroom discourse—focused, relevant
discussion , not just listening—supports learning.Clear articulation of one's thinking, even just to oneself, helps develop that thinking.
What this paper adds
The common languages we use for classroom mathematics—natural language for conveying the meaning and context of mathematical situations and for explaining our reasoning; and the formal (written) language of conventional mathematical notation, the symbols we use in mathematical expressions and equations—are both essential but each presents hurdles that necessitate the other. Yet, even together, they are insufficient especially for young learners.
Programming, appropriately designed and used, can be the third language that both reduces barriers and provides the missing expressive and creative capabilities children need.
Appropriate design for use in regular mathematics classrooms requires making key mathematical content obvious, strong and the ‘driver’ of the activities, and requires reducing tech ‘overhead’ to near zero.
Continued usefulness across the grades requires developing children's sophistication and knowledge with the language; the powerful ways that children rapidly acquire facility with (natural) language provides guidance for ways they can learn a formal language as well.
Implications for policy and/or practice
Mathematics teaching can take advantage of the ways children learn through experimentation and attention to the results, and of the ways children use their language brain even for mathematics.
In particular, programming—in microworlds driven by the mathematical content, designed to minimise distraction and overhead, open to exploration and discovery
en route to focused aims, and in which childrenself ‐evaluate—can allow clear articulation of thought, experimentation with immediate feedback.As it aids the mathematics, it also builds computational thinking and satisfies schools' increasing concerns to broaden access to ideas of computer science.