Big Numbers and Small kids: Preschoolers’ Learning of Multi-digit Numbers

• In Event: 2-051 - Learning Before School

Integrative Statement

Mastery of the symbolic number system is foundational to success in mathematics. But, numerous studies have shown that many school-aged children err at learning the place-value concept of multi-digit numbers. Recent studies, however, hinted that young children may start to acquire an implicit understanding of multi-digit numbers early on. It remains unclear: a) what kinds of learning experience can lead to such impressive early knowledge, and b) what learning mechanisms can support this learning. We provide experimental evidence that casual activities (e.g., picture-book reading) that allow children to map spoken multi-digit number words and their written forms can lead to rapid learning and generalization of the principles underlying symbolic multi-digit numbers.

Fifty-seven 3- to 5-year-olds were randomly assigned to a training condition (N = 40) or a control condition (N = 17). At pre- and post-test, children were asked to identify a multi-digit number by name in a two-alternative-forced-choice task and to indicate which of the two written multi-digit numbers represents a larger magnitude. The testing items included both trained and untrained numbers to test transfer effects. During the three days of training, the training group was provided with a small set of name-number associations through picture-book reading or making multi-digit numbers with cards. For example, children were presented with a story (Fig. 1): “Johnny wants to save money to buy a bike. Do you know how much it costs? It costs sixty dollars” while seeing the written number “60” on the page. The control group was also given opportunities to map spoken words to written forms, but the experiences were about name-letter associations (“cat” - > CAT).

A linear mixed effect model revealed a significant interaction between time and condition, β = 0.32, SE = 0.15, p = .04 (Fig. 2). The training group demonstrated rapid learning from pre- (M = 60%, SD = 48%) to post-test (M = 68%, SD = 46%), t (39) = 4.5, p = 0.0001, d = .71, whereas the control group did not (Mpre = 60%, SDpre = 49%, Mpost = 60%, SDpost = 48%), t (16) = 0.24, p = 1, d = .06. The training group also demonstrated great generalization—they improved significantly even on the untrained items, t (39) = 3.3, p = .002, d = .51. Thus, children in the training group have built implicit knowledge of multi-digit numbers--although they may not be able to articulate the place-value concept explicitly--and can generalize such knowledge to never-encountered numbers.

Thus, early experiences with hearing and seeing multi-digit numbers (e.g., street address, calendar) can provide crucial learning opportunities for young children to discover the place value principle. Such learning may be supported by two crucial mechanisms: Structure mapping between number words and written numbers and statistical learning that aggregates multiple instances of such mapping. Experiential differences in the early learning environment may be the key contributing factor to individual differences in later place-value learning at schools, and providing such experiences has the potential for addressing these early gaps.

Authors

• Lei Yuan, Indiana University
  Presenting Author

• Linda B Smith, Indiana University
  Non-Presenting Author