Abstract
Recent studies showed that kindergarten children solve addition, subtraction, doubling and halving problems using the core system for the approximate representation of numerical magnitude. In Study 1, 34 first-grade students in their first week of schooling solved approximate arithmetic problems in a number range up to 100 regarding all four basic operations. Children solved these problems significantly above chance.In Study 2, 66 first graders were tested for their approximate arithmetic achievement, working memory capacity, groupitizing, phonological awareness, naming speed and early arithmetic concepts at the beginning of first grade and again at the beginning of second grade. It appears that approximate arithmetic achievement is independent from most other cognitive variables and correlates most with other variables of the mathematical domain. Furthermore, regression analyses revealed that school success was only predicted by groupitizing and central executive capacity, but not approximate arithmetic achievement, when controlling for other cognitive variables.
Highlights
Helping students understand formal arithmetic is one of the main concerns of schools worldwide
The latest TIMS study showed that one third of all fourth graders did not reach the intermediate benchmark they were expected to reach with proper formal schooling (Gonzales et al, 2008)
This leads us to the question: how primary schooling can affect a better learning of formal arithmetic? These basic skills are needed for later school and vocational careers
Summary
Approximate arithmetic achievement predicts school success one year later, even when controlling for other variables (working memory, core system 2, naming speed, phonological awareness, and early arithmetic concepts). During addition problems children saw two sets of blue dots falling behind an occluder on the left side, afterwards they were shown a set of red dots on the right side and had to decide which character had more dots. During multiplication problems two (or three) cartoon characters were shown with a set of dots on the left side of the screen. During division problems there were two (or three) characters on the left side of the screen. These characters had a set of blue dots, which they wanted to share . On the right side of the screen was a single character with a set of red dots. We tested for several alternative, non-arithmetic strategies in Appendix A.1 to Gilmore et al (2010)
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