Diverse mathematical knowledge among indigenous Amazonians

Abstract

We investigate number and arithmetic learning among a Bolivian indigenous people, the Tsimane', for whom formal schooling is comparatively recent in history and variable in both extent and consistency. We first present a large-scale meta-analysis on child number development involving over 800 Tsimane' children. The results emphasize the impact of formal schooling: Children are only found to be full counters when they have attended school, suggesting the importance of cultural support for early mathematics. We then test especially remote Tsimane' communities and document the development of specialized arithmetical knowledge in the absence of direct formal education. Specifically, we describe individuals who succeed on arithmetic problems involving the number five-which has a distinct role in the local economy-even though they do not succeed on some lower numbers. Some of these participants can perform multiplication with fives at greater accuracy than addition by one. These results highlight the importance of cultural factors in early mathematics and suggest that psychological theories of number where quantities are derived from lower numbers via repeated addition (e.g., a successor function) are unlikely to explain the diversity of human mathematical ability.

Keywords: arithmetic development; education; mathematical cognition.

Fig. 1.

(A) Stacked histogram of child knower levels per year of education (N = 812). (B) Percentages of child knower levels per year of education. (C) Stacked histogram of adult knower levels (N = 332) by year of education. (D) Percentages of adult knower levels per year of education.

Fig. 2.

(Left) Jatata sheets sell for 5 Bolivianos (Bs) each in the remote community. They are used to roof houses but also as currency (units of 5) to pay off outstanding accounts with river traders. (Right) Plantains are also priced in multiples of 5, depending on the size of the bunch.

Fig. 3.

Study 2: (A) Sellers outperformed nonsellers in both addition and multiplication (both phrasings); (B) Among themselves, sellers performed better in both addition and multiplication when questions were phrased as practical words problems but were notably stronger in multiplication.

Fig. 4.

Study 2: Market vs. nonmarket addition problems (whole-sample performance by item).

Fig. 5.

Study 3: Nonprice addition performance on $+$1 and $+$5 (whole sample).