Based on an empirical study, we explore children’s primary and secondary perceptions on infinity. When discussing infinity, children seem to highlight three categories of primary perceptions: processional, topological, and spiritual. Based on their processional perception, children see the set of natural numbers as being infinite and endow Q with a discrete structure by making transfers from N to Q. In a continuous context, children are more likely to mobilize a topological perception. Evidence for a secondary perception of arises from students’ propensities to develop infinite sequences of natural numbers, and from their ability to prove that N is infinite. Children’s perceptions on infinity change along the school years. In general, the perceptual dominance moves from sequential (processional) to topological across development. However, we found that around 11–13 years old, processional and topological perceptions interfere with each other, while before and after this age they seem to coexist and collaborate, one or the other being specifically activated by the nature of different tasks.
- RT @shankerinst: We are devastated to report the death of David K. Cohen, a founding member of the Albert Shanker Institute’s board of dire… 4 months ago
- Check this out! twitter.com/SLSingh/status… 5 months ago
- I really appreciated the keynote by @deborah_ball #TWSummerInstitute To quote some of her closing words: "It's coll… twitter.com/i/web/status/1… 7 months ago
- RT @TeachingWorks: Today is the day! If you signed up to join us, the link to view our #TWSummerInstitute keynote address today is waiting… 7 months ago
- Looking forward to the lecture by @deborah_ball at #TWSummerInstitute 7 months ago