The number line estimation task is frequently used to measure children's numerical magnitude understanding. It is unclear whether the resulting straight, horizontal, left-to-right-oriented estimate patterns indicate task constraints or children's intuitive number--space mapping. Three- to six-year-old children (N = 72, M[subscript age] = 4.89, 56%…

The ability to solve mathematical problems has been an interesting research topic for several decades. Intuition is considered a part of higher-level thinking that can help improve mathematical problem-solving abilities. Although many studies have been conducted on mathematical problem-solving, research on intuition as a bridge in mathematical…

Recent research shows that preverbal infants can reason about single-case probabilities without relying on observed frequencies, adapting their predictions to relevant dynamic parameters of the situation (Téglás, Vul, Girotto, Gonzalez, Tenenbaum & Bonatti, [Téglás, E., 2011]; Téglás, Girotto, Gonzalez & Bonatti, [Téglás, E., 2007]). Here…

In this paper two studies are reported in which two contrasting claims concerning the intuitiveness of the law of large numbers are investigated. While Sedlmeier and Gigerenzer ("J Behav Decis Mak" 10:33-51, 1997) claim that people have an intuition that conforms to the law of large numbers, but that they can only employ this intuition…

The ubiquity of the subject of percentages in our everyday life demands that math teachers and pre-service math teachers demonstrate a profound knowledge and thorough understanding of the concept of percentages. This work, which originated from one specific lesson in an 8th grade math class, studies the conceptual understanding and problem-solving…

A major source of errors in rational number tasks is the inappropriate application of natural number rules. We hypothesized that this is an instance of intuitive reasoning and thus can persist in adults, even when they respond correctly. This was tested by means of a reaction time method, relying on a dual process perspective that differentiates…

Evidence evaluation is a crucial process in many human activities, spanning from medical diagnosis to impression formation. The present experiments investigated which, if any, normative model best conforms to people's intuition about the value of the obtained evidence. Psychologists, epistemologists, and philosophers of science have proposed…

This study is concerned with the development of children's intuitive understanding of nonlinear processes. The ability to estimate linear and exponential growth was examined in 7-, 9-, 11-, and 13-year-old children and adults (N=160). Whereas linear growth was judged correctly at all ages, estimations of exponential growth were in line with…

This report focuses on prospective secondary mathematics teachers' understanding of irrational numbers. Various dimensions of participants' knowledge regarding the relation between the two sets, rational and irrational, are examined. Three issues are addressed: richness and density of numbers, the fitting of rational and irrational numbers on the…