Insight into early precursors of proportional reasoning is necessary to further our theoretical understanding of mathematical development and to guide early interventions. Although several researchers have suggested patterning as a possible precursor for proportional reasoning, there is little empirical evidence to support this assumption,…

Several studies have shown that children do not only erroneously use additive reasoning in proportional word problems, but also erroneously use proportional reasoning in additive word problems. Traditionally, these errors were contributed to a lack of calculation and discrimination skills. Recent research evidence puts forward an additional…

Comparing probabilities is a useful skill in life. Binary choice tasks are popular means in research on probabilistic reasoning. Falk, Yudilevich-Assouline, and Elstein ("Educational Studies in Mathematics," 81(2), 207-233 2012) noted that many of these tasks contain design flaws. We designed and evaluated an extended and improved binary…

Previous research has shown that early numerical abilities are predictive of later mathematical achievement. In line with these previous studies, we investigated whether early numerical abilities are also associated with later probabilistic reasoning abilities. In the present study, we examined children's numerical abilities in the second grade of…

Previous research demonstrated that some children inappropriately solve multiplicative missing-value word problems additively, while others inappropriately solve additive missing-value word problems multiplicatively. Besides lacking skills, children's preference for additive or multiplicative relations has been shown to contribute to those errors.…

The present study longitudinally investigated proportional reasoning abilities in early elementary school before the start of its instruction. Three aims were put forward: (a) distinguishing the different developmental states in young children's understanding of missing-value proportional situations, (b) investigating how children transition…

Students often show difficulties in understanding rational numbers. Often, these are related to the natural number bias, that is, the tendency to apply the properties of natural numbers to rational number tasks. Although this phenomenon has received a lot of research interest over the last two decades, research on the existence of qualitatively…

Word problems are among the most difficult kinds of problems that mathematics learners encounter. Perhaps as a result, they have been the object of a tremendous amount research over the past 50 years. This opening article gives an overview of the research literature on word problem solving, by pointing to a number of major topics, questions, and…

Understanding rational numbers is a complex task for primary and secondary school students. Previous research has shown that a possible reason is students' tendency to apply the properties of natural numbers (inappropriately) when they are working with rational numbers (a phenomenon called "natural number bias"). Focusing on rational…

Proportionality can be considered among the most important mathematical notions in the middle school math curriculum (grades 5 to 8). It is the capstone of elementary arithmetic, number, and measurement concepts, and at the same time one of the most elementary understandings one needs for more advanced mathematics. Understanding proportionality is…

In this commentary we take a critical look at the various studies being reported in this issue about the relationship between cognitive neuroscience and mathematics, from a mathematics education viewpoint. After a discussion of the individual contributions, which we have grouped into three categories--namely neuroscientific studies of (a)…

Recent research on the phenomenon of improper proportional reasoning focused on students' understanding of elementary functions and their external representations. So far, the role of basic function properties in students' concept images of functions remained unclear. We add to this research line by investigating how accurate students are in…

Background: Rational numbers are of critical importance both in mathematics and in other fields of science. However, they form a stumbling block for learners. One widely known source of the difficulty learners have with rational numbers is the natural number bias, that is the tendency to (inappropriately) apply natural number properties in…

Inhibitory control--the ability to ignore salient but unhelpful stimuli and responses--seems to be important for learning mathematics. For instance there is now robust evidence that performance on classic measures of inhibition, such as the Stroop Task, correlate with school-level mathematics achievement. At the same time, a great deal of…

The Monty Hall dilemma (MHD) is a counterintuitive probability problem in which participants often use misleading heuristics, such as the equiprobability bias. Finding the optimal solution to the MHD requires inhibition of these heuristics. In the current study, we investigated the relation between participants' equiprobability bias and their MHD…