The purpose of this study was to analyze participants' levels of hemoglobin as they performed arithmetic mental calculations using Optical Topography (OT, helmet type brain-scanning system, also known as Functional Near-Infrared Spectroscopy or fNIRS). A central issue in cognitive neuroscience involves the study of how the human brain encodes and…

The current study was designed to extend the current literature to study scale drift in CAT as part of improving quality control and calibration process for ACCUPLACER, a battery of large-scale adaptive placement tests. The study aims to evaluate item parameter drift using empirical data that span four years from the ACCUPLACER Arithmetic…

Background: In order to fully specify the profiles of risk and protective factors of developmental disorders, a better understanding of the conditions under which they co-occur is required. So far, empirical evidence on comorbidities of specific learning disorders in arithmetic, reading and spelling is scarce. Methods: Prevalence and gender ratios…

Arithmetic skills are generally claimed to be preserved in semantic dementia (SD), suggesting functional independence of arithmetic knowledge from other aspects of semantic memory. However, in a recent case series analysis we showed that arithmetic performance in SD is not entirely normal. The finding of a direct association between severity of…

"Mathematical habits of mind" include reasoning by continuity, looking at extreme cases, performing thought experiments, and using abstraction that mathematicians use in their work. Current recommendations emphasize the critical nature of developing these habits of mind: "Once this kind of thinking is established, students can apply it in the…

The aim of this 2 year longitudinal study was to explore whether children's individual differences in spontaneous focusing on numerosity (SFON) in kindergarten predict arithmetical and reading skills 2 years later in school. Moreover, we investigated whether the positive relationship between SFON and mathematical skills is explained by children's…

In a previous article of the same journal, we have discussed the interrelations of students' beliefs and self-efficacy beliefs for the use of representations and their respective cognitive performance on the learning of fraction addition. In the present paper, we confirm a similar structure of cognitive and affective factors on using…

It is a pity that for so many people not involved in Teaching, and for a surprising number who are, mathematics in schools is "chiefly" all about the ability to know a set of facts, multiplication tables and addition bonds in particular, rather than the capacity to reason and explore patterns and relationships in Number and Shape.…

Fraction division is generally introduced in sixth or seventh grade with this rule: "Invert and multiply." The authors examined current commercial curricula and found that few textbooks use context as a way to build meaning for the division of fractions. When context is used, the connection between the invert-and-multiply rule and the context is…

In the late seventies, Guy Brousseau set himself the goal of verifying experimentally a theory he had been building up for a number of years. The theory, consistent with what was later named (nonradical) constructivism, was that children, in suitable carefully arranged circumstances, can build their own knowledge of mathematics. The experiment,…

Counting abilities have been described as determinative precursors for a good development of later arithmetic abilities. Mastery of the stable order, the one-one-correspondence and the cardinality principles can be seen as essential features for the development of counting abilities. Mastery of the counting principles in kindergarten was assessed…

The arithmetical performance of typically achieving 5- to 7-year-olds (N=29) was measured at four 6-month intervals. The same seven tasks were used at each time point: exact calculation, story problems, approximate arithmetic, place value, calculation principles, forced retrieval, and written problems. Although group analysis showed mostly linear…

The Lorentz velocity addition formula for one-dimensional motion presents a number of problems for beginning students of special relativity. In this paper we suggest a simple rewrite of the formula that is easier for students to memorize and manipulate, and furthermore is more intuitive in understanding the correction necessary when adding…

A number derivative is a numerical mapping that satisfies the product rule. In this paper, we determine all number derivatives on the set of integers modulo n. We also give a list of undergraduate research projects to pursue using these maps as a starting point.

Children's failure on equivalence problems (e.g., 5 + 4 = 7 + __) is believed to be the result of misunderstanding the equal sign and has been tested using symbolic problems (including "="). For Study 1 (N = 48), we designed a nonsymbolic method for presenting equivalence problems to determine whether Grade 2 children's difficulty is due…