Adult and developing humans share with other animals analog magnitude representations of number that support nonsymbolic arithmetic with large sets. This experiment tested the hypothesis that such representations may be more accurate for addition than for subtraction in children as young as 3 1/2 years of age. In these tasks, the experimenter hid…

There is a very natural way to divide a four-digit number into 2 two-digit numbers. Applying an algorithm to this pair of numbers, determine how often the original four-digit number reappears. (Contains 3 tables.)

A simple view, which dates back to Turing, proposes that complex cognitive operations are composed of serially arranged elementary operations, each passing intermediate results to the next. However, whether and how such serial processing is achieved with a brain composed of massively parallel processors, remains an open question. Here, we study…

The author clarifies his position regarding what features of the examples used by Kaminski, Sloutsky, and Heckler (2008a) constitute substantive differences affecting performance. I also reiterate my hesitancy to extrapolate their findings to the broader realm of mathematics.

The identification of patterned responding in unmotivated test takers was investigated through the formation of a novel method. The proposed method relied on marginal proportions of answer choice options as well as the transitional proportions between responses on item pairs. A chi square analysis was used to determine the degree of significance…

In the September 2010 issue of "Mathematics Teaching," Tom O'Brien offered practical advice about how to teach addition, subtraction, multiplication, and division and contrasted his point of view with that of H.H. Wu. In this article, the author revisits Tom's examples, drawing on his methodology while, hopefully, simplifying it and giving it…

Depending on task combination, dual-tasking can either be performed successfully or can lead to performance decrements in one or both tasks. Interference is believed to be caused by limitations in central processing, i.e. structural interference between the neural activation patterns associated with each task. In the present study, single- and…

This article discusses how 13-year-old students with above-average numeracy skills and below-average reading skills cope with comprehending word problems. Compared to other students who are proficient in numeracy and are skilled readers, these students are more disadvantaged when solving single-step and multistep arithmetic word problems. The…

We examined the effects of early life stress (ELS) on intellectual ability in 2,725 20-year-old male participants, of whom 321 were separated temporarily (mean 1.7 years) from both their parents during World War II, at an average age of 4.3 years. Intellectual ability was tested when entering compulsory military service. The separated men had…

Division of fractions is often considered the most mechanical and least understood topic in elementary school. Enacting fraction division tasks in meaningful ways requires that teachers know not only "how" fraction division works but also "why" it works. The authors have created materials to help preservice teachers develop that knowledge. To…

Studies show the positive effects that video games can have on student performance and attitude towards learning. In the past few years, strategies have been generated to optimize the use of technological resources with the aim of facilitating widespread adoption of technology in the classroom. Given its low acquisition and maintenance costs, the…

Children with learning disabilities face problems in acquiring the basic skills needed for learning. Dyscalculia is one among those learning disorders which affects the ability to acquire arithmetic skills that are needed to perform mathematical calculations. However this is a learning difficulty which is often not recognized. The objectives of…

Writing is often considered secondary to the spoken language, as it is only coded sound-by-sound. But other scholars have demonstrated that writing is similar to "arithmetic": a cognitive structuring, a shift to the meta-level ("for the eye"). "Handwriting" (referred to here as the cursive writing in the sense of…

This paper surveys the fascinating mathematics of fair division, and provides a suite of examples using basic ideas from algebra, calculus, and probability which can be used to examine and test new and sometimes complex mathematical theories and claims involving fair division. Conversely, the classical cut-and-choose and moving-knife algorithms…

In this paper, we focus on Finnish pre-service elementary teachers' (N = 269) and upper secondary students' (N = 1,434) understanding of division. In the questionnaire, we used the following non-standard division problem: "We know that 498:6 = 83. How could you conclude from this relationship (without using long-division algorithm) what 491:6…