Arithmetic word problems are often presented accompanied by illustrations. The present study examined how different types of illustrations influence the speed and accuracy of performance of both good (n = 67) and poor arithmeticians (n = 63). Twenty-four arithmetic word problems were presented with four types of illustrations with increasing…

Calculia is considered to be the ability of performing arithmetic operations, the preconditions for the development of mathematical skills in the complex functioning of psychological functions represented in neuro-anatomical systems, as well in the interaction with the environment. Problems in acquiring arithmetic skills can be described as…

This study compared one lesson across four U.S. "traditional" textbook series, two U.S. reform-based textbook series, and one Chinese mathematics textbook series in teaching the connection between multiplication and division. The results showed the differences across U.S. and Chinese lessons in both the teaching and the practice parts of…

In this paper we present a model for computerized adaptive practice and monitoring. This model is used in the Maths Garden, a web-based monitoring system, which includes a challenging web environment for children to practice arithmetic. Using a new item response model based on the Elo (1978) rating system and an explicit scoring rule, estimates of…

This study examined the effect of training in math metacognition on fractional mathematics among primary school pupils, with a quasi-experimental design, specifically a post-test only control group design. Two intact classes were randomly selected and assigned to treatment and control conditions. Sixty primary six pupils constituted the sample…

This paper presents a computer based diagnostic tool developed to facilitate the learning process. The developed tool is capable of generating possible error syndromes associated with the answers received. The developed tool simulates the error pattern of the test results and then accordingly models the action plan to help in children's learning…

"Number Talks" is: (1) A five- to fifteen-minute classroom conversation around purposefully crafted computation problems that are solved mentally; and (2) The best part of a teacher's day. Whether you want to implement number talks but are unsure of how to begin or have experience but want more guidance in crafting purposeful problems, this…

Decimals are among the difficult subjects for the students because of its abstract nature. Therefore, the aim of this study is to develop instructional materials for students based on one of the four-stage models of constructivist approach related to the unit of "decimals". With this aim, a worksheet, analogy map and conceptual change…

Preschoolers' conceptual understanding and procedural skills were examined so as to explore the role of number-words and concept-procedure interactions in their additional knowledge. Eighteen three- to four-year-olds and 24 four- to five-year-olds judged commutativity and associativity principles and solved two-term problems involving number words…

As the U.S. economy begins to show signs of improvement, executives say they need a workforce fully equipped with skills beyond just the basics of reading, writing, and arithmetic (the three Rs). Skills such as critical thinking and problem solving, communication, collaboration, and creativity and innovation (the four Cs) will become even more…

In a large sample (N = 439) of literacy impaired and unimpaired elementary school children the predictions of the temporal processing theory of dyslexia were tested while controlling for (sub)clininal attentional deficits. Visual and Auditory Temporal Order Judgement were administered as well as three subtests of a standardized attention test. The…

We report the development of a multiple-choice instrument that measures the mathematical knowledge needed for teaching arithmetic with fractions, decimals, and proportions. In particular, the instrument emphasizes the knowledge needed to reason about such arithmetic when numbers are embedded in problem situations. We administered our instrument to…

In a 3-year longitudinal study, 471 children were classified, based on their performances on arithmetic tests in first and second grade, as having persistent arithmetic disabilities (AD), persistent low achieving (LA), persistent typical achieving, inconsistent arithmetic disabilities (DF1), or inconsistent low achieving in arithmetic. Significant…

Arithmetic and cognitive skills of children with mathematical difficulties (MD-only), with comorbid reading difficulties (MD-RD), with reading difficulties (RD-only), and normally achieving children were examined at 3 points from Grades 3-4 to Grades 5-6 (age range, 9-13 years). Both MD groups displayed severe weaknesses in 4 domain-specific…

The number Pi (approximately 3.14159) is defined to be the ratio C/d of the circumference (C) to the diameter (d) of any given circle. In particular, Pi measures the circumference of a circle of diameter d = 1. Historically, the Greek mathematician Archimedes found good approximations for Pi by inscribing and circumscribing many-sided polygons…