We studied the acquisition of the ordinal meaning of number words and examined its development relative to the acquisition of the cardinal meaning. Three groups of 3-, 4-, and 5-year-old children were tested in two tasks requiring the use of number words in both cardinal and ordinal contexts. Understanding of the counting principles was also…

Adults are prone to treating percents, one representational format of rational numbers, as novel cases of natural number. This suggests that percent values are not differentiated from natural numbers; a conceptual shift from the natural numbers to the rational numbers has not yet occurred. This is most surprising, considering people are inundated…

In two experiments, participants judged the average numerosity between two sequentially presented dot patterns to perform an approximate arithmetic task. In Experiment 1, the response was given on a 0-20 numerical scale (categorical scaling), and in Experiment 2, the response was given by the production of a dot pattern of the desired numerosity…

Motivating middle school students to learn can be challenging. One proven method for doing so is through an integrated curriculum. Educational philosophers and curriculum theorists have long noted the benefits of an integrated curriculum, which recognizes that the subject areas within the curriculum are connected to one another and to the real…

Studies reveal that students as well as teachers have difficulties in understanding and learning of decimals. The purpose of this study is to investigate students' as well as pre-service teachers' solution strategies when solving a question that involves an estimation task for the value of a decimal number on the number line. We also examined the…

Teachers and researchers have known for decades that the use of storybooks can have a positive impact on students' experiences with mathematics. This article describes how first graders in an urban public school actively engage with mathematics by using the story "Bean Thirteen" as a context for developing number sense. This…

The study aimed to investigate students' conceptions on the notion of absolute value and their abilities in applying the specific notion in routine and non-routine situations. A questionnaire was constructed and administered to 17-year-old students. Data were analysed using the hierarchical clustering of variables and the implicative method, while…

A facility with signed numbers forms the basis for effective problem solving throughout developmental mathematics. Most developmental mathematics textbooks explain signed number operations using absolute value, a method that involves considering the problem in several cases (same sign, opposite sign), and in the case of subtraction, rewriting the…

The basis of this intervention study is a distinction between numerical calculus and relational calculus. The former refers to numerical calculations and the latter to the analysis of the quantitative relations in mathematical problems. The inverse relation between addition and subtraction is relevant to both kinds of calculus, but so far research…

As students contribute to social and sociomathematical norms, they will often reorganize their own understandings. As such, the purpose of this article is to describe the ways in which prospective elementary teachers contributed to the norms that were established and "re"-established throughout an entire semester in an undergraduate…

In this article, we present an integer sequence approach to solve the classic water jugs problem. The solution steps can be obtained easily by additions and subtractions only, which is suitable for manual calculation or programming by computer. This approach can be introduced to secondary and undergraduate students, and also to teachers and…

The current study examined the development of two effects that have been found in single-digit multiplication errors: relatedness and distance. Typically achieving (TA) second, fourth, and sixth graders and adults, and sixth and eighth graders with a mathematics learning disability (MLD) performed a verification task. Relatedness was defined by a…

This article shows how to modify classroom evaluation items to avoid four potential difficulties that limit a teacher's insight into students' mathematical understanding by addressing these issues: (1) poor choice of numbers; (2) implausible or inappropriate contexts; (3) inclusion of graphics that do not help make learning visible; and…

Although students' invented strategies typically prove to be effective in the improvement of students' mathematical understanding, little is known about how preservice teachers interpret and respond to student-invented strategies on whole number multiplication. This study investigated the nature of 25 preservice teachers' interpretations of and…

Deaf Children usually achieve lower scores on numerical tasks than normally hearing peers. Explanations for mathematical disabilities in hearing children are based on quantity representation deficits (Geary, 1994) or on deficits in accessing these representations (Rousselle & Noël, 2008). The present study aimed to verify, by means of symbolic…