The intention of the present study is to know how the pupils can learn to make a group of ten to understand the idea of unitizing. The pupils were given a contextual problem "Counting the Beads" in order to promote their understanding about the idea of unitizing. The process of designing the problem was based on the 5 tenets of…

We share results from a quasi-experimental study in which we compared achievement between traditional face-to-face and computer-based sections of Intermediate Algebra on a common multiple choice exam as well as performance on open-response tasks. Students in the computer-based group performed better on the final exam and were also more likely to…

To promote a relational understanding of the equal sign (=), students may require exposure to a variety of equation types (i.e., 3 = 8 - 5; 2 + 3 = 1 + 4; 9 - 3 = 6). The purpose of this study was to evaluate 8 elementary curricula for degree of exposure to equation types. Across 6 elementary grade levels, curricula were coded for the number of…

Three studies explore arithmetic tasks that support both substitutive and basic relational meanings for the equals sign. The duality of meanings enabled children to engage meaningfully and purposefully with the structural properties of arithmetic statements in novel ways. Some, but not all, children were successful at the adapted task and were…

A new method for obtaining Russell-Saunders terms of atomic configurations is reported. This new method is significantly different from, while at the same time complementary to, previously published methods for obtaining atomic terms. This novel procedure is elicited by the method used to determine the splitting of S, P, D terms in weak ligand…

A cumulative body of research has shown that children typically shift from an "operational" to a "relational" conception of the equals sign as they move through schooling. Jones (2008) argued that a truly relational conception of the equals sign comprises a "substitutive" component and a "sameness"…

The debate about whether making a risky choice is based on a weighting and adding process has a long history and is still unresolved. To address this long-standing controversy, we developed a comparative paradigm. Participants' eye movements in 2 risky choice tasks that required participants to choose between risky options in single-play 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…

It has been well-documented that many students do not understand the meaning of the equal sign. Thus, researchers have called for instruction that specifically addresses misconceptions about the equal sign, and have indicated that such work must start at the elementary level. In response to these recommendations, some state curriculums require…

The ability to represent numerical quantities in symbolic form is a necessary foundation for mathematical competence. Variables are particularly important symbolic representations for learning algebra and succeeding in higher mathematics, but the mechanisms of how students link a variable to what it represents are not well understood. Research…

The language of mathematics is unique and complex. One feature of the mathematical register is the use of symbols and abbreviations. Whilst it may be possible for a student to think mathematically in the absence of symbols, the written communication of mathematical ideas cannot be achieved concisely without the use of mathematical symbols.…

In this article, I explore tensions of care in the context of school mathematics by examining two accounts of a classroom moment involving labelling an angle. In particular, I draw attention to how caring for students and caring for mathematical ideas interplay in complex ways by inquiring into the two accounts through ideas of care and…

This study examined ways in which students make use of a graphing calculator and how use relates to comfort and understanding with mathematical symbols. Analysis involved examining students' words and actions in problem solving to identify evidence of algebraic insight. Findings suggest that some symbols and symbolic structures had strong…

This article reports results from a study investigating the impact of a sustained, comprehensive early algebra intervention in third grade. Participants included 106 students; 39 received the early algebra intervention, and 67 received their district's regularly planned mathematics instruction. We share and discuss students' responses to a written…

A solid foundation of chemistry principles is only gained through a true comprehension of the material as opposed to pure memorization. One of the most fundamental concepts in chemistry is that of determining the amount of product formed in a chemical reaction when one of the reactants is limiting. To increase students' comprehension of this…