This article reports on an empirical study that investigates the way students' performance in solving arithmetical tasks may be related to their performance in solving algebraic tasks. The sample consisted of 203 Grade 6 students. The arithmetical tasks involved arithmetical expressions with known quantities, whereas the algebraic tasks involved…

To understand the ways that manipulatives might support changes in students' reasoning about algebraic generalizations, a constructivist teaching experiment was conducted with two sixth-grade students. The students interpreted numerical situations with units of one and could construct units of units in mental activity. Initially, the students'…

This study lies within the field of early-age algebraic thinking and focuses on describing the functional thinking exhibited by six sixth-graders (11- to 12-year-olds) enrolled in a curricular enhancement program. To accomplish the goals of this research, the structures the students established and the representations they used to express the…

This paper builds on our previous research and investigates how students' fractional competence and reasoning can provide clear evidence of non-symbolic algebraic thinking and its progressive transition towards fully generalised algebraic thinking. In a large-scale study, 470 primary students completed a written paper and pencil test. This…

Procedural flexibility is an important skill for algebra. Although prior work has focused on measuring students' procedural flexibility using arithmetic problems, word problems may also capture students' flexibility because of their open-ended nature. To date, no published study has examined the use of word problems as another measure of…

Recent research has highlighted the role of functional relationships in introducing elementary school students to algebraic thinking. This functional approach is here considered to study essential components of algebraic thinking such as generalization and its representation, as well as the strategies used by students and their connection with…

Generalization is one of the core aspects of algebraic thinking, and research literature points to the importance of objectification when generalizing mathematical discourses. To increase the field's understanding of the objectification process in various algebra discourses, our study analyses Grade 6 teachers' use of words, symbols, routines and…

Representations are key to mathematical activities and meaning-making processes as they are part of modeling, connecting, communicating, and understanding mathematical ideas and concepts. The current study sought to examine a group of novice algebra learners' interactions with different representations from an onto-semiotic approach. A case study…

An alternating treatments design was used to analyze the effects of concrete and virtual manipulatives on the duration and number of correctly solved linear equations by three middle school students with cognitive disabilities. Participants physically manipulated algebra tiles to solve an equation during the concrete manipulative condition. During…

With the increase in the development of science and technology, contemporary technological requirements are seen as rising needs of the countries. In this regard, technology can be considered both a means and an end to reach science. Since gifted students are more prone to computer technologies due to their cognitive structures, instructional…

We conducted a descriptive exploratory study in which we analyzed 313 sixth to eighth grade students' answers to a word problem, accompanied by diagrams, involving generalization in an algebraic functional context. In this research, we jointly addressed two objectives: (a) to determine the strategies deployed by students to generalize and (b) to…

This study investigates sixth-grade Turkish students' pattern-generalization approaches among arithmetical generalization, algebraic generalization, and naïve induction. A qualitative case study design was employed. The data was collected from four sixth-grade students through the Pattern Questionnaire (PQ) and individual interviews based on the…

To date, of the many studies on early algebraic thinking, none, to our knowledge, has examined the relationships between algebraic thinking and negative numbers. Students encounter persistent difficulties in dealing with these numbers, and we believe that these could be addressed through the development of algebraic thinking. We are particularly…

This study explored whether initial skill moderated outcomes of Promoting Algebra Readiness, a Tier 2 sixth grade mathematics intervention targeting conceptual and procedural knowledge of fractions. The study analyzed data from a quasi-experimental pilot study in which at-risk students (n = 198) were assigned to the treatment or control condition…

This study explored whether initial skill moderated outcomes of Promoting Algebra Readiness, a Tier 2 sixth-grade mathematics intervention targeting conceptual and procedural knowledge of fractions. The study analyzed data from a quasi-experimental pilot study in which at-risk students (N = 198) from Oregon middle schools were assigned to the…