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…

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…

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…

Mathematics anxiety hinders students' mathematical achievement already in primary school, but research on its effects beyond whole number knowledge is limited. The main aim of the current study is to examine how state and trait mathematics anxiety relate to performance across five tasks that are relevant for the development of mathematics in…

Studies of errors in mathematics are essential for mathematics educators to design and contextualize a whole new instruction accordingly. Nonetheless, less attention has been given to the mathematical writing errors when compared to the mathematical conceptual and procedural errors. It is mainly because the former mistakes usually do not affect…

The equal symbol has been used in diverse mathematical frameworks, such as arithmetic, algebra, trigonometry, set theory, and so on. In mathematical terms, the equal sign has been used in fixed command of standings. The study reports on the students meaning and interpretations of the equal sign. The study involved Grade 6, 7, and 8 students in a…

This study explored how students develop meaning of functions by building on their understanding of expressions and equations. A teaching experiment using design research was conducted in a sixth-grade classroom. The data was analyzed using a grounded theory approach to provide explanations about why events occurred within this teaching episode…

The non-learning of school mathematics is now almost universally taken for granted, but this does not have to happen. This article takes a critical look at the root of this non-learning by pointing to the flagrant defects in the kind of mathematics--to be called TSM--that is predominant in almost all the school textbooks. By analyzing how the long…

The aim of this paper is to analyse the reasoning and symbolisations used by sixth grade Moroccan students in solving a task based on figurative patterns. Our analysis aims at identifying the systems of actions elaborated by the students to give the general expression of the sequence, according to their perceptions of the sequence of its patterns.…

The present study was conducted to compare the performances of high-achieving sixth grade students on written computation, symbolic representation, and pictorial representation tests. The study enrolled 107 sixth-grade students in three schools. Data were analyzed by using the Kruskal Wallis and Mann Whitney-U Tests and interviews were conducted…

Why is the use of letters in algebraic expressions and equations--variables--the source of such uncertainty for students and teachers? The authors studied a sixth-grade classroom and observed that students hold many misconceptions about variables. Some students hold an algebraic view of the equal sign. For them, it indicates an equation and…

This study describes the mathematical processes in TIMSS (Trends in Mathematics and Science Study) to reflect issues. A descriptive qualitative methodology was used in this analysis as the research approach. The research allocated the respondent to the 6th grade students of Muhammadiyah 6 in the sub-district of Dau, Malang regency, East Java,…

This paper presents strategies identified in Mexican rural school students in seeking structure on equivalence tasks that involve the equal sign and tasks that do not. The results arise from the pilot study of a research project on the structure of numbers and numerical operations -- a key aspect of early algebraic thinking. [For the complete…

This case study investigates, at three Swedish schools, primary school students' knowledge of the equal sign. The schools were chosen as representatives of schools whose students have different socioeconomic backgrounds. The data consist of Grade 3 and 6 students' responses to an assessment form based on Matthews et al. ("JRME,"…

The aim of this study is to investigate relationships between note-taking and the orchestrating of math-talk in whole-class teaching. A lesson on (average) velocity in a Swedish Grade 6 has been observed. Taking an inferentialist stance on human understanding, the study conceptualizes teaching and learning from the perspective of how students come…