Units coordination, defined by Steffe (1992) as the mental distribution of one composite unit (i.e., a unit of units) "over the elements of another composite unit" (p. 264) is a powerful tool for modeling students' mathematical thinking in the context of whole number and fractional reasoning. This paper proposes extending the idea of a…

South African learners' performance in mathematics, both locally and internationally, has raised significant concerns, particularly in the realm of algebra. To address this issue, a mixed-methods study was conducted to explore the effectiveness of using algebra tiles to teach algebraic expressions. The study aimed to investigate algebraic…

Units Coordination and Covariational Reasoning are powerful frameworks for modeling students' mathematics in arithmetic reasoning and construction of relationships between changing quantities, respectively. This case study of an advanced stage 2, 8th-grade algebra student, Daniel, investigated connections between his units coordination and…

The aim of this study is to examine how middle school mathematics teachers diagnose and attempt to eliminate students' misconceptions in algebra. The study employed a case study method and embedded single-case design. The research was conducted with three mathematics teachers working in different state schools and having different professional…

Students often perform arithmetic using rigid problem-solving strategies that involve left-to-right-calculations. However, as students progress from arithmetic to algebra, entrenchment in rigid problem-solving strategies can negatively impact performance as students experience varied problem representations that sometimes conflict with the order…

Previous research has established the importance of definitions in mathematics and have distinguished the difference between extracted and stipulated definitions. Much remains unknown, however, about the role definitions serve in developing students' disciplinary literacy. In this study, we analyze how definitions from four US Algebra 1 textbooks…

Understanding equivalence is fundamental to STEM disciplines, yet misunderstandings and misconceptions inhibit students from fully appreciating or leveraging the concept. Using the game-based algebraic notation system, From Here to There! (FH2T), students explore ideas of equivalence by dynamically transforming expressions or equations among…

In this study, the authors highlight the differences in classroom-, teacher-, and school-level factors in 8th and 9th grade algebra experiences along socioeconomic and racial/ethnic lines using nationally representative survey data from the American Mathematics Educator Study. Several takeaways emerge from this analysis. The analysis shows that…

Central in the frameworks that describe algebra from K-12 is the idea that algebraic thinking is not a single construct, but consists of several algebraic thinking strands. Validation studies exploring this idea are relatively scarce. This study used structural equation modeling techniques to analyze data of middle school students' performance on…

In this study, we highlight the differences in classroom-, teacher-, and school-level factors in 8th and 9th grade algebra experiences along socioeconomic and racial/ethnic lines using nationally representative survey data from the American Mathematics Educator Study. Several takeaways emerge from our analysis. First, we show that highest-poverty…

To efficiently solve mathematical expressions and equations, students need to notice the systemic structure of mathematical expressions (e.g., inverse relation between 3 and 3 in 3 + 5 - 3). We examined how symbols--specifically variables versus numbers--and students' algebraic knowledge impacted seventh graders' problem-solving strategies and use…

Purpose: WebQuests are employed for many different instructional aims by offering students to take an active role and encouraging their critical thinking skills to construct their own meaning about an inquiry. The purpose of the study was to explore pre-service mathematics teachers' decisions about the organization of information sources in which…

This study, firstly, aimed at investigating the various types of the multiple math representations and transitions among them in the 8th grade math textbook, and secondly, teachers' use of these representations in teaching. The current study employed the content analysis approach to investigate the multiple mathematical representations and…

Middle school is a critical time when students begin formal study of functional relationships in algebra. However, many students struggle in understanding functions as relationships between quantities that change according to a dependency relationship. We report on the influence of Scaling Continuous Covariation in fostering productive ideas about…

The aim of this study was to examine 6th-grade students' mathematical abstraction processes related to the concept of variable by using the teaching experiment method and to reveal their learning trajectories in the context of the RBC+C model. A teaching experiment was administered to a class of 29 middle school students for 3 weeks. Observations,…