The present study investigates the effect of the separator lines on the learning of 8th grade students in simplifying algebraic expressions with parenthesis. An experimental study was designed to achieve this goal involving 60 girl students in 8th Grade (13 and 14 years old) randomly selected and assigned to two experimental and control groups.…

One typical challenge in algebra education is that many students justify the equivalence of expressions only by referring to transformation rules that they perceive as arbitrary without being able to justify these rules. A good algebraic understanding involves connecting the transformation rules to other characterizations of equivalence of…

Purpose: It is crucial for teachers to understand what students already know and what they are thinking, before conducting their lessons, because identification of the cause is the first step of remedy. This study analyses students' conceptions that underlie the errors they make in algebraic expressions under two categories of conceptual…

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…

In this article, we examine eighth graders' incorrect responses to a specific task on a national standardized assessment of mathematics. The task asked students to write the formula for the perimeter of a given figure as a function of a variable. We focus on incorrect responses to better understand students' difficulties with the algebraic…

The purpose of the study was to develop mathematical instructional card game titled "algebrameter" and determine its efficacy in remediating junior secondary school (JSS) students' learning difficulties in algebra and geometry. The study employed research and development design. A sample of 120 JSS II students drawn from a population of…

The transition between arithmetic and algebraic thinking is challenging for students. One notable difficulty for students is understanding algebraic symbols--pronumerals. Researchers are exploring pedagogical approaches in seeking to address this issue. The current paper is contributing to this body of literature by illustrating how an online card…

Although positive effects of lesson study on teachers learning are reported, only some studies have investigated teacher noticing as an analytical tool for supporting teachers with an explicit focus, as in LS, and more empirical evidence is needed. This qualitative interpretive case study design aims to investigate the noticing processes of a…

Student focusing and noticing, which drive reasoning, are important but under researched aspects of student learning. Quadratic functions representations are perceptually and conceptually complex and thus, offer much for students to focus on and notice. Our study compared a teacher's goals for student focusing and noticing during quadratic…

The purpose of this article is to present and discuss two recommended sequences of learning the areas of polygons, starting from the area of a rectangle. Exploring the algebraic derivations of the two sequences reveals that both are valid teaching progressions for introducing the area formula for various polygons. Further, it is suggested that…

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…

One does not have to teach for very long to see students applying the wrong formula in the wrong situation (e.g., Kirshner and Awtry 2004; Tan-Sisman and Aksu 2016). Students can become overreliant on the power of the formula instead of thinking about the relationships it describes. It is not surprising that students can see formulas as a way to…

"Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014) gives teachers access to an insightful, research-informed framework that outlines ways to promote reasoning and sense making. Specifically, as students transition on their mathematical journey through middle school and beyond, their knowledge and use of…

Simplifying symbolic expressions is usually perceived in middle school algebra as an algorithmic activity, achieved by performing sequences of short drill-and-practice tasks, which have little to do with conceptual learning or with creative mathematical thinking. The aim of this study is to explore possible ways by which ninth-grade students can…

This article describes a learning trajectory on expressions and equations based on the sixth-grade Common Core State Standards for Mathematics (NGA/CCSSO, 2010). A classroom teaching experiment using design research (Lamberg & Middleton, 2009) was conducted. The data was analysed using Corbin and Strauss' (2014) Constant Comparative method and…