In this study I explore the construction of algebraic structure sense through engaging students in task sequences designed to elicit the development of competencies related to this understanding. The primary task-design principle employed in this study is strategic variation, in which certain components of items within task sequences vary while…

The COVID-19 global pandemic widely affected education across the world and engendered unprecedented scenarios that required expeditious responses. In South Africa, the pandemic came on top of pre-existing inequalities in the education system. Using a qualitative research method of exploratory and descriptive nature, this study engaged a social…

The current study aimed to reveal the changes to the identities of two tenth graders in mathematics learning at a Japanese high school during the COVID-19 pandemic from the perspective of learning from home versus learning in the classroom. The following research questions are raised: How has the pandemic situation affected and changed Japanese…

This brief "Math for Real" article introduces Ohanna, a seventh grader who lives in New York City and regularly takes the bus to get around the city. Ohanna pays $2.50 per bus ride when using her MetroCard. She earns a 5% bonus when she refills the card with a minimum of $5.00. For example, if she adds $10.00 on her MetroCard, her…

Research tells us that success in algebra is a factor in many other important student outcomes. Emerging research also suggests that students who are started on an algebra curriculum in the earlier grades may have greater success in the subject in secondary school. What's needed is a consistent, algebra-infused mathematics curriculum all…

This study investigates students' conceptions of absolute value (AV), their performance in various items on AV, their errors in these items and the relationships between students' conceptions and their performance and errors. The Mathematical Working Space (MWS) is used as a framework for studying students' mathematical work on AV and the…

Paolo Ruffini (1765-1822) may be something of an unknown in high school mathematics; however his contributions to the world of mathematics are a rich source of inspiration. Ruffini's rule (often known as "synthetic division") is an efficient method of dividing a polynomial by a linear factor, with or without a remainder. The process can…

We analyse the "two-dice horse race" task often used in lower secondary school, in which two ordinary dice are thrown repeatedly and each time the sum of the scores determines which horse (numbered 1 to 12) moves forwards one space.

This study examined whether secondary students in an urban school district perceived racial differences in opportunity to be successful in mathematics, whether those perceptions differed between students of color and white students, and the relation of those perceptions to teachers' choice and implementation of mathematical tasks. The results of…

The purpose of this study was to investigate secondary mathematics teachers' conceptions of mathematical literacy, which are important to consider when is essential to address in designing and implementing effective approaches. Data sources included semi-structured interviews with 16 in-service mathematics teachers from different types of…

We explore the effects of a statewide policy change that increased the number of high school math courses required for admission to four-year public universities in North Carolina. Using data on cohorts of eighth-grade students from 1999 to 2006, we exploit variation by district over time in the math course-taking environment encountered by…

The 2-year Philippine Senior High School (SHS) commenced only in 2016. This phenomenographic study aimed to describe, explain and explore the teaching of SHS Mathematics to include problems encountered and interventions done by the teachers. Two schools in Quezon City were purposively chosen to be the study site with a maximal variation sampling…

Learning progressions (LPs) describe the development of domain-specific knowledge, skills, and understanding. Each level of an LP characterizes a phase of student thinking en route to a target performance. The rationale behind LP development is to provide road maps that can be used to guide student thinking from one level to the next. The validity…

College students may be seen as near-peers to high school students and high school students are often able to see themselves in the college students who are but one step ahead. This nearness in maturity and educational level may place college students in a particularly powerful position when it comes to reaching out to high school students to…

This paper reports the results of a research exploring the mathematical connections of pre-university students while they solving tasks which involving rates of change. We assume mathematical connections as a cognitive process through which a person finds real relationships between two or more ideas, concepts, definitions, theorems, procedures,…