Developing both conceptual and procedural knowledge is important for students' mathematics competence. This study examined whether U.S. Grade 9 general education mathematics teachers' self-reported use of concept-focused instruction (CFI) and procedure-focused instruction (PFI) were associated differently with ninth graders' algebra achievement…

Meaningful collaborative interactions in asynchronous online mathematics teacher professional development (PD) may provide teachers with valuable opportunities to learn. We studied collaborative interactions in online teacher PD activities that involved embedded videos, prompts, discussions, and multiple online tools. Analysis of teacher responses…

There is a strong relationship between the quality of education, teachers' decisions and instructional actions, and knowledge. All of them have an important role outcome of the lesson and students' learning. The focus of this study was to discover how the process of students' learning or incapability of learning was affected by teaching practices.…

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'…

Textbook is one of the most tangible resources for teaching and learning mathematics, offering valuable opportunities for both teachers and students. This study compared the mathematical tasks in 6th-grade textbooks from the United States and Turkey, focusing on three dimensions of the tasks: representation, contextual features, and cognitive…

A controversial, equity-focused mathematics reform in the San Francisco Unified School District (SFUSD) featured delaying Algebra I until ninth grade for all students. This study examines student-level longitudinal data on mathematics course-taking across successive cohorts of SFUSD students who spanned the reform's implementation. We observe…

Seeds of Algebraic Thinking comes from the Knowledge in Pieces (KiP) perspective of learning. KiP is a systems approach to learning that stems from the constructivist idea that people learn by building on prior knowledge. As people experience the world, they acquire small, sub-conceptual knowledge elements. When people engage in a particular…

A theoretical model describing Grade 7 students' rational number sense was formulated and validated empirically (n = 360), hypothesizing that rational number sense is a general construct consisting of three factors: basic rational number sense, arithmetic sense, and flexibility with rational numbers. Data analysis suggested that rational-number…

Mathematical problem-posing and modeling are essential skills in developing students' analytical thinking and problem-solving abilities. This study aims to examine correlation between 9th-grade students' problem-posing and mathematical modeling skills within the learning domain of numbers and algebra. Additionally, it evaluates students'…

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…

In 2014, a team of educators and all of the eighth-grade students at a "failing school" in Nashville, Tennessee, took up the challenge of teaching and learning Algebra 1. This was in the context of a constrained standardized-test-driven public school environment in which less than 20 percent of these students had achieved proficiency in…

This qualitative study aims to investigate the mediation strategies employed by teachers who participated in a professional development (PD) course, focusing on the teaching of Grade 9 linear equations. Within the context of the PD course, teachers engaged with various pedagogical approaches for teaching linear equations and other secondary school…

This quantitative correlational study examines school-level longitudinal outcomes of eighth-grade algebra universal acceleration in 15 U.S. school districts when compared with selective acceleration in 289 school districts. Universally accelerated school districts had higher enrollments, with large effect sizes, in geometry, algebra 2, and…

Providing students with the appropriate math support can ensure they develop the skills and confidence they need to succeed. This Spotlight explores effective strategies for providing targeted math support, addressing math anxiety, and promoting student success. From combating math anxiety to leveraging in-school tutoring, these articles offer…