In mathematics education, researchers often contrast conceptual and procedural teaching approaches, although labels and conceptualizations often vary across studies. Prior research has extensively examined empirical relationships between the two teaching approaches and mathematics achievement. In our study, we aimed to extend this research by…

This study examined repeating and growing pattern knowledge and their associations with procedural and conceptual arithmetic knowledge in a sample of U.S. children (N = 185; M[subscript age] = 79.5 months; 55% female; 88% White) and adults (N = 93; M[subscript age] = 19.5 years; 62% female; 66% White) from 2019 to 2020. Three key findings emerged:…

When, how, and why students use conceptual knowledge during math problem solving is not well understood. We propose that when solving routine problems, students are more likely to recruit conceptual knowledge if their procedural knowledge is weak than if it is strong, and that in this context, metacognitive processes, specifically feelings of…

The purpose of this study was to examine the psychometric properties of the Precalculus Concept Assessment (PCA), a 25-item multiple-choice instrument designed to assess student reasoning abilities and understanding of foundational calculus concepts (Carlson et al., 2010). When this study was conducted, the extant research on the PCA and the PCA…

It has become increasingly clear that the early use of decomposition for addition is associated with later mathematical achievement. This study examined how younger children execute a base-10 decomposition strategy to solve complex arithmetic (e.g. two-digit addition). 24 addition problems in two modalities (WA: Written Arithmetic; OA: Oral…

This study aims to determine the relationship of junior high school students' spatial and mathematical logical intelligence based on understanding the concepts. Spatial intelligence indicators in this study are reviewed from students' abilities in using images as a tool for solving problems, connecting data with concepts that have been held, and…

Math anxiety negatively predicts young children's math achievement. While some researchers have suggested that math anxiety may stem from poor math ability, others have argued that math anxiety occurs at all levels of math ability. An important question is whether math anxiety predicts math achievement over and above foundational math skills. We…

Informal best fit lines frequently appear in school curricula. Previous research collectively illustrates that the adjective informal does not translate to cognitive simplicity. Using existing literature, we create a hypothetical framework of cognitive processes associated with studying informal best fit lines. We refine the framework using data…

Math anxiety negatively predicts young children's math achievement. While some researchers have suggested that math anxiety may stem from poor math ability, others have argued that math anxiety occurs at all levels of math ability. An important question is whether math anxiety predicts math achievement over and above foundational math skills. We…

Purpose: The purpose of this descriptive study is to investigate why some elementary children have difficulties mastering addition and subtraction calculation tasks. Design/methodology/approach: The researchers have examined error types in addition and subtraction calculation made by 697 Portuguese students in elementary grades. Each student…

Introduction: The macroscopic perspective is one of the frameworks for research on problem solving in mathematics education. Coming from this perspective, our study addresses the stages of thought in mathematical problem solving, offering an innovative approach because we apply sequential relations and global interrelations between the different…

Are there differential benefits of training sequential number knowledge versus spatial skills for children's numerical and spatial performance? Three- to five-year-old children (N = 84) participated in 1 session of either sequential training (e.g., what comes before and after the number 5?) or non-numerical spatial training (i.e., decomposition of…

This research focused on performance indicators for elementary and middle school students. Performance indicators are factors that could hinder or enhance early childhood education. For instance, poverty affects a child's development and educational outcomes beginning in the formative years, both directly and indirectly through mediated,…

One crucial issue in mathematics development is how children come to spontaneously apply arithmetical principles (e.g. commutativity). According to expertise research, well-integrated conceptual and procedural knowledge is required. Here, we report a method composed of two independent tasks that assessed in an unobtrusive manner the spontaneous…

This article presents activities appropriate for the first half of a general introductory statistics course. All activities revolve around the same data set collected early in the course. The activities require students to make decisions about how they should proceed. (Contains 2 tables and 5 figures.)