Prompting learners to generate examples has been proposed as an effective way of developing understanding of a new concept. However, empirical support for this approach is lacking. This article presents two empirical studies on the use of example-generation tasks in an online course in introductory university mathematics. The first study compares…

A new classification for semantic structures of one-step word problems is proposed in this paper. The classification is based on illustrations of word problem situations in Common Core State Standards (CCSSM, 2010) and related historical studies (e.g. Weaver, 1973, 1979, 1982), as well as conceptual elaborations of embodied and grounded nature in…

This exploratory and experimental research aims to describe randomness expressed in 5 to 6-year-old children's drawings. This study considers a six-day activity developed in 5 Chilean kindergartens, with a total of 142 participants. The activity on the mosquito's flight considered the corporal movements to generate the idea of randomness in…

The purpose of this meta-analysis was to investigate the effectiveness of the use of games as part of mathematics instruction on academic achievement in grades Kindergarten to 12 in the United States. There were 17 studies selected for investigation published from 2010 to 2023 that focused on game-based learning and mathematics. This meta-analysis…

This observational study used data from 270 second-grade students to investigate the association between students' strategy use for multidigit addition and subtraction and their mathematics achievement. Based on strategies they used during a mathematics interview, students were classified into the following strategy groups: (a) standard algorithm,…

We share a subset of the 41 underlying strategies that comprise five ways of reasoning about integer addition and subtraction: formal, order-based, analogy-based, computational, and emergent. The examples of the strategies are designed to provide clear comparisons and contrasts to support both teachers and researchers in understanding specific…

This study investigated the cognitive and social processes through which high school students acquire the differential concepts through communication in a dynamic geometry environment through some cases. Additionally, we observed how a dynamic geometry environment affects these processes. To achieve this objective, eight students were recruited by…

The National Council of Teachers of Mathematics (NCTM) has been emphasizing the importance of teachers' pedagogical communication as part of mathematical teaching and learning for decades. Specifically, NCTM has provided guidance on how teachers can foster mathematical communication that positively impacts student learning. A teacher may have…

We investigated how high school mathematics course placement contributes to inequalities in college preparation for students categorized as "English Learners" (ELs), especially "long-term" English Learners (LTELs). We devised a base-2 enumeration approach that allowed us to process complex transcript data from one school…

English Learners (ELs) enrollment in the U.S. public schools continues to increase. ELs have various linguistic needs including listening, reading, speaking, and writing English. Often this group of students does not perform well academically on state assessments since these assessments are normally written in English and require substantial…

The sequence in which problems of different concepts are studied during instruction impacts concept learning. For example, several problems of a given concept can be studied together (blocking) or several problems of different concepts can be studied together (interleaving). In the current study, we demonstrate that the 2 sequences impact concept…

As technology become more ubiquitous in the classroom, teachers need to overcome two types of barriers to use it effectively: access to resources (including the development of knowledge) and the development of appropriate beliefs. To assist teachers in overcoming these barriers, we must understand the relationships that exist among them. We…

Prior research has shown that EL classification is consequential for students, however, less is known about how EL classification impacts students' outcomes. In this study, we examine one hypothesized mechanism: teacher perceptions. Using nationally-representative data (ECLS-K:2011), we use coarsened exact matching to estimate the effect of EL…

This study was conducted to compare two grade-ten mathematics textbooks according to Bloom's Taxonomies. In the Arabic version, 37 out of 70 periods (55.29%) were given to plane geometry and trigonometry, whereas 29 out of 70 periods (41.41%) were allocated for geometry and trigonometry. Also, 12 periods (17.14%) were allocated for algebra in the…

In online educational systems we can easily collect and analyze extensive data about student learning. Current practice, however, focuses only on some aspects of these data, particularly on correctness of students answers. When a student answers incorrectly, the submitted wrong answer can give us valuable information. We provide an overview of…