Students with autism spectrum disorder (ASD) are included in the general education classroom more often than ever before. Despite mathematical strengths and early success, these students experience poor outcomes (academic and employment) compared to their typically developing peers. The language of mathematics increases in complexity, use, and…

The limitations of traditional education models and the advancement of technology have revealed the need to transform the learning experience. The "Flipped Learning" approach, born out of this need, is a model where students study learning materials in advance and participate in more interactive and hands-on activities in the classroom.…

The authors define two mathematical cognitive verbs which are fundamental to the development of mathematical thinking and reasoning. They distinguish between 'describing' and 'explaining' in relation to doing mathematics, rather than using them interchangeably.

This study provides the first large-scale quantitative exploration of mathematical language use in U.S. classrooms. Our approach employs natural language processing techniques to describe variation in the use of mathematical language in 1,657 fourth and fifth grade lessons by teachers and students in 317 classrooms in four districts over three…

This study explores volitional and affective responses to instructional activities aimed at developing geometric and spatial vocabulary of a neurodivergent student. Using teaching experiment methodology across 15 instructional sessions, we observed how the student responded to games, direct instruction, and vocabulary support embedded in spatial…

Despite the proliferation of video-based instruction and its benefits--such as promoting student autonomy and self-paced learning--the complexities of online teaching remain a challenge. To be effective, educators require extensive training in digital teaching methodologies. As such, there's a pressing need to examine and comprehend the…

Problem-solving is one of the 21st-century skills. However, students still have difficulty solving sequences and series word problems. The purpose of this research is to analyze students' errors in solving sequences and series word problems based on problem-solving steps of Polya. The research method is descriptive qualitative. The research…

The main purpose of this study was to test the effects of word-problem (WP) intervention, with versus without embedded language comprehension (LC) instruction, on at-risk 1st graders' WP performance. We also isolated the need for a structured approach to WP intervention and tested the efficacy of schema-based instruction at 1st grade. Children (n…

Teaching simulations such as scriptwriting tasks offer a novel way to support pre-service teachers in gaining diagnostic competencies and in guiding students to work through difficulties. We first report on the theory-driven development of a scriptwriting task, specifically the theoretically-founded language- and accompanying content-related…

Gestures are associated with powerful forms of understanding; however, their causative role in mathematics reasoning is less clear. We inhibit college students' gestures by restraining their hands, and examine the impact on language, recall, intuition, and mathematical justifications of geometric conjectures. We test four mutually exclusive…

The COVID-19 epidemic had caused one of the most significant disruptions to the global education system. Many educational institutions faced sudden pressure to switch from face-to-face to online delivery of courses. The conventional classes are no longer the primary means of delivery; instead, online education and resources have become the…

Influenced by COVID-19, online learning has become one of the most important forms of education in the world. In the era of intelligent education, knowledge tracing (KT) can provide excellent technical support for individualized teaching. For online learning, we come up with a new knowledge tracing method that integrates mathematical exercise…

Assessment data from the United States and international reports of student achievement indicate that upper elementary students are failing to meet basic levels of proficiency in fractions and writing, and that this is particularly prevalent with students with or at-risk for learning disabilities in mathematics. Proficiency with fractions has been…

Mathematics has been defined by researchers as a 'second or third language' and, as a result, it should be taught as a second language. Results of the literature reviewed from the theories on the teaching of mathematics and English as a second language, as well as on mathematics learning and English as a second language acquisition, have resulted…

This archival data study examined the relations between cognitive abilities and math reasoning for Hispanic English learner (EL) students in grades 1 through 5 with an identified learning disability. The 295 student participants were referred for an initial psycho-educational Spanish or English evaluation due to academic concerns by their school…