The teaching and learning of mathematical modelling is an important research field all over the world. In this paper we present a survey of the state-of-the-art on empirical studies in this field. We analyse the development of studies focusing on cognitive aspects of the promotion of modelling, i.e. the promotion of modelling abilities resp.…

Ratio and proportional relationships, along with the interrelated topics of fractions,decimals, and percent, provide a critical foundation for algebra (National Mathematics Advisory Panel, 2008). Proportional reasoning, which not only requires understanding the concept of ratios and that two or more ratios are equal, also requires the ability to…

We describe the findings from a randomized evaluation of a one-year kindergarten math enrichment program, the High 5s program. The program was designed to provide small-group math enrichment in a fun, club-like format to children who had received enriched math instruction the prior year. Participants included 655 kindergarten students in 24…

Augmented reality (AR) and mobile devices show promise for promoting mathematics practices and an increase in perseverance. Using an experimental pre-/posttest comparable condition group design, this study investigated (a) whether differences exist in students' number sense outcome scores based upon the type of board game they played with…

This multiple probe across participants design evaluated the effectiveness of teaching early number sense skills (ENS) to young children (age 4) with autism spectrum disorder (ASD) using Number Talks with supports. Following participation in Number Talks with supports, young children with ASD learned the ENS skills of subitizing, one-to-one…

This dissertation reports the research methodology and findings of three studies focused on mathematical modeling as a structured problem-solving process where the student translates relevant details from a situation, event, or phenomena in daily life into mathematical language with mathematically-defined structures and operations, which form the…

Spatial skills are consistently linked to mathematical reasoning, and are sensitive to intervention. One important spatial skill is spatial scaling. We evaluated whether (1) a playful scaling game might promote learning by providing feedback during play, and (2) spatial scaling is related to number-line estimation based on the mutual reliance on…

Spatial skills are consistently linked to mathematical reasoning, and are sensitive to intervention. One important spatial skill is spatial scaling. We evaluated whether (1) a playful scaling game might promote learning by providing feedback during play, and (2) spatial scaling is related to number-line estimation (NLE) based on the mutual…

The overarching goal of this 2-phase study was to investigate the contributions of relational reasoning to mathematical thinking and performance for 790 primary and middle-school Chinese students. Phase I of the study was undertaken to establish the reliability and validity of the Test of Relational Reasoning-Junior (TORRjr), a 32-item measure…

We illustrate how early adolescents use different patterns of ability feedback to promote a positive self-concept of ability (SCA) in mathematics. Students can simultaneously use ability appraisals from parents and teachers, while also drawing information from peer, dimensional, and temporal comparisons. Although we find these five sources are…

During a time when students are accessing instruction virtually because of COVID-19, reflecting on the sixth of the Standards for Mathematical Practice (SMP 6) is a vital step for educators to take. Although the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010) identifies SMP 6 as Attend to precision, associated expertise…

Despite historical emphasis on "specific" learning disabilities (SLDs), academic skills are strongly correlated across the curriculum. Thus, one can ask how specific SLDs truly are. To answer this question, we used bifactor models to identify variance shared across academic domains (academic "g"), as well as variance unique to…

The research focuses on the diagnostics and stimulation of socially disadvantaged children of a preschool age, which is a crucial component of inclusive education. The aim of the research was to experimentally verify through input and output orientation diagnostics the effectiveness of the stimulation program for 5 to 6 year old socially…

This study aimed to explore mother's views and home literacy practices for their children on literacy skills acquisition. In the study carried out in 2020, twenty-five mothers of children aged 6 years were assessed by means of a semi-structured qualitative interview. Two mother views were identified; (1) family is responsible (FR) and (2) teacher…

The purpose of this study was to determine the effectiveness of a video-based instruction packet for teaching math-based vocational skills delivered through augmented reality (AR) to three adults with intellectual disabilities. The dependent variable was the percentage of steps performed correctly to solve each selected type of math problem. The…