This paper is devoted to the design, description and validation of the Android application TEAtreves, which focuses on structured arithmetic problem-solving for students with autism spectrum disorder (ASD). The application contains multiple adaptations to make it suitable for users with ASD. Validation was carried out with five students with ASD,…

The purpose of this study was to examine the effects of a number line intervention with supported self-explanation on student understanding of fraction magnitude and quality of explanation. Participants were three U.S. middle school students with significant behavior problems. Participants were given eight lessons containing explicit instruction…

We build on mathematicians' descriptions of their work and conceptualize mathematics as an aesthetic endeavor. Invoking the anthropological meaning of practice, we claim that mathematical aesthetic practices shape meanings of and appreciation (or distaste) for particular manifestations of mathematics. To see learners' spontaneous mathematical…

Children's understanding of fractions, including their symbols, concepts, and arithmetic procedures, is an important facet of both developmental research on mathematics cognition and mathematics education. Research on infants', children's, and adults' fraction and ratio reasoning allows us to test a range of proposals about the development of…

The low performance of Grade 4 learners in the mathematical concept of word problems involving multiplication remains a concern for many researchers in mathematics education. Several studies conducted have largely focused on improving learners' performance on bare problems involving multiplication, with little focus on contextual problems. The…

Elementary school children (ages 7-11) struggle to understand mathematical equivalence, a foundational prealgebraic concept. Some manipulations to the learning environment, including well-structured nontraditional arithmetic practice alone, have been shown to improve children's understanding; however, improvements have been modest. The goal of…

Fractions are an important mathematical concept; however, fractions are also a struggle for many students with disabilities. This study explored a new framework adapted from the evidence-based concrete-representational-abstract framework: the virtual-representational-abstract (VRA) framework. The VRA framework involves teaching students to solve…

Mathematical reasoning is important in conceptual understanding and problem solving. In current reform-based, discourse-oriented mathematics classrooms, students with learning disabilities (LD) encounter challenges articulating or explaining their reasoning processes. Enlightened by the concept of conversational repair borrowed from the field of…

Researchers have speculated that children find it more difficult to acquire conceptual understanding of the inverse relation between multiplication and division than that between addition and subtraction. We reviewed research on children and adults' use of shortcut procedures that make use of the inverse relation on two kinds of problems:…

Proportional reasoning is an important cornerstone in children's mathematical development. This sort of reasoning has been shown to develop across the early years of schooling (ages 8 to 10) through the middle years (ages 11-14). In the early years, children tend to use additive reasoning to generate solutions to problems, while later comparisons…

The purpose of this study was to examine children's mathematical understandings related to participation in tithing (giving 10% of earnings to the church). Observations of church services and events, as well as interviews with parents, children, and church leaders, were analyzed in an effort to capture the ways in which mathematical problem…

Dot enumeration (DE) and number comparison (NC) abilities are considered markers of core number competence. Differences in DE/NC reaction time (RT) signatures are thought to distinguish between typical and atypical number development. Whether a child's DE and NC signatures change or remain stable over time, relative to other developmental…

This paper describes the use of quantities in video games by young people as part of a broader effort to understand thinking and learning across naturally occurring contexts of activity. Our approach to investigating the use of quantities in game play is ethnographic; we have followed eight children over a six-month period as they play their own…

Examined the relationship between 6- to 8-year olds' conceptual understanding of additive composition, commutativity, and associativity principles and addition problem-solving procedures. Results revealed that conceptual understanding was related to using order-indifferent, decomposition, and retrieval strategies and speed and accuracy in solving…

After figuring out why many kids hate math, these longtime educators Bob and Ellen Kaplan created an after-school program in which children as young as 5 formulate equations of their own--and actually enjoy doing it. This paper discusses the experiences of the Kaplan couple, Bob and Ellen, on their Math Circle class during after-school sessions…