Manipulative-based instructional sequences have proven to be successful with students with disabilities. However, instruction must not only support the acquisition of conceptual and procedural knowledge but also build on students' strengths. This article describes how teachers can use manipulative-based instructional sequences to support the…

This article illustrates how teachers can use number lines to support students with or at risk for learning disabilities (LD) in mathematics. Number lines can be strategically used to help students understand relations among numbers, approach number combinations (i.e., basic facts), as well as represent and solve addition and subtraction problems.…

This article is about problems that children may have when learning mathematics, problems that are also typified in publications as 'dyscalculia'. We consider two questions. The first: Is a child a dyscalculic if it runs into trouble learning mathematics? The second: Does a child have problems when learning mathematics because it experiences…

We investigated the extent to which one elementary school child with working-memory differences made sense of number as a composite unit and advanced her reasoning. Through ongoing and retrospective analysis of eight teaching-experiment sessions, we uncovered four shifts in the child's real-time negotiation of number over time: (a) initial…

In this study, it was aimed to teach the addition and subtraction to a student with dyscalculia who is in third grade at elementary school. Before preparing individualized program, the student was given a pretest to measure about his level of the subject. The instruction was carried out in a room in the school, with a time of 40 minutes per day in…

Quality primary education is one of the 17 UN Sustainable Development Goals (SDGs). Undoubtedly, mathematics plays a key role in overcoming future challenges, and mathematical competence and problem-solving skills could help provide appropriate solutions to current and future social, environmental and economic challenges. The following paper deals…

To meet increasingly complex mathematics standards in late elementary school, students must conceptually understand and be fluent in the operations of multiplication and division. This includes understanding the operations' inverse relation. The purpose of the study was to investigate the effects of alternating concrete-representational-abstract…

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…

Implementing an integrated sequence of concrete-representational-abstract depictions of mathematics concepts (CRA-I) can improve the mathematics achievement of students with disabilities, and explicit instructional strategies involving problem-solving heuristics and student verbalizations can help facilitate students' conceptual understanding of…

Even in primary school, mathematics achievement depends upon the efficiency of cognitive, metacognitive and self-regulatory processes. Thus, for pupils to carry out a computation, such as a written calculation, metacognitive mechanisms play a crucial role, since children must employ self-regulation to assess the precision of their own thinking and…

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…

Place-value is an essential concept that is foundational for understanding our number system and for developing procedures for multidigit operations, but there has been limited research into the place-value understanding of students with learning disabilities. This research is a two-part mixed-methods study that links basic research to…

This paper introduces a revised model for the development of basic computation skills. The model draws on four key phases, which have proven to be important for the development of calculation strategies and stresses the use of gestures and the verbalisation of concrete and mental images. This seems to be of crucial importance for children with…

The Common Core Standards require demonstration of conceptual knowledge of numbers, operations, and relations between mathematical concepts. Supplemental instruction should explicitly guide students with specific learning disabilities (SLD) in these skills. In this article, we illustrate implementation of the concrete-representational-abstract…

Counting abilities have been described as determinative precursors for a good development of later mathematical abilities. However, an important part of variance in mathematical achievement has also been associated with differences between instruction methods given in schools. In this study counting and instruction as predictors for mathematical…