When teachers listen to, and learn from, students, they begin to see the world from a child's perspective, and this helps make what they teach more accessible to students. Thus it is important for teachers and educators to understand mathematics from the children's perspectives to help them improve their classroom instructions, by anticipating…

Cognitive diagnostic models (CDMs) attempt to uncover latent skills or attributes that examinees must possess in order to answer test items correctly. The DINA (deterministic input, noisy "and") model is a popular CDM that has been widely used. It is shown here that a logistic version of the model can easily be fit with standard software for…

This study investigated the effectiveness of "Math Explorer" at enhancing the word problem-solving skills of students with mathematics difficulties (MD). The study, which had a multiple-probe-across-subjects design, was conducted over 18 weeks. Four students with MD in Grades 2 and 3 participated. All students were able to use the four-step…

The researcher used a simultaneous prompting procedure to teach 3 Kindergarten students who had or who were at risk for a developmental delay. She taught a paraprofessional to use two instructional formats to teach skills (i.e., phonics or subtraction). On an alternating schedule, she used the simultaneous prompting procedure with a massed trial…

Ever since "mental arithmetic" was updated to "mental calculation," official documents have succeeded in perpetuating several basic misconceptions and misunderstandings about this topic. This situation does not augur well for the successful teaching of mental calculation strategies to young children. In this article, the author…

Many sets of state and national mathematics standards have come and gone in the past two decades. The Common Core State Mathematics Standards (CCSMS), which were released in June of 2010, have been adopted by almost all states and will be phased in across the nation in 2014. The main difference between these standards and most of the others is…

Patterns of problem-solving among 5-to-7 year-olds' were examined on a range of literacy (reading and spelling) and arithmetic-based (addition and subtraction) problem-solving tasks using verbal self-reports to monitor strategy choice. The results showed higher levels of variability in the children's strategy choice across Years 1 and 2 on the…

Three studies addressed children's arithmetic. First, 50 3- to 5-year-olds judged physical demonstrations of addition, subtraction and inversion, with and without number words. Second, 20 3- to 4-year-olds made equivalence judgments of additions and subtractions. Third, 60 4- to 6-year-olds solved addition, subtraction and inversion problems that…

The effect of a mathematic flashcard application on a hand-held computing device was examined across three individual second grade students with learning and behavioral disabilities. All of the students improved their subtraction scores by an average of 17% as measured by the district-created, curriculum-based assessment. The results of this study…

A 3-week problem-solving practice phase was used to investigate concept-procedure interactions in children's addition and subtraction. A total of 72 7- and 8-year-olds completed a pretest and posttest in which their accuracy and procedures on randomly ordered problems were recorded along with their reports of using concept-based relations in…

This study was designed to investigate the cognitive level of development and mathematical fluency of first grade children. A total of (N = 100) 6- and 7-year-olds from two low socioeconomic level elementary schools participated in this study. Piaget's conservation-of-liquid task was administered to children to determine their cognitive level of…

This paper reports on a research project on information and communication technology (ICT)-based dynamic assessment. The project aims to reveal the mathematical potential of students in special education. The focus is on a topic that is generally recognised as rather difficult for weak students: subtraction up to 100 with crossing the ten. The…

The main challenge for theories of multitasking is to predict when and how tasks interfere. Here, we focus on interference related to the problem state, a directly accessible intermediate representation of the current state of a task. On the basis of Salvucci and Taatgen's (2008) threaded cognition theory, we predict interference if 2 or more…

This paper examines the contribution of mathematical knowledge for teaching (MKT) and curriculum materials to the implementation of lessons on integer subtraction. In particular, it investigates the instruction of three teachers with differing MKT levels using two editions of the same set of curriculum materials that provided different levels of…

Little research has focused on an informal understanding of subtractive negation (e.g., 3 - 3 = 0) and subtractive identity (e.g., 3 - 0 = 3). Previous research indicates that preschoolers may have a fragile (i.e., unreliable or localized) understanding of the addition-subtraction inverse principle (e.g., 2 + 1 - 1 = 2). Recognition of a small…