The aim of this study was to examine if--and to what extent--a sensory modality's conceptual congruency influences learning in digital environments. Building on previous work in multimedia and embodied learning, the study used custom software to systematically vary the conceptual congruency of two sensory modalities (aural and bodily-kinesthetic).…

Students with learning disabilities/difficulties in mathematics often apply ineffective procedures to solve word problems. Given that current mathematics curriculum standards emphasize conceptual understanding in problem solving as well as higher-order thinking and reasoning, the purpose of this study was to evaluate the impact of a model-based…

Young children's symbolic magnitude understanding, or knowledge of how written numerals and number words can be ordered and compared, is thought to play an important role in their mathematical development. There is consistent evidence that symbolic magnitude skills predict mathematical achievement in later childhood and adulthood. Yet less is…

In this paper we explored primary school teachers preference for different game modes to support mathematics teaching and learning. Eighty-four teachers played digital and non-digital addition and subtraction games that were functionally equivalent during professional learning workshops. Most teachers indicated that they would be more likely to…

The literature dealing with student understanding of integration in general and the Fundamental Theorem of Calculus in particular suggests that although students can integrate properly, they understand little about the process that leads to the definite integral. The definite integral is naturally connected to the antiderivative, the area under…

Many related studies have studied many different models in the teaching of the concept of integer, which have reported that counters failed to completely help with the understanding of the concept of and operation modeling in integers. The purpose of the present research is presenting the "opposite model", which is a quantitative model,…

Although basing instruction on a learning trajectory (LT) is often recommended, there is little direct evidence to support the premise of a "LT approach"--that to be maximally meaningful, engaging, and effective, instruction is best presented one LT level beyond a child's present level of thinking. The present report serves to address…

This observational study used data from 270 second-grade students to investigate the association between students' strategy use for multidigit addition and subtraction and their mathematics achievement. Based on strategies they used during a mathematics interview, students were classified into the following strategy groups: (a) standard algorithm,…

Because word problems present mathematical information through a scenario, they are language-intensive and require mathematical and reading comprehension skills to solve them. In addition, they are linguistically complex, which makes them challenging for all learners, especially multilingual learners. Given the rising number of dual-language…

This study addresses first graders' conceptual knowledge exhibited in addition strategies in relation to instructional practices and teachers' beliefs in a suburban Alabama school. To address the purpose of the study, the central question was "What is the nature of the relationship between curricular practices and beliefs and students'…

To improve understanding of identities and inverses, and to provide a stronger foundation for future mathematics, Sandra Miles designed a two-part lesson that makes the relationship between identities and inverses explicit. This article illustrates Miles' teaching of the first part of the lesson, focused on addition and subtraction, and then gives…

The present study aimed to examine the opinions of in-and preservice middle school mathematics teachers about teaching four operations with integers through "number line" and/or "counters". Participants were 42 middle school mathematics teachers and 51 pre-service mathematics teachers. The data were collected through open-ended…

This study explored the relationships between task beliefs about the empty number line (ENL), mathematical ability, gender, and voluntary ENL use in multi-digit subtraction and addition. One hundred twenty-three Dutch third-grade students and nine teachers from six schools participated in this study. The multilevel path analysis showed that task…

CBM for mathematics assesses growth in accuracy and fluency of basic math skills using content from a student's curriculum. CBM for mathematics can include single-skill measures (SSM), skill-based measures (SBM), and general-outcome measures (GOM). Past research on growth rates in CBM for mathematics has focused on GOMs and has relied on…

These four chapters describe studies of using models for integer addition and subtraction. The models draw principally on the two grounding metaphors of object collection and motion along a path. A strength of all chapters is detailed analysis of how the models are and can be implemented and how they influence student's learning. Together the…