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).…

Teacher-directed and self-directed learning have been compared across various contexts. Depending on the settings and the presentation of material, mixed benefits are found; the specific circumstances under which either condition is advantageous are unclear. We combined and reanalyzed data from two experimental studies investigating the effects of…

We report on 25 Year 5-6 students' written responses to two items taken from an assessment of mental computation fluency with multiplication, alongside their reasoning of the strategy they had employed, which may or may not have made use of the associative property. Coding of this interview data revealed four distinct levels of conceptual…

This research paper reports strategies used by Grade 6 learners in multiplying whole numbers in five selected primary schools in Kavango East and West regions. A total of 200 learners' mathematics exercise books were analysed in order to identify the commonly used strategies by learners in multiplying whole numbers. A total of ten teachers…

This article focuses on how two mathematics teachers (Amy and Beth -- pseudonyms) cope with the changes of meanings in multiplication due to the changes of contexts. It highlights the qualitative similarities and differences between these two teachers in the sense-making process of multiplication. A potentially useful framework of supportive and…

Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

This article examines the importance of developing the notion of place value as a rate of ten. In exploring how to nurture this concept, the author looks at the role of the language of value, the problem types of multistep multiplication and addition along with measurement division, each with ten as an organizing unit, as well as strategically…

This paper examines a problem described as widespread and long-standing in mathematics education: supporting pupils into multiplicative reasoning, a form of reasoning that has been noted as central to large tracts of secondary mathematics and beyond. Also noted, however, is a persistent perception of multiplicative situations only in terms of…

Curricular analysis indicates that the U.S. students are introduced to multiplication in additive terms (as the replication of equal groups and repeated addition). But the virtue of this introduction for supporting students' understanding of the full range of multiplicative relationships is unclear. This paper reports an analysis of all grade 4…

Strategy flexibility, adaptivity, and the use of clever shortcut strategies are of major importance in current primary school mathematics education worldwide. However, empirical results show that primary school students use such shortcut strategies rather infrequently. The aims of the present study were to analyze the extent to which Dutch sixth…

This article investigates how students in third grade learn to reason on multiplication when they first encounter that concept in the classroom context. By analysing the data from 24 classrooms focused on teaching and learning multiplication, the article aims at contributing to the research and conceptualisations about how students learn to…

The current study examines the mental computation performance owned by students at fifth grade. This study was carried out with 118 fifth graders (11-12-year-olds) studying at 3 randomly selected primary schools that served low and middle socio-economic areas in a city of Turkey. "Mental Computation Test (MCT)" has been used to reach how…

Mathematical relationships are crucial elements to consider for learning mathematics. However, too often students pay more attention to the calculations to be done rather than the reasons for doing them. Relying on the relational paradigm to support elementary school students, we proposed two specially designed tasks to help students recognize and…

Many general and special education teachers teach mathematics word problems by defining problems as a single operation and linking key words to specific operations. Unfortunately, teaching students to approach word problems in these ways discourages mathematical reasoning and frequently produces incorrect answers. This article lists eight common…

Many general and special education teachers across the U.S. teach word problems by defining problems as a single operation (e.g., "Today, we're working on subtraction word problems") and linking key words (e.g., more, altogether, share, twice) to specific operations (e.g., share means to divide). Unfortunately, teaching students to…