This report presents dual analyses of an undergraduate student, Cassie, whose work provides nice contrasts between Grounded Theory (GT) analysis and Knowledge Analysis (KA). The analyses highlight particular methodological differences, such as grain size of findings, positioning of novices and more general implications about expert-novice studies.…

The recent proliferation of technological devices with natural user interfaces (e.g., touchscreen tablets) is regenerating scholarship on the role of sensorimotor interaction in conceptual learning. Some researchers of mathematical education have adopted views from constructivism, phenomenology, enactivism, and ecological dynamics to interpret…

International research suggests that early mathematical competences predicts later mathematical outcomes. In this paper, we build on our previous study of young children's mathematical competencies (MacDonald & Carmichael, 2015) to explore the relationship between mathematical competencies at 4-5 years, as measured by teacher ratings, and…

We aggregated and analyzed single-case research targeting math-fact fluency to investigate whether learning (behavior change) data were sufficient to summarize and compare intervention outcomes or if learning rate (learning/cumulative instructional time) data would provide divergent effect size (ES) results. We also extracted the curricular scope…

A critical component in enhancing academic success is identifying children at risk of later academic difficulties. Although significant efforts have been devoted to design effective assessment processes in elementary school, fewer efforts (particularly for mathematics) have been made for preschool. The focus of this study was to design and…

By means of three case studies, we will present two mathematical modelling activities that are suitable for students enrolled in senior high school and the first year of mathematics at university level. The activities have been designed to enrich the learning process and promote the formation of vital modelling skills. In case studies one and two,…

This research study examines the development of the ability of pre-service teachers to notice signs of students' understanding of the derivative concept. It analyses preservice teachers' interpretations of written solutions to problems involving the derivative concept before and after participating in a teacher training module. The results…

Kyle, a kindergartner from a low-income family, is shown a set of three black dots on a white mat. His teacher then hides the dots with a small box lid and lays down an additional set of two dots. She pushes the two dots under the cover, one at a time. Kyle must now choose the number of dots "hiding" under the box from a set of four…

This paper investigates how an online test ("Self-Test" developed at the University of Southern Queensland) can enrich students' understanding of their academic numeracy, through a purpose-built, self-assessment tool aligned with online modules. Since its creation and evaluation, the tool has been developed and tailored to suit other…

This event-related fMRI study investigated the differences between learning from examples and learning from verbal directions in mathematical problem solving and how these instruction types affect the activity of relevant brain regions during instruction and solution periods within problem-solving trials. We identified distinct neural signatures…

This design research type development study aims at producing a set of PISA-like mathematics task which is valid and practical as well as has the potential effects. Then, activation of fundamental mathematical capabilities underlying mathematical process related to the mathematical literacy as the main potential effect of the developed PISA-like…

The purpose of this paper is to describe a trajectory of designing for particular forms of engagement with mathematics. The forms of engagement that were targeted through these design experiments involved making intentional choices about which procedures to leverage in order to support particular claims (what I call "critical…

While understanding rational numbers forms an essential part of mathematical literacy, research has repeatedly shown that they form a stumbling block in education. A big source of difficulty is the inappropriate application of natural number knowledge. The research literature points at three main aspects where natural number knowledge is…

The natural number bias is known to explain many difficulties learners have with understanding rational numbers. The research field distinguishes three aspects where natural number properties are sometimes inappropriately applied in rational number tasks: density, size, and operations. The overall goal of this study was to characterize the…

As a Title I kindergarten teacher, Michelle Pace, second grade teacher at Lake Mary Elementary School in Florida, has seen firsthand how oral language can create roadblocks for students in all areas of the curriculum, both academically and socially. At the time this article was written, the state of Florida had recently adopted the Common Core…