In this paper we follow a hypothetical mathematician who is working on a problem that is eventually solved. We treat this problem as if it were difficult for the mathematician. In following the mathematician's work, we note both what she does and what she doesn't do in the process. By the latter, we consider the times when progress is not being…

Mathematical flexibility has been widely acknowledged as an important learning goal in mathematical education and has received increasing research attention in order to explore its nature, facilitating mechanisms, and promotion interventions. Given that researchers conceptualize, assess, and explain flexibility in mathematical problem solving from…

This study was designed to fill a need to explore the hypothesis that students who participate in middle school bands and or chorus have higher math cognitive functioning than their non-music peers. Using the Measure of Academic Progress (MAP), this study identified specific math domains that middle school music students showed higher functioning…

The design principles of cognitive load theory and learning by analogy has independently contributed to our understanding why an instruction will or will not work. In an experimental study involving 97 Year 9 Australian students conducted in regular classrooms, we evaluated the effect of the unguided problem-solving approach, worked examples…

The COVID-19 public health emergency has been characterized by an abundance of data in the form of numbers and charts. Although these data are readily available, there have been challenges associated with their interpretation--exacerbated by generally low numeracy rates. Consequently, people may underestimate the speed at which the disease spreads…

In this report, we present cases where students constructed new quantities through operating on quantities that does not fit the definitions of existing theories on quantitative operations. As a result, we identified five quantitative operators--operators that can be used on single qualities in order to transform the quantity to a new…

The construct of static and emergent shape thinking (Moore & Thompson, 2015) characterizes differences in students' reasoning about graphs. In our previous work with middle school students, we found that this construct may also be useful in characterizing students' reasoning about other representations such as simulations and tables. In this…

Finger gnosia and fine motor skills (FMS) are assumed to play a key role in the development of arithmetic abilities, but their contribution to early numerical skills (i.e., enumeration skills and cardinality) has received little attention so far. The purpose of this study was to investigate the predictive value of finger gnosia and FMS to…

Increasing use of intelligent tutoring systems in education calls for analytic methods that can unravel students' learning behaviors. In this study, we explore a latent variable modeling approach for tracking learning flow during computer-interactive artificial tutoring. The study considers three models that give discrete profiles of a latent…

Concerns about low mathematics achievement have created a push to increase national mathematics proficiency levels through research and policy. Efforts have largely focused on early mathematics interventions for students with or at risk for mathematics learning difficulties implemented within multi-tiered response to intervention (RTI) frameworks.…

Does the mathematics course taught with logical reasoning methods have an effect on the success of students in skill-based questions and what are the students' views on teaching? Based on this problem, it was aimed to examine the effect of the mathematics course taught with logical reasoning methods on the success of students in skill-based…

This research is an ethnomathematical research that aims to explore the mathematical abilities of the Bugis people in weaving the "lipa' sabbe." This study applies a qualitative method with an ethnographic approach. The data were collected through observation, interviews, and documentation. Based on the results, it can be explained that…

As an interdisciplinary and multicultural educational framework takes the centrality of the delivery of 21st-century education across all levels, this study attempts to address the competencies that prospective and neophyte teachers need to possess to effectively design contextualized education. Through stepwise multiple regression analysis,…

This article investigates regional disparities in Romanian adults' numeracy and literacy skills. We analyse a novel data set that combines the assessment of numeracy and literacy competencies of the adult population in Romania with information about regional economic conditions and educational administrative data. Using a background questionnaire…

This study examined a 6-week intervention in which fourth grade students either played fluency games or used pictorial flashcards to develop fluency with their basic multiplication facts. Students who played fluency games showed more growth than the pictorial flashcards, but an analysis of variance showed that there was no statistically…