In this paper we report on two assessment tasks extracted from a larger study. The tasks involved number-line placements on two different number lines (0-to-10 and 0-to-20) and place-value understanding. Participants were 119 children from four different classes (Years 1-3). Children's placements were more accurate on the 0-to-20 than the 0-to-10…

This case study narrative reports on the journey of *Sammy as her mindset as a learner of mathematics is challenged. Often students who are mathematically highly capable are viewed as being privileged, they are rarely placed with the cohort of struggling students. Children like Sammy who are mathematically highly capable or gifted, however, are…

The benefit of interleaving cognitive content has gained attention in recent years, specifically in mathematics education. The present study serves as a conceptual replication of previous work, documenting the interleaving effect within a middle school sample through brief homework assignments completed within ASSISTments, an adaptive tutoring…

Early mathematics content that is taught in elementary school lays the foundation for students' advanced mathematics performance. Thus, researchers show it is important that pre-service elementary teachers build a strong background in numbers and operations, as well as efficacy beliefs in mathematics instruction. This study expands the literature…

Reviewing the research on teachers' diagnostic competences shows that most findings focus on the correspondence between teachers' diagnostic judgments and students' actual achievement, while cognitive processes and cognitive resources of teachers in diagnostic situations have been examined much less. We intend to extend this state of research from…

Findings from an empirical study on prospective elementary teachers' argument productions are reported. In order to analyse the data, a generative study was conducted to develop a framework for expressed actions that afforded the communication of viable arguments for generalizations. Identified are three types of technical handles that appear…

School districts altered instructional delivery from solely in-person to a combined virtual/in-person model in the 2020-2021 school year in response to the COVID-19 pandemic. The Houston Independent School District (HISD) offered in-person and virtual instruction to early learners at school-based programs (SBP), early childhood centers (ECC), and…

One of the major benefits of the face-to-face teaching environment is that social interaction opportunities are a natural part of the course: Learners meet in the same room for the same allotted period of time each week. This social opportunity is not organic to online courses; therefore, to have this social interaction as a part of online classes…

Students' difficulties in mathematics and science may stem from interference of irrelevant salient variables. We focus on the comparison of perimeters task, in which area is the irrelevant salient variable. A previous fMRI brain-imaging study related to the comparison of perimeters task suggested that increasing the level of salience of the…

This study examined the effects of a teacher-delivered intervention with online mathematics mini-games on special education students' multiplicative reasoning ability (multiplication and division). The games involved declarative, procedural, as well as conceptual knowledge of multiplicative relations, and were accompanied with teacher-led lessons…

Counting skills are foundational for young children to build number concepts in mathematics. Multitiered instruction that involves core instruction as well as supplemental interventions is implemented to support young children in the learning process and promote early intervention of basic skills. Researchers show that explicit instruction is…

This article offers a reflection on the findings of three PhD studies, in the domains of, respectively, subtraction under 100, fractions, and algebra, which independently of each other showed that Dutch students' proficiency fell short of what might be expected of reform in mathematics education aiming at conceptual understanding. In all three…

Children in the elementary grades are expected to solve equations to demonstrate prealgebraic proficiency. Prealgebraic differences may emerge based equation type (i.e., standard vs. nonstandard), the operation shown or required for solution (i.e., addition or subtraction), and the position of the unknown. Prealgebraic differences may also be…

This article explores some of the common mathematical difficulties that 11- to 16-year-old students experience with respect to their learning of physics. The definition of "understanding" expressed in the article is in the sense of transferability of mathematical skills from topic to topic within physics as well as between the separate…

In many scientific contexts, students need to be able to use mathematical knowledge in order to engage in scientific reasoning and problem-solving, and their understanding of scientific concepts relies heavily on their ability to understand and use mathematics in often new or unfamiliar contexts. Not only do science students need high levels of…