This study investigates school-age children's arithmetic operations performance while solving larger-size problems which produces interferences in memory. Complex problems can trigger competing responses in working memory, which are irrelevant to a task goal and increase the likelihood of interference from previously learned problems (De Visscher…

Background: The Mental Starters Assessment Project (MSAP) seeks to address poor performance in Grade 3 mathematics. The programme focusses on eliminating inefficient counting methods and promoting strategic mathematical skills, including numerical sense, mental calculation and rapid recall skills. Additionally, MSAP supports teachers' professional…

When a number sentence includes more than one operation, students are taught to follow the rules for the order of operations to get the correct result. In this context, brackets are used to determine the operations that should be calculated first. However, it seems that the written format of an arithmetical expression has an impact on the way…

George Spencer-Brown's Laws of Forms was first published in 1969. In the fifty years since its publication, it has influenced mathematicians, scientists, philosophers, and sociologists. Its influence on mathematics education has been negligible. In this paper, I present a brief introduction to the theory and its philosophical underpinnings. And I…

In the first main section of this thesis, I investigate superirreducible polynomials over fields of positive characteristic and also over [set of rational numbers] and [set of integers]. An n-superirreducible polynomial f(x) is an irreducible polynomial that remains irreducible under substitutions f(g(x)) for g of degree at most n. I find…

Students need to create mental models for different types of addition and subtraction situations in order to develop a broad and viable understanding of these operations. Although most students succeed when changing or combining sets, situations that demand a quantitative comparison of sets seem considerably more difficult in the first school…

The study tested the hypotheses that boys will have an advantage learning the fractions number line and this advantage will be mediated by spatial abilities. Fractions number line and, as a contrast, fractions arithmetic performance were assessed for 342 adolescents, as was their intelligence, working memory, and various spatial abilities. Boys…

Solving mathematical (math) word problems (MWP) automatically is a challenging research problem in natural language processing, machine learning, and education (learning) technology domains, which has gained momentum in the recent years. Applications of solving varieties of MWPs can increase the efficacy of teaching-learning systems, such as…

Children's knowledge of arithmetic principles is a key aspect of early mathematics knowledge. Knowledge of arithmetic principles predicts how children approach solving arithmetic problems and the likelihood of their success. Prior work has begun to address how children might learn arithmetic principles in a classroom setting. Understanding of…

Although basing instruction on a learning trajectory (LT) is often recommended, there is little evidence regarding 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. This hypothesis was evaluated for an empirically-validated…

Although basing instruction on a learning trajectory (LT) is often recommended, there is little evidence regarding a premise of a LT approach--that to be maximally meaningful, engaging, and effective, instruction is best presented 1 LT level beyond a child's present level of thinking. We evaluated this hypothesis using an empirically validated LT…

Differing research worldviews have typically resulted in interpretations at odds with one another. Yet, leveraging distinct perspectives can lead to novel interpretations and theoretical construction. Via an empirically grounded research commentary, we describe the value of such activity through the lens of previously reported findings. This…

For schools implementing Response-to-Intervention, it is important to understand how to efficiently intensify interventions. Treatment intensity, or intervention design, is a critical yet overlooked and understudied aspect in math. More frequent dosage results in greater student gains. However, questions remain regarding how teaching episodes…

The aim in the current study is to examine the conceptualizations of zero in arithmetic operations among students with learning disabilities (LD) and no learning disabilities (N-LD). The similarities and differences in the understandings of students with LD and N-LD of zero in arithmetical operations will be discussed. The study is a multiple case…

This systematic review analyses the research results of low-achieving grade K-3 children's numeracy competencies by investigating the research approaches used, the definitions of low achievers and the numeracy competencies reported. 18 articles, identified in ERIC, PsycINFO and Web of Science, were selected for further analysis. The results show…