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…

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…

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…

Students often perform arithmetic using rigid problem-solving strategies that involve left-to-right-calculations. However, as students progress from arithmetic to algebra, entrenchment in rigid problem-solving strategies can negatively impact performance as students experience varied problem representations that sometimes conflict with the order…

In this paper, we describe an experiment in using history to work on problem-solving and the relationship between arithmetic and algebra. The students involved attended the first year of the Italian upper secondary school (grade 9). The original sources we used are problems from Italian treatises on arithmetic and algebra that appeared in the…

This study focused on capturing the research landscape of past studies related to mathematics problem solving in elementary education from 1969 to 2021 through a bibliometric analysis. All the 159 bibliographic data involved were extracted from the Scopus database. The findings show an increasing trend in publication and citation over the years.…

Several working memory processes have been hypothesized to influence different arithmetic operations. Working memory has been compartmentalized into a number of different sub-processes, such as phonological memory and visuospatial memory that are believed to have unique contributions to the performance of two distinct arithmetic operations:…

Objective: When students learn or solve problems, attentional resources are depleted; rest breaks may restore cognitive functioning in support of learning. Research framed by attention restoration theory holds that exposure to natural environments may be another means to restore attentional resources. The study investigated the effects of…

Diagnostic tests have been developed previously to measure algebraic thinking skills; however, the tests do not specifically address algebraic problem-solving. Thus, an Algebraic Thinking Test (ATT) Instrument was developed to measure algebraic thinking skills in problem-solving involving linear equations. ATT comprises nine open-ended questions…

Background: Traditional math instruction that emphasizes procedures and rote memorization is common in math classes, particularly within the United States. Students may be able to perform steps and recite information, but flexible thinking in math is also an important ability. Lay theories assume that extensive experience in math would lead to…

We analyzed the solution pathways and errors found in the written responses of 469 prospective teachers solving an equation containing fractions. The majority (332, or 70%) used an algebraic method; 141 of the 332 (42%) were correct, and 22% of the algebraic methods were abandoned before a solution was obtained. We identified the steps in the…

The aim of the exploratory method research centered on the presence of mathematical tools in STEM through three main questions: Is mathematics an essential tool in the field of STEM? Can mathematics complete projects solely with mathematical and digital tools? Does understanding mathematical modeling affect STEM teaching? A better understanding of…

The aim of this study is to determine the primary school fourth-grade students' understanding of four operation symbols, using them in arithmetic operations and word problems. Phenomenology research design, one of the qualitative research methods, was used in the research. The participants of the research consist of 123 students, attending the…

Context: Students with special educational needs in the area of learning (SEN-L) attend vocational trainings to be provided with qualifications for the labor market. Competences in arithmetic operations and comparing quantities such as weights and lengths are indispensable for obtaining a vocational qualification. Therefore, the study investigates…