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…

"University of Chicago School Mathematics Project (UCSMP)" is a core mathematics curriculum that includes materials and a routinized instructional approach with an option for teacher training. The curriculum uses an inquiry-based approach with a focus on active learning where students frequently engage in hands-on activities and…

"University of Chicago School Mathematics Project (UCSMP)" is a core mathematics curriculum that includes materials and a routinized instructional approach with an option for teacher training. The curriculum uses an inquiry-based approach with a focus on active learning where students frequently engage in hands-on activities and…

Several factors seem important to understand the nature of mathematical learning. Byrnes and Miller combined these factors into the Opportunity-Propensity model. In this study the model was used to predict the number-processing factor and the arithmetic fluency in grade 4 (n = 195) and grade 5 (n = 213). Gender, intelligence and affect (positive…

Mathematics learning is illustrated as a developmental progression in the direction of concrete-to-abstract by educational theorists. Various studies rooted in this notion were conducted in the past. This study aimed to profile the landscape of research rooted in this notion which was published from 1968 to 2021. The bibliographic data of 425…

Mathematics anxiety is the feeling of tension and fear which interferes with the manipulation of numbers in ordinary life and academic setting. This study aimed at exploring students' level of mathematics anxiety and teacher behavior and speech which intensifies and minimizes mathematics anxiety among secondary schools in Sokoto state, Nigeria. In…

Making accurate judgements and interpretations about student growth and progress in mathematics can be problematic when using open-ended assessments. This study reports on the development of a class-based assessment instrument and marking key designed to assess Year 2 students' mathematics competence to reflect their learning of mathematics…

The use of manipulatives to develop conceptual understanding appears to be a prevalent practice in many mathematical learning experiences, particularly in the early years of schooling. This study evaluates the impact of mathematical manipulatives on young children's attitudes towards mathematics (YCATM). The modified three-dimensional model of…

Prospective secondary mathematics teachers in Australia are typically taught by mathematics educators and mathematicians who work in different faculties and seldom collaborate--a situation that can lead to conflicting views about how to teach mathematics. This paper reports on findings from semi-structured interviews with three mathematics teacher…

The purpose of this study was to investigate the understanding of prospective elementary mathematics teachers of the formal definition of the limit of a sequence. The participants were 32 prospective mathematics teachers (8 male and 24 female) who were in their third year of study in a four-year mathematics teacher preparation programme Istanbul…

We re-examine a Malawian teacher's lessons which, using the framework of mathematic problem-solving developed by Polya, the typology of levels of task demand from Stein and colleagues and Malawi's description of learner-centred education (LCE), were described as teacher-centred and evaluated as 'not good'. We studied seven video-recorded circle…

There exist many studies on modeling competencies and their promotion; however, there is a need to investigate what modeling competencies are and how they vary in lower and higher-achieving groups of students in mathematics within the current modeling literature domain. This study examined how mathematical modeling competencies were displayed in…

We investigate aspects of reform enacted in 66 class observations from 18 institutions collected as part of the National Study of University Calculus in the US. We examined four aspects related to how problems were solved in class: the extent of student involvement, the representations and technology used, and specific features of the problems…

One of the key problems to be solved in mathematics education in England is that the demand for mathematics teachers is far in excess of the supply. Acknowledging that there are simply too few mathematics teachers, the UK government has invested significantly in retraining programmes. These programmes 'retrain' out-of-field teachers, that is,…

The study is based on the theory of teachers' knowledge of students, specifically those who have difficulties learning mathematics, and how their knowledge is expressed concerning students' self-identification. The participants in this study were Namibian high school mathematics teachers (N=6) and their 12th-grade students (N=23), all of whom…