Proof comprehension is an important skill for students to develop in their proof-based courses, yet students are rarely afforded opportunities to develop this skill. In this paper, we describe two implementations of an activity structure that was developed to give students the opportunity to engage with complex proofs and to develop their proof…

Abstraction is essential to learning mathematics because the mathematical concepts obtained through abstraction will be more meaningful than directly receiving these concepts. This study aims to describe the pre-service teachers' abstraction in constructing relationships among quadrilaterals. This research method was explorative qualitative…

Knowledge required to teach mathematics at the university level is a current and relevant research topic in Mathematics Education. Thus, the case study presented in this article pertains to one mathematics lecturer whose knowledge is examined focusing on his delivery of a Multivariable Calculus course. The data required were gathered via classroom…

This study aims to analyze possible connections among the noticing skills of pre-service mathematics teachers, and specifically the skills of attending to students' thinking, interpreting students' mathematical understanding, and proposing teaching alternatives. We characterized these connections in terms of coherency, i.e., the extent to which…

This study aimed to describe students' semantic representation obstacles in solving geometric problems. There are three types of obstacles, that are ontogeny, epistemology, and didactics obstacles. This study was carried out on three subjects with different obstacles and focused on math semantic representations in solving geometry problems. The…

Algebraic thinking is the ability to generalize about numbers and calculations, find concepts from patterns and functions and form ideas using symbols. It is important to know the student's algebraic thinking process, by knowing the student's thinking process one can find out the location of student difficulties and the causes of these…

Previous literature has associated math literacy with linguistic factors such as verbal ability and phonological skills. However, few studies have investigated "linguistic synchrony," shown in mathematical discussions. This study modelled math literacy and examined the relationship of math literacy with linguistic synchrony between…

The study evaluated the effects of board games on children in a range of cognitive areas, considering both inclusion (i.e. pre- and post-comparisons, playing style [board games], participants belonging to PreKinder and Kindergarten, and experimental approach) and exclusion criteria (i.e. video games). Nineteen articles were selected using both…

Researchers from multiple disciplines have found that fractions and algebra knowledge are linked. One major strand of research has identified children's "units coordination" structures as crucial for success with fractions and algebra via multiplicative reasoning, whereas a second strand of research points to "magnitude…

Researchers from multiple disciplines have found that fractions and algebra knowledge are linked. One major strand of research has identified children's "units coordination" structures as crucial for success with fractions and algebra via multiplicative reasoning, whereas a second strand of research points to "magnitude…

The development of a set of rubrics for teachers and curriculum designers interested in the quality of numeracy tasks emerged from our struggle with an attempt to clarify the distinction between numeracy and mathematics. Shifting our perspective from asking what numeracy and mathematics are to asking what they are about led to the…

The theoretical reflection on the nature of school algebra and the development of algebraic thinking from the first educational levels is a relevant topic in mathematics education. In this paper, we first summarize and clarify the positions held on this topic by two theoretical frameworks: the Theory of Objectification and the Onto-semiotic…

Math computation is a foundational skill for students developing higher-level mathematics problem-solving skills and represents a primary deficit for students struggling in mathematics. Students with mathematics difficulties also tend to have difficulties with other executive functions. One domain that is systematically part of most mathematical…

Early arithmetic skills, and in particular the understanding of the part-whole relationship, are currently considered crucial for future arithmetic achievement. They are complex skills extending far beyond the mastery of counting procedures. In order to develop these arithmetic skills in kindergarten children, we developed a game-based approach…

This study aims to examine the opinions of the pre-service teachers, who are studying in the department of mathematics, on creativity and the concept of mathematical creativity. The study group of the study consisted of 32 pre-service teachers studying in the 4th grade in the department of mathematics teaching in a province located in the southern…