Mathematics professor Julie Cwikla decided that she needed to investigate young children's understandings and see what precurricular partitioning notions young minds bring to the fraction table. Cwikla realized that only a handful of studies have examined how preschool-age and early elementary school-age students solve fraction problems (Empson…

Pedagogical content knowledge is consisted of two components: student knowledge and teaching strategies. Teaching strategies was defined under two sub-headings as strategies for specific topics and specific strategies for any topic. The purpose of this study was to examine the method with which quadrilaterals were taught by mathematics teachers…

Mathematics and proof are two closely related concepts. Mathematics not only shows what is right or wrong, but it also teaches that it is not enough to know the latest formulas and results should be explained with causality. In this context, students learn the underlying meaning behind what mathematicians do by way of proofs. Accordingly, this…

In this article we explore the mechanisms through which one group of preservice teachers engage in "Collective Property Noticing"--a phenomenon in which group members integrate individual contributions such that the group, as a unit, notices mathematical properties of their collective image. Drawing on improvisational theory to help to…

In this empirical study, we investigate an early childhood education activity in mathematics on the concept of "pattern". The children participating in the study attend an intermediate form of schooling in Sweden called "the preschool class for six-year-olds", intended to facilitate their transition from preschool to school.…

Increased importance is being placed on statistics at both the K-12 and undergraduate level. Research divulging effective methods to teach specific statistical concepts is still widely sought after. In this paper, we focus on best practices for teaching topics in nonparametric statistics at the undergraduate level. To motivate the work, we…

In this paper we present a matrix-organised implementation of an experimental course in the history of the concept of a function. The course was implemented in a Danish high school. One of the aims was to bridge history of mathematics with the teaching and learning of mathematics. The course was designed using the theoretical frameworks of a…

Many papers have emphasized the need for and importance of particular examples and the underlying rationale for introducing a historical dimension in mathematics education. This article presents the development and implementation of a project, based on original sources, in a situation where the existing curriculum does not include history. The…

The central goals of most introductory linear algebra courses are to develop students' proficiency with matrix techniques, to promote their understanding of key concepts, and to increase their ability to make connections between concepts. In this article, we present an innovative method using adjacency matrices to analyze students' interpretation…

When designing lessons and units of study, teachers prepare problems that will make learning accessible, challenging, and targeted to goals. Experienced teachers often can predict classroom dialogue. This sense of déjà vu is even stronger when they teach the same course several times a day. The questions from the students are familiar and almost…

Finding patterns and making conjectures are important thinking skills for students at all levels of mathematics education. Both the Common Core State Standards for Mathematics and the National Council of Teachers of Mathematics speak to the importance of these thought processes. NCTM suggests that students should be able to recognize reasoning and…

This paper reports on a study that investigated the nature of the students' mathematical talk in an undergraduate mathematics study group. Study groups to support the learning of first year mathematics students are encouraged by mathematics educators. From nine recorded sessions, a session with a high quantity of mathematical talk and unfamiliar…

According to Stenhouse (1984), "research is systematic 'inquiry' made public". By bringing "inquiry" into teaching practice we promote learning in three layers: learning of mathematics; learning of the "teaching" of mathematics; and learning of the processes through which mathematics teaching and learning develop.…

The application to rational numbers of the procedures and intuitions proper of natural numbers is known as Natural Number Bias. Research on the cognitive foundations of this bias suggests that it stems not from a lack of understanding of rational numbers, but from the way the human mind represents them. In this work, we presented a fraction…

The answers offered by computer algebra systems (CAS) can sometimes differ from those expected by the students or teachers. The comparison of the students' answers and CAS answers could provide ground for discussion about equivalence and correctness. Investigating the students' comparison of the answers gives the possibility to study different…