The notion of definition is a central building block of mathematics. In addition to specific definitions, it is desirable that students learn about meta-mathematical aspects of definitions such as their role of classification, and about characteristics of definitions such as arbitrariness. We investigated how such meta-mathematical aspects emerge…

This study is a contribution to efforts to promote practices for dealing with the difficulties encountered by learners in probabilistic modeling situations. We attempt to elucidate as precisely as possible the types of difficulties that secondary school students face in the process of modeling with probability tools. By referring to a large and…

Prompting learners to generate examples has been proposed as an effective way of developing understanding of a new concept. However, empirical support for this approach is lacking. This article presents two empirical studies on the use of example-generation tasks in an online course in introductory university mathematics. The first study compares…

We report on an innovative design of algorithmic analysis that supports automatic online assessment of students' exploration of geometry propositions in a dynamic geometry environment. We hypothesized that difficulties with and misuse of terms or logic in conjectures are rooted in the early exploration stages of inquiry. We developed a generic…

There is a growing interest in conducting research in educational mathematics in the area of the didactics of probability, where the main difficulties that students have in understanding the concepts related to statistical inference have been revealed. For this research, the concept of the empirical rule and a practical application created by…

Research Findings: This study investigated teachers' Concept development (CD) strategy use in whole-group math teaching and its associations with children's higher-order thinking processes in 25 Chinese preschool math lessons. We utilized the CD dimension within the Classroom Assessment Scoring System (CLASS) to guide our exploration. CD…

This study investigated the cognitive and social processes through which high school students acquire the differential concepts through communication in a dynamic geometry environment through some cases. Additionally, we observed how a dynamic geometry environment affects these processes. To achieve this objective, eight students were recruited by…

Reversibility of concepts, a key aspect of mathematical development, is often problematic for learners. In this theoretical paper, we present a typology we have developed for categorizing the different reverse concepts that can be related to a particular initial concept and explicate the relationship among these different reverse concepts. We…

I present my perspective on the design process in this article, arguing for a focus on student learning and "slow design" that stems from knowledge of mathematics and their support system in the learning process. I have a question about the design process academization and task design research direction. Numerous examples from my work at…

The purpose of this paper is to account for the advancement of questioning in mathematics education. Four sections focus on: (1) Importance of Questioning in Education (a historical perspective of questioning from the 1960s through the 1990s); (2) Cognitive Classification of Questions (Costa's Levels of Thinking, Webb's Depth of Knowledge, and…

Background: Students' ability to construct and coordinate units has been found to have far-reaching implications for their ability to develop sophisticated understandings of key middle-grade mathematical topics such as fractions, ratios, proportions, and algebra, topics that form the base of understanding for most STEM-related fields. Most of the…

This study focuses on how prospective teachers learn about students' mathematical thinking when (1) anticipating secondary students' answers reflecting different characteristics of understanding, and (2) propose new activities in relation to the classification of quadrilaterals. The data were collected from forty-eight prospective secondary school…

Concept inventory tests are one method to evaluate conceptual understanding and identify possible misconceptions. The multiple-choice question format, offering a choice between a correct selection and common misconceptions, can provide an assessment of students' conceptual understanding in various dimensions. Misconceptions of some engineering…

The aim of this study was to determine preservice mathematics teachers' personal figural concepts and hierarchical classifications about quadrilaterals and to investigate the relationships between them. The participants were 57 preservice primary mathematics teachers in their senior year at a state university in Turkey. The preservice mathematics…

A study of how Swedish students understand the concept of complex numbers was performed. A questionnaire was issued reflecting the student view of own perception. Obtained answers show a variety of concept images describing how students adopt the concept of complex numbers. These concept images are classified into four categories in order to…