The study reported in this paper contributes to the exploration of the development of children's mathematical drawing. 36 preschool children produced drawings of 'something tall and something short'. Open-ended analysis of the forms and structures of the drawings revealed four categories ranging from scribble to the base-line comparison of two…

This paper investigates the interplay of words and expressions with students' efforts to indicate times on a clock. We consider how elementary students interpret precise times (e.g., 2:30, 4:30) as compared to relative times (e.g., half past 11) as they describe this intangible quantity using a clock. Interviews with students in grades 2 and 4 (n…

The purpose of this study was to explore the ways elementary pre-service teachers responded to hypothetical student misconceptions about area measurement topics, framed in the context of their existing understanding and the Mathematical Knowledge for Teaching framework. Data collection consisted of written pre-assessments, followed by…

Using correct definitions of the mathematical concepts is crucial for learning and teaching of any mathematical content. Being able to make mathematically correct definition of the concepts is an indicator of teachers' content knowledge. The purpose of this study is to determine how preservice middle school mathematics teachers define the concept…

Understanding is one of the four key proficiencies in the "Australian Curriculum: Mathematics" and arguably the pivot on which mathematics depends. This case study investigated preservice teachers' understanding and ability to articulate some measurement concepts. Data were gathered from 23 preservice teachers who voluntarily…

In this study, external representations and the problems encountered related transformation process between representations towards limit concept were investigated. "Limit Representation Conversion Test" was administered to 41 preservice mathematics teachers studying at a state university in central Turkey during 2018-2019 academic…

The literature emphasizes the interest and need to learn the concept of continuity with understanding, although this meaning it is not consensual nor specified how it may emerge and be developed in the learning process. In this paper we report the results of a study aiming to analyse Brazilian preservice mathematics teachers' understanding of the…

This study introduces inferentialism and, particularly, the "Game of Giving and Asking for Reasons" (GoGAR), as a new theoretical perspective for investigating qualities of procedural and conceptual knowledge in mathematics. The study develops a framework in which procedural knowledge and conceptual knowledge are connected to limited and…

"When you hear hoofbeats, look for horses, not zebras." This common saying in medicine (often attributed to Theodore Woodward, MD, of the University of Maryland School of Medicine) advises doctors to stick to the expected or likely diagnosis, rather than anticipating an unusual or atypical one. As a result, uncommon medical diagnoses are…

This article shares the learning experienced by my seventh-grade students during a lesson incorporating LEGO robotics into my mathematics class. I provide evidence of my students' learning, which represents how LEGO robotics can benefit students in the mathematics classroom to support engagement and development of understanding.

Teacher training is a key aspect for the success of any educational system and it is a prior challenge to face in-depth in Zambia. This study explores some dimensions of prospective secondary mathematics teachers' subject-matter knowledge and pedagogical content knowledge restricted to the topic of the function concept. Data were collected by…

Mathematics teachers' ability to translate and make connections between representations of functions requires investigation. Consequently, this qualitative case study article focuses on pre-service mathematics teachers' nature of understanding of the tangent function; a function bearing unique characteristics compared with the sine and cosine…

This paper gives a blueprint for reacting to the various issues that an instructor will face in their day-to-day life as the manager of a Mastery-Based Testing (MBT) classroom. For example, I created a rubric to compare traditional testing with MBT, adapted my office hours to accommodate more retake opportunities, and required effort between…

Textbooks, which form the staples of a teacher's set of resources, play a critical role in deciding what and how mathematics is taught in classrooms. However, textbooks do not always present concepts in ways that enhance understanding by students, nor are they always comprehensive in the treatment of a topic. In this exploratory study, we analyse…

Global economic and societal shifts are causing movement from manufacturing economies to knowledge and information industries. As a result, learners must be equipped with the 21st century skills necessary for lifelong skill development and prosperity. Communication is identified as one of the essential 21st century skills for preparing students…