In this paper, we focus on two particularly problematic concepts in teaching mathematics: the complex unit i and angles. These concepts are naturally linked via De Moivre's theorem but are independently misused in numerous contexts. We present definitions, notations, and ways of speaking about these terms from mathematics education that are not…

This study aims to analyze the problem-posing skills of primary school mathematics teacher candidates with problem-posing experience and their views on problem posing. The case study, one of the qualitative studies, was used in the study. The study group is ten prospective elementary mathematics teachers who were selected using the purposive…

In quantum mechanics, probability amplitudes are complex numbers and the relative phases between the terms in superposition states have measurable effects. This article describes an investigation into sophomore- and junior-level students' reasoning patterns in relating relative phases and real-world quantum phenomena. The investigation involved…

It has been stated that a criterion of a threshold concept is that it is troublesome or difficult to understand. However, not all difficult concepts are also threshold concepts. This article explores this difference through the context of students' difficulties in learning prosthetics and two models of describing threshold concepts. Students and…

This study explores the similarities and differences between English and Arabic numeral-based formulaic expressions, and difficulties that student-translators have with them. A corpus of English and Arabic numeral-based formulaic expressions containing zero, two, three, twenty, sixty, hundred, thousand…etc., and another corpus of specialized…

We introduce a methodology for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We studied 12 pre-service teachers as they solved a set of fractions tasks, ranked by cognitive demand. We present the unit transformation graphs for one of those pre-service teachers, to illustrate how she experienced and met…

Preparing for the future during ongoing activities is an essential skill. Yet it is currently unclear to what extent we can prepare for the future in parallel with another task. In two experiments, we investigated how characteristics of a present task influenced whether and when participants prepared for the future, as well as its usefulness. We…

This paper reports the results of an investigation into the ways pre-service teachers engaged in structured problem solving as part of their first-year mathematics education course. The purpose of this study was to determine the preferred problem solving strategies of pre-service teachers and the types of difficulties they experienced. The written…

Scaffolding is defined as help that can assist students to solve problems or understand concepts that were not able to complete independently. In modern times, the concept of technology-based Scaffolding in learning has developed. In this study an educational game called "Telolet" was designed with the aim of providing Scaffolding to…

Proportional reasoning is important to the field of mathematics education because it lies at the crossroads of additive reasoning in the elementary school and multiplicative reasoning needed for more advanced mathematics. This research reports on the representations used by pre-service teachers (PSTs) as they responded to tasks involving…

When developing online classrooms it is necessary to ensure that all learners will be successful in the course regardless of the topic or discipline that is being discussed. This becomes especially important when the class involves numerical data. This paper outlines the difficulty of delivering online classes such as algebra, accounting, and…

This paper summarizes difficulties that chemistry students at all levels commonly exhibit when translating, manipulating, and interpreting mathematical expressions that contain logarithms, and offers approaches that the authors have found useful to help students overcome such difficulties. The online supplement provides problem sets created by the…

Mathematics lecturers have long expressed concern about their students poor mathematical background and the effect this has on performance in first mathematics courses at university level. This article explores a similar concern about students' numeracy in a statistics course for psychologists.

The first volume of the 29th annual conference of the International Group for the Psychology of Mathematics Education contains plenary lecture and research forum papers as listed below. Short oral communications papers, poster presentations, brief summaries of discussion groups, and working sessions are also included in the volume. The plenary…