This study examines the development of learning designs based on Realistic Mathematics Education (RME) on the probability topic at the eighth-grade junior high school level. Probability abounds in everyday life, and the RME approach is believed to develop students' mathematical communication skills. This learning design development used the Plomp…

In order to improve instruction, teachers need to make sense of and evaluate the critical events that have the potential to strengthen the understanding of students' mathematical thinking. Mathematics instruction has shifted toward inquiry teaching which leaves many teachers attempting to change their practices accordingly. While there are…

Researchers often develop instruments using correctness scores (and a variety of theories and techniques, such as Item Response Theory) for validation and scoring. Less frequently, observations of children's strategies are incorporated into the design, development, and application of assessments. We conducted individual interviews of 833…

Recent research has boosted the inclusion of introductory group theory into secondary and undergraduate mathematics education due to manifold potentials, e.g., with regards to the promotion of students' abstract thinking. However, in addition to research on cognitive processes, learners' affective characteristics have largely remained unexplored…

This study investigated how problem-solving videos can be used in video-mediated professional learning to support secondary preservice mathematics teachers (PMTs) in developing teacher knowledge for noticing student thinking in the context of the derivative concept in calculus. A model of the trajectory of PMTs' noticing was constructed as six…

In issue 31(2) of the "Australian Senior Mathematics Journal", Kok (2017) describes a useful four-step process for investigating number patterns and identifying the underlying function. The process is demonstrated for both linear and quadratic functions. With respect to the quadratic example, I provide an additional idea relevant to step…

This study analyses learning aspects of undergraduate mathematics students' first encounter with the subgroup test, using the commognitive theoretical framework. It focuses on students' difficulties as these are related to the object-level and metalevel mathematical learning in group theory, and, when possible, highlights any commognitive…

Modern calculus textbooks carefully illustrate how to perform integration by trigonometric substitution. Unfortunately, most of these books do not adequately justify this powerful technique of integration. In this article, we present an accessible proof that establishes the validity of integration by trigonometric substitution. The proof offers…

In this response paper to Hoyles' contribution "Transforming the mathematical practices of learners and teachers through digital technology" (EJ1200112) focuses on three points. First, more knowledge is needed on why teaching and learning practices should transform, into what will they transform, and by what or by whom will they be…

The purpose of this study was to explore how university students construct the relationship between the concepts of differential and derivative with the integration of GeoGebra and the ACODESA method. The participants in this study were 33 pre-service mathematics teachers. An open-ended questionnaire, knowledge test, tasks, and participants'…

Teachers whose mathematical meanings support understanding across different contexts are likely to convey them in productive ways for coherent student learning. This exploratory study sought to elicit 67 secondary mathematics pre-service teachers' (PSTs) meanings for quadratics with growing pattern creation and multiple translation tasks. A…

Examples are an essential part of mathematics teaching and learning, used on a daily basis to teach and practice content. Yet, selecting good examples for teaching is complex and challenging. This article presents ideas to consider when selecting examples, drawn from a research study with algebra 2 teachers.

This article examines a common proportional reasoning problem used in schools, often referred to as the Orange Juice task. The authors show how these six strategies described by Nikula (e.g., Unitizing, Norming, etc.) and one additional strategy can be used to either solve or make progress in the Orange Juice task. The article presents work from…

Due to the COVID-19 pandemic, countries have had to adapt their usual teaching environment and processes to distance education. The purpose of this study was to investigate the Grade 9 geometry course contents shared on the Education Information Network (EBA) platform in terms of mathematics values (mathematical values and mathematics educational…

While focusing on numeracy is essential in preschool classrooms with deaf and hard of hearing (DHH) children, it is also important that concepts of numeracy be taught in a way that incorporates executive functions, introduces computational thinking, and prepares students for life in a 21st-century world. Technology-enhanced teaching resources…