This paper describes the conceptions about complex numbers that a group of university students has, these were built from the application of an activity sequence centered on these numbers. This sequence is based on the APOS theory, some aspects of semiotic representation theory, and the use of digital technology. Particularly, both the general…

When to introduce negative integers to children is an important issue in school mathematics; delaying their introduction can lead to lasting misconceptions such as one cannot subtract a larger whole number from a smaller. Yet understanding negatives involves a complex extension of whole-number knowledge. It is not known whether this extension is…

This paper reports the methods and findings from a research project investigating the professional learning and development (PLD) facilitation practices that influence and support the development of middle leaders in secondary schools. The participants for this research are expert facilitators employed by the University of Auckland delivering…

Calls for a crisis in community college leadership have been replete over the past 15 years. Now, the impact of the changing of the guard in leadership positions is gaining momentum. Coupled with the exodus of long-serving leaders is a reticence among mid-level leaders in seeking advancement. This paper reports on interviews with cabinet level…

Is the natural number 7 rational? Is it complex? We argue that the answers to these questions relate to the ways numbers are taught. Commonly, a new kind of numbers is presented as an expansion of a previously familiar kind of numbers, which results in a nested image of the relations between number sets. In this article, we introduce an…

Students' construction, coordination, and abstraction of units underlie success across multiple mathematics domains. Structures for coordinating units underscore notions of numbers as composite units (e.g., five is a unit of five and five units of one). In this working group, we seek to facilitate collaboration amongst researchers and educators…

Research supports the premise that various mathematical topics can be categorized as being performed better by the left or right brain hemisphere. Hemispheric lateralization is defined as a learner's preferred hemisphere of control. Torrence's "Human Information Processing Survey" was given to 170 black female college students enrolled in…

This paper synthesizes research evidence pertaining to several so-called 21st century skills: critical thinking, creativity, collaboration, metacognition, and motivation. We provide a rationale for focusing on these five skills and explain their importance as educational outcomes. We then summarize peer-reviewed research published in education and…

The paper describes two experiments conducted to improve writing skills of learning disabled adolescents. Experiment 1 used creative prompts plus a cut and paste editing strategy. In experiment 2, the same creative prompts were used with the Bank Street word processing program. Writing samples were scored for composition quality (holistic, number…

The principles of cognitive psychology as they relate to rational number learning and instruction are discussed. Issues of knowledge acquisition, organization, retrieval and transfer are reviewed as they affect this area of the elementary school curriculum. Specific problems in learning about rational numbers and systematic student errors are…

An extensive number of studies acknowledge the transformed nature of literacies by building on the complexity of multimodal semiotic repertoires and available digital resources (Reinhardt & Thorne, 2019; Toffoli, 2020). The exposure to such resources and tools makes digital literacies dynamic as environments provide students with opportunities…

This paper discusses the performance of 20 disabled secondary readers, on Carol Chomsky's tests of five stages of language development. These results, which indicated a low level of lingusitic competence for 18 of the 20 subjects, are reviewed against related studies. Analyses of the reading of these subjects indicated that they made most of their…

Collaborative problem solving (CPS) is a 21st-century skill essential for learning gains, workplace success, and tackling increasingly complicated global problems. Group diversity plays a vital role during collaborative activities, especially in a digital space. Although CPS involves dynamic communication behaviors, few studies have considered the…

Spatial visualization skills are essential and fundamental to studying STEM subjects, and sketching is an effective way to practice those skills. One significant challenge of supporting practice using sketching questions is the vast number of possible mistakes, making it time-consuming for instructors to provide customized and actionable feedback…

Multiplicative thinking is a critical stage in mathematical learning and underpins much of the mathematics learned beyond middle primary years. Its components are complex and an inability to understand them conceptually is likely to undermine students' capacity to develop beyond additive thinking. Of particular importance are the ten times…