In this survey paper, we describe the state of the field on linear algebra research. We synthesize themes, questions, results, and perspectives emphasized in the papers that appear in this issue, as well as a selection of those published between 2008 and 2017. We highlight the extensive base of empirical research detailing how students reason…

The project team for the National Monitoring Study of Student Achievement (NMSSA) has recently begun writing reports focussed on how insights generated by the study can be used to promote learning and teaching. The reports are written primarily for teachers. This short article introduces the reports with a special emphasis on the mathematics and…

Student ability to demonstrate mathematical creativity positively affects their mathematical learning. Further, creativity-based mathematical instruction (CBMI) may enhance divergent thinking and precipitate a highly creative mathematical learning environment. In this literature review and discussion, it is posited that CBMI has distinctively…

We describe here lessons learned in designing an early algebra curriculum to measure early algebra's impact on children's algebra readiness for middle grades. The curriculum was developed to supplement regular mathematics instruction in Grades K-5. Lessons learned centered around the importance of several key factors, including using conceptual…

In this article, a cognitive framework for observing learning activities based on human-computer coupling is proposed. The observation is based on the vectorization of a learning situation along with human-computer interaction factors. An evolutionary high-dimensional topology of learning cognitive flow is introduced for human-computer…

As we move further into the digital age, the acquisition of digital literacy (DL) and computational thinking (CT) skills is emerging internationally as an essential goal for students in contemporary school curricula. As the world becomes more uncertain and volatile due to impacts of artificial intelligence (AI), international unrest, climate…

A learning trajectory describes the progression of student thinking and strategies over time in terms of sophistication of both conceptual understanding and procedural fluency. Currently, learning trajectories exist in the research literature for many mathematical domains, including counting, addition and subtraction, multiplicative thinking,…

This article continues to challenge the robust myth that mathematical smartness is exemplified in individuals who consistently complete mathematics problems quickly and accurately. In so doing, I present a set of counterstories from three students in one ninth-grade Algebra 1 classroom. These students described transformative experiences in their…

The Australian Council for Educational Research (ACER) is one of the world's leading educational research centres. Since it was established in 1930, ACER has built a strong reputation as a provider of reliable support and expertise to education policymakers and professional practitioners. Each year, ACER is involved in a large number of research…

The authors investigated the degree to which school-level teacher characteristics and resources are related to the mathematics learning of kindergarten children using a sample drawn from a large US database. Kindergarten-level teacher characteristics were operationalised as collective teacher efficacy, teacher experience and teacher preparation;…

Latvian Education Foundation presents methods and tools to reach comprehension and develop creative thinking. The Web page www.goerudio.com contains wordings of conceptions and patterns under training standards, as well as appropriate models/examples created by students and teachers, which interprets mentioned conceptions and patterns by use of…

Research has demonstrated that second language immersion is an effective means of facilitating primary school students' second language acquisition without undermining their competence in their first language. Despite the rapid growth of Chinese-English bilingual programmes in China, limited empirical research has been conducted thus far by which…

The concept of learning progressions offers one promising approach to developing the knowledge needed to define the "track" that students may be on, or should be on Learning progressions can inform teachers about what to expect from their students. They provide an empirical basis for choices about when to teach what to whom Learning…

In its mathematics standards, National Council of Teachers of Mathematics (NCTM) states that problem solving is an integral part of all mathematics learning and exposure to problem solving strategies should be embedded across the curriculum. Furthermore, by high school, students should be able to use, decide and invent a wide range of strategies.…

In 2007, the federal government appointed a group of education professionals, researchers, and stakeholders to study and advise on ways to "foster greater knowledge of an improved performance in mathematics among American students...with respect to the conduct, evaluation and effective use of the results of research relating to proven-effective…