Teachers' beliefs about students' errors are influenced by structural factors and by other beliefs towards education and students that teachers may hold. The literature on this topic has provided some evidence and some mixed results. Furthermore, some structural aspects related to errors have not been considered in framing teachers' beliefs about…

Algebra is critical in shaping future mathematics success and is integral to the K-12 curriculum. Despite its inclusion, a common challenge arises as students' progress to higher grades without a solid foundation, resulting in challenging learning experiences. This action research study focuses on the algebraic learning experience of a Grade 7…

This extensively updated teaching resource provides over 100 engaging, full-color visuals with explanations of how they can be used to stimulate mathematics learning, to explain mathematical concepts, and to assess students' mathematical understanding in grades K-8. Readers are provided with a strong mathematical background, downloadable copies of…

Academically gifted students or high potential learners don't feel challenged in regular classrooms. Teachers in schools are also not quipped with pedagogical interventions to meet the advanced learning needs of gifted students. Mentoring is considered an effective method to guide, motivate and optimize learning abilities of gifted students. The…

Using the "Middle School Student Mathematics Learning Non-intellectual Questionnaire," a total of 1,400 middle school students in 11 districts and counties of Tianjin were surveyed. According to the data, using the raw score normalization method and the formula "T = 50+10×Z", the non-intellectual overall and sub-dimension norm…

Purpose: When using embedded, student-centered assessment tools for maker education, understanding the characteristics of a body of evidence can help teachers guide the assessment process. This study aims to examine assessment artifacts from a makerspace program and present a set of qualities that emerged, which researchers and maker educators can…

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…

This study was aimed to explore the teacher's knowledge and understanding of mathematical literacy, especially on the PISA survey, understanding of mathematical literacy, aspects, and processes of evaluating mathematical literacy in the PISA survey and the learning process carried out by respondents in their respective classes. The research used a…

This book seeks to illustrate the research on mathematics competencies and disposition in China according to the conceptual development and empirical investigation perspective. Mathematics education in China has a distinguishing feature a focus of attention to mathematical competency. Paradoxically, there has not been an explicit, refined, and…

In new generation schooling contexts, the interaction of human activity, space, and objects, co- produce spatialised practices. There is the fluid use and continuous re-design of learning spaces, where dynamic socio-material practices support the ongoing and negotiated development of curriculum, pedagogy and assessment. Links are forged in this…

This article seeks to substantiate the need for the prognostic assessment of the degree to which school students are prepared to master new types of activity, which underlie their design of an individual learning route at an appropriate senior stage of learning. The authors discuss the concept of project competence as an integral characteristic of…

This paper discusses issues arising in the design of questions to use in an on-line computer-based formative assessment system, focussing on how best to identify the stages of a learning hierarchy for reporting to teachers. Data from several hundred students is used to illustrate how design decisions have been made for a test on interpreting line…

Educational Badges are touted as an alternative assessment that can increase learner motivation. We considered two distinct models for educational badges; merit badges and videogame achievements. To begin unpacking the relationship between badges and motivation, we conducted a study using badges within an intelligent-tutor system for teaching…

We describe efforts toward the development of a hypothetical learning progression (HLP) for the growth of grade 7-14 students' models of the structure, behavior and properties of matter, as it relates to nanoscale science and engineering (NSE). This multi-dimensional HLP, based on empirical research and standards documents, describes how students…

There has been a recent upsurge of interest in exploring how choices of methods and timing of instruction affect the rate and persistence of learning. The authors review three lines of experimentation--all conducted using educationally relevant materials and time intervals--that call into question important aspects of common instructional…