Understanding how students learn is important for both researchers and teachers. In terms of mathematics, constructing a new mathematical structure depends on conceptual understanding and connection with previous construct and they needs to be consolidated. A construct can be consolidated when the construct is recognized and used in the further…

Attributes of teaching and learning contexts provide rich information about how students participate in learning activities. By tracking and analyzing snapshots of these attributes captured continuously throughout the duration of the learning activities, teachers can identify individual students who need special attention and apply different…

In this paper, we report on primary-school students' views of their learning experiences when they engaged with mathematical phenomena through apps. The students commented on how they used a range of digital tools within the apps to solve problems, and we consider how the affordances of the mobile technologies, including multi-representation,…

The importance of mathematical visual images is indicated by the introductory paragraph in the Statistics and Probability content strand of the Australian Curriculum, which draws attention to the importance of learners developing skills to analyse and draw inferences from data and "represent, summarise and interpret data and undertake…

Students hold many misconceptions as they transition from arithmetic to algebraic thinking, and these misconceptions can hinder their performance and learning in the subject. To identify the errors in Algebra I which are most persistent and pernicious in terms of predicting student difficulty on standardized test items, the present study assessed…

Lina, a Mexican American second grader, bilingual in Spanish and English, used a strategy for adding two two-digit numbers that the authors share as an example of the importance of listening to the mathematical ideas of children, especially when these ideas do not align with how mathematics is traditionally represented in the classroom. The…

The focus on Computer Science Education at the K-12 level has been increasingly highlighted due to today's need for a populace with computational thinking skills, in addition to the expansion of careers related to computing and computer science. Programming helps facilitate students' examination of the nature of a problem and helps students to…

Research in psychology and in mathematics education has documented the ubiquity of "intuition traps" -- tasks that elicit non-normative responses from most people. Researchers in cognitive psychology often view these responses negatively, as a sign of irrational behaviour. Others, notably mathematics educators, view them as necessary…

The research examined the calculation methods used by pupils in Grades 3-6 when they were presented with problems that could be worked out efficiently and flexibly by applying number sense. The study was conducted with a convenience sample of 179 pupils between the ages 7 years and 10 months to 12 years and 10 months. in mainstream education in…

A well-known mathematical puzzle regarding a worm crawling along an elastic rope is considered. The resulting generalizations provide examples for use in a teaching context including applications of series summation, the use of the integrating factor for the solution of differential equations, and the evaluation of definite integrals. A number of…

This paper reports a study about how a teacher educator shared knowledge with teachers when they worked together to implement mathematical problem posing (MPP) in the classroom. It includes feasible methods for getting practitioners to use research-based tasks aligned to the curriculum in order to encourage children to pose mathematical problems.…

Algebraic structures are a necessary aspect of algebraic thinking for K-12 students and teachers. An approach for introducing the algebraic structure of groups and fields through the arithmetic properties required for solving simple equations is summarized; the collective (not individual) importance of these axioms as a foundation for algebraic…

This study examined the longitudinal effects of a middle school reform mathematics curriculum on students' open-ended problem solving in high school. Using assessment data from a large, longitudinal project, we compared the open-ended problem-solving performance and strategy use of high school students who had used the Connected Mathematics…

Making sense of mathematical concepts and solving mathematical problems may demand different forms of reasoning. These could be either domain-based, such as algebraic, geometric or statistical reasoning, while others are more general such as inductive/deductive reasoning. This article aims at giving visibility to a particular form of reasoning…

The very nature of algebra concerns the generalization of patterns (Lee 1996). Patterning activities that are geometric in nature can serve as powerful contexts that engage students in algebraic thinking and visually support them in constructing a variety of generalizations and justifications (e.g., Healy and Hoyles 1999; Lannin 2005). In this…