To date, of the many studies on early algebraic thinking, none, to our knowledge, has examined the relationships between algebraic thinking and negative numbers. Students encounter persistent difficulties in dealing with these numbers, and we believe that these could be addressed through the development of algebraic thinking. We are particularly…

Common divisor is one of the concepts that started to be learned in secondary school and forms the basis of many concepts. But students generally have difficulty in making sense of it. The purpose of this study is to investigate concept formation processes of common divisor through a case study on seven sixth grade students. To do this, we…

Reading is regarded as one of the basic learning processes that provides multiple skills and abilities for daily life. The study reported on here arose from evidence of reading comprehension difficulties of middle school students in Colombia, and from reflection on the didactic strategies used for the promotion and teaching of reading. The purpose…

In this study, the purpose was to make use of metaphors to determine the difficulties experienced by secondary school 6th and 7th grade students in the process of learning the subject of circle. In the study, the phenomenological research design, one of qualitative research methods, was used. The research data were collected from a total of 140…

In this article we show how students' productive struggle on a mathematical task can lead to collective mathematical creativity. We use observable (co)actions and interactions from a video record that features three Grade 6 students in a problem-solving session to document the emergence of collective creativity leading to a solution. We discuss…

Self-efficacy in mathematics is related to engagement, persistence, and academic performance. Prior research focused mostly on examining changes to students' self-efficacy across large time intervals (months or years), and paid less attention to changes at the level of lesson sequences. Knowledge of how self-efficacy changes during a sequence of…

Background: Helping upper elementary and lower secondary school students develop an awareness of various aspects of the nature of science (NOS) and nature of technology (NOT) is a widely recognized goal of science teaching. In this study, we focus on the connections between science and technology (S&T). Purpose: We report on the design,…

Diagnostic assessments are intended to support teachers' instructional decision making by providing instructionally relevant information. In this article, we propose that using cognitive theories of learning to design diagnostic assessments can provide teachers with two diagnostic outcomes: (a) the location of a student's thinking within the…

The purpose of this research was to identify the common errors made in English writing by Malaysian Chinese primary year 6 ESL students and to determine the extent of the influence of the first language, Mandarin in ESL writing. The Mandarin language uses a logographic writing system while the English language is written in alphabetic scripts. The…

This study tests a hypothesized learning progression for the concept of energy. It looks at 14 specific ideas under the categories of (i) Energy Forms and Transformations; (ii) Energy Transfer; (iii) Energy Dissipation and Degradation; and (iv) Energy Conservation. It then examines students' growth of understanding within each of these ideas at…

The current study focused on the role of feedback on students' prediction accuracy (calibration). This phenomenon has been widely studied, but questions remain about how best to improve it. In the current investigation, fifty-seven students from sixth grade were randomly assigned to control and experimental groups. Thirty pictures were chosen from…

Across Canada there is increased attention to the important relationship between the quality of learning environments--particularly effective teaching--and student achievement. "What did you do in school today?" proposes a multi-dimensional framework of student engagement as a core idea for improving the quality of teaching and learning…