In this article, I examine how a focus on preciseness in the mathematics classroom could affect group activity. The preciseness relates to the ways mathematical concepts, in this case angles are described in discourse between students. In this context, I consider how 'micro-invalidations', can limit students' opportunities to learn in a social and…

The study and interest of figurate numbers can be observed even in ancient Greece. On the other hand, it becomes very important the historical understanding about an evolutionary process and the particular generalization of such 2D, 3D and m-D figurate numbers and they remain the interest of current scientific investigations. On the other hand, in…

Recently, Gauthier introduced a method to construct solutions to the equations of motion associated with oscillating systems into the mathematics education research literature. In particular, Gauthier's approach involved certain manipulations of the differential equations; and drew on the theory of complex variables.Motivated by the work of…

The mathematics education field recognizes the importance of noticing children's mathematical thinking as a means for supporting children in learning mathematics (Sherin et al. Mathematics teacher noticing. Routledge, New York, 2010). Using the existing literature base around teachers' knowledge of children's mathematical thinking and…

Through a series of explorations, this article will demonstrate how the Kentucky Derby winning times dataset provides various opportunities for introductory and advanced topics, from data processing to model building. Although the final goal may be a prediction interval, the dataset is rich enough for it to appear in several places in an…

In the paper a software solution is presented for the generation of instances of exercises. The focus is on education in mathematics but the approach can be adopted in other fields such as computer science and natural science. The present solution uses the R environment for the generation process and LaTeX for the content presentation. In the…

Students' personal interest is hypothesized to be an important resource for learning, but only a few empirical studies have investigated the effect of interest on academic achievement and motivational outcomes of university studies. This lack of empirical studies is remarkable, because inadequate individual prerequisites are considered one reason…

This study is part of wider research that seeks to investigate the existence (or not) of socio-didactic-mathematical norms in the discourse arises within a group of pre-service secondary mathematics teachers when they are solving a didactic-mathematical task. In addition, we try to analyze whether any of these norms could have relationships with…

The difficulty in the process of trigonometry teaching, served as a stimulus for the present research, in which the objective consisted of designing and proposing the use of a Trigonometric Cicular Geoplane for the construction of meaningful learning in the area of Mathematics at Israel Technological University. For Its development, a field…

The cognitive relationship between intuition and proof is complex and often students struggle when they need to find mathematical justifications to explain what appears as self-evident. In this paper, we address this complexity in the specific case of open geometrical problems that ask for a conjecture and its proof. We analyze four meaningful…

Background: Tasks that involve retrieving information from memory, such as answering short answer questions, are more effective at improving learning than restudying, concept mapping, and other study techniques. However, little is known about how often teachers naturally provide these retrieval practice opportunities during lectures and classroom…

This article maps out existing research regarding the effectiveness of subject-integrated school garden teaching. The school subjects of interest are mathematics, languages and science, and subject integration is defined as a link between these subjects and school garden teaching. The article is based on an integrative review and is derived from…

The aim of this study was to compare the use of coherence relations in the school textbooks of four primary school subjects. A corpus of 1,882 texts, corresponding to the genres used to teach in the school textbooks of Science, Language, Mathematics, and History, was analyzed. The analysis was performed manually using a taxonomy that incorporates…

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 aim of this paper is on the one hand to discuss from an APOS (Action-Process-Object-Schema) theory perspective the mental constructions involved in the learning of linear algebra, through examples concerning the linear transformation concept and related notions. On the other hand, methodological issues related to the design of research…