The author has been influenced throughout his time in mathematics education by the work of Caleb Gattegno. Gattegno made extensive use of the word awareness whereas much educational literature from a psychological perspective talks about memory (for example, Justicia-Galiano, MartÌn-Puga, Linares & Pelegrina, 2017). This has, amongst other…

The notions of meaning and sense, which are closely related to understanding, play an essential role in educational processes in general and, therefore, in the teaching and learning of mathematics. However, the terms 'meaning' and 'sense' are unevenly used in the theory of language, semiotics, philosophy and psychology. After describing the main…

The rapid development of education informatization has accumulated a large amount of data for learning analytics, and adopting educational data mining to find new patterns of data, develop new algorithms and models, and apply known predictive models to the teaching system to improve learning is the challenge and vision of the education field in…

In this paper we present a collaborative 3D modeling and printing experience within a Project Based Learning (PBL) activity, carried out with two different groups of participants: pre-service teachers at the Universidad Autónoma de Madrid (Spain), and school students of Primary and Secondary level taking part in an extra-curricular activity.…

This research aimed to determine the effectiveness of the issue, discussion, establishment, and application (IDEA) learning model in embedding mathematical concepts understanding. It is a quantitative study with a quasi-experimental approach. This research was conducted at Malang Islamic University with students majoring Mathematics education…

Several factors seem important to understand the nature of mathematical learning. Byrnes and Miller combined these factors into the Opportunity-Propensity model. In this study the model was used to predict the number-processing factor and the arithmetic fluency in grade 4 (n = 195) and grade 5 (n = 213). Gender, intelligence and affect (positive…

The study aims to investigate the analysis of student metacognition skill in solving the rainbow connection problem under the implementation of the research-based learning model. The method used in this study is a mixed method. The research subjects were the 4th semester of students of higher education consisting of 30 students of experimental…

We present a model that employs "cultural-historical activity theory" (CHAT) concepts to inform research with designated Educational Leaders in early years settings. We theorise practice change in early years mathematics education in terms of motive objects of activity and mediation by cultural tools. We show how CHAT can be used to lead…

The new model of Polish education was designed by the Komisja Edukacji Narodowej (KEN). The Commission, established in 1773, was the first ministry of education in Europe. It dealt not only with problems related to the learning-teaching process, but also promoted scientific development. The present analysis is an attempt at examining the process…

The authors of this article strongly advocate for a change to the current Australian model of primary education in order to, among other things, establish the concrete practicalities of systematic mathematics thinking thereby limiting the "re-teaching" time required of secondary school mathematics teachers; bring a clear focus to the…

In light of conceptual metaphor theory, historical mathematicians' and students' difficulty with negative numbers reveals that the collecting objects metaphor may be a cognitive obstacle to those first learning about negative numbers. Moreover, consistency of physical motions with targeted ideas is a factor of cognition. Thus, this…

This research study aims at exploring the use of some dimensions and theoretical-methodological tools suggested by the model of Didactic-Mathematical Knowledge (DMK) for the analysis, characterization and development of knowledge that teachers should have in order to efficiently develop within their practice. For this purpose, we analyzed the…

In acquiring number words, children exhibit a qualitative leap in which they transition from understanding a few number words, to possessing a rich system of interrelated numerical concepts. We present a computational framework for understanding this inductive leap as the consequence of statistical inference over a sufficiently powerful…

Our paper is an analytical review of the design, development and reporting of learning progressions and teaching sequences. Research questions are: (1) what criteria are being used to propose a "hypothetical learning progression/trajectory" and (2) what measurements/evidence are being used to empirically define and refine a "hypothetical learning…

This paper reports on an investigation into managing cognitive conflict in the context of student learning about decimal magnitude. The influence of prior constructs is examined through a brief review of the literature. A micro-genetic approach was used to capture detail of the teaching intervention used to facilitate development in student…