In this article, the authors share their favorite "Construct It!" activity, which focuses on rate of change and functions. The initial approach to instruction was procedural in nature and focused on making use of formulas. Specifically, after modeling how to find the slope of the line given two points and use it to solve for the…

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…

This article reports on an empirical study that investigates the way students' performance in solving arithmetical tasks may be related to their performance in solving algebraic tasks. The sample consisted of 203 Grade 6 students. The arithmetical tasks involved arithmetical expressions with known quantities, whereas the algebraic tasks involved…

Is the natural number 7 rational? Is it complex? We argue that the answers to these questions relate to the ways numbers are taught. Commonly, a new kind of numbers is presented as an expansion of a previously familiar kind of numbers, which results in a nested image of the relations between number sets. In this article, we introduce an…

Adaptive learning support provided by kindergarten teachers before and after (macro-adaptive learning support) as well as during mathematical learning activities (micro-adaptive learning support) is a cross-cutting concept of teaching quality. Effective adaptive learning support enhances children's learning. However, providing it is challenging…

This study delves into the correlation between the beliefs of five university mathematics teachers regarding the teaching of mathematics and their instructional practices. Adopting a case study methodology, this research aimed to thoroughly investigate this relationship. The collection of data was carried out through questionnaires, and the…

Background: The growing necessity of providing better education, notably through the development of Adaptive Learning Systems (ALSs), leveraged the study of several psychological constructs to accurately characterize learners. A concept extensively studied in education is engagement, a multidimensional construct encompassing behavioral expression…

In this article, the authors provide some insight into how teachers can potentially facilitate among students' representations and activities on mathematical tasks: between or among -- (1) student representations and the context; (2) multiple forms of student representations; and (3) processes in student representations. The authors use the…

Although student covariation reasoning has been explored in depth to improve understanding of the correspondence between variables, research has focused on studying existing reasoning about variables in Cartesian representations. The working method had a qualitative approach, with a descriptive exploratory scope, the spontaneous representations…

This study delves into the intricate relationship between pre-service teachers' (PSTs') Mathematical Knowledge for Teaching Fractions (MKTF) and its influence on their teaching practices. Grounded in the premise that MKTF domains exhibit interconnectivity, shaping the constructs of teaching practices, the study employed the mathematical task…

This study explores how kindergarten students from a multilingual sample (n=131) representing 23 different languages differ in response to intervention, based on their skill in mathematics and domain general cognitive skills. Analyses for this study indicate significant correlations between initial math skill, phonological memory, working memory,…

This study explores how kindergarten students from a multilingual sample (n = 131) representing 23 different languages differ in response to intervention, based on their skill in mathematics and domain general cognitive skills. Analyses for this study indicate significant correlations between initial math skill, phonological memory, working…

This study presents the preliminary qualitative results of a larger mixed methods study. The qualitative phase utilized task-based clinical interviews to examine the non-symbolic and symbolic linear generalizations of middle-grades students. This investigation identified similarities and differences in the students' generalizations, and…

This study explores indigenous pedagogical methods for teaching geometry in three secondary schools within the Kalomo District of Zambia. The study addresses three primary objectives: (1) exploring the utilization of Indigenous pedagogical methods in teaching geometry, (2) assessing the impact of integrating traditional knowledge on student…

This article outlines a series of lessons the author led to help students understand gerrymandering, which is the practice of drawing district boundaries to favor a particular group or party and which undermines the fairness of a representative democracy. These lessons were developed to capture student interest and engagement by linking…