This paper reports findings related to the pursuit of describing a lived knowing for teaching mathematics. Specifically, we used an enactivist perspective to describe the knowing exhibited by three experienced high school teachers in their instructional actions while leading whole-class instruction on the topic of the equations of exponential…

Current gaps in achievement among students from diverse backgrounds and their culturally dominant counterparts imply that theoretical ideas, such as culturally responsive teaching (CRT), that focus on increasing the achievement of diverse populations are sound yet difficult to translate into everyday practice. CRT is intricate and complex and…

Mathematical modelling is emphasised in curricula worldwide. Since 2006, mathematical modelling has been considered a fundamental process in the mathematics subject in Norwegian upper secondary schools. This study aimed to identify tensions in the approaches to mathematical modelling expressed in teacher interviews (N = 4) and framework discourses…

This article reports on the evolution of prospective secondary teachers' knowledge (meanings for dy/dt) and beliefs (about teaching and learning mathematics) in a semester-long inquiry-oriented differential equations class. Students entered the course with limited, primarily procedural, meanings for dy/dt. Throughout the semester, they engaged in…

This study aims to examine mathematics teachers' interpretations of students' thinking within the scope of teaching experiments as a professional development activity. The method used in this study is a teaching experiment. The participants are 3 elementary school mathematics teachers. The teaching experiment consists of 5 teaching episodes and…

Two broad categories of instructional practices, (a) explicitly attending to concepts and (b) fostering students' opportunities to struggle, have been consistently linked to improving students' mathematical learning and achievement. In this article, we describe an effort to build these practices into a framework that is useful for a diverse set of…

We report on mixed methods research that explored pre-service teachers' pedagogical content knowledge in basic musical methods for teaching and learning of basic fractions within the framework of Vygotsky's Theory of Scaffolding. Vygotsky's use of scaffolding opines that knowledge, skills and prior experiences, create the foundation for potential…

We report on mixed methods research that explored pre-service teachers' pedagogical content knowledge in basic musical methods for teaching and learning of basic fractions within the framework of Vygotsky's Theory of Scaffolding. Vygotsky's use of scaffolding opines that knowledge, skills and prior experiences, create the foundation for potential…

This article examines the development of professional knowledge in pre-service mathematics teachers. From the discussion of a task associated with the multiplication of consecutive integer numbers, generalization is recognized as a process that allows to explore, to explain, and to validate mathematical results, and as an essential ability to…

Existing studies have defined and assessed disciplinary literacy, mathematical literacy, and general academic language. However, there is a need to define and assess mathematics discipline-specific language (MDL), particularly for elementary school teachers. Therefore, the purpose of this study was to develop a research instrument to assess the…

Stephens (2008) described structural thinking as an awareness of the way different occurrences of a mathematical property develop into correct generalisations. Many primary pre-service teachers (PSTs) graduate from their tertiary studies without the ability to notice structural thinking. In this study, two primary PSTs learned to notice structural…

Recognising teachers' knowledge as one of the main factors influencing their practices and student learning, we aim to contribute to obtaining a better and deeper understanding of the specificities of teachers' mathematical knowledge. A case study involving one 8th-grade Chilean mathematics teacher is presented in the context of rational numbers.…

In response to the call for research on integrating best general practices in teaching with those that promote equity and access, we present a two-part study focused on instructional strategies that may remove learning barriers for English Language Learners. We theoretical developed and empirically explored supplemental components for traditional…

Researchers have generated a powerful framework that identifies three aspects of noticing students' mathematical thinking: attending to, interpreting, and deciding how to respond to student thinking. Previous research has tended to focus on evaluating how "well" teachers engaged in noticing, and how "well" they connected the…

This article presents a study that investigated potential misconceptions presented in third grade mathematics classrooms and the association of these potential misconceptions with Mathematical Knowledge for Teaching (MKT) and standards-based teaching practices (as measured by the Mathematics Scan). A sequential explanatory mixed methods model was…