This article reflects critically on the guidance offered to South African teachers in two canonical texts: the Curriculum and Assessment Policy Statements (CAPS) and Mathematics teaching and learning framework for South Africa: Teaching mathematics for understanding (TMU). I make explicit my philosophical orientation, and how 'teaching mathematics…

Worked examples and self-explanations studies have been conducted predominantly with college students in controlled laboratory settings. While there is evidence showing the independent effects of these learning strategies with college students, little is known about the combined effects with K-12 students in ecologically-valid environments.…

The present study aimed to examine the extent of utilizing Open Educational Resources (OER) in mathematics instruction for the intermediate school in Riyadh, Saudi Arabia. It also aimed at identifying the benefits, the challenges, and the opportunities of applying OER in the educational process. For achieving the study objectives, the descriptive…

The 2016 Guidelines for Assessment and Instruction in Statistics Education (GAISE) College Report emphasized six recommendations to teach introductory courses in statistics. Among them: use of real data with context and purpose. Many educators have created databases consisting of multiple datasets for use in class; sometimes making hundreds of…

Linear algebra differs from other mathematics courses because of the special difficulties that students have in understanding the concepts. Teaching without concretizing the concepts of Linear Algebra encouraged students to memorize definitions of concepts and rules has been articulated. Many researches show that technology-supported teaching is…

Many educators use informal math language to make the content more accessible for middle school students, yet this use of informal language may have unintended consequences. Informal language may hinder students' development of a deep math lexicon and understanding of concepts and procedures across grade levels. Becoming proficient with math…

This paper explores different ways in which mathematics students read a section of a prescribed mathematics textbook. In this case, the students are mathematics teachers learning new mathematics in a self-study calculus course. Two students were video-taped, while they studied a prescribed portion of the textbook. The reading styles of these two…

These notes discuss several related propositions in geometry that can be explored in a dynamic geometry environment. The propositions involve an unexpected property of quadrilaterals.

During the 2013-2014 school year, the Maryland State High School Assessment in Algebra with Data Analysis (HSA) was a requirement for high school graduation in Maryland. At Frederick High School, only 27 percent of students who took the test that year passed. To respond to such an alarming failure rate, three teachers and the author developed and…

Classroom discourse is critical to helping students learn mathematics. Interacting with peers and the teacher within a classroom community assists students in building their understanding of mathematical concepts. A discourse community, sometimes referred to as a math-talk learning community, is "a classroom community in which the teacher and…

There are fundamental questions that teachers should ask themselves and their students as they prepare lessons on calculating area. Area measurement is commonly used in everyday life (perhaps to carpet a room or organize a space) and plays a foundational role in mathematics from multiplication all way up to calculus. Despite the usefulness of area…

Prior research acknowledges the need to further develop undergraduate mathematics instruction. The aim of this study is to investigate the relationship between instructional design and quality of learning. This quantitative study approaches the learning environment by comparing students' approaches to learning, self-efficacy, and experiences of…

Fully articulating validation arguments in the context of classroom assessment requires connecting evidence from multiple sources and addressing multiple types of validity in a coherent chain of reasoning. This type of validation argument is particularly complex for assessments that function in close proximity to instruction, address the fine…

The use of recorded lecture videos (RLVs) in mathematics instruction continues to advance. Prior research at the post-secondary level has indicated a tendency for RLV use in mathematics to be negatively correlated with academic performance, although it is unclear whether this is because regular users are generally weaker mathematics students…

In this study, we aim to explore the extent of mathematics pre-service teachers' ability to apply their procedural understanding combined with spatial perception for drawing conceptual conclusions related to angles in a pyramid. The participants are 16 pre-service high school mathematics teachers. They have studied solid geometry during one…