Learners are all different and teachers are all different, so why do we often ignore this reality when trying to explain, or demystify, some aspect of mathematics in the classroom? Enabling learning can be challenging, demanding of creativity, and needy of alternatives if understanding is the real goal. Here the authors offer ideas that are aimed…

Traditionally, a considerable part of teaching and learning algebra has focused on routine practice and the application of rules, procedures, and techniques. Although today's computerized environments may have decreased the need to master algebraic skills, procedural competence is still a central component in any mathematical activity. However,…

In this article, we describe how using prediction during instruction can create learning opportunities to enhance the understanding and doing of mathematics. In doing so, we characterize the nature of the predictions students made and the levels of sophistication in students' reasoning within a middle school algebra context. In this study, when…

In some secondary mathematics curricula, there is a topic called Stereometry that deals with investigating the position and finding the intersection, angle, and distance of lines and planes defined within a prism or pyramid. Coordinate system is not used. The metric tasks are solved using Pythagoras' theorem, trigonometric functions, and sine and…

Proving and refuting mathematical claims constitute a significant element in the development of deductive thinking. These issues are mainly studied during geometry lessons and very little (if at all) in lessons of other mathematical disciplines. This study deals with high school students' perceptions of proofs in the geometry. The study explores…

Many students have trouble grasping algebra. In this book, bestselling authors Judith, Gary, and Erin Muschla offer help for math teachers who must instruct their students (even those who are struggling) about the complexities of algebra. In simple terms, the authors outline 150 classroom-tested lessons, focused on those concepts often most…

Symmetry is found in the visual arts, architecture and design of artefacts since the earliest time. Many natural objects, both organic and inorganic, display symmetry: from microscopic crystals and sub-atomic particles to macro-cosmic galaxies. Today it features strongly in higher mathematics such as Linear and Abstract Algebra, Projective and…

Continuous feed and bleed ultrafiltration, modeled with the gel polarization model for the limiting flux, is shown to provide a rich source of non-linear algebraic equations that can be readily solved using numerical and graphical techniques familiar to undergraduate students. We present a variety of numerical problems in the design, analysis, and…

Pre-engineering is increasingly being taught as a high school subject. This development presents challenges as well as opportunities for the physics education community. If pre-engineering is taught as a separate class, it may divert resources and students from traditional physics classes. However, design modules can be used as physics teaching…

The exploration of number patterns as a pedagogical approach to introducing algebra has been advocated by many mathematics educators. French (2002) comments that the introduction of algebra through what is potentially a wide range of pattern generalisation activities may be effective in assisting pupils to see algebra as both meaningful and…

Video recordings of instruction have been a mainstay for supporting conversations about teaching by representing particularities of instruction and by presenting the viewer with a multitude of details for interpretation. In this essay, we contrast non-fictional videotapes of actual classroom interaction with fictional animations of classroom…

The flipped classroom approach was implemented across three semesters of a College Algebra course. This paper is part of a larger design and development research study and focuses on student perceptions of the flipped classroom teaching approach. Qualitative methodology was used to describe how students perceived the instruction of their College…

The m-rater scoring engine has been used successfully for the past several years to score "CBAL"™ mathematics tasks, for the most part without the need for human scoring. During this time, various improvements to m-rater and its scoring keys have been implemented in response to specific CBAL needs. In 2012, with the general move toward…

The purpose of this study was to understand how students' attitudes were connected to their mathematics learning. This investigation was specific to web-based homework in developmental courses in the community college environment. The mixed-methods approach was used to analyze the relationship between students' attitudes and mathematical…

Classroom observation of teachers is a significant part of educational measurement; measurements of teacher practice are being used in teacher evaluation systems across the country. This research investigated whether observations made live in the classroom and from video recording of the same lessons yielded similar inferences about teaching.…