Mathematical Argumentation skills have historically been overlooked in assessment, but the inclusion of Mathematical Argumentation in the Common Core State Standards (CCSS) as one of the Standards of Mathematical Practice challenges assessment developers to assess this mathematical practice. Explanation and justification of one's own thinking to a…

This study aims to investigate the effectiveness of the Emporium instructional method in a course of college algebra and trigonometry by comparing to the traditional lecture method. The math emporium method is a nontraditional instructional method of learning math that has been implemented at several universities with much success and has been…

As with previous reports of activity at the annual Institute of Mathematics Pedagogy, this does not disappoint. The tasks used to support teaching and learning in mathematics can vary in so many ways, but this variation is compounded when learners begin to access the tasks. A task that really motivates and challenges one learner is likely to…

Over the past two decades, mathematical patterns have been acknowledged as important early components of children's development of algebraic reasoning (NCTM 2000). In particular, growing patterns have attracted significant attention as a context that helps students develop an understanding of functional relationships (Lee and Freiman 2006; Moss et…

Abstract algebra enjoys a prestigious position in mathematics and the undergraduate mathematics curriculum. A typical abstract algebra course aims to provide students with a glimpse into the elegance of mathematics by exposing them to structures that form its foundation--it arguably approximates the actual practice of mathematics better than any…

This paper describes a model for building cognition-and-instruction-based goal trajectories (GT) in the context of a study that examines the validity of curriculum-embedded assessments. The model consists of six design processes and two constraints. The GT is constructed from curriculum-specified learning goals as well as developmental…

Students' experience in using formulas for volumes is often limited to substituting numbers into given formulas. An activity presented in this article may help students make connections between the formulas for volumes of prisms and volumes of pyramids. In addition, some interesting facts from number theory arise, demonstrating strong connections…

Many integrals require two successive applications of integration by parts. During the process, another integral of similar type is often invoked. We propose a method which can integrate these two integrals simultaneously. All we need is to solve a linear system of equations.

One of the most significant steps in learning algebra is understanding the change in the role of letters in mathematical expressions from unknowns to variables. We describe the historical development of this change in usage, starting with the ancient use of mathematical unknowns, detailing several important changes in practice that allowed for the…

Students often complain that the rules of mathematics are being changed. A short conversation between a professor and a class of college algebra students dramatizes this in the realm of complex numbers and the legal realm of speed limits.

We summarize the most important facts about the Steiner point of a triangle and find formulas for its distance to each vertex in terms of the side-lengths of the triangle.

Algebraic notation has been bedazzling learners for generations, yet despite research, learned papers, comparative studies, and a great deal of hard work on the part of classroom practitioners the situation remains a stubborn constant. In this article some small-scale research has highlighted some issues that might find a resonance in many…

Calculators with computer algebra systems (CAS) are powerful tools when working with equations and algebraic expressions in mathematics. When calculators are allowed to be used during assessments but are not available or provided to every student, they may cause bias. The CAS calculators may also have an impact on the trustworthiness of results.…

The Peer Enabled Restructured Classroom (PERC) is an instructional innovation developed to address gaps in science, technology, engineering, and math (STEM) in urban high schools. The PERC model changes instruction from teacher led to peer led by bringing peer students into the classroom to lead small-group work. Our study sought to provide…

Number sense is one's ability to understand what numbers mean, perform mental mathematics, and look at the world and make comparisons. Researchers show instruction that teaches children how to classify numbers, put numbers in sequence, conserve numbers effectively, and count builds their number sense skills. Targeted instruction that teaches…