After teaching last 10 years and analyzing student work, I realize that in developmental and Elementary Algebra courses there is a disconnection between the students conceptual understanding in context in contrast to their procedural fluency. In some cases, students can perform the procedure, but do not understand when the procedure is valid. In…

In agreement with the main tenets of the anthropological theory of the didactic (ATD), this study uncovers dependencies between what students can learn, the established curriculum and the current state of mathematicians' mathematics ('scholarly mathematics'). One main result is that the mathematics taught, too often taken for granted by curriculum…

Solving problems involving absolute value is one of the hardest topics for students learning in elementary algebra course. This is an important topic in student's mathematics life since absolute value functions are important example of a function which is continuous on the real line but not differentiable at the origin. A deep understanding of…

In this paper, we derive the result of the classical gambler's ruin problem using elementary linear algebra. Moreover, the pedagogical advantage of the derivation is briefly discussed.

Multicomponent solution calculations can be complicated for students and practiced chemists alike. This article describes how to simplify the calculations by representing a solution's composition as a point in a "concentration space," whose axes are the concentrations of each solute. The graphical representation of mixing processes in a…

A newspaper numbers game based on simple arithmetic relationships is discussed. Its potential to give students of elementary algebra practice in semi-"ad hoc" reasoning and to build general arithmetic reasoning skills is explored. (Contains 3 figures, 7 tables and 3 notes.)

This article examines the attitudes of some precalculus students to solve trigonometric and logarithmic equations and systems using the concepts of elementary algebra. With the goal of enticing the students to search for and use connections among mathematical topics, they are asked to solve equations or systems specifically designed to allow…

Research shows that when students have access to advanced coursework opportunities, they work harder and are more engaged in school, have fewer absences and suspensions and higher graduation rates. Unfortunately, many Black and Latino students and students from low-income backgrounds lack equitable access to advanced coursework opportunities, such…

A recent trend in school mathematics has been to launch student inquiry with real-world contexts that capture student interest and intrigue (Meyer 2011, 2012; Kane 2015). Often these starting points harness the immediacy and power of the Internet to provide strong visuals and timely relevance. The goal of the resulting student inquiry is to foster…

The statistics about community college developmental math level and completion rates can seem disheartening, especially for those who work with these students day-to-day and know their life stories. When it comes to teaching her students, the author chooses not to focus on the statistics. Instead, she pays attention to their varied career goals…

Research shows that when students have access to advanced coursework opportunities, they work harder and are more engaged in school, have fewer absences and suspensions and higher graduation rates. Unfortunately, many Black and Latino students and students from low-income backgrounds lack equitable access to advanced coursework opportunities, such…

We present a detailed description of a Cryptography and Computer Security course that has been offered at Knox College for the last 15 years. While the course is roughly divided into two sections, Cryptology and Computer Security, our emphasis here is on the Cryptology section. The course puts the cryptologic material into its historical context…

Research shows that when students have access to advanced coursework opportunities, they work harder and are more engaged in school, have fewer absences and suspensions and higher graduation rates. Unfortunately, many Black and Latino students and students from low-income backgrounds lack equitable access to advanced coursework opportunities, such…

Research shows that when students have access to advanced coursework opportunities, they work harder and are more engaged in school, have fewer absences and suspensions and higher graduation rates. Unfortunately, many Black and Latino students and students from low-income backgrounds lack equitable access to advanced coursework opportunities, such…

Learning progressions have become an important construct in educational research, in part because of their ability to inform the design of coherent standards, curricula, assessments, and instruction. In this paper, I discuss how a learning progressions approach has guided our development of an early algebra innovation for the elementary grades and…