This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students' initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students' thinking and learning over time in relation to a set of tasks…

In this article, the author contributes to the growing body of scholarship on critical mathematics pedagogy. In particular, the author advances this scholarship by outlining how critical pedagogy in the mathematics classroom can support students to engage in transformational resistance. Using a critical practitioner research approach, the author…

The transition to Common Core State Standards for Mathematics has created a need for high-quality professional learning on content and pedagogy. This is especially true for algebra 1 teachers in Florida, where students must pass a standards-based exam as a requirement to earning a high school diploma. Time, distance, and cost constraints can get…

This dissertation investigated whether math course sequence from 8 th to 9th grade influenced 9th grade math motivation, defined as perceived competence in math, sense of belonging in math, importance of math, and math anxiety. Two competing hypotheses were proposed suggesting that a more accelerated math curriculum (Algebra 1 in 8th grade versus…

I describe a method of evaluating the integral of 1/r[superscript 2] with respect to r that uses only algebra and the concept of area underneath a curve, and which does not formally employ any calculus. This is useful for algebra-based introductory physics classes (where the use of calculus is forbidden) to derive the work done by the force of one…

Acid-base equilibrium is one of the most important and most challenging topics in a typical general chemistry course. This article introduces an alternative to the algebraic approach generally used in textbooks, the graphical log "C" method. Log "C" diagrams provide conceptual insight into the behavior of aqueous acid-base systems and allow…

In recent years, the usefulness of affect detection for educational software has become clear. Accurate detection of student affect can support a wide range of interventions with the potential to improve student affect, increase engagement, and improve learning. In addition, accurate detection of student affect could play an essential role in…

The concept of exponents has been shown to be problematic for students, especially when expanding it from the domain of positive whole numbers to that of exponents that are negative and later rational. This paper presents a theoretical analysis of the concept of exponentiation as a continuous operation and examines the deficiencies of existing…

The roots of the general quadratic equation y = ax[superscript 2] + bx + c (real a, b, c) are known to occur in the following sets: (i) real and distinct; (ii) real and coincident; and (iii) a complex conjugate pair. Case (iii), which provides the focus for this investigation, can only occur when the values of the real coefficients a, b, and c are…

This article re-considers some interrelations among Pythagorean triads and various Fibonacci identities and their generalizations, with some accompanying questions to provoke further development by interested readers or their students. (Contains 3 tables.)

With the Common Core State Standards' emphasis on transformations, teachers need a variety of approaches to increase student understanding. Teaching matrix transformations by focusing on row vectors gives students tools to create matrices to perform transformations. This empowerment opens many doors: Students are able to create the matrices for…

The article begins with a well-known property regarding tangent lines to a cubic polynomial that has distinct, real zeros. We were then able to generalize this property to any polynomial with distinct, real zeros. We also considered a certain family of cubics with two fixed zeros and one variable zero, and explored the loci of centroids of…

This study investigates prospective teachers' understanding of the connections between algebraic and graphical representations of the functions and their development of the concept via process-object conceptions in each of these situations. The results indicated that most of the participants were dependent upon an algebraic expression to think…

This paper reports on a study of twelve 10th grade students using Cognitive Tutor, a math software program, to learn linear algebra word concept. The study's purpose was to examine whether students' mathematics performance as it is related to using Cognitive Tutor provided evidence to support Koedlinger's (2002) four instructional principles used…

In this article, the authors examine the mathematics identity development of six Black male students over the course of a 4-year The Algebra Project Cohort Model (APCM) initiative. Mathematics identity here is defined as participation through interactions and positioning of self and others. Data collection included nearly 450 minutes of video…