Given the Common Core State Standards for Mathematics, California's history of math acceleration in the middle grades, and the concern for correct math course placement for all students, this brief examines patterns from the past to shed light on considerations for the future. The brief, written by WestEd's Tony Fong and Neal Finkelstein, presents…

Although urban Latinas/os have participated in mathematics workshops in urban universities for over three decades as part of the Emerging Scholars Program (ESP), few studies have explored Latina/o students' perspectives of how and why these learning environments support them in attaining mathematical success. This article presents an in-depth case…

Many researchers, policymakers, and university administrators have called for more students to major in Science, Technology, Engineering and Mathematics (STEM) fields to address the critical need for a diverse and technically skilled workforce that is prepared to address national problems and educate its future STEM leaders. One of the questions…

Recently, there has been an increasing interest in collegiate mathematics education, especially teaching and learning calculus (e.g., Oehrtman, Carlson, & Thompson, 2008; Speer, Smith, & Horvath, 2010). Of many calculus concepts, the derivative is known as a difficult concept for students to understand because it involves various concepts…

Rate is an important, but difficult, mathematical concept. Despite more than 20 years of research, especially with calculus students, difficulties are reported with this concept. This paper reports the results from analysis of data from 20 Australian Grade 10 students. Interviews targeted students' conceptions of rate, focussing on the influence…

The refraction problem, well-known in calculus and physics, continues to reveal new insights. This paper presents a geometric solution in which the trammel of Archimedes plays the prominent role. When properly configured, the trammel generates an ellipse and its family of normal lines. One normal line in particular intersects the boundary…

Poor class attendance is detrimental to student success. This is especially true in entry-level college mathematics courses, where habitual non-attendance can have lasting effects that greatly limit a student's options for continued academic success. The purpose of this study was to design an attendance incentive and to evaluate its impact on…

The literature has revealed that many students encounter substantial difficulties in applying the first law of thermodynamics. For example, university students sometimes fail to recognize that heat and work are independent means of energy transfer. When discussing adiabatic processes for an ideal gas, few students can correctly refer to the…

In this paper we give a general solution to the problem of the damped harmonic oscillator under the influence of an arbitrary time-dependent external force. We employ simple methods accessible for beginners and useful for undergraduate students and professors in an introductory course of mechanics.

Derivation of the law of radioactive decay is considered without prior knowledge of calculus or the exponential series. Calculus notation and exponential functions are used because ultimately they cannot be avoided, but they are introduced in a simple way and explained as needed. (Contains 10 figures, 1 box, and 1 table.)

Student ability, teacher expectations, respective degrees of difficulty, and curriculum and instructional practices all work together to provide students experiences leading to differing levels of success in respect to mathematical translations. Herein, we discuss teacher beliefs and instructional practices, investigate why some translations seem…

This article presents our response to Oud and Folmer's "Modeling Oscillation, Approximately or Exactly?" (2011), which criticizes aspects of our article, "Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes" (2011). In this response, we present a conceptual explanation of the derivative-based estimation…

Students rarely use their graded exams to study. An alternative method of grading exams, based on self-reflection, encourages students to use their mistakes as a learning resource. In this grading method, the test is returned with each question simply marked as "right" or 'wrong." Students can then go over their exams and resubmit them with…

The limit concept plays a foundational role in calculus, appearing in the definitions of the two main ideas of introductory calculus, derivatives and integrals. Previous research has focused on three stages of students' development of limit ideas: the premathematical stage, the introductory calculus stage, and the transition from introductory…

One of the neglected elements when teaching at a distance is establishing what learners already know at the beginning of the course or module. Unlike the face-to-face environment, in distance learning there is no opportunity for administering diagnostic activities just before the onset of instruction. This means that both the weak and more…