College students enrolling in the calculus sequence have a wide variance in their preparation and abilities, yet they are usually taught from the same lecture. We describe another pedagogical model of Individualized Additional Instruction (IAI) that assesses each student frequently and prescribes further instruction and homework based on the…

Today's classrooms are much different from those of yesterday. The increased diversity of learners, students' familiarity and attraction to technology, and the improved availability of technology in education have made it increasingly possible for teachers to use various forms of technology in instruction. The responsibility for addressing these…

Last year the United States unveiled the Common Core State Standards (CCSS) in English and Mathematics for grades K-12. In particular, the authors included two possible sequences of 8-12 mathematics courses that would fulfill the standards. Most notably, the courses titled "3a" and "3b" in these two sequences have become…

This study examined relationships between students' personal variables (gender, prior achievements, age and academic major) and their success in the first year undergraduate calculus course. The study sample consisted of 59 first year undergraduate students taking Math 154 Calculus II course. A written test about integral, sequence and series…

To find the number of distinct real roots of the cubic equation (1) x[caret]3 + bx[caret]2 + cx + d = 0, we could attempt to solve the equation. Fortunately, it is easy to tell the number of distinct real roots of (1) without having to solve the equation. The key is the discriminant. The discriminant of (1) appears in Cardan's (or Cardano's) cubic…

In a first calculus course, it is not unusual for students to encounter the theorems which state: If f is an even (odd) differentiable function, then its derivative is odd (even). In our paper, we prove some theorems which show how the symmetry of a continuous function f with respect to (i) the vertical line: x = a or (ii) with respect to the…

Improving college performance and retention is a daunting task for colleges and universities. Many institutions are taking action to increase retention rates by exploring their academic programs. Regression analysis was used to compare the effectiveness of ACT mathematics scores, high school grade point averages (HSGPA), and demographic factors…

The California Department of Education is in the process of revising the Career and Technical Education (CTE) Model Curriculum Standards. The Educational Policy Improvement Center (EPIC) conducted an investigation of the draft version of the Health Sciences and Medical Technology Standards (Health Science). The purpose of the study is to…

Engineering technology students can attain a meaningful mathematics learning if they are allowed to actively participate in hands-on activities. However, the current dissemination of knowledge in the classroom still focuses on teacher-centered paradigm of teaching. A study to explore lecturers' views regarding a newly developed integral calculus…

In this article we use data from the Longitudinal Study of American Youth to examine the influence of parent education on pathways to science, technology, engineering, mathematics, and medicine (STEMM) professions. Building on a general model of factors related to STEMM education and employment, we employ a two-group structural equation model to…

This tricentennial tribute commemorates Euler's major contributions to mathematical and physical sciences. A brief biographical sketch is presented with his major contributions to certain selected areas of number theory, differential and integral calculus, differential equations, solid and fluid mechanics, topology and graph theory, infinite…

The common understanding within the mathematics community is that the role of the college algebra course is to prepare students for calculus. Though exceptions are emerging, the curriculum of most college algebra courses and the content of most textbooks on the market both reflect that assumption. This article calls that assumption into question…

The paper focuses on analysing grade 12 learner errors and the misconceptions in calculus at a secondary school in Limpopo Province, South Africa. As part of the analysis the paper outlines the nature of mathematics errors and misconceptions. Coding of learners' errors was done through the lens of a typological framework. The analysis showed that…

This study adds momentum to the ongoing discussion clarifying the merits of visualization and analysis in mathematical thinking. Our goal was to gain understanding of three calculus students' mental processes and images used to create meaning for derivative graphs. We contrast the thinking processes of these three students as they attempted to…

This article discusses a three-step method that was used in a college calculus course. The three-step method was developed to help students understand the course material and transition to be more independent learners. In addition, the method helped students to transfer concepts from short-term to long-term memory while lowering cognitive load.…