For various reasons there has been a recent trend in college and high school calculus courses to de-emphasize teaching the Partial Fraction Decomposition (PFD) as an integration technique. This is regrettable because the Partial Fraction Decomposition is considerably more than an integration technique. It is, in fact, a general purpose tool which…

PreCalculus students can use the Completing the Square Method to solve quadratic equations without the need to memorize the quadratic formula since this method naturally leads them to that formula. Calculus students, when studying integration, use various standard methods to compute integrals depending on the type of function to be integrated.…

In this note, we introduce and discuss convolutions of two series. The idea is simple and can be introduced to higher secondary school classes, and has the potential of providing a good background for the well known convolution of function.

Empirical research shows that students often use reasoning founded on copying algorithms or recalling facts (imitative reasoning) when solving mathematical tasks. Research also indicate that a focus on this type of reasoning might weaken the students' understanding of the underlying mathematical concepts. It is therefore important to study the…

Place value is a phenomenon that has ominous implications for developing number sense and meaning and for using alternative algorithms and alternative representations within whole number arithmetic. For the most part, school programs examine place value at a surface level, with a primary focus on having the student identify or state a number value…

In this paper, I analyze the association between workplace sex ratios and partnership formation and dissolution. I find that the risk of dissolution increases with the fraction of coworkers of the opposite sex at both the female and male workplace. On the other hand, workplace sex ratios are not important for the overall transition rate from…

Students manipulate data algebraically, and statistically to create models applied to a falling ball. They also borrow tools from arithmetic progressions to examine the relationship between the velocity and the distance the ball falls. (Contains 2 tables and 5 figures.)

Probability is an important idea with a remarkably wide range of applications. However, psychological and instructional studies conducted in the last two decades have consistently documented poor understanding of probability among different populations across different settings. The purpose of this study is to develop a theoretical framework for…

There have been calls for at least 30 years in American education for a return to basics in mathematics instruction. The problem lies in defining what is basic. Mathematics is more than arithmetic. It is a fabric of ideas, relationships, principles and procedures. But all too often the emphasis in classroom instruction is on static facts and…

Formerly, the "prisoners" problem was used by the author in his teaching chiefly as a process activity, with the intention of promoting certain investigative techniques: the idea of starting with a smaller problem (say, 10 prisoners, guards and cells, rather 100), and the importance of finding an effective method for displaying what was going on.…

Responsiveness to Intervention (RtI) is recommended both as an essential step before identifying learning disabilities (LD) and as a mechanism for preventing learning difficulties. The use of evidence-based multi-tiered interventions is of critical importance when implementing RtI. This article presents the results of a study that examined the…

General Certificate of Secondary Education (GCSE) mathematics assessment previously included a piece of coursework that required learners to develop a general equation to describe the relationship between two groups of numbers on a number grid. In this author's experience, it became clear that Year 10 students often struggled to form a link…

This article presents an instructional approach to constructing discovery-oriented activities. The cornerstone of the approach is a systematically asked question "If a mathematical statement under consideration is plausible, but wrong anyway, how can one fix it?" or, in brief, "If not, what yes?" The approach is illustrated with examples from…

The current study compared the effects of technological environments with that of the paper-and-pencil environment on reasoning about the concept of derivatives in the context of maximum and minimum problems. The data consisted of clinical interviews conducted with three pre-service secondary mathematics teachers and a newly registered graduate…

As state and school leaders across the country push to have more students take algebra in 8th grade, a new study argues that middle schoolers struggling the most in math are being enrolled in that course despite being woefully unprepared. "The Misplaced Math Student: Lost in Eighth Grade Algebra," scheduled for release by the Brookings Institution…