LOGO and turtle graphics were an influential movement in primary school mathematics education in the 1980s and 1990s. Since then, technology has moved forward, both in terms of its sophistication and pedagogical potential; and learner experiences, preferences and ways of thinking have changed dramatically. Based on the authors' previous work and a…

Researchers have noticed a shift in education, with science and social studies taking a backseat to mathematics and literacy (Marx & Harris, 2006; Rodriguez, 2006). Some school districts are operating on a rotating basis with science instruction--one month on and one month off (Marx & Harris, 2006). A better approach would be to encourage students…

Data-driven instruction began its spread across the country about a decade ago, in the footsteps of the No Child Left Behind requirement that schools administer yearly achievement tests. Those tests didn't help teachers spot and backfill learning gaps, though. Scores came back after everyone had moved on to the next grade, and anyway, the tests…

This study examined prospective middle grade mathematics teachers' knowledge of algebra for teaching with a focus on knowledge for teaching the concept of function. 115 prospective teachers from an interdisciplinary program for mathematics and science middle teacher preparation at a large public university in the USA participated in a survey. It…

This What Works Clearinghouse (WWC) review focuses on mathematics interventions for elementary school students in kindergarten through grade 5 designed to impact student achievement, including curriculum-based interventions, instructional techniques, and products designed to deliver content and monitor student progress. Systematic reviews of…

This What Works Clearinghouse (WWC) evidence review protocol focuses on mathematics interventions for middle school students in grades 6 through 8 designed to impact student achievement, including curriculum-based interventions, instructional techniques, and products designed to deliver content and monitor student progress. Systematic reviews of…

We present a "base x height" approach to familiar results of Archimedes on the area of a parabolic sector. (Contains 1 figure.)

Several new and sharp inequalities involving the constant e and the sequence (1 + 1/n)[superscript n] are proved.

More often than one might at first imagine, a simple trick involving integration by parts can be used to compute indefinite integrals in unexpected and amusing ways. A systematic look at the trick illuminates the question of whether the trick is useful enough to be called an actual technique of integration.

Automobile sunshades always fold into an "odd" number of loops. The explanation why involves elementary topology (braid theory and linking number, both explained in detail here with definitions and examples), and an elementary fact from algebra about symmetric group.

In order to find its circumference, Archimedes famously boxed the circle between two polygons. Ending the first of a series of articles (MT179) with an aside, Francis Lopez-Real reverses the situation to ask: Which polygons can be boxed between two circles? (The official term for such polygons is "bicentric".) The sides of these polygons are…

The notion of equivalence relation is arguably one of the most fundamental ideas of mathematics. Accordingly, it plays an important role in teaching mathematics at all levels, whether explicitly or implicitly. Our success in introducing this notion for its own sake or as a means to teach other mathematical concepts, however, depends largely on our…

It is known that the ratios of consecutive terms of Fibonacci and Tribonacci sequences converge to the fixed ratio. In this article, we consider the generalized form of Tribonacci numbers and derive the "golden proportion" for the whole family of this generalized sequence. (Contains 2 tables.)

What factors affect transfer of knowledge is a complex question. In recent research, the authors demonstrated that concreteness of the learning domain is one such factor (Kaminski, Sloutsky, & Heckler, 2008). Even when prompted and given no time delay, participants who learned a concrete instantiation of a mathematical concept failed to…

The purpose of this study was to examine the effects of a Tier 2 supplemental intervention focused on rational number equivalency concepts and applications on the mathematics performance of third-grade students with and without mathematics difficulties. The researcher used a pretest-posttest control group design and random assignment of 19…