A grandmother attempts to teach her four-year-old granddaughter the multiplication tables using simple repetition, but they repeatedly start over at 'three fives'; the child keeps coming up with 'thirty-five'. We consider three possible explanations: self-perpetuating frequency of behavior, saliency of memory and Vygotsky's next or proximal zones…

This study examined whether students were reaching automaticity with single digit multiplication facts. A fourteen question interview was used to collect data. The first three questions asked the student basic information about themselves and their current math teacher. The next seven questions were math facts. The math facts chosen for the…

This quasi-experimental study was conducted with two fifth grade classrooms to investigate the effect of scent on students' acquisition and retention of multiplication facts and math anxiety. Forty participants received daily instruction for nine weeks, using a strategy-rich multiplication program called Factivation. Students in the Double Smencil…

Although learning mathematics certainly depends upon accurate understanding of the facts of multiplication, it requires much more. This study examines the relationship between a meaningful understanding of arithmetic operations and the mastery of basic facts. The study began with a joke about a mistaken mathematical fact. The children appreciated…

There is evidence for both semantic and asemantic routes for naming Arabic digits, but neuropsychological dissociations suggest that number-fact retrieval (2x3=6) can inhibit the semantic route for digit naming. Here, we tested the hypothesis that such inhibition should slow digit naming, based on the principle that reduced access to multiple…

In this article, the author presents an innovative approach to teaching multiplication facts for children in middle school or younger. After introducing the dangers of some contradictions that persist, relating a brief summary of related research and guidelines regarding math facts and their relation to strategic approaches to more complex math,…

This paper proposes that there are some students who understand mathematics but just can't remember the rules to use it, and others who have accurate rote memory but can't apply the facts they know or do not understand the concepts behind them. The guided discovery approach to teaching mathematics is introduced. This approach promotes a system of…

The author's secondary school mathematics students have often reported to her that quadratic relations are one of the most conceptually challenging aspects of the high school curriculum. From her own classroom experiences there seemed to be several aspects to the students' challenges. Many students, even in their early secondary education, have…