In Probability and Statistics taught to mathematicians as a first introduction or to a non-mathematical audience, joint independence of events is introduced by requiring that the multiplication rule is satisfied. The following statement is usually tacitly assumed to hold (and, at best, intuitively motivated): If the n events E[subscript 1],…

An adapted alternating treatments design with initial baseline and final best treatment phase was used to evaluate and compare the effects of two classwide interventions, detect--practice--repair (DPR), and self-mediated iPad instruction, on the multiplication math facts fluency in an inclusive third-grade classroom. Twelve students participated…

Leslie Steffe, among the foremost mathematics education researchers in the world, has had a profound influence on three generations of researchers. In 2006, he received the first-ever Senior Scholar Award from the AERA Special Interest Group: Research in Mathematics for the excellence and seminal nature of his work. Steffe shares his thoughts…

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…

This study examines preservice elementary teachers' (PTs) knowledge for teaching the associative property (AP) of multiplication. Results reveal that PTs hold a common misconception between the AP and commutative property (CP). Most PTs in our sample were unable to use concrete contexts (e.g., pictorial representations and word problems) to…

Piagetian theory describes mathematical development as the construction and organization of mental operations within psychological structures. Research on student learning has identified the vital roles of two particular operations--splitting and units coordination--play in students' development of advanced fractions knowledge. Whereas Steffe and…

The purpose of the present study was to examine the effectiveness of a strategic training program for improving students' performance in solving multiplication problems. The participants were 3 third graders with math difficulties. In this teaching experiment, microgenetic analysis was used to analyze improvement in students' strategic development…

Poor mathematics achievement in middle school students is evident in many countries. While some of the difficulties can be attributed to student related factors, there is considerable evidence that computational automaticity is essential for mathematics achievement. A QuickSmart (QS) mathematics intervention program was trialled with a group of…

The 43rd meeting of Canadian Mathematics Education Study Group (CMESG) was held at St. Francis Xavier University in Antigonish, Nova Scotia (May 31-June 4, 2019). This meeting marked only the third time CMESG/GCEDM (Groupe Canadien d'Étude en Didactique des Mathématiques) had been held in Nova Scotia (1996, 2003), and the first time it had been…

The transition from whole numbers to integers involves challenges for both students and teachers. Leadership in mathematics education calls for an ability to translate depth of understanding into effective teaching methods, and this landscape includes alternative treatments of familiar topics. Noting the multiple meanings associated with the…

This report describes the longitudinal development of one student, Drew, in terms of his unit concepts in area and volume measurement situations across Grades 2 through 5. Data were collected during individual interviews and an open-response assessment within the context of a four-year longitudinal teaching experiment. Results indicate that Drew's…

This paper shares research from a pilot study in which young children were introduced to multiplication and division problems in their first year of school. The focus was on building children's conceptual understanding of the idea of "repeated groups" as a fundamental aspect of multiplication and its relation to division. The particular…

We present a synthesis of findings from constructivist teaching experiments regarding six schemes children construct for reasoning multiplicatively and tasks to promote them. We provide a task-generating platform game, depictions of each scheme, and supporting tasks. Tasks must be distinguished from children's thinking, and learning situations…

The Common Core State Standards for Mathematics (CCSSM) call for an in depth, integrated look at elementary school mathematical concepts. Some topics have been realigned to support an integration of topics leading to conceptual understanding. For example, the third-grade standards call for relating the concept of area (geometry) to multiplication…

The equipartitioning learning trajectory (Confrey, Maloney, Nguyen, Mojica & Myers, 2009) has been hypothesized and the proficiency levels have been validated through much prior work. This study solidifies understanding of the upper level of co-splitting, which has been redefined through further clinical interview work (Corley, Confrey &…