This article reports on a study in which researchers asked children to "make up as story and a picture about marbles for this number sentence: 3 x 5 = 15." Students in this study came from pre - dominantly low- to average-income families living in three distinct geographical areas within the United States. A similar division task was…

In this study, I use a systemic functional linguistics approach to examine mathematics classroom discourse with the aim of providing a plausible explanation of how students could actively participate in productive classroom discussions without adopting ways of reasoning that were accepted in the classroom community. In this way, I work in the…

This study explored the potential of a rich assessment task to reveal students' multiplicative thinking in respect to a hypothetical learning trajectory. Thirty pairs of students in grades 5 and 6 attempted the task. Twenty-two pairs applied multiplicative structure to find the number of items in arrays. However counting and computational errors…

Lorraine Day and Derek Hurrell provide a convincing argument for using arrays to promote students' understandings of mental computation strategies for multiplication. They also provide a range of different examples that illustrate the benefits of arrays in the primary classroom.

When viewed through a lens of embedded cognition, algorithms may enable aspects of the cognitive work of multi-digit multiplication to be "offloaded" to the environmental structure created by an algorithm. This study analyses four multiplication algorithms by viewing different algorithms as enabling cognitive work to be distributed…

Multiplicative thinking is a "big idea" of mathematics that underpins much of the mathematics learned beyond the early primary school years. This article reports on a recent study that utilised an interview tool and a written quiz to gather data about children's multiplicative thinking. Our research has so far revealed that many primary…

In this article, the authors discuss a special type of multiplication-and-division-of-fractions problem that elementary school teachers can use to promote children's understanding of fractional quantities and their relationships. These problems are accessible to students working at different levels of fraction understanding, and they can be solved…

In this case study, we examine the usage of language -- how teachers used and regulated their language when teaching English language learners (ELLs) with learning disabilities (LD) how to solve mathematics multiplication problems. We focus on types of scaffolds used by teachers to identify how scaffolding helps ELLs with LD build better…

Multiplication of numbers from 1 to 10 is very important as it provides the basis for learning multiplication of other larger numbers as well as other related mathematical operations. How do students learn multiplication? Usually students just memorize the results of multiplication. This is often performed without a complete comprehension of the…

Based on Common Core Standards (2010), mathematics interventions should emphasize conceptual understanding of numbers and operations as well as fluency. For students at risk for failure, the concrete-representational-abstract (CRA) sequence and the Strategic Instruction Model (SIM) have been shown effective in teaching computation with an emphasis…

Lesson study cultivates teachers' capacity for formative assessment by placing student thinking front and center throughout. Lesson study is a form of professional development in which a team of teachers determines a mathematical focus, collaboratively studies student thinking about the topic, designs a lesson about this content, implements the…

In this article, the authors summarize results from 5 randomized controlled trials assessing the effects of intervention to improve the fraction performance of fourth-grade students at risk for difficulty in learning about fractions. The authors begin by explaining the importance of competence with fractions and why an instructional focus on…

Proficiency in mathematics across the United States has become an area of concern as performance on state accountability tests continues to demonstrate that less than 50% of students in 4th and 8th grade are proficient in mathematics (NCES, 2013). With such large numbers of students lacking proficiency in mathematics, systematic interventions that…

The complex nature of multiplicative thinking can be challenging for students and teachers to navigate. We report on the impact on student learning of school-based professional learning that targeted teachers' pedagogical content knowledge related to Multiplicative Thinking. Analysis of Year 4 students' longitudinal data indicated greater growth…

In this case study with Devin (pseudonym), which was part of a larger, constructivist teaching experiment with students identified as having learning difficulties in mathematics, we examine how a fourth grader constructed a dual anticipation involved in monitoring when to start and when to stop the simultaneous count of composite units (numbers…