This study aims to explain the thinking process of students in solving combination problems considered from assimilation and accommodation frameworks. This research used a case study approach by classifying students into three categories of capabilities namely high, medium and low capabilities. From each of the ability categories, one student was…

A first application of multilevel latent class analysis (MLCA) to educational large-scale assessment data is demonstrated. This statistical technique addresses several of the challenges that assessment data offers. Importantly, MLCA allows modeling of the often ignored teacher effects and of the joint influence of teacher and student variables.…

In general, units coordination refers to the relationships that students can maintain between various units when working within a numerical situation. It is critical that middle school students learn to coordinate three levels of units not only because of their importance in understanding fractions but also because of their implications for…

Background: It has been shown that mathematical representations can aid children's understanding of mathematical concepts but that children can sometimes have difficulty in interpreting them correctly. New advances in eye-tracking technology can help in this respect because it allows data to be gathered concerning children's focus of attention and…

We used event-related potentials (ERPs) to determine the time course of mechanisms underlying strategy selection. Participants had to select the better strategy on multiplication problems (i.e., 51 × 27) to find approximate products. They could choose between rounding up and rounding down both operands to their nearest decades. Two types of…

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…

The purpose of this study was to examine adult developmental mathematics (ADM) students' knowledge of fraction addition and subtraction as it relates to their demonstrated fraction schemes and ability to disembed in multiplicative contexts with whole numbers. The study was conducted using a mixed methods sequential explanatory design. In the first…

The Smarties-Box Challenge encourages students to apply several different mathematical capabilities and concepts--such as, estimation, multiplication, and the notion of being systematic--to solve a complex, multistep problem. To effectively engage in the Smarties-Box Challenge, students are required to demonstrate aspects of all four proficiency…

This article investigates the impact of research findings on the representation of proportional reasoning in two commonly used Swedish mathematics textbook series for grades 7-9. A research-based framework that identifies five learning goals for understanding of proportional reasoning was used to analyse the textbooks. The results brought to…

This analytical study analyzed the performance in Basic Mathematics of the indigenous students, the Aeta students (Grade 6) of Sta. Juliana Elementary School, Capas, Tarlac, and the APC students of Malaybalay City, Bukidnon. Results were compared with regular students in rural, urban, private, and public schools to analyze indigenous students'…

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…

We investigated a new phenomenon that sheds light on age-related differences in strategy selection: the strategy repetition phenomenon (i.e., tendency to repeat the same strategy over consecutive items). Young and older adults had to provide the best estimates of multiplication problems like 47 × 86. They had to select the best of 2 rounding…

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…

This investigation examined the degree to which prospective elementary teachers had developed a meaningful and conceptual understanding of what integers are and explored their development of models for multiplication with integers that are related to everyday activities. Additionally, this study explored how these understandings informed…