The goal of this study is to develop the professional noticing abilities of preservice elementary teachers in the context of the Stages of Early Arithmetic Learning. In their mathematics methods course, the preservice elementary teachers participated in a researcher-developed multi-session module that progressively nests the three interrelated…

This experiment tested the hypothesis that organizing arithmetic fact practice by equivalent values facilitates children's understanding of math equivalence. Children (M age = 8 years 6 months, N = 104) were randomly assigned to 1 of 3 practice conditions: (a) equivalent values, in which problems were grouped by equivalent sums (e.g., 3 + 4 = 7, 2…

This study investigated how the use of virtual manipulatives in integer instruction impacts student achievement for integer addition and subtraction. Of particular interest was the influence of using virtual manipulatives on students' ability to create and translate among representations for integer computation. The research employed a…

Much attention has been devoted in the literature to students' struggles with fraction division. With regard to the traditional invert and multiply algorithm, researchers and educators have examined such areas as typical errors, how to help students understand why this method works, and what alternatives are available that might be more intuitive.…

Modern Hindu-Arabic numeration is the end result of a long period of evolution, and is clearly superior to any system that has gone before, but is it optimal? We compare it to a hypothetical base 5 system, which we dub Predator arithmetic, and judge which of the two systems is superior from a mathematics education point of view. We find that…

This study was designed to investigate preservice elementary school teachers' (PSTs') responses to written standard place-value-operation tasks (addition and subtraction). Previous research established that PSTs can often perform but not explain algorithms and provided a four-category framework for PSTs' conceptions, two correct and two incorrect.…

This study investigated the role of strategy instruction and working memory capacity (WMC) on word problem solving accuracy in children with (n = 100) and without (n = 92) math difficulties (MD). Within classrooms, children in Grades 2 and 3 were randomly assigned to one of four treatment conditions: verbal-only strategies (e.g., underlining…

Early algebraic thinking in a primary context is not about introducing formal algebraic concepts into the classroom but involves reconsidering how one thinks about arithmetic. Early algebraic thinking assists young students to engage effectively with arithmetic in ways that support engagement with arithmetic structure rather than arithmetic as a…

The purpose of this study was to assess student knowledge of numeric, visual and algebraic representations. A definite gap between arithmetic and algebra has been documented in the research. The researchers' goal was to identify a link between the two. Using four "Guess My Number" problems, seventh and tenth grade students were asked to write…

In this innovative book, two experienced educators present a fresh and engaging approach to mathematics learning in the middle grades with the transition from arithmetic to algebra. The authors provide a collection of balanced, multi-dimensional assessment tasks designed to evaluate students' ability to work with mathematical objects and perform…

The data used for the qualitative analysis reported here were generated as part of a larger study to understand and characterize teacher practice related to engaging students in algorithmic thinking associated with the fraction operations of addition, subtraction, multiplication and division. This paper presents ways in which teachers used…

Single Display Groupware (SDG) allows multiple people in the same physical space to interact simultaneously over a single communal display through individual input devices that work on the same machine. The aim of this paper is to show how SDG can be used to improve the way resources are used in schools, allowing students to work simultaneously on…

The involvement of working memory (WM) was examined in two types of mental calculation tasks: exact and approximate. Specifically, children attending Grades 3 and 4 of primary school were involved in three experiments that examined the role of verbal and visuospatial WM in solving addition problems presented in vertical or horizontal format. For…

For community college faculty and administrators who wish to find a higher degree of successful outcomes in a developmental arithmetic course, this study examined whether a conceptual developmental arithmetic instructional approach affects the overall performance of community college students and if it differentially affects the performance of low…

This study investigates the extent to which pre-service elementary teachers (PETs) use their realworld knowledge to solve problems for which the result of the arithmetic operation is problematic, if one takes into consideration the reality of the context. A paper-and-pencil test was administered to 566 PETs enrolled in mathematics content courses.…