Division-With-Remainder (DWR) problems are particularly complex, as suggested in many studies. The purpose of this work was to establish whether students' difficulties in DWR problems came from an inadequate initial representation or from an inadequate final interpretation of the numerical answers, and whether remainders could be grouped into two…

The GeoGebra software is attracting a lot of interest in the mathematical community, consequently there is a wide range of experience and resources to help use this application. This article briefly outlines how GeoGebra will be of great value in statistical education. The release of GeoGebra is an excellent example of the power of free software…

The author discusses how she made up some dice problems for a child's birthday. She presents some activities that can be used with younger and older children based on dice. (Contains 4 figures.)

Recognizing meaning in students' mathematical ideas is challenging, especially when such ideas are different from standard mathematics. This study examined, through a teaching-scenario task, the reasoning and responses of prospective elementary and secondary teachers to a student's non-traditional strategy for dividing fractions. Six categories of…

This note presents demonstrations of mathematics that emerges when problems are posed with respect to a combined 12 x 12 multiplication table showing multiplier and multiplicand. Through processes such as recognizing and extending patterns, specializing and generalizing particular functional relationships between the diagonal and row sequences are…

Little research has focused on an informal understanding of subtractive negation (e.g., 3 - 3 = 0) and subtractive identity (e.g., 3 - 0 = 3). Previous research indicates that preschoolers may have a fragile (i.e., unreliable or localized) understanding of the addition-subtraction inverse principle (e.g., 2 + 1 - 1 = 2). Recognition of a small…

"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Standards on Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained through decades of mathematics teaching and research,…

This dissertation examines the manner in which young school-age children construct quantitative mental imagery and act upon these constructions for arithmetic ends. After conducting dyadic teaching experiments with three first grade students who were participating in mathematics intervention, I found the connection between the participants'…

While there is evidence for an association between the development of reading and arithmetic, the precise locus of this relationship remains to be determined. Findings from cognitive neuroscience research that point to shared neural correlates for phonological processing and arithmetic as well as recent behavioral evidence led to the present…

Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…

Language and arithmetic are both lateralized to the left hemisphere in the majority of right-handed adults. Yet, does this similar lateralization reflect a single overall constraint of brain organization, such an overall "dominance" of the left hemisphere for all linguistic and symbolic operations? Is it related to the lateralization of specific…

This study examined the effects of a yearlong Mediational Intervention for Sensitizing Caregivers (MISC; Klein, 1992) on: (a) the quality of interactions between rehabilitation day center paraprofessional staff (n=10) and their adult consumers (n=19) with severe intellectual disability (ID) and (b) the consumers' cognition, autonomy, and…

The use of difference and differential equations in the modelling is a topic usually studied by advanced students in mathematics. However difference and differential equations appear in the school curriculum in many direct or hidden ways. Difference equations first enter in the curriculum when studying arithmetic sequences. Moreover Newtonian…

According to this author, when it comes to data-based decision making, many educators are looking in the wrong place. This is one reason why this potentially powerful practice has too often under-delivered. Many schools rush headlong into analyzing data without considering if the data they are reviewing is worth the effort, if other data might…

This new study is being released as an advance excerpt of the 2008 Brown Center Report on American Education. This new report finds that the nation's push to challenge more students by placing them in advanced math classes in eighth grade has had unintended and damaging consequences, as some 120,000 middle-schoolers are now struggling in advanced…