This study used units coordination as a theoretical lens to investigate how whole number and fraction reasoning may be related for preservice teachers at the conclusion of a math methods class. The study contributes quantitative evidence that units coordination provides a common foundation for both mathematical knowledge for teaching whole number…

A robust understanding of place value is essential. Using a problem-based approach set within meaningful contexts, students' attention may be drawn to the multiplicative structure of place value. By using quotitive division problems through a concrete-representational-abstract lesson structure, this study showed a powerful strengthening of Year 3…

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…

The basis of this intervention study is a distinction between numerical calculus and relational calculus. The former refers to numerical calculations and the latter to the analysis of the quantitative relations in mathematical problems. The inverse relation between addition and subtraction is relevant to both kinds of calculus, but so far research…

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…

Action research (AR) is defined by Macintyre to be: "an investigation, where, as a result of rigorous self-appraisal of current practice, the researcher focuses on a problem,or a topic or an issue which needs to be explained, and on the basis of information, plans, implements, then evaluates an action then draws conclusions on the basis of…

High academic standards are an important first step in ensuring that all Alaska's students have the tools they need for success. These standards reflect the collaborative work of Alaskan educators and national experts from the nonprofit National Center for the Improvement of Educational Assessment. Further, they are informed by public comments.…

The primary objective of this study was to provide an experimental model of children's representations of addition and subtraction concepts viewed as constructed schemes. How children with different counting schemes differ in their addition and subtraction concepts and how the types of problems children solve correlate with the addition and…

The author examines a well known number trick, in other number bases, and finds that equivalent results arise. (CT)

Problems focusing on number theory that can make good use of the calculator in discovering and proving simple theorems are proposed. The focus is on the properties of subtracting the smaller of a three digit number and its mirror number from the larger in a process that leads to zero. (MP)

Material included in this bulletin provides an overview of research studies which pertain to teaching addition and subtraction of whole numbers in the primary grades. The studies mentioned relate directly to the following questions: (1) What foundation for addition and subtraction do children have upon entering school? (2) What is the relative…

Five-frames are proposed as manipulative material to increase children's ability to identify the number of objects without direct counting. How to use frames and beansticks to construct basic facts without counting is discussed. (MNS)

This article argues that the reason the mathematics performance of students with mild disabilities is so limited is the mathematics. Using illustrations from subtraction, the article proposes number sense be a primary goal and that within the realm of number sense, big ideas be included among the dependent variables. (Contains references.)…

This paper reports the formative evaluation of six curriculum units related to initial number sentence writing. These units were used for a coordinated study carried out by the Mathematics Work Group of the Wisconsin Research and Development Center for Individualized Schooling. The units were tried during the 1977-78 and 1978-79 school years at a…