We examine whether the array representation can support children's understanding and reasoning in multiplication. To begin, we define what we mean by understanding and reasoning. We adopt a "representational-reasoning" model of understanding, where understanding is seen as connections being made between mental representations of concepts, with…

Second-grade students struggle with writing about mathematical topics during math class, so the teacher begins to integrate mathematical topics into their Writing Workshop. Content journals are used during math, and students are encouraged to write about personal connections to mathematical situations, as well as incorporate mathematical concepts…

Introduction: In this document we stress the importance of developing in children a structure for advanced numerical-algebraic thinking that can provide an element of control when solving mathematical situations. We analyze pupils' conceptions that induce errors in algebra due to a lack of control in connection with their numerical thinking. We…

This study explores the use of cogenerative dialogue (cogen) in an Adult Basic Education (ABE) program located in New York City, and the ways in which students and teachers collaborated to cogenerate resources that afforded a positive and equitable learning environment built on solidarity and new perspectives on teaching and learning of…

The research described in this dissertation explores the impact of utilizing a LEGO-robotics integrated engineering and mathematics program to support fifth grade students' learning of ratios and proportion in an extracurricular program. The research questions guiding this research study were (1) how do students' test results compare for students…

Since the dawn of civilization, pictorial representations and symbols have been used to communicate simple statistics. Efficient and effective, they are still used today in the form of pictures and graphs to record and present data. Who can tie their shoes? How many calories are in your favorite food? Make data and graphs relevant and interesting…

Although current reform movements have stressed the importance of developing prospective middle school mathematics teachers' subject matter knowledge and understandings, there is a dearth of research studies with regard to prospective middle school teachers' confidence and knowledge with respect to quadratic functions. This study was intended to…

Two experts on education offer a rich and diverse selection of children's literature and teaching strategies for the K-8 mathematics classroom. To date, a vast majority of classrooms continue to fall short in the implementation and direction of NCTM Principles and Standards for School Mathematics (PSSM), in part because most of these classrooms…

Teaching computer programming to young children has been considered difficult because of its abstract and complex nature. The objectives of this study are (1) to investigate whether an innovative educational technology tool called Scratch could enable young children to learn abstract knowledge of computer programming while creating multimedia…

This book is loaded with hands-on measurement and geometry activities that will get students rolling up their sleeves, excited to use their math skills. The author has created these activities to supplement a teacher's existing math curriculum. They are flexibly designed for use as either introductory, reinforcement, or assessment activities. This…

This paper presents an alternative version of formulas of conditional probabilities and Bayes' rule that demonstrate how the truth table of elementary mathematical logic applies to the derivations of the conditional probabilities of various complex, compound statements. This new approach is used to calculate the prior and posterior probabilities…

Combating the perception of many adults and children that mathematics is difficult, irrelevant and not for them is a major task for teachers and one that is not easily achieved. Attempts to place mathematics in real-life situations or to use contexts to alleviate the apparent separation of school mathematics and out-of-school mathematics have been…

In this article, the author uses a range of simple materials to facilitate students' understandings of measurement concepts. The six activities presented are essentially about looking at different configurations of a given volume. (Contains 6 figures.)

The orders of presentation of pre-calculus and calculus topics, and the notation used, deserve careful study as they affect clarity and ultimately students' level of understanding. We introduce an alternate approach to some of the topics included in this sequence. The suggested alternative is based on years of teaching in colleges within and…

This paper describes the procedures of reconstructing ancient architecture using solid modeling with geometric analysis, especially the Golden Ratio analysis. In the past the recovery and reconstruction of ruins required bringing together fragments of evidence and vast amount of measurements from archaeological site. Although researchers and…