This study focused on how to help students translate word problems so that they understand how to solve them, and so they are successful with word problems. I have created three research questions to focus on during this research project. First, how will direct instruction of word meaning help clarify the operation needed, affect the achievement…

Finding real-world examples for middle school algebra classes can be difficult but not impossible. As we strive to accomplish teaching our students how to solve and graph equations, we neglect to teach the big ideas of algebra. One of those big ideas is functions. This article gives three examples of functions that are found in Arches National…

This article describes a teacher and class as they discover that their reading comprehension strategies cross over into mathematical problem solving. The students practice using visualization techniques to improve their understanding of word problems. (Contains 5 figures.)

The effects of using homework guides, and homework logs on students' abilities to solve word problems involving basic addition and subtraction facts were studied. Students received one of three versions of addition and subtraction timed tests once per week--every Thursday--that focused on measuring automaticity of basic addition and subtraction…

This study examined average-, high- and top-performing US fourth graders' rational number problem solving and their understanding of rational number representations. In phase one, all students completed a written test designed to tap their skills for multiplication, division and rational number word-problem solving. In phase two, a subset of…

The problem solving performance of 24 learning disabled and 24 non-disabled second and fourth grade children was investigated using embedded irrelevant linguistic and numerical information within addition word problems. Irrelevant numerical information but not irrelevant linguistic information affected performance of all groups; however, LD…

This article describes a method of solution that Ramanujan may have used in solving the following puzzle: The number of a house is both the sum of the house numbers below it on the street and the sum of those above it. (The houses on a street are numbered consecutively, starting with 1.)

We present and discuss three examples of misapplication of the notion of conditional probability. In each example, we present the problem along with a published and/or well-known incorrect--but seemingly plausible--solution. We then give a careful treatment of the correct solution, in large part to show how careful application of basic probability…

This article offers an engaging application that adds meaning to the binomial theorem. (Contains 8 figures.)

This study employs the Excel function to design dynamic visual activities for factors and multiples word problem learning. A teaching experiment was carried out eight times in 4 weeks on three fifth grade students. The result showed that after using multiple-linked representations activities, students made greater progress in understanding target…

Teachers must be prepared to recognize valid alternative representations of arithmetic problems. Challenging examples involving mixed fractions and division are presented along with teacher's discussion from a professional development workshop. (Contains 6 figures and 1 table.)

This note presents a teaching suggestion, using the history of mathematics, to give students from middle school and high school the possibility of facing problems found in old mathematics books and comparing their solutions with those given in those books. (Contains 3 figures and 1 table.)

This case study investigates a professional development initiative in which a first-grade bilingual teacher engages in learning and teaching Cognitively Guided Instruction, a framework for understanding student thinking through context-rich word-problem lessons. The study explores (a) the impact of classroom-based professional development on a…

This paper is an attempt at clarifying the concept of "problem," in order to improve the teaching of problem solving. Four categories are employed in the analysis: formulation, context, solutions, and methods of approach. Examples are included. (MNS)

Uses the spot problem to illustrate the importance of inductive and deductive reasoning and the connections among algebra, graph theory, geometry, and combinatorics. (Author/NB)