Bill and Karen are special education teachers who have entirely different knowledge and skill profiles. Bill is a special educator with 20 years of experience. He teaches reading to third-, fourth-, and fifth-grade students in a high-poverty elementary school resource classroom. His school is currently engaging in a schoolwide Reading First effort…

All learners, including those who qualify for special education services, should have access to learning mathematical concepts. This study examined the efficacy of using hands-on sets of materials to teach two high school students with mental retardation the four situations for subtraction. This is a mixed methods study using a simple…

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…

In the article we compare the approaches of 3 in-service teachers and 3 student teachers when they tried to solve a verbal arithmetic problem in the classroom. Each interaction was studied using a System of Analysis that takes into account the cognitive processes involved in the solution of a mathematic problem and describes the interaction at…

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)

Research indicates that students have great difficulty solving certain algebra word problems. These solutions, moreover, appear to be due to some situational factors characteristic of algebra problems, e.g., presentation and response format. This study investigates students' preconceptions, post facto alternative concepts based on key features of…

This paper is an exploration of the conceptual issues that have arisen in the course of building a natural language generation (NLG) system for automatic test item generation. While natural language processing techniques are applicable to general verbal items, mathematics word problems are particularly tractable targets for natural language…

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)

Provides a model for teachers to engage children in understanding problems and communicating their solutions in order to lead them toward becoming mathematically powerful learners. (Author/NB)

Presents solutions to the Pumpkin Puzzler problem that appeared in the October 2001 issue of this journal. (Author/NB)

Presents solutions to the Football Frenzy problem that appeared in the November 2001 issue of this journal. (Author/NB)

Provides problems to illustrate the potential power of mathematical intuition when confident problem solvers take the time to "play" with a problem and follow their instincts. (MKR)