Learning by Seeing by Doing: Arithmetic Word Problems

Learning by doing in pursuit of real-world goals has received much attention from education researchers but has been unevenly supported by mathematics education software at the elementary level, particularly as it involves arithmetic word problems. In this article, we give examples of doing-oriented tools that might promote children\u27s ability to see significant abstract structures in mathematical situations. The reflection necessary for such seeing is motivated by activities and contexts that emphasize affective and social aspects. Natural language, as a representation already familiar to children, is key in these activities, both as a means of mathematical expression and as a link between situations and various abstract representations. These tools support children\u27s ownership of a mathematical problem and its expression; remote sharing of problems and data; software interpretation of children\u27s own word problems; play with dynamically linked representations with attention to children\u27s prior connections; and systematic problem variation based on empirically determined level of difficulty

A study of the impact of instructional approach on community college students’ problem solving and metacognitive abilities in the developmental mathematics course, Introductory Algebra

The purpose of this quasi-experimental study was to examine the cognitive, metacognitive, affective and instructional constructs that influence students’ problem solving development in a community college Introductory Algebra course. The study addressed the lack of success that developmental mathematics students in a community college have in the Introductory Algebra course and in subsequent curriculum mathematics courses. Research suggests that the prevalent procedural-oriented instructional methodology used in most mathematics classrooms may be contributing to the lack of student success. The community college students (N = 140) in this study were enrolled in an Introductory Algebra course. The study investigated the relationships among the constructs self-regulation, students’ problem solving development, and instructional methods used in the Introductory Algebra course. A correlational design established the quantitative relationships among the constructs. The aim of this study was to heighten the awareness of both the cognitive and non-cognitive aspects of adult student learning, as well as, the importance of attending to the students’ conceptual understanding of mathematics