Describes an exploratory teaching experiment carried out to test the hypothesis that it is feasible to develop a disposition toward more realistic mathematical modeling in pupils. The learning and transfer effects of an experimental class of 10- and 11-year-old students that were compared to the results of two control groups support this…

Focuses on the strategies young children (N=115) use to solve rectangular covering tasks before they have been taught area measurement. Children's solution strategies were classified into five developmental levels. Emphasizes the importance of understanding the relationship between the size of a unit and the dimensions of the rectangle in learning…

Report provides new data concerning children's accuracy as measured by previous studies and clarifies progress of first graders during entire year on difficult single-digit addition and subtraction problems. Discussion focuses on advantages of an adding on interpretation of subtraction and the importance of emphasizing conceptual understanding…

Examined is the relationship between junior high school students' directional reasoning about rates and numerical reasoning on proportion-related word problems. The relationship between the ability to solve context-free fraction exercises and the ability to solve mathematically similar word problems is discussed. (KR)

Described are the general problem-solving strategies and their nature and functions. The importance of integrating different types of general problem-solving strategies with content-specific teaching in mathematics classes is discussed. (KR)

Twelve middle school students, working in pairs, used a computer microworld to explore introductory geometric transformational concepts. Despite a tendency for symbolic overgeneralization, the students were able to use visual feedback from the microworld and discussions with partners to correct their own mistakes. (Author/JJK)

A study asked 24 first grade children from 3 different classes to write number sentences and select appropriate alternative number sentences for addition and subtraction word problems. Results indicated that children could be characterized into five clusters according to their flexibility in accepting alternative number sentences and that…

Researchers from four projects with a problem-solving approach to teaching and learning multidigit number concepts and operations describe a common framework of conceptual structures children construct for multidigit numbers, and categories of methods children devise for multidigit addition and subtraction. Conceptions include unitary, decade and…

Discussed is the research project that used small-group problem solving as a primary instructional strategy of second grade mathematics for an entire year. The mutual construction of classroom norms for cooperative learning style is illustrated and examples of resulting learning opportunities are given. (MDH)

Investigates issues of conceptual understanding in teaching and learning mathematics provided conceptually based instruction on place value and two-digit addition and subtraction without regrouping in four first grade classrooms. Conventional textbook-based instruction was provided in two first grade classrooms. Experimental-group students scored…

Examined the effects of intervention in the instruction of 12 male seventh-grade students for the purpose of developing number sense. Results indicate that after instruction students were more likely to use strategies to solve number magnitude, mental computation, and computational estimation problems that reflected number sense. (Contains 50…