Cross-sectional and longitudinal data from students as they advance through the middle school years (grades 6-8) reveal insights into the development of students' pattern generalization abilities. As expected, students show a preference for lower-level tasks such as "reading the data," over more distant predictions and generation of abstractions.…

This study presented contextual problems involving rational numbers and proportional reasoning to 7th-grade students with different curricular experiences. Evidence indicates that students in reform curricula, who are encouraged to construct their own conceptual and procedural knowledge of proportionality through collaborative problem-solving…

Explores strategies to encourage students' understanding of proportional reasoning. Conducts a study to compare the proportional reasoning of students studying one of the new standards-based curricula with that of students from a control group. (ASK)

This article presents specific instructional approaches and examples to develop the algebraic reasoning skills of middle and secondary students with mild disabilities. Discussion of the National Council of Teachers of Mathematics standards identifies general principles, content standards, and process standards. Discussion of effective instruction…

Defines the mathematical concept of proportionality. Uses graphs of linear relationships to explore and make generalizations about the characteristics of proportional situations to help students critically evaluate problems involving proportions. (MDH)

Describes several short geometry tasks that go beyond the simple recognition of figures and properties. Presents scoring rubrics and questions that might be useful to middle school teachers developing short open-ended questions that encourage and assess students' thinking. (ASK)

Identifies the types of reasoning involved in middle grade mathematics with regard to multiplicative structures and the difficulties students have with the concepts, why these difficulties might occur, and the interconnections within this content area. Offers four recommendations for the preparation and professional development of teachers.…

Preservice elementary teachers worked cooperatively to explore the relationship between the measure of the central angle and the number of sides of regular polygons using the reflection of a line in a hinged mirror. The experience involved conjecture and experimentation, communication, and building connections between science, geometry, and…