BrainPOP Science is a research-based program that has been shown to be effective in improving and quickly developing students' scientific reasoning skills. This white paper presents a comprehensive case study conducted in school districts in the Southeastern United States. BrainPOP Science is one of the leading supplemental middle school programs.…

We report on findings from two one-on-one teaching experiments with prospective middle school teachers (PTs). The focus of each teaching experiment was on identifying and explicating the mental processes and types of intermediate, supporting reasoning that each PT used in their development of combinatorial reasoning. The teaching experiments were…

Reports survey results on proof conceptions. Presents an overview of responses at the end of year 8 (age 13 years) and year 9 (age 14 years). Distinguishes three strategies--empirical, focused-empirical, and focused-deductive--that represent shifts in attention from an inductive to a deductive approach. Indicates some progress from year 8 to year…

Examines the criteria that middle school students, nonscientist adults, technicians, and scientists used to rate the validity of conclusions drawn by hypothetical students from a set of evidence. The sources of the groups' differing epistemic criteria rest in their different spheres of cultural practice. Explores implications of this perspective…

One of the most challenging daily experiences of teaching young adolescents is helping them transition from Piaget's concrete to the formal operational stage of cognitive development during the middle school years. Students who have reached formal operations can design and test hypotheses, engage in deductive reasoning, use flexible thinking,…

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)

Contrasts students' presymbolic and symbolic procedures in generalizing activities. Uses the semiotic-cultural theoretical approach and focuses on the role of body, discourse, and signs when students refer to mathematical objects. Identifies types of generalizations and discusses a specific kind of rupture in the ostensive gestures and…

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)

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.…

The need for developing cognitive skills in early adolescents as they move from concrete thinking to more abstract operations has been documented. College students seeking the middle school endorsement in education were trained to utilize matrices as graphic constructs of textual materials. By examining these content matrices, prepracticum…

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…

Presents three typical lab activities involving the breathing rate of fish, the behavior of electromagnets, and tests for water hardness to demonstrate how labs can be modified to teach process skills. Discusses how basic concepts about experimentation are developed and ways of generating and improving science experiments. Includes a laboratory…