Replies to Lerman, who presented Vygotsky as an irreconcilable opponent to Piaget's genetic epistemology and von Glasersfeld's radical constructivism. Argues that Lerman's stance does not reflect von Glasersfeld's opinion of Vygotsky's work, nor does it reflect Vygotsky's opinion of Piaget's work. Establishes compatibility between analytic units…

Analyzes instructional actions designed to help a student understand distance, time, and speed. Focuses on the mathematical knowledge that guided instructional decisions and actions and discusses implications for content preparation of teachers. Contains 48 references. (Author/MKR)

Investigates whether elementary school students can construct operations of thought for integers and integer addition crucial for understanding elementary algebra. Two sixth graders were taught using a computer. Results included both students being able to construct mental operations for negating arbitrary integers and determining sign and…

Fourth grade children (n=20) were matched on a pretest and randomly assigned to either a wooden base-10 block or computerized microworld group. Instruction was designed to establish relationships between notation and meaning, extending whole number numeration to decimal numeration. Neither group changed whole-number notational methods nor had…

Examines how one teacher's way of knowing mathematics was reflected in language used in teaching concepts of rate to one student. The teacher's conceptualizations of rate were encapsulated in the language of numbers and operations which undermined his effort to help the student understand rates conceptually. (Contains 27 references.) (Author/MKR)

Discusses the interactions between technology and research in mathematics education, including computer-assisted instruction, role of technology in learning, use of computer environments to study students' mathematical concept formation, research methodologies, interactive technologies, and lack of technology-related research in the "Journal for…