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The NAEP testing over the past decade shows gradual improvement of test scores at the eighth-grade level, contrary to what many say about stagnant scores. However, by 2000, only one-fourth of eighth graders performed at the proficient level. (Contains 2 tables and 6 figures.)

Debates about the future of school mathematics in the United States often center on whether standards-based instruction is improving or undermining students' achievement. Critical for making progress in these debates is information about the actual nature of classroom practice in U.S. classrooms. This article focuses on one key element of classroom practice--teaching--and presents the results of two studies of randomly selected, nationally representative U.S. eighth-grade mathematics lessons that were videotaped as part of the TIMSS 1995 and 1999 Video Studies. (Contains 4 figures, 6 tables and 11 footnotes.)

Presents results from the mathematics portion of the Third International Mathematics and Science Study (TIMSS) 1999 Video study, which examined classroom teaching practices in eighth-grade mathematics and science in seven countries. Identifies some general features among the countries, but discernible variation in teaching methods and topics covered. (SLD)

Describes the way in which 12 primary-grade teachers responded to reform-minded teaching of multidigit addition and subtraction. Discusses the nature of effective teacher-development programs. Contains 21 references. (ASK)

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 significantly higher than control-group students on items measuring understanding place value and addition and subtraction with regrouping. (Author/MDH)

Reported are the effects of a conceptually oriented unit on decimal fractions. The relationships between short-term changes in solving processes and the stability of these processes over time, performance of students, and entry achievement level and the long-term effects of conceptually based instruction are discussed. (KR)

Based on the premise that meaningful learning in mathematics occurs when children link their understandings with the symbols and procedures they are taught, three places are identified where children can link symbols and their referents, procedural rules and conceptual knowledge, and answers to problems with other knowledge about what is reasonable. (MBR)

Teachers need to understand why students use certain methods in solving mathematical problems so that they can assess the students' understanding of the concepts behind such solutions. Students who simply memorize rules are bound to encounter difficulties when they face a new set of problems while those who truly understand the logic behind procedures can modify them. The concept of place value, for example, can be learned by students if teachers give them exercises which will allow them to relate key ideas with written notations and sharing this knowledge with others., Marcy and Angela were each solving the following problem in their second-grade classroom: The school cafeteria has 347 ice-cream bars in one box and 48 in another box. How many [...]

Examines the methodology of instruction and cognitive change in mathematics. Distinction between teaching and learning; Approaches in cognitive psychology; Identification of an instructional sequence in the cognitive processes.