Argues that mathematics is, to a large extent, the study of patterns. Presents an activity in which students search for patterns in the Fibonacci sequence and Pascal's Triangle. (ASK)

The approximation of functions such as the sine, cosine, and exponential by polynomials is significant and interesting enough for students to learn about. Presents Maclaurin's theorem, examples employing the theorem, and applications of the theorem. (ASK)

Discusses the commercial for Skittles candies and asks the question "How many flavor combinations can you find?" Focuses on the modeling for a Skittles exercise which includes a brief outline of the mathematical modeling process. Guides students in the use of the binomial theorem and Pascal's triangle in this activity. (ASK)

Suggests scales as alternative representations of numerical concepts and operations that can be used as arithmetic-mean machines, adding machines, multiplication machines, and geometric-mean machines. (ASK)

Presents a brief history on the evolution of the National Council of Teachers of Mathematics' (NCTM) standards and reform efforts in mathematics education. Discusses the advantages of having standards. Mentions some research results stating dramatic increases in reading and mathematics achievement for schools with the highest implementation of…

The teacher's role in discourse is to initiate and orchestrate classroom interactions that contribute to students' understanding of mathematics. Describes instructional thoughts, struggles, and actions in order to establish and maintain an interactive mathematics-classroom discourse by emphasizing the teacher role in discourse. Provides a…

Presents an activity in which students use mathematical ideas to understand how the intensity of light changes as light passes through water or similar partial barriers, by using a calculator-based laboratory device to record light intensity. Continues with a structured series of questions involving the use of difference equations with which…

Discusses the need for well-developed rubrics in mathematics education. Compares rubrics with partial credit, and describes different types of rubrics. Provides an example of a general rubric used for holistic scoring, and issues that arise when applying the rubric to student responses. Contains 16 references. (ASK)

Introduces a technique for developing tasks suitable for group investigation where students work from sets of numerical examples toward making generalizations. (ASK)

Discusses the changes that have evolved in teaching and learning practices in mathematics classrooms by reflecting on issues in the past and present. Examines what should be done to prepare students for the future. Contains 16 references. (ASK)

Reports findings from a five-day summer institute conducted with 27 practicing primary grade teachers that was part of a year-long professional development project that supported teachers' thinking about children's arithmetical understanding. Indicates that teachers developed two hypotheses about children's thinking and what it means for children…

Provides a framework of four constructs that can be used to analyze various forms of classroom communication. Develops and uses these constructs as two preservice teacher's concepts of communication and their corresponding classroom practices are considered. (Contains 33 references.) (Author/ASK)

Listening to students' mathematical thinking is one of the reform-minded visions of mathematics teaching. Examines how a mathematics letter exchange between grade 4 students provided an occasion for prospective teachers to learn about students' mathematical thinking and examine their interpretive practices. (Contains 26 references.) (Author/ASK)

Describes the International Conference on Mathematics Teacher Education (ICMTE) held in Taipei, Taiwan whose program consisted of plenary talks, research reports, panel discussions, and a workshop on multimedia interactive learning environments in teacher education. Highlights issues raised by presenters during the conference. Lists 29 conference…

Describes the Chinese normal education system which differs from that of other countries, particularly in the uniqueness of its curriculum design, its admission process for normal students, and its training of students during their normal education. Highlights preservice teacher education in China. (Author/ASK)