Describes a classroom problem of probability as follows: How many people do you need in a group to ensure that the probability of at least two of them having the same birthday is greater than one-half? Answer: 23. The probability principles needed are simple enough to be accessible to advanced high school students. (PVD)

Describes a classroom activity based on the practice of fishermen tying knots in boat anchor ropes to determine river or lake depth. Knot-tying provides a simple hands-on context for students modeling in algebra. Students were actively involved in measuring, collecting data, fitting a line to data, finding an equation for a line, and checking a…

Reprints three items that appeared in the media that were developed into mathematical problems. Items include a commentary called Junk the Penny, a sale advertisement for a department store, and a sports column with statistics. Eighteen questions are provided along with answers. A graphing calculator is suggested for some problems. (PVD)

Describes a classroom activity designed to give students hands-on experience using technology and geometric visualization, as well as to explore fractal geometry in a cooperative classroom environment. Natural phenomena is the context of these activities. Enriches understanding of Euclidean geometry and infinite sequences. Lists materials,…

Describes some ways to assess students' achievement of objectives in the Assessment Standards for School Mathematics. Suggests alternative methods of assessment that are appropriate to answer questions about connections and reasoning. Discussion is divided into two sections: (1) Assessment as Culminating Activity and Evaluation-An Example from…

Describes computer or calculator-graphing technology to develop parametric representations which help students connect mathematical topics from algebra and trigonometry through algebraic, graphical, and numerical representations. Computer or calculator graphing utilities instantly transform algebraic expressions into visual and numerical displays…

Suggests ways to analyze and modify typical classroom tests that are objective, easy to implement, and in accordance with the types of changes and recommendations being discussed to improve assessment. Sections include Criteria for Analyzing Classroom Tests; Modifying Test Items; Needed Steps; Cautions; and Conclusions. Uses actual classroom test…

Describes the study of a physics teacher whose teaching changed as his beliefs about mathematics changed. Following a week-long institute on using graphing calculators, the teacher became an advocate of calculator use and his algebraic thinking progressed as he realized the importance of functions. (DDR)

Lists some ways that sequences were incorporated into mathematics lessons and explains a teacher's observations about the caliber of thinking and questioning that students develop as they learn appropriate ways to use numbers. Provides a number of questions that have been raised by students and the thinking prompted by a discussion of those…

Describes a technique that uses cellular telephones and their rates to enliven the topic of linear equations in a college algebra course. Uses mathematics to select a cellular telephone plan from a vendor. Enables students to use and connect the ideas of functions, equations, graphs, and applications. (DDR)

Presents an activity devised as a method of introducing periodic functions that can enable students to gain a deeper understanding of the concept of function. Employs a calculator-based laboratory, a light sensing probe, and an appropriate calculator. Calculator programs and sample data are included. (DDR)

Discusses the implications of a research study of more than 2000 students aged 11 to 15 that explored why the students interpret algebra in certain ways. Recommends strategies that can help teachers deal with prior knowledge that students may bring to their study of algebra. (DDR)

Describes a game used in precalculus that builds interest and confidence in the uses of inverse functions. The game is preceded by a worksheet that enables students to discover that f(x) and f-1(x) are mirror images of the line y=x. (DDR)

Introduces students to the study of dynamical systems through a number of learning activities that explore functions in general and linear and exponential functions in particular. Students use calculators to interpret graphs, find patterns in tables of data, and also use algebra. (DDR)

Focuses on Standard 4: Knowing Mathematical Pedagogy from the "Professional Teaching Standards" from the National Council of Teachers of Mathematics. Uses the profile of an algebra teacher and his pedagogy to explore how this standard might be exemplified in practice. (DDR)