Discusses how students fail to recognize the underlying equivalence when the same set of points is represented by a graph or an equation or a table. Presents activities in which more than one form of representations of the same information are included. (ASK)

Presents an assignment given to students to produce a report on perfect numbers and their properties. Summarizes the history of perfect numbers and their features. Recommends spreadsheet, theoretical, and programming activities on perfect numbers. (ASK)

Describes one possible approach to solving the following problem: given a pentagon ABCDE in which triangles ABC, BCD, CDE, DEA, and EAB all have area=1, is the area of the pentagon determined? (AIM)

Describes the solution to a geometric problem by two ninth-grade mathematicians using The Geometer's Sketchpad computer software program. The problem was to divide any line segment into a regular partition of any number of parts, a variation on a problem by Euclid. The solution yielded two constructions, one a GLaD construction and the other using…

Describes a lesson that uses the graphing calculator to prompt the proof of the mean-value theorem. Students, through guided questioning, proposed the idea of using a difference function to find where a tangent line is parallel to a secant line. Through the use of graphing technology, students conjectured the essential fact that the constructed…

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…

Presents an interesting problem intended to introduce students to an application of algebra and to help them make the transition from arithmetic to algebra. Uses different problem representations including making successive approximations, interpreting graphs, and solving equations. Discusses pedagogical issues involved. Contains 11 references.…

Presents examples of how students can create drawings of sets of lines whose envelopes are parabolas, cardioids, epicycloids, or hypocycloids. Provides students with experience in problem solving, reasoning, communication, and connections between numbers and geometry, between mathematics and art, and between mathematics and other applications.…

Describes the development of a method of generating problems that are easy to present in classroom settings because all the important points to be graphed are single-digit integers. Uses an algorithm that generates intersection problems that fit the criteria. A proof of the algorithm is included. (DDR)

Describes the incorporation of math concepts into snacktime for prekindergarten students through a self-serve center with a snack menu. Children gain experience in counting, sequencing, and measuring continuous quantities; understand the concepts of sets, uniform units, more and less, equal quantities, fractions, zero, and patterns. (KB)

Explores the relationship between classroom discourse and mathematical development in a first-grade classroom. Addresses issues such as the teacher's role and the role of symbolization in supporting reflective shifts in the discourse. Contrasts the analysis of reflective discourse with Vygotskian accounts of learning that also stress the…

Explored whether a system between written place-value system and base-10 manipulatives helped children understand place-value. Found evidence that the intermediate system helped children differentiate between face values and complete values of digits in multidigit place-value number representations, and to grasp that the sum of the digits'…

Presents activities that explore step-cut dissections of whole rectangles. Provides students with the opportunity to discover patterns, which allows them to solve more and more complex problems that offer a context within which students can think about and use different mathematical concepts. (JRH)

Addresses difficulty levels and the importance of providing experience at all levels. Levels are count and land, at which children do not understand if the number arrived at is reasonable; number sense and relationships, where children are developing a sense of reasonableness; and parts of numbers, when children are able to work flexibly with…

Demonstrates the use of hexagonal dot paper in integrating algebra, geometry, and trigonometry within a single problem-solving setting rather than treating them in isolation. Suggests other related mathematically challenging activities for enrichment. (AIM)