Defines spatial structuring as the mental operation of constructing an organization or form for an object/set of objects. Examines in detail students' structuring and enumeration of two-dimensional rectangular arrays of squares. Concludes that many students do not see row-by-column structure. Describes various levels of sophistication in students'…

Caring and compassionate teachers can engage sullen, uncooperative students by inviting them on learning journeys that utilize various abilities and intelligences. The best teachers help students as they struggle to understand both core concepts and answers to essential questions. Two teachers' innovative strategies are described. (MLH)

Describes an activity on fractal geometry in which students built a 19-foot-tall Sierpinski pyramid in the Minneapolis Convention Center in conjunction with the National Council of Teachers of Mathematics' (NCTM) 75th Annual Meeting in April, 1997. Contains 13 references. (ASK)

Features a brief description of fractals and their characteristics, some example activities, and an argument for including fractals in the mathematics curriculum. (ASK)

Describes an interdisciplinary unit on robotics that includes teaching parts of a circle, constructing and programming robots, and incorporating language arts. (JOW)

Provides examples of geometry writing projects and discusses goals and difficulties of using these projects. Explores the process of grading and allowing student revisions of these projects by using a time-saving grading method. (Author/ASK)

Shares experiences with a series of lessons for fourth and fifth grade students in the elementary school and sixth, seventh, and eighth grade students at the middle school with the aim of showing ways in which architects use mathematics. Asks students to become architects and design buildings using geometrical shapes. (ASK)

Introduces handling data as conceived by Euclid, which provides some interesting possibilities for students to investigate fundamental geometrical ideas as well as relating some elementary geometry with elementary trigonometry. (ASK)

Considers teaching strategies to help children overcome misconceptions and difficulties with the mathematical concept of angles. (ASK)

Compares a teaching program designed to enhance schema acquisition with one of worked examples, traditionally used to teach geometry. Shows that both groups of subjects had improvements in the number of problems solved, with those exposed to non-goal-specific procedures demonstrating greater rates of improvement and greater efficacy in…

Presents an activity using geoboards to recognize similar and different relationships of triangles. (ASK)

Recognizing geometric shapes and noting their special properties are important steps in learning geometry. Offers the use of geoboards and emphasizes that much of what teachers want students to learn about squares, rectangles, and trapezoids can be accomplished with geoboard figures. Presents activities on quadrilaterals using geoboards. (ASK)

Presents a framework for differentiating between five levels of extension of knowledge: basic features, forms, rules, application, and elaboration. Comparison of the extent of knowledge use exhibited by (n=14) Year-11 Australian students on a range of plane geometry problems found that high-achieving students exhibited greater extension of…

Documents students' use of Cabri-Geometry to work on tasks that led them to construct particular relationships and explore and connect different mathematical themes or ideas. (Author/MM)

Surveys recent literature on the use and value of the history of geometry in mathematics education. Makes the case that arguments can be divided into conceptual, (multi-) cultural and motivational ones. Details about content and purpose of the literature surveyed are presented in two appendices. (Author/MM)