The ability of students to sort cards based on surface features and deep patterns is investigated. The effect of the presence of variables and what makes a pattern difficult or easy for students to recognize are discussed. Study revealed that students are unsuccessful at making connections between expressions, sentences, and sequences which share…

Stresses recognition and application of the identity property of 1 across the mathematics curriculum to help students overcome difficulties. (MKR)

EQUALS is a teacher education program that helps elementary and secondary educators acquire methods and materials to attract minority and female students to mathematics. It supports a problem-solving approach to mathematics which has students working in groups, uses active assessment methods, and incorporates a broad mathematics curriculum…

Middle-school students were asked to determine the dimensions of a hotel atrium so that guests could enjoy the maximum area of scenic view, given that 650 feet of brass railing could be used around each floor. Several solution approaches are described. (MKR)

Assessment of general reasoning processes, elementary algebraic understanding, and novel problem solving of (n=147) seventh- and eighth-grade students found that abilities to generalize from patterns and tables of data and understanding variable constructs contributed significantly to application of algebraic concepts and processes. Questions…

Lists questions and answers for mathematical investigations that teachers should ask when they consider using alternative approaches to teach new content. Presents an example of a mathematical investigation on concepts of area, symmetry, pattern, function, algebraic rules, and Pythagorean theorem. Argues that investigations offer opportunities for…

Describes how graphing calculators can be used to explore different functions, from linear to higher degree polynomials. "Globs" (circles) are drawn around randomly plotted points on the screen, and students devise functions that pass through as many of these globs as possible. Variations on the game are also mentioned. (DPM)

This review of the introductory instructional substance of functions and graphs analyzes research on the interpretation and construction tasks associated with functions and some of their representations (algebraic, tabular, and graphical). The nature of learning is analyzed in terms of intuitions and misconceptions. (TJH)

This study explores seventh- and eighth-grade students' thinking about mathematical patterns. Interviews were conducted in which students solved problems about sequential perimeter and area problems modeled with pattern blocks and tiles, generalized the relationships related to the patterns and represented the relationships symbolically,…

Presents an extended activity consisting of a sequence of tasks organized so that students can visit several mathematical concepts concurrently and explore connections among them. Students build solids using bendable straws to form the skeletons of various polyhedra. Topics covered include tables and charts, algebraic expressions, surface area,…

Describes a project in which students, in groups, wrote a chapter on factoring polynomials. Gives general format of the activity and excerpts from student writings. (10 references) (MKR)

Describes the underlying philosophical and cultural changes associated with classroom organizational changes in one eighth-grade teacher's attempts to implement National Council of Teachers of Mathematics standards. Observations and interviews indicated that there were two distinct cultures ("book world" and organic or…

Presents an activity through which students develop mathematical concepts connected to area and perimeter in a rich, real-life setting and use tables, graphs, diagrams, and spreadsheets to explore the problem, see relationships, and make and test conjectures about those relationships. Encourages algebraic thinking. (SYB)

One of five articles in the second section, "Deepening Relationships through PDS Brings Change in Practice," this article describes a collaborative research project between a middle school mathematics teacher and a university mathematics professor. (SM)

The focus of this paper is to further understanding of the distribution and the effects of an expanded conception of opportunity to learn on student mathematics achievement. In addition to descriptive statistics, a set of two-level hierarchical linear models was employed to analyze a subset of the restricted-use National Education Longitudinal…