Describes how constructing concept maps and writing accompanying interpretive essays can be used in a Calculus I course to improve students' understanding of important concepts and help teachers assess students' knowledge. This combined approach allows students to explicitly communicate their knowledge and a chance to view mathematics as a…

Presents a mathematics activity that introduces proof by contradiction in a nonformal setting. This activity has the added benefit of helping students gain a greater understanding of the electoral college. (ASK)

Argues that teachers need help developing the knowledge and habits of mind to construct practices that embody the integration of assessment with instruction. Describes a study in which teachers try to link assessment with instruction through cases. (ASK)

Presents activities on writing and learning about cuneiform numerals and some mathematical and numerical topics in the context of Mesopotamian culture. Includes resources for further reading. (ASK)

States that thinking about numerical procedures starts in the elementary grades and continues in successive grades until students can eventually express and reflect on the procedures using algebraic symbolism. Outlines how such thinking can progress to algebraic reasoning. Illustrates how computers can be used to promote this progression through…

Contributes to the emerging picture of children's development of understanding in geometry and the kinds of teaching that can support it. Describes how teachers can use episode writing to capture student thinking and make instructional decisions. (ASK)

Describes an open-ended activity in which students try to determine the factors that contribute to an unusual chemical reaction. Uses a case study approach to show students how the presence of chlorine in tap water can interfere with a pH indicator. Includes assessment guidelines and extension activities. (WRM)

Presents examples of students' work when they are engaged in problem solving and reasoning tasks as they determine how to fill bottles with water to create musical notes by blowing across the tops of the bottles, and as they create mathematical models that represent these notes. (ASK)

Describes vortex tessellation in which an individual tile becomes smaller, and swirls or spirals inward to the center. Provides mathematical uses of this type of tessellation. (ASK)

Features activities for advanced second-year algebra students in grades 11 and 12. Introduces three random variables and considers an empirical and theoretical probability for each. Uses coins, regular dice, decahedral dice, and calculators. (ASK)

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

Describes possible uses of spirographs in mathematics classrooms to study parametric equations and symmetry. (ASK)

Suggests that assessing problem-solving activities is more complex than assessing other activities. Addresses one method of assessment for a particular mathematical problem-solving activity that is an analytic scoring rubric. (ASK)

Presents a set of tasks using a child's invented strategy and a nonstandard algorithm to illustrate one way to facilitate the development of mathematical and pedagogical dispositions. (ASK)

Describes young students' development of mathematical understanding as they dramatize, read, write, and draw about mathematics after reading the story "Benny's Pennies." (ASK)