A presentation on the Budapest Seminars in Mathematics Education website, inspired the author to try a new approach while teaching a unit on quadrilaterals in his Geometry for K-8 Teachers course, a class primarily composed of undergraduate students interested in teaching at the elementary or middle school level. The author designed a lesson that…

How students interpret problems influences how they solve them. Lists lessons learned at the end such as how fair assessment of mathematics set in contexts requires having students explain their reasoning or assumptions, and is done most effectively and accurately over time. (ASK)

Shares two lessons in which students help teachers pose problems and discover the importance of posing problems properly. Presents a fifth-grade lesson in which students found a mistake in a proportion problem, and an eighth-grade lesson that discusses a geometry problem with insufficient information. (ASK)

Describes students' enthusiasm for Tuesdays in an American community school in Greece when they get together in small groups to explore, conjecture, analyze, and solve mathematics problems. (ASK)

Presents the discussion of three teachers who were searching for understanding of problem-centered instruction in mathematics education. Aims to help readers reflect on how they see problem solving in their own classrooms and to reconsider ways in which they use problems in instruction. (ASK)

Presents two problems with multiple approaches concerning the one hundredth of something. Describes student attempts at solving these nonroutine problems using a variety of strategies. (ASK)

Illustrates a modeling approach used by Singapore educators to teach mathematical skills and concepts in a problem-solving environment. (Contains 11 references.) (YDS)

Describes the use of the measures of fluency, flexibility, and originality to assess students' responses to open-ended problems in mathematics classrooms. Contains 12 references. (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 problem that requires solving a card problem by exploring patterns that will lead to a logical solution. Involves students in developing and analyzing their own algorithms as well as discussing their reasoning with peers. (ASK)

In today's society, changes in technology have made estimation skills more important than ever in the development of mathematical power. Presents a schoolwide activity in which students participate in a mathematical contest on estimation. Concludes that, in devising their estimates, students have practiced their problem-solving and sense-making…

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)

Describes a mathematics fair prepared by the University of Missouri Mathematics Teachers Organization (UM2TO) which includes games involving numbers and computation, logic puzzles, geometry and spatial-visualization exploration, and probability and statistics activities. Presents tips for developing a mathematics fair. (ASK)

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)