Today we find common agreement that effective mathematics instruction in the elementary grades incorporates liberal use of concrete materials. Articles in the Arithmetic Teacher no longer exhort us to use concrete materials, nor does the Professional Standards for Teaching Mathematics (NCTM 1991) include a standard on the use of concrete materials. The use of concrete materials seems to be assumed unquestioningly.

The mathematics curriculum in Norfolk Public School is arranged in a spiral, with concepts from twelve basic strands continually reviewed and developed. An emphasis is placed on connecting new ideas with previously studied concepts and on using models and manipulatives to understand the underlying operations.

In the old days, the Richest Man in the World was, of course, the Fattest Man in the World. He lived in the Biggest House in the World, all alone except for 100 cooks and 3 vice presidents. Four weeks before his fortieth birthday he instructs these cooks and vice presidents to bake him the Biggest Birthday Cake in the World.

The National Council of Teachers of Mathematics's Curriculum and Evaluation Standards for School Mathematics (1989) reflects the importance of understanding the development of knowledge at the K-4 level. The standards document recognizes that current instructional and curricular content must focus on students' active construction of mathematical knowledge. Instructional practices need to be conceptually oriented, involve children actively, emphasize the development of mathematical thinking and application, and include a broad range of content.

Three years ago, the mathematics teachers from grades 4-12 in our school met for two weeks during the summer for an in-service program related to assessment and decided to begin using portfolios with our students in the fall. I was enthusiastic, although I had no idea at that time how drastically my approach to assessment—and to teaching in general—would change a a result of the portfolio decision.

In Everybody Counts, a document from the National Research Council (1989), we are told that the major objective of elementary school mathematics should be to develop number sense. This strong statement, if taken seriously, can change the way many—but not all—teachers teach mathematics in elementary school.

Too often when teachers plan for instruction, such mathematical skills as two-digit subtraction, multiplication facts, and equivalent fractions take precedence over thinking-and-reasoning strategies. Planning for instruction that promotes the development of children's thinking and reasoning about mathematics not only helps them make sense of the content they are studying but also helps them learn ways of thinking that later will enable them to make sense of new content.