Double number lines, area models, and other diagrams power up students'ability to solve and make sense of various problems.
“A mile wide and an inch deep” is an oftenrepeated criticism of U.S. mathematics curriculum. In 2006, NCTM published Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence to suggest important areas of emphasis for instruction. Many states produced new standards that were informed by the book. However, Charles (2008/2009) argues that we must address not only the mile-wide issue, by reducing the number of skill-focused standards, but also the inch-deep issue, by making essential understanding more explicit. Charles suggests that many useful resources are available to deal with the latter.
The results from the Third International Mathematics and Science Study (TIMSS) have renewed American interest in Japanese mathematics education (U.S. Department of Education 1996, 1997, 1998). Although many people are impressed with the high level of achievement of Japanese mathematics students, mathematics educators, both in and outside Japan, also realize the shortcomings of the Japanese educational system. For example, Nagasaki (1998) points out that a gender gap exists in both mathematics achievement and attitudes toward mathematics. He also points out that many Japanese children do not see the relevance of mathematics to their daily lives.
Let's Eliminate Fractions from Primary Curricula!
As the statement above shows, Principles and Standards for School Mathematics (NCTM 2000) calls for focused and cohesive school mathematics curricula. To create such curricula, we must make hard decisions about what topics to include and what to remove from the curricula. What, then, are the “big ideas” in mathematics for primary grades? The current crowded state of primary curricula is the result of our inability to make hard decisions. It is about time that we tackle this difficult issue.
Fraction concepts continue to be one of the most challenging topics for elementary and middle school children (see, e.g., Kouba, Zawojewski, and Strutchens ). One important factor in teaching and learning fractions is the use of representations. This article addresses four issues surrounding this topic: (1) tools for representing fractions, (2) methods of representing fractions, (3) fraction notations, and (4) fraction language.
Young children are introduced to simple fractions, such as one-half, as early as kindergarten, even though a formal introduction of fractions in most curricula does not begin until third or fourth grade.
How Japanese curriculum treats fractions. Several questions are raised concerning the way fractions are typically taught in North America, and readers are able to reflect on their teaching style versus that of Japanese teachers
Amy F. Hillen and Tad Watanabe
Conjecturing is central to the work of reasoning and proving. This task gives fourth and fifth graders a chance to make conjectures and prove (or disprove) them.
Tad Watanabe, Robert Hanson, and Frank D. Nowosielski
A ninth-grade student was the featured speaker at a special mathematics colloquium at Towson State University's Mathematics Department and the Center for Mathematics and Science Education in May 1994. A colloquium in the mathematics department was nothing unusual, but the age of the speaker distinguished this one. In this article, we describe what made the colloquium so intriguing and the subsequent activities it generated.
Tad Watanabe and Dorothy White
Over the past three years, 2001–2004, we had the privilege of serving on the Editorial Panel of Teaching Children Mathematics. During this time, many readers have expressed a desire for more articles written by classroom teachers. As members of the TCM Editorial Panel, we have tried to encourage classroom teachers to submit manuscripts, but with little success. We realize that classroom teachers are extremely busy and have to juggle many different responsibilities; however, we would like to present five reasons why classroom teachers should consider writing articles for TCM (or other professional journals).