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Julie Sarama and Douglas H. Clements

Zachary's grandmother was walking him out of preschool. He looked at the tiled walk-way and yelled, “Look, Grandma! Hexagons! Hexagons all over the walk. You can put them together with no spaces!”

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Douglas H. Clements and Julie Sarama

This is the second in a series of articles exploring the use of the National Council of Teachers of Mathematics' (NCTM's) 2006 publication, Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence. The series introduction by NCTM President Skip Fennell, explaining what Curriculum Focal Points are and why NCTM developed them, appeared in the December 2007/January 2008 issue of Teaching Children Mathematics (page 315). In this and subsequent TCM articles, the authors of the various grade bands discuss the Focal Points for one or two grade levels. Because one principle of Curriculum Focal Points is that of cohesive curriculum, in which ideas develop across the grades, we encourage teachers of all grade levels to read the full series.

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Julie Sarama and Douglas H. Clements

This is the third in a series of articles exploring the use of the 2006 National Council of Teachers of Mathematics (NCTM) publication, Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence. The series introduction from NCTM President Skip Fennell, explaining what the Curriculum Focal Points are and why NCTM developed them, appeared in the December 2007/January 2008 issue of Teaching Children Mathematics (page 315). In subsequent TCM articles, the authors of the various grade bands discuss focal points for one or two grade levels. Because one principle of Curriculum Focal Points is that of cohesive curriculum, in which ideas develop across the grades, we encourage teachers of all grade levels to read the full series.

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Edited by Douglas H. Clements and Julie Sarama

If you ask, teachers will tell you about the advantages that they find in using computers. For example, writers have reported that fourand five-year-olds from an urban, economically disadvantaged population began making new friends as they asked others to join them in working at the computer. For the first time, they sought help from one another (Bowman 1985). An egocentric child learned cooperation and problem solving. Children's cooperative play paralleled the proportion of cooperative play in the block center and provided a context for initiating and sustaining interaction that could be transferred to play in other areas as well, especially for boys (Anderson 2000). Are these examples unique, or are such advantages widespread? We know that computers are increasingly a part of preschoolers' lives. From 80 percent to 90 percent of early childhood educators attending the annual conference of the National Association for the Education of Young Children report using computers (Haugland 1997). Such use is no surprise— research on young children and technology indicates that we no longer need to ask whether the use of technology is “developmentally appropriate” (Clements and Nastasi 1993).

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Douglas H. Clements and Julie Sarama

When we talk about our prekindergarten curriculum development project,

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Barbara Wilmot

Edited by Douglas H. Clements

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Douglas H. Clements and Julie Soromo

Try this problem: Write an equation using the variables S and P to represent this statement: “There are six times as many students as pro-lessors at this university.” Use S for the number of students and P for the number of professors.

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Michael Battista and Douglas H. Clements

Elementary school students have considerable difficulty determining the number of cubes that are contained in three-dimensional rectangular buildings like the one shown in figure 1 (Battista and Clements 1996). The reasoning required to complete such tasks is important because it builds the cognitive frame-work for understanding the measurement of volume and the formulas for determining volume. This article describes typical student strategies for enumerating cubes in cube buildings and illustrates why these problems are so difficult for students. It also describes instructional tasks that can help students develop more powerful ways of thinking about such problems.

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Julie Sarama and Douglas H. Clements

Computers help students develop algebraic thinking. Why? They can act as dynamic “function machines,” allowing students to explore variables and relationships among variables. They “run” and reveal patterns, helping students see relationships as they emerge. They serve as a bridge between concrete examples and algebraic representations.

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Douglas H. Clements and Julie Sarama

If used properly, manipulatives can support the learning of mathematics and motivate students. The intelligent use of manipulatives takes advantage of their features, especially the extra features of computer manipulatives (Clements and McMillen 1996). The use of manipulatives must be integrated into a sound mathematical lesson. In this article, we present one example of an activity that capitalizes on the particular advantages of physical and computer pattern blocks.