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  • Author or Editor: Lyn D. English x
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Lyn D. English

Three core components in developing children's understanding and appreciation of data—establish a context, pose and answer statistical questions, represent and interpret data—lay the foundation for the fourth component: use data to enhance existing context.

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Lyn D. English

The study investigated the strategies that 7-to 12-year-old children spontaneously apply to the solution of novel combinatorial problems. The children were individually administered a set of six problems involving the dressing of toy bears in all possible combinations of tops and pants (two-dimensional) or tops, pants, and tennis rackets (three-dimensional). Two sets of solution procedures were identified, each comprising a series of five increasingly complex strategies ranging from trial-and-error approaches to sophisticated odometer procedures. Results suggested that experience with the two-dimensional problems enabled children to adopt and subsequently transform their efficient 2-D odometer strategy (where one item is held constant) into the most sophisticated 3-D odometer strategy, which involved working simultaneously with two constant items. The study highlights the importance of discrete mathematics as a source of problem-solving activities in which children are motivated to create, modify, and extend their own theories.

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Lyn D. English

This study investigated the problem-posing abilities of third-grade children who displayed different profiles of achievement in number sense and novel problem solving. The study addressed (a) whether children recognize formal symbolism as representing a range of problem situations, (b) whether children generate a broader range of problem types for informal number situations, (c) how children from different achievement profiles respond to problem-posing activities in formal and informal contexts, and (d) whether children's participation in a problem-posing program leads to greater diversity in problems posed. Among the findings were children's difficulties in posing a range of problems in formal contexts, in contrast to informal contexts. Children from different achievement profiles displayed different response patterns, reflected in the balance of structural and operational complexity shown in their problems.

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Lyn D. English

Our children live in a highly sophisticated world composed of interlocking complex systems. An appreciation and understanding of such systems is critical for making effective decisions about our lives as individuals and as community members. The activities presented in this article provide rich opportunities for children to experience an introduction to complex systems during which they think mathematically about relevant relationships, patterns, and regularities in dealing with authentic problems (English 2006; Lesh and Doerr 2003).

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Lyn D. English

Children have traditionally solved our problems—problems that we think will be of interest and relevance to them. We need to shift some of this responsibility to students and let them pose problems that they consider to be worthwhile pursuing.

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Lyn D. English

Help first-grade students learn to competently generate, test, revise, and represent data before being formally taught to do so.

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Lyn D. English and Nicholas G. Mousoulides

A sixth-grade engineering-based modeling activity asks students to select the best possible design for a reconstructed bridge.

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Lyn D. English and Donna T. King

Contributors to the iSTEM (Integrating Science, Technology, Engineering, and Mathematics) department share ideas and activities that stimulate student interest in the integrated fields of science, technology, engineering, and mathematics (STEM) in K–grade 6 classrooms. This article is a comprehensive Earthquake Engineering activity that includes the Designing an earthquake-resistant building problem. The task was implemented in sixth-grade classes (10–11-year-olds). Students applied engineering design processes and their understanding of cross-bracing, tapered geometry, and base isolation to create numerous structures, which they tested on a “shaker table.”

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Bharath Sriraman and Lyn D. English

For many students, combinatorics is associated with negative experiences calculating permutations and combinations, often confusing one with the other. What exactly is combinatorics? Combinatorics can be defined as the art of counting, or more specifically, as “an area of mathematics in which we study families of sets (usually finite) with certain characteristic arrangements of their elements or subsets, and ask what combinations are possible and how many there are” (Rusin 2002).

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Lyn D. English and Anthony Standen