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Patricia F. Campbell

Problem solving is a topic of current interest for mathematics teachers and researchers (National Council ofTeachers of Mathematics, 1980, 1981). One focus of this concern has been to study the thinking processes children use when solving mathematical problems. A common methodology is to interview children, asking them to “think aloud” as they solve a problem. The interview is tape-recorded to produce a protocol for identifying and making inferences about the child's problem-solving processes. Some researchers use the tape recording as the data source; others use a transcript of the recording.

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Patricia F. Campbell

One method that primary mathematics textbooks currently use to communicate mathematical concepts to children is dynamic drawings in conjunction with written numeral statements. These dynamic illustrations may be either single pictures or sequences of pictures with motion portrayed by use of postural cues (e.g., picturing legs of the characters in a state of nonequilibrium) or conventional cues (e.g., using lines, vibration marks, or clouds of dust about the characters). In a previous study, Campbell (1978) noted that initially viewing and interpreting sequences provided first-grade students with a learning experience that significantly affected their interpretation of single pictures; however, the overall analysis concerning the effect of the number of pictures yielded differing results.

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Patricia F. Campbell

Picture a school-board meeting or a meeting of a school district's elementary curriculum committee. Raise the issue of integrating microcomputers into the elementary school's mathematics curriculum, and a debate will ensue. Focus the discussion on the use of microcomputers in the primary classroom, and the remarks will become intense and passionate. Although the diversity of comments prompted by such a discussion cannot be anticipated, two views will probably be voiced. Seeking the promise of a supposed competitive edge, one faction will favor microcomputer use while questioning whether the calculator threatens children's learning of the basics, that is, arithmetic. Citing the added danger of producing socially isolated children who are obsessed with the lure of microcomputers, another group will reject any form of technology in the primary classroom.

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Patricia F. Campbell

In communicating with words it is obvious that if the receiver does not know the language he will not be able to decode the message. It is obvious that reading is a skill which must be learned. It is not obvious—indeed it is sometimes completely unnoticed—that a parallel condition exists in the case of pictures. Children must learn bow to “read” pictures.

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Patricia F. Campbell

Young children's pre chool years are filled with three-dimensional objects as the children come to understand spatial and topological idea. These idea, such a nearness order or enclosure are based on the child's experiences and sensory impressions of shape and solids. However. too often early school experience with geometric concepts are limited to plane figure. This is because solid are difficult to represent on paper or the blackboard and young children have difficulty constructing model of three-dimensional figure with cardboard and paste. The “cut and paste” method of constructsion also produces permanent figures that are difficult to store.

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Patricia F. Campbell

According to the National Council of Teachers of Mathematics (1980), the focus of school mathematics in the 1980s must be on problem solving. Furthermore, computation is to be a tool for problem solving. The importance of problem solving as a goal in mathematics education cannot be disputed; however, the de-emphasis of computation may cause fee lings of uneasiness for many primary-level teachers. These feeling can be accentuated by such statements as “Primary-level curricula contain practically no mathematical problem-olving experiences” (Greenes 1981). Where does this dilemma leave the typical primary-level teacher, given the existing primary mathematics curriculum and the demands from pa rents and school administrators that young children develop a mastery of addition and subtraction?

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Patricia F. Campbell

An examination of current primary mathematics textbooks reveals that one method of communicating mathematical concepts to children is with dynamic pictures used in conjunction with written numeral statements. These pictures portray motion and are meant to serve as a reference either to assist the students in solving a related problem or to define a context within which the problem may be interpreted. However, it is necessary for the children to relate or assimilate the characters depicted in these pictures and to perceive the action portrayed before they can associate these pictures with the addition or subtraction of whole numbers.

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Patricia F. Campbell

Over the last fifteen years, much research has investigated children's learning of mathematics. This research indicates that when permitted, children frequently devise approaches to solve problems that are distinct from those typically used by adults.

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Patricia F. Campbell and Cynthia Langrall

The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) speaks of the necessity of providing effective mathematics education for all students. Noting that “the social injustices of past schooling practices can no longer be tolerated” (p. 4), the standards document calls for a mathematics content that is “what we believe all students will need if they are to be productive citizens in the twenty-first century. If all students do not have the opportunity to learn this mathematics, we face the danger of creating an intellectual elite and polarized society” (p. 9), Similarly, the National Research Council's Mathematical Sciences Education Board noted that two themes underlie current analysis of American education: “equity in opportunity and… excellence in results” (1989. 28–29). Although the NCTM's standards and other reform documents have been critiqued as addressing the issue of equity in terms of “enlightened self-interest” as opposed to seeking justice (Secada 1989), these documents have called attention to educational disparity. The issue today is how to make the goal of equity a reality in classrooms. To do otherwise would be to assign “mathematics for all” to the status of a slogan, a catchy phrase but having no meaning in practice.

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Patricia F. Campbell and Nathaniel N. Malkus

A three-year study found that those responsible for coaching math teachers positively affected student academic progress in grades 3, 4, and 5. Read why this effect took time to emerge.