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Adding + It Up: Helping Children Learn Mathematics
Students are less fluent in operating with rational numbers, both common and decimal fractions. The most recent NAEP in 1996 contained few computation items, but earlier assessments showed that about 50% of 13-year-olds correctly completed problems like and 4.3–0.53. Again, this level of performance has remained quite steady since the advent of NAEP. One conclusion that can be drawn is that by age 13 many students have not fully developed procedural fluency. Although most can compute well with whole numbers in simple contexts, many still have difficulties computing with rational numbers.
Results from NAEP dating back over 25 years have continually documented the fact that one of the greatest deficits in U.S. students’ learning of mathematics is in their ability to solve problems. In the 1996 NAEP, students in the fourth, eighth, and twelfth grades did well on questions about basic whole number operations and concepts in numerical and simple applied contexts. However, students, especially those in the fourth and eighth grades, had difficulty with more complex problem-solving situations. For example, asked to add or subtract two- and three-digit numbers, 73% of fourth graders and 86% of eighth graders gave correct answers. But on a multistep addition and subtraction word problem involving similar numbers, only 33% of fourth graders gave a correct answer (although 76% of eighth graders did). On the 23 problem-solving tasks given as part of the 1996 NAEP in which students had to construct an extended response, the incidence of satisfactory or better responses was less than 10% on about half of the tasks. The incidence of satisfactory responses was greater than 25% on only two tasks.61
Performance on word problems declines dramatically when additional features are included, such as more than one step or extraneous information. Small changes in problem wording, context, or presentation can yield dramatic changes in students’ success,62 perhaps indicating how fragile students’ problem-solving abilities typically are.
Several kinds of items measure students’ proficiency in adaptive reasoning, though often in conjunction with other strands. One kind of item asks students to reason about numbers and their properties and also assesses their conceptual understanding. For example,