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Executive Summary
Pages 1-14

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From page 1...
... Adding It Up: Helping Children Learn Mathematics is about school mathematics from pre-kindergarten to eighth grade. It addresses the concerns expressed by many Americans, from prominent politicians to the people next door, that too few students in our elementary and middle schools are successfully acquiring the mathematical knowledge, the skill, and the confidence they need to use the mathematics they have learned.
From page 2...
... The usefulness of numerical ideas is enhanced when students encounter and use was a multiple representations for the same concept. Second, the numbers and operations of school mathematics are organized as number systems, such as the whole numbers, and the regularities of each system can help students learn with understanding.
From page 3...
... Because studies that touch on a key question and yield unequivocal findings are rare in educational research, we have sought to point out when we have used professional judgment and reasoned argument to make connections, note patterns, and fill in gaps. In the final chapter of the report, we have also called for additional research in areas where it could improve educational practice.
From page 4...
... Despite efforts over the last half-century to set higher learning goals for U.S. school mathematics and to provide new instructional materials and better assessments, most students in grades pre-K to 8 encounter a rather shallow curriculum.
From page 5...
... The Mathematical Knowledge Children Bring to Spoof Children begin learning mathematics well before they enter elementary school. Starting from infancy and continuing throughout the preschool period, they develop a base of skills, concepts, and misconceptions.
From page 6...
... Furthermore, not all children enter school with the informal understanding of number assumed by the elementary school curriculum. Developing Proficiency with Whole Numbers Whole numbers are the easiest numbers to understand and use.
From page 7...
... A variety of instructional approaches (using physical materials, special counting activities, and mental computation) are effective in helping students learn multidigit arithmetic by focusing on the base-ten structure and encouraging students to use algorithms that they understand.
From page 8...
... These new approaches offer considerable promise for avoiding the difficulties many students now experience. lust as the elementary and middle school mathematics curriculum should prepare students for the study of algebra, so it should also include attention to other domains of mathematics.
From page 9...
... The quality of instruction depends, for example, on whether teachers select cognitively demanding tasks, plan the lesson by elaborating the mathematics that the students are to learn through those tasks, and allocate sufficient time for the students to engage in and spend time on the tasks. Effective teachers have high expectations for their students, motivate them to value .
From page 10...
... Despite the common myth that teaching is little more than common sense or that some people are just born teachers, effective teaching practice can be learned. lust as mathematical proficiency itself involves interwoven strands, teaching for mathematical proficiency requires similarly interrelated components: conceptual understanding of the core knowledge of mathematics, students, and instructional practices needed for teaching; proceduralfluency in carrying out basic instructional routines; strategic competence in planning effective instruction and solving problems that arise while teaching; adaptive reasoning in justifying and explaining one's practices and in reflecting on those practices; and a productive disposition toward mathematics, teaching, learning, and the .
From page 11...
... These observations lead us to five principal recommendations regarding mathematical proficiency that reflect our vision for school mathematics. The full report augments these five with specific recommendations that detail policies and practices needed if all children are to become mathematically ~ .
From page 12...
... Unfortunately, just as students' opportunities to learn mathematics effectively have been insufficient, so have teachers' opportunities to learn more about mathematics, students' learning and thinking, and their teaching practice. Regular time needs to be provided for teachers to continue their professional development, conferring with one another about common problems and working together to develop their teaching proficiency.
From page 13...
... Materials for instruction need to develop the core content of school mathematics in depth and with continuity. In addition to helping students learn, these materials should also support teachers' understanding of mathematical concepts, of students' thinking, and of effective pedagogical techniques.
From page 14...
... Evidence from such research, together with information from evaluations of current and future programs of curriculum and professional development, will enable the United States to make the genuine, lasting improvements in school mathematics learning that have eluded it to date. Conclusion The goal of mathematical proficiency is an extremely ambitious one.


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