Everyday Mathematics

Abstract: Adding It Up explores how students in pre-K through 8th grade learn mathematics and recommends how teaching, curricula, and teacher education should change to improve mathematics learning during these critical years. The committee identifies five interdependent components of mathematical proficiency and describes how students develop this proficiency. With examples and illustrations, the book presents a portrait of mathematics learning: * Research findings on what children know about numbers by the time they arrive in pre-K and the implications for mathematics instruction. * Details on the processes by which students acquire mathematical proficiency with whole numbers, rational numbers, and integers, as well as beginning algebra, geometry, measurement, and probability and statistics. The committee discusses what is known from research about teaching for mathematics proficiency, focusing on the interactions between teachers and students around educational materials and how teachers develop proficiency in teaching mathematics.

Abstract: This article focuses on the subject matter knowledge of preservice elementary and secondary mathematics teachers. In order to examine what teacher candidates understand about mathematics as they enter formal teacher education, results from questionnaires and interviews with 252 prospective teachers participating in a large study of teacher education are discussed. The results reveal the mathematical understandings that these elementary and secondary teacher candidates brought with them to teacher education from their precollege and college mathematics experiences, understandings that tended to be rule-bound and thin. Based on these data, the article challenges 3 common assumptions about learning to teach elementary or secondary mathematics: (1) that traditional school mathematics content is not difficult, (2) that precollege education provides teachers with much of what they need to know about mathematics, and (3) that majoring in mathematics ensures subject matter knowledge. These assumptions underlie cu...