Irrational Numbers, Square Roots, and Quadratic Equations

To improve mathematics achievement of U.S. students and to assure that "what and how students are taught should reflect not only the topics within a certain academic discipline, but also the key ideas that determine how knowledge is organized and generated within that discipline" are dual...

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Bibliographic Details
Published inMathematics teaching in the middle school Vol. 20; no. 8; pp. 467 - 474
Main Author Popovic, Gorjana
Format Journal Article
LanguageEnglish
Published National Council of Teachers of Mathematics 01.04.2015
Subjects
Academic Standards
Equations (Mathematics)
Mathematical Concepts
Mathematics Achievement
Mathematics Instruction
Mathematics Teachers
Middle School Teachers
Middle Schools
Numbers
Secondary School Mathematics
State Standards
Teaching Methods
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Summary:To improve mathematics achievement of U.S. students and to assure that "what and how students are taught should reflect not only the topics within a certain academic discipline, but also the key ideas that determine how knowledge is organized and generated within that discipline" are dual goals of the Common Core State Standards for Mathematics (CCSSI). CCSSI defines what students should understand and be able to do in their study of mathematics, but they "do not dictate the curriculum or teaching methods." Therefore, individual State Boards of Education have created curriculum scope and sequence documents aligned with the standards to serve as resources for teachers. The purpose of this article is to respond to questions raised by middle school mathematics teachers about irrational numbers and square roots and about solving quadratic equations. The hope is that the discussion not only provides a meaningful explanation of each individual concept but also connects the concepts and explores a possible way to elicit classroom discussions that emphasize making conjectures, constructing viable arguments, and critiquing the reasoning of others. A bibliography is included.
ISSN:1072-0839