Most any students can explain the meaning of "a[superscript b]", for "a" [element-of] [set of real numbers] and for "b" [element-of] [set of integers]. And some students may be able to explain the meaning of "(a + bi)[superscript c]," for "a, b" [element-of] [set of real numbers] and for…

Thomas Kuhn (1962/2012) introduced the term "paradigm shift" to the scientific literature to describe how knowledge in science develops. The aims of this article are to identify paradigm shifts, or revolutions, that have occurred in mathematics, and to discuss their relevance to teaching mathematics in schools. The authors argue that…

To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for advanced math. But students who take Algebra I in grade 8 and skip other math courses, such as grade 8 general math, might miss opportunities to develop the foundational…

To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for advanced math. But students who take Algebra I in grade 8 and skip other math courses, such as grade 8 general math, might miss opportunities to develop the foundational…

These are the appendixes for the report, "What Grade 7 Foundational Knowledge and Skills Are Associated with Missouri Students' Algebra I Achievement in Grade 8?" To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for…

To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for advanced math. But students who take Algebra I in grade 8 and skip other math courses, such as grade 8 general math, might miss opportunities to develop the foundational…

Two-Way Immersion (TWI) programs have demonstrated positive outcomes in students' academic achievement in English, yet less is known about content teaching and learning in the non-English language in these programs. This study uses math instruction as a lens to identify pedagogical strategies and challenges in the teaching of math in Korean to…

In the September 2010 issue of "Mathematics Teaching," Tom O'Brien offered practical advice about how to teach addition, subtraction, multiplication, and division and contrasted his point of view with that of H.H. Wu. In this article, the author revisits Tom's examples, drawing on his methodology while, hopefully, simplifying it and giving it…

This new addition to Math Solutions "Supporting English Language Learners in Math Class series" offers a wealth of lessons and strategies for modifying grades 6-8 instruction. Section I presents an overview of teaching math to English learners: the research, the challenges, the linguistic demands of a math lesson, and specific strategies and…

The paper details a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts to force limit discussion into the language of individual real numbers and equality. The system of near-numbers…

Presents an activity using fractal cards--eye-catching pop-up cards--by applying simple iterative processes to single sheets of paper. This activity incorporates the concepts of measurement, number systems, sequences, series, limits, recursion, iteration, self-similarity, and fractional dimensions. Contains 12 references. (ASK)

This is part two of a two-part SMSG mathematics text for junior high school students. Key ideas emphasized are structure of arithmetic from an algebraic viewpoint, the real number system as a progressing development, and metric and non-metric relations in geometry. Chapter topics include real numbers, similar triangles, variation, polyhedrons,…

This book is written to answer commonly asked homework questions of fourth, fifth, and sixth graders. Included are facts, charts, definitions, explanations, examples, and illustrations. Topics include ancient number systems; decimal system; math symbols; addition; subtraction; multiplication; division; fractions; estimation; averages; properties;…

The introductory level curriculum guide for bilingual education for Serbocroatian-speaking children in the Chicago public schools is divided into three difficulty levels and is designed to facilitate acquisition of mathematical concepts by presenting them in the children's native language. At each level, the concepts covered include the meaning of…

The introductory level curriculum guide for bilingual education for Spanish-speaking children in the Chicago public schools is divided into four difficulty levels and is designed to facilitate acquisition of mathematical concepts by presenting them in the children's native language. At each level, the concepts covered include the meaning of…