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The article examines some views of algebraic reasoning, discusses a controversy on patterns, and describes the use of three types of patterns in the development of teachers' algebraic reasoning. It references the book "Principles and Standards for School Mathematics," which focuses on four major themes of algebraic reasoning for grades Pre-K-12. It suggests teachers to develop their own algebraic reasoning and understanding of the role of patterns.

The article presents a reprint of the article "Algebra in the Elementary Schools," by James H. Shipley, which originally appeared in the June 1912 issue of "Mathematics Teacher." The article expresses the author's dissatisfaction with students' knowledge of fractions. He provides his suggestions on what should be included in elementary school curriculum, including mechanical drawing and algebra. He believes that introducing algebra in elementary school will make the subject more easy to understand.

The article offers reflections on the teaching of algebra in elementary schools in reference to the article "Algebra in the Elementary Schools," by James H. Shipley in 1912. Shipley proposed an algebraic approach to teaching arithmetic. The author of this article addresses issues related to mathematics curriculum, mathematics testing, misconceptions of students' capabilities, and the purpose of mathematics study. The author remarks that the goal of teachers today is to educate everyone and believes that the education system of the United States is resistant to change.