Although recently revised in the sixth edition, this new version reorganizes the chapter around five critical themes of algebraic thinking: generalization from arithmetic and from patterns in all of mathematics, meaningful use of symbols, study of structure in the number system, study of patterns and functions, and the process of mathematical modeling, which integrates the first four. In addition, there is increased attention to developing meaningful contexts for algebraic thinking across grades Pre-K-8, including connections to other subject areas.
Teachers must understand both mathematics itself and how students learn mathematics in order to teach it effectively. Learning through problem solving is another major theme of this book. Students solve problems not just to apply mathematics, but also to learn new mathematics.
Effective problems will take into account where students are, the problematic or engaging aspect of the problem must be due to the mathematics that the students are to learn and not be diluted by non-mathematical activities such as cutting or pasting, and the problem must require justifications and explanations for answers and methods. Learning then becomes an outcome of the problem solving process. The book also addresses in more detail than any other book on the market the effect that the trends of standards-based education, increased pressure to test, and increased teacher accountability have had on teaching mathematics
