Thinking Mathematically: A Critical Approach to Mathematical Pedagogy

Thinking Mathematically: A Critical Approach to Mathematical Pedagogy

Thinking mathematically illustrates how the elements, standards, traits and abilities of critical thinking guide a better teaching method for mathematics. Applying the elements of critical thinking shows that we are not now providing students with real abilities in mathematics. Linking mathematics to language makes learning mathematics more natural. The concept of zero, rules and operations, cardinal and ordinal use of numbers are discussed. Examples are taken from history and special numbers: perfect, amicable and sociable numbers. The Roman numbering system shows operations without a symbol for zero; the eleven axioms grounding our mathematics system show how operations arise from rules, and numerical concepts arising from generalized operations. A puzzle analysis shows how operations can be used to obscure the rules.