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Direct linkWhite, Jonathan J. – PRIMUS, 2017
A problem sequence is presented developing the basic properties of the set of natural numbers (including associativity and commutativity of addition and multiplication, among others) from the Peano axioms, with the last portion using von Neumann's construction to provide a model satisfying these axioms. This sequence is appropriate for…
Descriptors: Numbers, Sequential Learning, Active Learning, Inquiry
Blanton, Maria; Brizuela, Bárbara M.; Gardiner, Angela Murphy; Sawrey, Katie; Newman-Owens, Ashley – Journal for Research in Mathematics Education, 2015
The study of functions is a critical route into teaching and learning algebra in the elementary grades, yet important questions remain regarding the nature of young children's understanding of functions. This article reports an empirically developed learning trajectory in first-grade children's (6-year-olds') thinking about generalizing functional…
Descriptors: Young Children, Elementary School Students, Grade 1, Mathematics Instruction
