Learning Progressions
How do children progress in their learning of math? My colleagues and I developed the following concept maps to explain what it looks like as kids learn words and how to represent things, justify things, and solve problems. We consulted two textbooks by John Van de Walle: Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades K-2 (Volume I) (2nd Edition) and Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II) (2nd Edition).
Word Knowledge
Word knowledge is recognizing a word, understanding what the word means in context, and being able to use the words in speech or writing. Here is the sequence of levels of understanding and skill: