What’s the Difference in Reasoning Abstractly and Quantitatively?

I recently attended a fabulous professional development which discussed the Eight Mathematical Practices for Common Core Standards.  One of these practices is having students reason abstractly and quantitatively.  I have always required students to label the answers to their equations when supporting an open ended question, but I didn’t realize the depth of what I was requiring.  Consider this.  Which is more– 5 or 8?  We would all agree that 5<8.  This is an example of reasoning abstractly.  Now, consider this.  Which is more–5 quarters or 8 pennies?  We would all agree that 5 quarters > than 8 pennies.  This is an example of reasoning quantitatively.  When students answer a word problem by labeling each component of their equation, they are reasoning quantitatively.  When students merely solve a “naked numbers” problem without labeling the quantities with which they are reasoning , then they are reasoning abstractly.  When students are reasoning with specific quantities, then the foundation being built is stronger for them to then build abstractly.  Just think.  The math textbooks are backwards.  Quantitative reasoning problems follow abstract reasoning, however students understanding is built first with quantitative problems and should be followed with abstract understanding.