Counting by 10s: Memorizing vs. Understanding

I have been thinking a great deal about the importance of gaining a true understanding of math concepts as opposed to the "old school" way of having students memorize facts and formulas.  While I believe there is a place for memorization (memorizing times tables, for example), I thought I had come to a comfortable place in terms of believing that conceptual understanding must come first.  Students should not be allowed to simply memorize something that they have no understanding of.

Then, I was confronted by my own daughter's understanding (or lack thereof) of counting by 10s.  Emma is in the first grade.  In Kindergarten they begin to learn to count by 5s and 10s.  Emma can dutifully count in these ways.  The other night I was helping her with her math homework.  Part of the assignment was a series of problems such as: 24 + 10 = , 28 + 10 = etc.  For the assignment, they were allowed to use their number lines.  After the fourth problem, I asked her whether she saw a pattern.  At first, she was unable to see it.  I asked her about counting by 10s.  She dutifully counted by 10s.  I asked her what she was doing when she was counting that way.  She had no idea.  I went back and we began adding together.  We struggled together for awhile.  I realized she had memorized this pattern without gaining an understanding of it.  At the same time, her homework seemed to suggest that they did not expect students to fully understand this concept.  I went in and talked to my Mentor Teacher who happens to teach the first grade -- very convenient!  She said that I should not be worried that she does not yet fully "see" all of the patterns.  Most first graders don't.

So I now wonder whether there isn't a different place for memorization than I was originally thinking about.  Perhaps memorization, rather than being the antithesis or bad cousin to understanding, is actually part of learning a concept.  Memorizing a pattern such as counting by 10s does not mean a student understands how the pattern works but it is an important piece of being exposed to a concept and, over time, as students are exposed to more math, they will begin to understand and see the pattern more conceptually.  This also fits in with the concept of spiraling curriculum in which it is not expected that students understand everything about a concept they are exposed to.  They will be exposed to it again (and again) over time and each time gain a slightly better idea of it.  So this makes sense in some ways but I wonder if it is true or whether I am just trying to comfort myself with the knowledge that Emma will eventually come to understand what she has now only memorized.