One of the reasons why we teach is because we want our students to experience the JOY of mathematics. Mathematics should be about questioning, wondering, and the joy of discovery…and math classes should leave students wanting to know more math and do more math thinking. We cannot build an appreciation of math through content standards alone. Math classes should be filled with opportunities for students to have voice and a choice. At the very least, they need a voice in making meaning of problems and a choice in how they go about seeking a pathway to a solution.
But sometimes we (or our textbooks) squash all the joy out of a math lesson. We rob them of their right to notice math things, wonder about math ideas, or do messy math stuff. And lessons that focus on “measurable outcomes” with “explicitly defined objectives” often euthanize mathematical curiosity.