During our tutoring session, I attempted to ask her questions that guided her towards using skills she already had demonstrated in novel problems. She repeatedly asked me to just "tell her the answer" and said that she would understand. Additionally, she did not want to continue working on particular problems, saying she would "get it later." When pressed for an explanation of her work, she simply replied, "it doesn't matter." I am supremely worried for this girl since - to me and many math teachers - the content we teach is not as important as the justification of an answer or the explanation of a train of thought.
In theory, however, changes are afoot that will modify the classroom to ensure these requirements.
The Common Core that has been mostly adopted by 45 states across the US is supposed to foster those changes through its reinvented Standards for Mathematical Practice. While not the most succinct document, it explains how students need to be pushed to persevere in their struggles, learn the tools of the trade, find structures and patterns and use them effectively, and more. My fellow math teachers and I love doing this and - to be honest - probably would be doing so even without the new standards. The only way to ensure these ideas are followed is to put them into a solid curriculum that is very different from generations past.
If teachers, administrators, parents, and community members truly want to make the 21st century classroom model what the Standards preach, we need to be more focused on innovative techniques to engage students. Many teachers understand that their role is not that of a banker "depositing" information into the brains of their students. Instead, it is to help foster ideas and question their students in order to build skill in justification and reasoning. When I ask a student to explain their work and hear the response, "I can't explain it, but I know it," I want to scream and yell that without the evidence of an explanation, there is no true understanding.
Current math teachers across the country are locked in a battle whereby they are being required to innovate but are not sure how to do so nor are they being given the resources. Additionally, they are being pushed into an atmosphere of state testing that has aggravated parents and community members too, all while not truly understanding the goals of the Common Core.
If we really want our students to gain more math knowledge and be prepared to challenge others on a global scale we need to make sure we actively search programs and trainers to make sure our teachers understand what they should - and should not - be doing in their classrooms.