When students catch their own mistake and seek to understand what misunderstanding led to the error, they are much less likely to make the mistake again. If the teacher works hard to point out every logical flaw, the students will continue to sit back and relax and let us do the hard work. Checking is part of that internal dialogue that students must make part of their mathematical being. Back to Affect As mathematical coach, the teacher has countless difficult decisions to make. Knowing how and when to help our students get stuck and unstuck requires many understandings, most important of which is a knowledge of each student and where they are in their development as a mathematician.
Confidence is essential if students are to respond productively to being stuck.
They need to be able to bring us their anxieties, questions, and ramblings. In response, we have to be cheerleaders, good listeners who can pose good questions, and mentors who can offer opinions about fruitful directions to follow. Throughout the research process, we must be completely open about what each stage should provide for our students. What is appropriate at one point in the process may still not be effective if a student does not understand how they are to respond to new information. One student confessed to a teacher, at the end of months of meetings, that she dreaded the meetings because she knew she would be asked questions that she could not answer.