In the context of instruction, letting students construct their own knowledge at their own pace makes taxing demands on teachers' mastery of the subject matter. The most successful teachers have a commitment to making connections , both between different mathematical ideas and children's current state of understanding. However, making connections on individual levels of understanding calls for flexibility of content knowledge that comes with a reasonable proficiency in the subject matter. The latter is usually not assumed of elementary school teachers who instruct in several subjects. Lastly, education is a multistage process.
Every stage assumes a certain degree of knowledge presumably acquired in previous stages.
A well defined curriculum plays the role of a goal setter for admission to and successful performance in the next stage. Unless the whole system undergoes a fundamental overhaul, we may expect that teachers will be more comfortable with curriculum as a framework for specific content and target skills than as a set of open-ended activities. Noted Niss, One observation that a mathematics educator can hardly avoid to make is the widening gap between researchers and practitioners in mathematical education. The very existence of a gap is neither surprising nor worrying. The course for concern is that it is widening.