These days it seems like everyone’s getting excited about project-based learning, to reduce the anxiety for students who hate exams and essays. Few people talk about the dark side of project-based learning, though, so here are several things to consider before you integrate it into your classroom.
First, there is the matter of projects requiring a significant amount of time to complete. Even small projects, when they involve groups, often result in much of the time being spent creating an effective work dynamic, which, while a useful skill, steals from the already limited amount of time teachers have to teach all the math required by the curriculum. In order for the project to be worthwhile, students need to be able to learn efficiently, and projects may or may not be the most efficient means of learning for all students.
Surprisingly, many students who are linear thinkers tend to prefer exams and assignments to projects, so that they are able to define precisely which topics to study, and they know immediately whether they understand or not. Projects can cause some anxiety to them if they have less control over their final grade. Also on the topic of grading, it can be difficult for the teacher to summatively assess projects (i.e. give grades), since the requirements of projects tend to be less precise. Because not every school prefers formative assessment over summative, this can be a significant issue.
There is also the matter of finding a project that is appropriate to the students. It is often quite difficult to apply more advanced mathematical concepts to models (though more of them are surfacing online), and thus it can be tricky to create a project that actually increases student understanding. Older students may feel condescended to if they are given a more basic project.
Overall, it is my opinion that projects have their place in the classroom, but like so many other approaches to education, project-based learning is but one useful technique among hundreds of techniques that may be appropriate sometimes and counterproductive other times.