One concern is that PBL may be inappropriate in mathematics, the reason being that mathematics is primarily skill-based at the elementary level. Transforming the curriculum into an over-reaching project or series of projects does not allow for necessary practice of particular mathematical skills. For instance, factoring quadratic expressions in elementary algebra requires extensive repetition.
On the other hand, a teacher could integrate a PBL approach into the standard curriculum, helping the students see some broader contexts where abstract quadratic equations may apply. For example, Newton's law implies that tossed objects follow a parabolic path, and the roots of the corresponding equation correspond to the starting and ending locations of the object.
Another criticism of PBL is that measures that are stated as reasons for its success are not measurable using standard measurement tools, and rely on subjective rubrics for assessing results.
In PBL there is also a certain tendency for the creation of the final product of the project to become the driving force in classroom activities. When this happens, the project can lose its content focus and be ineffective in helping students learn certain concepts and skills. For example, academic projects that culminate in an artistic display or exhibit may place more emphasis on the artistic processes involved in creating the display than on the academic content that the project is meant to help students learn.