The big one in the United States is the role of quantitative measures of learning in the measuring process. Many of these have been mandated by legal requirements, and as most recognize, one shoe does not fit all students.
The next big one in the US is reading proficiency in the early years, whole word or aural based, or a combination. The issue is not settled, especially for boys.
Another issue is competency in math, and the role of calculators versus rote memorization (such as multiplication tables). The issue really boils down to whether to use instructional time on practice spaced over time, or not.
There are other, mostly centering on social values (teaching religious mores, evolution, life skills). These probably in the long run have little competence when measured against reading proficiency, math proficiency, and understanding of history, and the scientific method.
On emerging area is the use and teaching of collection and use of large scale information networks, such as internet.