The group expressed an enthusiastic consensus that the mathematics of the early grades should be connected to what the students will learn later on. Whether this be called vertical integration or early introduction of advanced ideas is not important. Likewise, some members expressed doubt that we have a sufficiently sharp definition of algebraic thinking to distinguish it from other types of mathematical thought, but that the precise distinction is not so important as the early introduction of good mathematical ideas in general. In particular, geometric concepts should be part of the curriculum from the very beginning. The concern came up more than once that elementary school teachers need support in implementing this idea, since many are not comfortable with more advanced mathematical concepts, and won't see the connections with what they are teaching.
Matrices are notation for transformations.
This is probably too deep to really treat in high school, but it can be told to students. Rotations are given by rotation matrices. This makes sense out of the addition formulas for sines and cosines, in terms of the group law for rotation matrices. A specific bit of 20th-century mathematics was provided by a member. We thought that an exposition of some of the relations between Gaussian and ordinary binomial coefficients may add some zest to a traditional secondary school subject.