Relational Understanding vs. Instramental Understanding

Three things that made you "stop" as you read this piece, and why
1. "By many, probably a majority, his attempts to convince them that being able to use the rule is not enough will not be well received." 
Is this really true? Multiple times I have heard students question why what they're learning is relevent and when they would be able to use it. Clearly these students are wanting a deeper understanding. Furthermore, when students realize that the rule they learned isn't working anymore or if the context of the problem is changed, they will be confused and not know what to do or they will get the question wrong. 

2. "Over-burdened syllabi. Part of the trouble here is the high concentration of the information content of mathematics."
Although having a dense curriculum would make it difficult to go deeper into a topic and spend enough time to have relational understanding, I don't think it is completely to blame. If students have a firm grasp of the early concepts in early years, they will be confident in them going into the next year and can build upon them. I wonder if it would be easier for students to learn a topic in a year than move on to a new topic the next year. This way teachers could focus on one topic and build upon it at their own pace without having to do lots of recap to help the students remember the previous material.

3. "Difficulty of assessment of whether a person understands relationally or instrumentally."
I found it very interesting how Skemp proposes that mathematics students are examined orally. It would be beneficial for the students who find it difficult to get their thoughts on paper and are more comfortable with vocalizing the steps they are doing. I think this should be an option for those students who have an understanding of math but are unable to effectively communicate that understanding via pencil and paper. In order to have a record of the assessment, I would keep a recording of the conversation so that I could have something to reference. It would also be useful to the student to reflect back on their assessment.

Where you stand on the issue Skemp raises, and why
I believe students should be taught relationally initially. However, I am not opposed students learning and using "the rules" once they have relationally understood the concept. It is irresponsible mathematics to give students a formula/trick for particular problems without offering an explanation of why it works. Once students have a grasp on the concept, I don't see a problem with them using some short cuts or rules. Since mathematics is constantly building on prior concepts, it is to the students benefit to be comfortable with prior concepts. Furthermore, being able to complete certain problems quickly (such as factoring polynomials) will help the students focus on the new material being presented. I do think it would be beneficial to revisit the old material briefly before moving onto the new material so that the students could see the connection.