A Relationally Instrumental Understanding

 All true friends in Wonderland are of course faux amis, or my favorite, falsche Freunde.

The point Richard R. Skemp makes is one that I've very much been buying into over my mathematical learning journey. I suppose a little history of myself, I actually failed high school. At the time, as I told my teacher when I skipped school to play a World of Warcraft expansion at launch, "I care more about video games than school." Much of my learning journey happened after high school when I had the great idea to become an engineer despite having no prerequisite knowledge or credits. So I of course had no foundation for any of my learning. I started out taking catch-up courses at Langara, and I kept learning things instrumentally. This got me quite far in engineering, but after I finished and started mathematics I kept finding holes in my knowledge that slowed me down and hampered my understanding of the mathematical problems I was presented with. 

I've come to have a great respect for relational understanding of math, and it's now the goal to have it for myself and the accompaniment of my teaching. Obviously there will be students like my former self who will reject the relational understanding in favor of the simple instrumental one to get problems done. I cannot convert every student into a "born again relationalist." As such, I wish to teach a relational understanding where I can, but bow down to the instrumentalist when all else fails. 

I hope my own journey will motivate students to appreciate and desire a relational understanding for themselves, as I hope not to have any falsche Freunde in my classroom.