Sept 14 Entrance Ticket

First, Skemp’s pointed out that a student can get the right answer without understanding the mathematics is totally reasonable. His idea of instrumental understanding is knowing the rules / algorithms without knowing the reasons behind them, this idea made me think about how often teachers do this without realizing it. I am definitely a victim of this, and I need to be more mindful of this. Second, I thought it was interesting that Skemp does recognize the benefits of instrumental learning, despite it being somewhat against what we have discussed in class so far. We as teachers should be explaining why methods and algorithms work the way they do, rather than just memorizing them, However, getting a right answer quickly can certainly help build student confidence. Therefore, instrumental understanding still has its uses. Lastly, Skemp’s example of comparing learning mathematics to navigating a town is a very interesting example, definitely was not expecting that while reading the article.

 

For me, I think an approach I could try is: first do instrumental methods to build algorithmic skills, and just to make sure students get the right answers first, then connect to simple proofs or real life examples to reinforce learning.