Instrumental vs Relational ways of Knowing in Mathematics - Skemp

The mention of the goal of the students is to understand instrumentally while the teacher wants them to understand rationally stuck out to me. As a student and math tutor I connect to both sides, however as I have continued in my education I have found the importance in understanding the WHY a rule works, as it promotes general application of the rule to different contexts. As well, the idea that if math is taught instrumentally, success will likely be achieved quicker leading to a re-establishment of self confidence. This made me stop and think as I have witnessed how necessary this is for certain students, in order for their motivation towards learning to continue. While reading, I stopped and had to think, when the benefits of relational mathematics were being explained in terms of learners actively taking charge of their own learning. I found it interesting that this aspect of relational mathematics shared similar principles to the new teaching and learning practices that are being encouraged. Where students are encouraged to further explore topics they are interested in, creating lifelong learners. 

I can relate with aspects of both instrumental and relational understanding in mathematics, but I believe that deciding which way of knowing and understanding to use in mathematics could be dependent on the goal of the math class or the goal of the student. Some students may only need to know particular techniques so relational understanding would take too long given they only need to know certain facts. Whereas, students who intend to further their math education, or continue in the science field and enjoy taking charge in their own learning would benefit from a relational understanding. As someone who hopes to teach, I see the importance of a relational understanding, particularly in math. Although there will be more content to learn, once the material is learnt, it will likely be easier for students to recall and apply generally.