This is understanding how and why the rules and procedures work. Students who are taught relational understanding usually have an easier time remembering certain procedures because they had a deeper meaning of why they work. These students will also retain all their learned knowledge longer and are also less likely to make common mistakes. Some students will be lacking motivation and determination and others may be too ready to accept your help because they are not used to thinking things through for themselves. Through their growth as learners students will make sense of math and will soon be less worrisome.
“Those with a relational understanding can learn new concepts easier, retain previous concepts, and are able to deviate from formulas/rules given different problems easier because of the connections they have made.”
When a student wants to make sense of learned concepts but are not given the time and conditions to experience math, they will come to believe that they are not good at math or they will say “they are not math people”. There are a few ways to try and remedy this; notice instrumental teaching, learn how to move from one to the other, and align assessment practices to meet with relational understanding. When you are unaware of your teaching style it was believe that you are doing a good job because your students are clearly learning something. By becoming more aware of your teaching style you can stop the behaviors that are like instrumental teaching and start transitioning to relational teaching.