Relational Understanding vs. Instrumental Understanding

After reading Mr. Skemp’s article, I have got mixed feelings towards both approaches. Through many years’ of study, I have got math teachers try to explain things in a marvellous (relational) way. But after the whole class, we are still at a loss regarding steps to solve the questions. By saying “Relational knowledge can be effective as a goal in itself”, Mr. Skemp have admitted that teaching in the relational way is a daunting task to accomplish by itself. Especially for students at young ages, their understandings and experiences are very limited. One relational explanation, which the teacher feels to be excellent, might be harder to understand than the original question for students. Thus, we need an explanation for the explanation. For example, on page 6, Mr. Skemp used the music teaching as an analogy to prove his point. For those readers who are familiar with music, they might feel the analogy is excellent. But for those readers who aren’t music fans, the words such as “stave, minim, crotchets, and quaver” took a whole course to explain well. Not to say let the readers understand what the author is trying to prove. Nor do I agree that math be taught purely instrumentally. For this part, I feel Mr. Skemp has done a good job to prove the point. See quote 4 and 5. In summary, the approach I suggest is: First, teach the students instrumentally. Give them a crutch to help them walk on their own. Second, when the students get an idea of what’s going on but still confused why they do this, give them relational explanation to clarify. The students will suddenly realize what they have done make sense and they will have a firm understanding of how to do it. [ Quotes ] 1: knowledge can be effective as a goal in itself 2: Imagine that two groups of children are taught music as a pencil-and paper subject. 3: Within its own context, instrumental mathematics is usually easier to understand; sometimes much easier. 4: It (Relational understanding) is more adaptable to new tasks. 5: It (Relational understanding) is easier to remember.