Entry #2

Although instrumental and relational understanding have both advantages and disadvantages, relational understanding is more beneficial to students, especially in the long term. Relational understanding includes knowing not only how to do something, but also knowing the reasoning behind the action. Skemp explains, throughout his argument, that instrumental understanding, the ability to know how to do something, is actually contained within relational, meaning that when a student is learning through relational understanding, that student is still gaining the instrumental understanding as well. Skemp examines why teachers choose to teach instrumental mathematics when clearly relational is the better option because it incorporates both types of understanding and has a longer lasting effect. He found three advantages associated with instrumental understanding. He says that it is easier to understand, the results are more immediate, and the answers could be found more quickly. Along with this, the main disadvantage that Skemp emphasizes in his article is that instrumental understanding only lasts for the short term and is only useful within a limited context. However, he states that relational understanding had four basic advantages. He explains that relational understanding is easier to apply to new tasks, can be an effective goal in itself, and causes the students to reason and understand things for themselves. The last advantage of relational understanding is that it is easier to remember. It takes more time and effort to learn as well as to teach relational understanding, but once it is learned, the result is more lasting. Skemp does not identify any real disadvantages associated with relational understanding, but he explains some of the factors that add to the difficulty of using relational understanding. He says that it is hard to test whether or not a student actually understands relationally just by their test answers, and that sometimes the curriculum is so large that it is hard to be able to make the time to teach everything using relational understanding. Also, he explains that it is difficult to change the ways of both teaching, and the ways for students to learn. The focus of mathematics in schools is often placed on instrumental understanding, so it is difficult to make that switch to relational understanding, even though relational understanding is more beneficial to students. Students will be able to use what they learned from relational understanding because the effects are longer lasting and are easier to connect to other ideas and new tasks.