Chapter 4 summary p. 87-105
This chapter focuses on the question, “Why are abstract ideas so difficult to comprehend and so difficult to apply when they are expressed in new ways?”The cognitive principle that guides this chapter is “We understand new things in the context of things we already know, and most of what we know is concrete.”
Students understand new ideas by relating them to old ideas. So if every new idea builds on ideas that the student already knows, we as teachers need to know what our students already know so we are able to give them concrete familiar examples.
The author claims that “understanding is remembering in disguise”. We must ensure that the right ideas from long term memory are accessed and moved into working memory so that students are able to comprehend the new ideas.
When we contrast shallow knowledge (some understanding of the material, but limited understanding) to deep knowledge (knowing not just the parts but also the whole) we see where students with deep knowledge are able to apply the knowledge to many different contexts and discuss it in different ways. We as teachers want our students to have deep knowledge; so it is up to us to provide them with the experiences they need to gain deep knowledge. The questions that we pose in our classrooms need to be more than factual questions and students need to be given time to contemplate them. Our projects and tests should also demand deep understanding. We need to stay realistic in our expectations of our students and how quickly they can grasp new information. Deep knowledge is achieved through practice.
Chapter 5 p. 107-125
The question for this chapter, “is drilling worth it?” questions whether the cognitive benefit makes it worth the potential cost to motivation. The cognitive principle that guides this chapter is “It is virtually impossible to become proficient at a mental task without extended practice.”
Practice helps our students to gain competence and to improve. But it also reinforces the basic skills required for the learning of more advanced skills, protects against forgetting, and improves transfer.
I enjoyed the explanation in this chapter about working memory, which is the site of thinking. When you are combining information in new ways you have to think about it. Our working memory space is limited and could create a bottleneck if we try to put too much information into it. (There is only a limited amount of working memory and no amount of practice will change that.) The way that we are able to “cheat” this limitation is to keep more information in working memory by “chunking,” which treats several things as a single unit and stores it in our long term memory. Two ways to do this is to increase your factual knowledge and to manipulate information to be more efficient. Examples given were tying your shoes or driving a car. At first they take a lot of working memory, but with practice, they become automatic, requiring little or no working memory capacity.
The quote I am including comes from the great philosopher Alfred North Whitehead. “It is a profoundly erroneous truism, repeated by all copybooks and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them.”
The chapter went on to discuss studying practices and information retention. Cramming allows us to do well on immediate tests; however the information will not be retained long term. The suggested manner of studying in several sessions with delays between them allows a person to remember material longer.
Practice also is an important provider to good transfer. Information transfer is more likely when the new problem is similar to the structure of problems seen before.
It was refreshing for me to read chapter 5 because I think that in our math programs we don’t stress the drilling of math facts like we used to and I see how long it takes middle school students who haven’t learned their facts to complete work that should be automatic. This chapter reinforced the value of spending time to make these basic facts automatic so we’ll have more room in our working memory.
Sorry my post is so long. There was a lot of information in those 2 chapters and I hated to leave anything out. The quote was interesting to me because I often think, my students just don't think when they are doing their work! I guess the reason "not thinking" sometimes is not good, is the students doesn't have enough knowledge to do the work automatically without thinking the information through.
ReplyDeleteAll learners must make those connections. We make connections to our self, text, or the world. We understand new things in the context of the things we know and most of what we know is concrete. When we encounter an abstract principle we want to go back to our known comfort level - so we ask for concrete examples to help us understand.
ReplyDeleteIs drilling worth it? I think yes is the right answer, and I also think no is the right answer! For example, when students only work on their math through rote learning, the learning is very shallow. They must have a deeper understanding of the process. We know they understand when they can show transfer of old knowledge to a new problem. However, at some point some learning like math facts must become automatic to speed up other learning and to make more room in working memory. Thus we improve competence and proficiency. The author went on to state that then there is also an increased likelihood that learning will transfer.