The beginning of section three the author starts by talking about memory and memory that lasts. He talks about his high school Geometry class and how much of the material that he has forgotten over the years. The author then talks about research that has been done about studying for tests. He talks about cramming for tests as opposed to studying in shorter increments over a period of several days. The research showed that cramming helped a student do well on a test, but they didn't remember it as long as the student that studied in shorter increments.
The author then talks about solving problems. People who practice math regularly are more likely to remember freshman algebra better than those who do not. Engineers are more likely to remember their old freshman Algebra problems, even though they are doing much more complicated math at work. The more this person practices doing math, the better that person can transfer that information to another problem, and have a better chance to solve that problem.
The author says that students that are more motivated to learn will be able to retain that information for a longer time and increase that opportunity of that learning tranferring to new situations.
Chapter 6 talks about the difference between teaching students facts and information and teaching them to think beyond just the facts and think about why things happen. The author talks about getting students to take information and process it to solve problems. To thinks like mathematicians, scientists, and historians.
The author talks about adjusting teaching styles for different types of learners. The author claims that although all students have different interests and abilities, most students share the same learning style.
UGH! I just had this well-written thought out post and for some reason it "wouldn't take"! This one may just be short and sweet!
ReplyDeleteIn an earlier section Willingham talked about the gaps that our students are coming to us with. He talked about the privileged and the underprivileged and because of their different background knowledge, they had different skills. In this section he made the comment, "The fact that we understand new ideas by relating them to things we already know helps us understand..." So, when students don't have the same background knowledge from the beginning it makes the job of the teacher even more difficult. I still have the question as to how and when those gaps get filled in? The money just isn't there. We do have some students pulled out at the middle school to focus on their reading skills which I think is great! However, what I am seeing is that they are working on the skills they missed, but that they are never really catching up. If anything, the gap is staying the same instead of getting bigger.
The title of Chapter 5 made this math teacher nervous because this debate goes on and on. My frustration at the middle school is that the students aren't coming to me knowing their multiplication facts. The argument is that they are coming to me with the strategies to solve multiplication facts. For example, they know that 7*8 is 7 groups of 8 and can draw me a proof picture to figure out its 56. That's great. But, as some point they really just need to know 7*8=56. As we continue to build on with division, fractions, and algebra if they have to draw pictures to show me 7*8 they get so frustrated because of how long it takes them to solve a problem. Willingham states, "It is virtually impossible to become proficient at a mental task without extended practice." It doesn't matter if it is math, reading, or basketball; I agree that to become better at something you need to practice. He later states that we need to practice for three reasons: "it reinforces the basic skills that are required for the learning of more advanced skills, it protects against forgetting, and it improves transfer." AMEN! Again, I don't care what the skill; to become better you must practice.
(I hope it posts this time!)
Damon,
ReplyDeleteThis section made me think that all that cramming that I did in high school and college was probaly not worth much. I guess it got me through college though, right?
When I think about how much we need our students to know the basic facts in math their is so much controversy between memorization and strategies to help the children understand the numbers. In third grade they are mastering their addition and subtraction facts and they are also beginning to learn their multiplication facts so they have a lot of numbers to know by the end of third grade. I now see that they just need lots of practice so they have the facts as background knowledge.
This section made me think about all of the information that we are just covering and not mastering. Students are exposed to various pieces of information throughout their years in school, and like Denise said often they cram to get by and the cramming doesn't carry on very far. I think that it is hugely valuable to require some basic memorization.
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