My blog is Grade A. It has nice multimedia features and will probably be updated even when I'm not taking a math methods course anymore as I make mathematical discoveries and reflect on student thinking. Where else can you find ants? I also point out the underlying connections between math and everything else in the universe.
Along those lines, any assessment that asks you to grade or rate yourself is quite flawed. The honest self-critical people - such as my natural self - will mark themselves down, while those wanting the A will just go for it. The only people that suffer are the self-critical ones. Assuming the instructor actually takes their self-criticism or self-grade of a B or a C seriously, they don't get their fair share of the A's and so on.
And along those lines, we need to keep people from eliminating themselves. Again, the honest well-intentioned people eliminate themselves. Ask 3rd graders "Who can hit this ball over the fence?" and most of them will raise their hand, even if they can't hit a ball. Meanwhile self-reflective Jonny or Brant eliminates himself. If it were up to me, only the 2-3 people that could actually do the task would raise their hands. But it's not.
Take this into math where there is the traditional trap of females thinking they are not as good at math and then they don't attempt as many problems (and teachers don't hold them to the same standard). Take the special ed kids who don't even try problems. If people could accurately discriminate things would be fine, but they can't. It's always better to go for as many opportunities as you can. Take risks. Get shot down, learn, move on, and so on. Not that I find what I just expressed that easy, but I know it's a better approach.
People who think "I could never work there." or "I'm not ready for the promotion. A leader has so much more initiative and speaks so well." are going to find those positions filled with incompetent people who didn't eliminate themselves and seldom deprecate themselves or their efforts. RISE UP AND DEMAND MORE FOR YOURSELF!
My brain is kind of mush right now.
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Tuesday, June 29, 2010
Wednesday, June 23, 2010
The Big Revelation, the Wisconsin context, the equation True or False test
The Big Revelation
I'm glad that Beth asked today how a second grader managed to get to second grade without being taught any strategies. This is actually pretty huge. I thought all of the video children had just been pulled from a regular classroom and asked to solve a word problem or two. Instead they are quite used to solving word problems. This doesn't change whether I think a child of a certain age or grade could do division or multiplication, but I didn't know that context. They have always seemed very comfortable turning to the manipulatives and/or white boards. When I work with my third graders, I have been disappointed that they haven't found my word problems as easy to navigate as the children in the videos.
The Wisconsin negative temperature context
While living in a cold climate could certainly build the concept in children's minds that there ARE such things as negative temperatures, I do not think it explains the familiarity in any way. The difference in temperatures would have to be so extreme like -50 F or 50 F for the negative to have a lot of impact. 14 F and -14 F are both extremely cold. All that said, I haven't grown up in a climate like that. Maybe parents really do go "Oh, 31 F? Just your winter jacket will do. But -5 F, hmmn, yeah, wear all your winter gear." Instead I'd suggest that they are exposed to negative numbers in their classroom.
4 = 3+1 and 3+2=5+1=6 Problems
I was really baffled by the class's response and YOU, Dr. Shih! About these problems. Very puzzled. I realized that I was relating to the questions very differently. HOWEVER: if you get out of it that they think number sentences can only be written one way... Excellent! Fine. The reaction of doing 5 + box = 11 is good.
To me that was the extent of the value of this test/survey. 5+2=3+4 works for me. I understand the idea behind it. It really is a matter of notation and symbols. Even the 3+2=5+1=6, I understand where it is going. If it is bad to think or teach that way, fine, message understood. But if I gave all of my third graders this tomorrow, I wouldn't make much of their answers. I just quizzed my wife over it. It was interesting to me that she would not accept 12 as a possible answer in 8+4=Box+5. She would accept it as less incorrect than 33 or another number, but to her, it was very wrong.
To put it another way. If I gave children 3i = 6... what do I really expect? If I gave it to my classmates what would I expect? It's not that meaningful unless you have been studying the i notation/operation (if that's how you want to approach it. And if it isn't i, then 3! = 6 which I think is 3x2x1 or it's an excited 3 that is so thrilled to be a 6. Read More......
I'm glad that Beth asked today how a second grader managed to get to second grade without being taught any strategies. This is actually pretty huge. I thought all of the video children had just been pulled from a regular classroom and asked to solve a word problem or two. Instead they are quite used to solving word problems. This doesn't change whether I think a child of a certain age or grade could do division or multiplication, but I didn't know that context. They have always seemed very comfortable turning to the manipulatives and/or white boards. When I work with my third graders, I have been disappointed that they haven't found my word problems as easy to navigate as the children in the videos.
The Wisconsin negative temperature context
While living in a cold climate could certainly build the concept in children's minds that there ARE such things as negative temperatures, I do not think it explains the familiarity in any way. The difference in temperatures would have to be so extreme like -50 F or 50 F for the negative to have a lot of impact. 14 F and -14 F are both extremely cold. All that said, I haven't grown up in a climate like that. Maybe parents really do go "Oh, 31 F? Just your winter jacket will do. But -5 F, hmmn, yeah, wear all your winter gear." Instead I'd suggest that they are exposed to negative numbers in their classroom.
4 = 3+1 and 3+2=5+1=6 Problems
I was really baffled by the class's response and YOU, Dr. Shih! About these problems. Very puzzled. I realized that I was relating to the questions very differently. HOWEVER: if you get out of it that they think number sentences can only be written one way... Excellent! Fine. The reaction of doing 5 + box = 11 is good.
To me that was the extent of the value of this test/survey. 5+2=3+4 works for me. I understand the idea behind it. It really is a matter of notation and symbols. Even the 3+2=5+1=6, I understand where it is going. If it is bad to think or teach that way, fine, message understood. But if I gave all of my third graders this tomorrow, I wouldn't make much of their answers. I just quizzed my wife over it. It was interesting to me that she would not accept 12 as a possible answer in 8+4=Box+5. She would accept it as less incorrect than 33 or another number, but to her, it was very wrong.
To put it another way. If I gave children 3i = 6... what do I really expect? If I gave it to my classmates what would I expect? It's not that meaningful unless you have been studying the i notation/operation (if that's how you want to approach it. And if it isn't i, then 3! = 6 which I think is 3x2x1 or it's an excited 3 that is so thrilled to be a 6. Read More......
Saturday, June 19, 2010
Wednesday, June 16, 2010
It all comes together
The ants are disturbing me a little. They seem to have blocked up all three entrances between the top area and the bottom sand. There are about 9 on the bottom and 6 up top. It seems the top ones are excavating the entrance hole to get back to the rest of the colony. But while three are moving pieces of sand around, there's an ant 1.5 centimeters below continuing to pile up sand to block the hole. I could use a skewer to unblock the hole, but I don't know that that's what they need.
Unfortunately this relates both to students and to my mother. My mother has been in the hospital since June 1. Last night she got put on a respirator again and intubated so she has a tube down her throat to her lungs, I think. She can't talk. Tonight she signaled that she wanted to write something. But my wife and I visiting was also stimulating or overstimulating her. She was also too tired to try to write. Basically a helpless feeling about how I can help her.
Then going to students: how long to wait while they are trying to solve a problem before trying to help. I think there's a Superman concept, of swooping in to the rescue. Teachers want to help students, but sometimes the best help is not giving any and letting their brains work. Maybe even not sometimes, but most of the time? Read More......
Unfortunately this relates both to students and to my mother. My mother has been in the hospital since June 1. Last night she got put on a respirator again and intubated so she has a tube down her throat to her lungs, I think. She can't talk. Tonight she signaled that she wanted to write something. But my wife and I visiting was also stimulating or overstimulating her. She was also too tired to try to write. Basically a helpless feeling about how I can help her.
Then going to students: how long to wait while they are trying to solve a problem before trying to help. I think there's a Superman concept, of swooping in to the rescue. Teachers want to help students, but sometimes the best help is not giving any and letting their brains work. Maybe even not sometimes, but most of the time? Read More......
Monday's "twist"
When I worked on classifying the measurement/rate problems and then trying to identify what they had in common on Monday, I honed in on the fact that all of the problems dealt with units (of measurement) which are divisible.
1. So problems had hours which can be broken down into minutes and seconds or grouped as days.
2. Miles can be expressed as yards or feet and so on.
3. Dollars can be divided into cents or the various denominations on bills.
Were these problems harder to classify? I would say no, but I have learned that they are [for students]. Where I can see them being trickier or more complex is if problem 4 were changed from:
Todd's tomato plants grow 4 inches a week. How many weeks will it take for them to grow 20 inches?
to:
Todd's tomato plant grows 4 inches a week. How many days will it take for them to grow one and a half feet?
Solving the problem now requires conversion of both time and distance. So that's where I could see the problem increasing in complexity. I think that such complexity is actually desirable, but not if it is causing confusion.
Once you know that a three-sided polygon is called a triangle, I think it is purely academic and impractical to tell students "Draw a three-sided polygon and color it yellow and write the word Caution in the middle of it." BUT if we know that a tortoise moves a yard every four seconds, I WOULD expect someone to predict how many feet it may have moved in a minute. We don't talk about 180 minutes passing, we just say 3 hours. But if a TV show is 90 minutes long, we should know that it's an hour and a half in duration. Read More......
1. So problems had hours which can be broken down into minutes and seconds or grouped as days.
2. Miles can be expressed as yards or feet and so on.
3. Dollars can be divided into cents or the various denominations on bills.
Were these problems harder to classify? I would say no, but I have learned that they are [for students]. Where I can see them being trickier or more complex is if problem 4 were changed from:
Todd's tomato plants grow 4 inches a week. How many weeks will it take for them to grow 20 inches?
to:
Todd's tomato plant grows 4 inches a week. How many days will it take for them to grow one and a half feet?
Solving the problem now requires conversion of both time and distance. So that's where I could see the problem increasing in complexity. I think that such complexity is actually desirable, but not if it is causing confusion.
Once you know that a three-sided polygon is called a triangle, I think it is purely academic and impractical to tell students "Draw a three-sided polygon and color it yellow and write the word Caution in the middle of it." BUT if we know that a tortoise moves a yard every four seconds, I WOULD expect someone to predict how many feet it may have moved in a minute. We don't talk about 180 minutes passing, we just say 3 hours. But if a TV show is 90 minutes long, we should know that it's an hour and a half in duration. Read More......
Monday, June 14, 2010
Ant Pic
That was from Saturday (Day 2 of having them). They've added a lot on since then.
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Thursday, June 10, 2010
Got Ants!
Today I found the fire ants, or at least a bunch of them on the way to science and then spent 20 minutes after science collecting about 14 of them. They are milling about in the giant ant farm. I will post pictures once they do something.
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