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.
Read More......
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.
Read More......
Wednesday, June 9, 2010
The Minds of Elementary School Teachers
My mother and I lived with my aunt and uncle in 7th grade during the Gulf War. This is when I failed math. My uncle was way into self-help and had a number of books on hypnotism. I read one of the most important books in MY life thanks to my uncle: The Magic of Thinking BIG by David Schwarz. I reread it dozens of times. But I also started reading about hynotism myself.
In high school I got a book on hypnotism myself (my experiences hypnotizing my two victims were interesting). Besides describing many manners of inducing hypnosis, tests or routines were also discussed in the book. Things like the hypnotized person trying to lift up their feet but finding that they could not.
One thing that could be done under hypnosis is to hypnotize a person to forget a number entirely. So if it were three, they will count "One, two, four, five." When asked "What's 5 minus 2?" the person might answer 2, 4, or a made-up number. There were two groups however who had HUGE problems with this sort of test or experiment. Very young children who had no concepts of numbers entirely AND elementary school teachers. For those with moderate math knowledge the name of 3 was not very important. To those with advanced math knowledge, like physicists or mathematicians, the name of 3 is also not very important too. But elementary school teachers are so used to teaching students the numbers that in their minds there can be nothing except the numbers they have spent so much time teaching to students, so they are generally unable to do away with a number. Read More......
Monday, June 7, 2010
Class Groups, Fractions, Confusion
This is a very long rambling post. Unfortunately I talk my way around an issue or problem and seldom straight through. My wife and I spent the early part of the evening collecting the materials I'll need for tomorrow's science lesson on making predictions and density. I'll also be teaching or presenting it on June 15 to the same entire group that was present in Dr. Olsen's hijacked classroom today.
Real Life Division or Classroom Groups
The human brain loves to identify patterns. If a 5th grade classroom teacher has divided her students into Orcas, Jellyfish, Dolphins, and Sea Urchins and there are 4 Orcas, 3 Sea Urchins, and the rest of the class is split between Dolphins and Jellyfish, what does that mean? As a sub in that class, I tried to piece together this grouping, came to my own conclusions, and explicitly asked the students. The Dolphins and Jellyfish said the 4 Orcas were troublemakers, but I knew this couldn't be it, because one of the most responsible students in the class was an Orca. The names also connoted something. Were the Dolphins all helpful and the Orcas predatory in the classroom? Are the Sea Urchins prickly students? Do the Jellies just float along?
In my Practicum 2 class, the teacher hands out poker chips to divide her class up to differentiate her math lessons and work with small groups. I became overly-focused on the fact that red chips seemed to connote the bright students who "get it", while "white chips" would spend time with the teacher being retaught. Preparing for my own lesson, I tried to clarify: what would happen if I gave a red chip student a blue chip or a white chip? It seemed the white chips held a stigma (to me at least). This puzzled my teacher. None of the kids, she said, ever complained about getting a white chip. Instead they are excited; they got to spend time with the teacher and oftentimes played math games with her. She happened to bring my chip-focusedness up with our site facilitator in a meeting last week, but the site facilitator too started reading into the chip colors, just like I did. When I told my wife about it, she too started making assumptions about what the color of the chips meant.
Unequal Fractions
Now that my third graders are onto fractions - and now that I'm paying closer attention to the specific vocabulary and terms used in the classroom - I keyed into the whole idea (bad pun) of fractions being equal parts. A pizza cut into 8 slices has 8 near-identical slices. Each slice is a congruent region to every other slice.
Ok, going off on a tangent here (better math pun): how confusing is it to use congruent to describe two shapes that are the same size and shape, yet we also can talk about lines being congruent? I've just had to do a little research to make sure I'm not even making up the idea of congruent lines vs. congruent shapes. Ah, they both can be congruent because it means "coinciding exactly when superimposed"
Anyways, getting back to fractions. Fractions are a way of dividing a whole into parts. A way? A representation? Yes, this is going to get long. Unequal fractions is apparently an actual term for something. I just mean fractions with unequal parts.
For example:
Dividing a 20 person class into 4 groups, normally would have 5 people in each group, but what if:
Red Group: 7
Blue Group: 3
Yellow Group:5
Green Group: 5
So we could talk about one fourth of the groups being confused about a concept, if all of Red Group does not get the idea of what I'm writing about here, because their group is ONE QUARTER of the class. But what if 2 members of Red Group do get it! They are 2/7ths of Red Group. Essentially I'm doing division of fractions, I guess. 2 sevenths of 1 fourth. But that's really convoluted. I'm talking about 2/20 of the class. I thought I was DIVIDING the fractions, but I was just multiplying them. I picked easier numbers. I know if one student out of the 20 does something, he is 1/20th the class. And if I say 1/5 of Green Group did x, I really am saying 1/5 of 1/4, so 1/5*1/4... Hmmn.
That doesn't make much sense, but it does highlight my confusion about the nature of fractions.
In my mind at least, fractions and decimals serve the same purpose. 0.25 is 1/4. But 0.25 makes no assumptions over how the other 0.75 is divided up. But 3/4 does seem to! What's going on here??? Read More......
Real Life Division or Classroom Groups
The human brain loves to identify patterns. If a 5th grade classroom teacher has divided her students into Orcas, Jellyfish, Dolphins, and Sea Urchins and there are 4 Orcas, 3 Sea Urchins, and the rest of the class is split between Dolphins and Jellyfish, what does that mean? As a sub in that class, I tried to piece together this grouping, came to my own conclusions, and explicitly asked the students. The Dolphins and Jellyfish said the 4 Orcas were troublemakers, but I knew this couldn't be it, because one of the most responsible students in the class was an Orca. The names also connoted something. Were the Dolphins all helpful and the Orcas predatory in the classroom? Are the Sea Urchins prickly students? Do the Jellies just float along?
In my Practicum 2 class, the teacher hands out poker chips to divide her class up to differentiate her math lessons and work with small groups. I became overly-focused on the fact that red chips seemed to connote the bright students who "get it", while "white chips" would spend time with the teacher being retaught. Preparing for my own lesson, I tried to clarify: what would happen if I gave a red chip student a blue chip or a white chip? It seemed the white chips held a stigma (to me at least). This puzzled my teacher. None of the kids, she said, ever complained about getting a white chip. Instead they are excited; they got to spend time with the teacher and oftentimes played math games with her. She happened to bring my chip-focusedness up with our site facilitator in a meeting last week, but the site facilitator too started reading into the chip colors, just like I did. When I told my wife about it, she too started making assumptions about what the color of the chips meant.
Unequal Fractions
Now that my third graders are onto fractions - and now that I'm paying closer attention to the specific vocabulary and terms used in the classroom - I keyed into the whole idea (bad pun) of fractions being equal parts. A pizza cut into 8 slices has 8 near-identical slices. Each slice is a congruent region to every other slice.
Ok, going off on a tangent here (better math pun): how confusing is it to use congruent to describe two shapes that are the same size and shape, yet we also can talk about lines being congruent? I've just had to do a little research to make sure I'm not even making up the idea of congruent lines vs. congruent shapes. Ah, they both can be congruent because it means "coinciding exactly when superimposed"
Anyways, getting back to fractions. Fractions are a way of dividing a whole into parts. A way? A representation? Yes, this is going to get long. Unequal fractions is apparently an actual term for something. I just mean fractions with unequal parts.
For example:
Dividing a 20 person class into 4 groups, normally would have 5 people in each group, but what if:
Red Group: 7
Blue Group: 3
Yellow Group:5
Green Group: 5
So we could talk about one fourth of the groups being confused about a concept, if all of Red Group does not get the idea of what I'm writing about here, because their group is ONE QUARTER of the class. But what if 2 members of Red Group do get it! They are 2/7ths of Red Group. Essentially I'm doing division of fractions, I guess. 2 sevenths of 1 fourth. But that's really convoluted. I'm talking about 2/20 of the class. I thought I was DIVIDING the fractions, but I was just multiplying them. I picked easier numbers. I know if one student out of the 20 does something, he is 1/20th the class. And if I say 1/5 of Green Group did x, I really am saying 1/5 of 1/4, so 1/5*1/4... Hmmn.
That doesn't make much sense, but it does highlight my confusion about the nature of fractions.
In my mind at least, fractions and decimals serve the same purpose. 0.25 is 1/4. But 0.25 makes no assumptions over how the other 0.75 is divided up. But 3/4 does seem to! What's going on here??? Read More......
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