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......

My mom

My mother passed away on Friday morning at 1:50 AM. She had just turned 65. Read More......

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......

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......

Ant Pic

That was from Saturday (Day 2 of having them). They've added a lot on since then. Read More......

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......

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......