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.
Read More......
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.
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......
Thursday, June 3, 2010
Math Vocab II and ASW2
Talking to my teacher during her prep today, she confirmed that I should study the math vocabulary from the [Envisions] book to learn it after I confessed that I would not have known what a number fact family is. The students are on fractions now. Most of them seem to be getting what fractions are.
For my ASW2 I am focusing on these two standards: (3)1.12 model and explain multiplication and division as repeated addition or subtraction [NS/PS 1.3.4] and (3)1.14 Immediately recall multiplication facts (products to 81).
In other news, my wife is now on summer vacation with 9-month schools ending yesterday. I also brought a glass jar with a lid to campus to try to capture some fire ants I saw. In one of the greatest disappointments of my life, when I got an ant farm last year for Christmas and ordered the ants... they showed up dead. So I have been biding my time ready to pounce on an unsuspecting ant colony. I think they are in hiding today because it is so hot out. Read More......
For my ASW2 I am focusing on these two standards: (3)1.12 model and explain multiplication and division as repeated addition or subtraction [NS/PS 1.3.4] and (3)1.14 Immediately recall multiplication facts (products to 81).
In other news, my wife is now on summer vacation with 9-month schools ending yesterday. I also brought a glass jar with a lid to campus to try to capture some fire ants I saw. In one of the greatest disappointments of my life, when I got an ant farm last year for Christmas and ordered the ants... they showed up dead. So I have been biding my time ready to pounce on an unsuspecting ant colony. I think they are in hiding today because it is so hot out. Read More......
Thursday, May 27, 2010
Today
To approach my teacher, to start hearing from her, I had to lower myself. I had to put aside the notion that we are peers or colleagues. I had to view her as the teacher and me as the student. And then conversations started to come forth and actual learning. There is really a big gulf between us. I have one of the best teachers with the most to teach, but then I have so much further to climb and learn. I have a lot of brain activity right now. My mind is trying to cope with my environment and make sense of things. It's a sign of actual learning, but it's uncomfortable.
I coasted through Practicum 1 with straight 3's. I had some problems, but they were resolved by my personality and not from me learning anything. My teacher now is the REAL DEAL.
I am not someone who likes challenge, but now I do have a challenge and I stand to gain so much from her. Read More......
I coasted through Practicum 1 with straight 3's. I had some problems, but they were resolved by my personality and not from me learning anything. My teacher now is the REAL DEAL.
I am not someone who likes challenge, but now I do have a challenge and I stand to gain so much from her. Read More......
Math Language
When I taught my lesson on Introducing Area (Envisions 16.5), one of the things that my PSMT kept telling the kids as she helped them later is: You know this, it's like an array....array....array. So I probably raised my eyebrows, but brought it up yesterday and asked about it and happened to mention that it's not really a standard vocabulary word. She responded something like oh but it is! (For them). They had learned mulltiplication by studying arrays.
What is an array? When I think of "an array", I think of an array of abilities or an array of numbers or a satellite array, so things which are linked and connected. A satellite or computer array is a series of connected computers that work together. In video games your character has an array of attributes that decide how well you shoot or jump. When I asked Debbie what an array is, she couldn't tell me. I'm certain she could do the multiplication that an array suggests to my 3rd grade classroom.
On the Daily Spiral Review my students will do today for my unit on volume, there is a question about lines of symmetry, prompting me to ask my teacher if her kids would know that. She said they'd been studying it since first grade. Other questions will ask about congruence or vertices, irregular vs. regular polygons.
Two or three years ago the Review-Journal published an article about failing math scores and included some of the test questions being given to our students. They had a similar sort of vocabulary. My mother's then-boyfriend and she, both college graduates, couldn't understand what the problems were asking. His degree was in physics and he helped to design the early programming of ICBMs during the Cold War for Boeing.
So.... our kids must be learning a lot, right? I don't think so. Maybe the NCTM would be thrilled by kids learning (or not really learning) what math terms mean, but it creates a disconnect for other generations trying to help students with problems they could actually help them with. Read More......
What is an array? When I think of "an array", I think of an array of abilities or an array of numbers or a satellite array, so things which are linked and connected. A satellite or computer array is a series of connected computers that work together. In video games your character has an array of attributes that decide how well you shoot or jump. When I asked Debbie what an array is, she couldn't tell me. I'm certain she could do the multiplication that an array suggests to my 3rd grade classroom.
On the Daily Spiral Review my students will do today for my unit on volume, there is a question about lines of symmetry, prompting me to ask my teacher if her kids would know that. She said they'd been studying it since first grade. Other questions will ask about congruence or vertices, irregular vs. regular polygons.
Two or three years ago the Review-Journal published an article about failing math scores and included some of the test questions being given to our students. They had a similar sort of vocabulary. My mother's then-boyfriend and she, both college graduates, couldn't understand what the problems were asking. His degree was in physics and he helped to design the early programming of ICBMs during the Cold War for Boeing.
So.... our kids must be learning a lot, right? I don't think so. Maybe the NCTM would be thrilled by kids learning (or not really learning) what math terms mean, but it creates a disconnect for other generations trying to help students with problems they could actually help them with. Read More......
Monday, May 24, 2010
Teaching Area tomorrow
So I resisted talking about the disappointing LOST finale last night in class, but a Math blog is the perfect place to mention the absence of the "numbers". Quite a let down.
Ok, here is something I'm working on for teaching area to the third graders tomorrow in my practicum. I am using the Legos to brace and keep the plaster squares at right angles with one another as I glue them down. I'm going to ask the class how many squares I'll need to fill in the inside of the rectangle I'm creating.
I enjoyed class today. It was fun figuring out how to arrange the layout. When I first saw the grid, I thought of comic book panels.
Type your summary here Read More......
Ok, here is something I'm working on for teaching area to the third graders tomorrow in my practicum. I am using the Legos to brace and keep the plaster squares at right angles with one another as I glue them down. I'm going to ask the class how many squares I'll need to fill in the inside of the rectangle I'm creating.
I enjoyed class today. It was fun figuring out how to arrange the layout. When I first saw the grid, I thought of comic book panels.
Type your summary here Read More......
Wednesday, May 19, 2010
Trouble in Paradise
I look forward to trying to figure out the columns and rows assignment with the 11 problems over the weekend.
I should admit that I am a skeptic of the modern math movement which was introduced today in class and which is implemented in most -if not all - CCSD classrooms. In my third grade classroom right now, for example, vertices were mentioned. When a rectangle was drawn the other day, the students called it a "rectangular prism" and when they saw a square, it was called a "cube". I hope to learn in this class why they are expected to learn such concepts in elementary school. I think they should be taught! But taught in middle school or high school. This mirrors the fact that at least one school in the CCSD students recite "digraph ph" when they see "ph" and "blend bl". Why do they need to know what a digraph or a blend is? It would be much better for them to be able to use that knowledge.
Instead of having automaticity with their arithmetic, most of the CCSD students I've encountered from subbing at 25 schools and in my practicum and observations have been very lacking in their ability to do arithmetic. I went to elementary school in the 1980s. I don't remember much about math, except that I found the multiplication facts around 12 very hard to master. At some point I did get them through repeated use. Many students do know know the helpful rule about 9 x a number (9x4 = 45, 4+5 = 9, 9x8 = 72, 7+2 = 9) It's not essential, of course. At one school though students have memorized number rules and the rule numbers themselves, so they say "Rule x: 5 times any number will have 0 or 5 at the end, Rule y: 2 times any number will always end in 0 or an even number.
Some school stuff behind the read more.
My title would be extra appropriate if I actually were teaching at Paradise ES this summer, but I'm not. What I've run into this first week and a half at my school is that I'm "engaging" my students too much. My natural personality is to jump right into things and then we were also encouraged to jump in at our Practicum Orientation.
This does relate to math. Math is the subject I see every day at my school. I try to help the kids as much as possible with the work. I don't do it for them, of course. I actually was teaching some counting strategies without realizing what I was teaching the last couple of days, not as a formal lesson, but as I coached some students through problems.
Anyways, I'm blabbering on. Read More......
I should admit that I am a skeptic of the modern math movement which was introduced today in class and which is implemented in most -if not all - CCSD classrooms. In my third grade classroom right now, for example, vertices were mentioned. When a rectangle was drawn the other day, the students called it a "rectangular prism" and when they saw a square, it was called a "cube". I hope to learn in this class why they are expected to learn such concepts in elementary school. I think they should be taught! But taught in middle school or high school. This mirrors the fact that at least one school in the CCSD students recite "digraph ph" when they see "ph" and "blend bl". Why do they need to know what a digraph or a blend is? It would be much better for them to be able to use that knowledge.
Instead of having automaticity with their arithmetic, most of the CCSD students I've encountered from subbing at 25 schools and in my practicum and observations have been very lacking in their ability to do arithmetic. I went to elementary school in the 1980s. I don't remember much about math, except that I found the multiplication facts around 12 very hard to master. At some point I did get them through repeated use. Many students do know know the helpful rule about 9 x a number (9x4 = 45, 4+5 = 9, 9x8 = 72, 7+2 = 9) It's not essential, of course. At one school though students have memorized number rules and the rule numbers themselves, so they say "Rule x: 5 times any number will have 0 or 5 at the end, Rule y: 2 times any number will always end in 0 or an even number.
Some school stuff behind the read more.
My title would be extra appropriate if I actually were teaching at Paradise ES this summer, but I'm not. What I've run into this first week and a half at my school is that I'm "engaging" my students too much. My natural personality is to jump right into things and then we were also encouraged to jump in at our Practicum Orientation.
This does relate to math. Math is the subject I see every day at my school. I try to help the kids as much as possible with the work. I don't do it for them, of course. I actually was teaching some counting strategies without realizing what I was teaching the last couple of days, not as a formal lesson, but as I coached some students through problems.
Anyways, I'm blabbering on. Read More......
Wednesday, May 12, 2010
Understanding Perimeter
Today I taught a lesson on understanding perimeter. I had asked my PSMT on Monday if I could start teaching as soon as possible and she said "How about perimeter and area tomorrow?" and I must have made a face and said something, so she said Wednesday was fine. But she was then in a meeting with our site facilitator anyways and only caught the tail end. She still had some good feedback to use.
If this were Livejournal I could use a LJ-cut tag and put my lesson there, so it's not too spammy. Did this work?
Brant Polkowski
Understanding Perimeter
3rd Grade
Standards/Objectives
Nevada Standard D.3-5 - Use physical models to explain he relationship between concepts and procedures
Objective: Students will use standard units to find the perimeter of a shape.
Materials/Technology Resources
Graph paper (handed out by an on-task student), personal white boards and markers (students already have), Scrabble board, pieces of Lego, pieces of Dungeons & Dragons square floor tiles, poster boards with class examples and assessment ones to work through.
TW call on on-task students to help in collecting and distributing materials.
Procedures
Opener: TW discuss family members' upcoming visit and mother's pool, draw it on the board, and then discuss how to prevent young nephews from falling in, leading into perimeter. Teacher will define the concept of perimeter and explain the concept with students copying class diagrams onto their graph paper. TW lead class through finding the perimeter in standard units (squares)
Class will find the perimeter of a Scrabble board.
TW pass out floor tiles to four groups and have students draw tiles on their paper. They will then find the perimeter of the tiles and hand back. TW hand out Lego tiles next and repeat.
Students will create their own shape and exchange their graph paper with another student and have that student find the perimeter of the object that they created.
Teacher will then hold up second whiteboard and show the two additional shapes. Students will be assessed using white boards on comprehension of perimeter concept before handing out Envisions worksheets to work through perimeter problems.
Extension: How would we find the perimeter of the model house I brought in? What do we notice about the perimeter of a square?
Closure: We will be working more with perimeter and its cousin area in the next few days. We won't always be using square shapes.
Student Assessment
Teacher will assess student comprehension by showing several shapes to the entire class. TW use 2 square-based shapes shown on the back of foamcore. Students will then find the perimeters of the shapes and hold up their whiteboards with the answers. TW monitor for comprehension. Read More......
If this were Livejournal I could use a LJ-cut tag and put my lesson there, so it's not too spammy. Did this work?
Brant Polkowski
Understanding Perimeter
3rd Grade
Standards/Objectives
Nevada Standard D.3-5 - Use physical models to explain he relationship between concepts and procedures
Objective: Students will use standard units to find the perimeter of a shape.
Materials/Technology Resources
Graph paper (handed out by an on-task student), personal white boards and markers (students already have), Scrabble board, pieces of Lego, pieces of Dungeons & Dragons square floor tiles, poster boards with class examples and assessment ones to work through.
TW call on on-task students to help in collecting and distributing materials.
Procedures
Opener: TW discuss family members' upcoming visit and mother's pool, draw it on the board, and then discuss how to prevent young nephews from falling in, leading into perimeter. Teacher will define the concept of perimeter and explain the concept with students copying class diagrams onto their graph paper. TW lead class through finding the perimeter in standard units (squares)
Class will find the perimeter of a Scrabble board.
TW pass out floor tiles to four groups and have students draw tiles on their paper. They will then find the perimeter of the tiles and hand back. TW hand out Lego tiles next and repeat.
Students will create their own shape and exchange their graph paper with another student and have that student find the perimeter of the object that they created.
Teacher will then hold up second whiteboard and show the two additional shapes. Students will be assessed using white boards on comprehension of perimeter concept before handing out Envisions worksheets to work through perimeter problems.
Extension: How would we find the perimeter of the model house I brought in? What do we notice about the perimeter of a square?
Closure: We will be working more with perimeter and its cousin area in the next few days. We won't always be using square shapes.
Student Assessment
Teacher will assess student comprehension by showing several shapes to the entire class. TW use 2 square-based shapes shown on the back of foamcore. Students will then find the perimeters of the shapes and hold up their whiteboards with the answers. TW monitor for comprehension. Read More......
Tuesday, May 11, 2010
PE Today
I met the last two students who were absent yesterday and then went to PE with the kids and met Miss Alexis and Mr. Petros. I volunteered to help at Field Day on Friday and will be doing some kind of putting game with 4th and 5th graders. A student gave me a yellow sucker today as a gift.
I want to get some of the students multiplication flash cards and even one: addition and subtraction, which I happen to have. I think I have some Spiderman $1 flashcards from Target. Read More......
I want to get some of the students multiplication flash cards and even one: addition and subtraction, which I happen to have. I think I have some Spiderman $1 flashcards from Target. Read More......
Monday, May 10, 2010
Welcome
Not that I'm an overachiever, but I am a little curious as to how blogger or Blogspot does its blogs, so I might be trying to test some things out and detailing the lives of each of my 32 cats starting with Mr. Peppers.
We had our first EDEL 433 Class today and Scott was our guest instructor. I really want to try to monetize this; I figure it means trying to make money off of your blog. Maybe this blog could pay for the class? Read More......
We had our first EDEL 433 Class today and Scott was our guest instructor. I really want to try to monetize this; I figure it means trying to make money off of your blog. Maybe this blog could pay for the class? Read More......
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