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14 Nov 2006 - 01:54
Coming to the end of our 4-day weekend here... Friday I learned from Christopher that on Tuesday (tomorrow) he would be taking a chapter test on probability. Seeing as how I don't know any probability, that was bad news. So I spent the weekend teaching to crammery, big-time. First I had to teach myself to crammery; then I had to teach Christopher to crammery; then I had to make Christopher learn how to draw tree diagrams; & after that I had to make him do a bunch of problems for practice & to see if he got them right. (He did.) By Sunday night Ed was in on the act, too, so 3 people in this household have spent a good portion of Veteran's day weekend teaching probability to crammery. You can make that 4 if you count my neighbor, the statistician. She spent the weekend on stand-by, fielding phone calls Saturday night and drawing tree diagrams Sunday afternoon. She loaned me her copy of Probability Demystified, which she used to teach probability to crammery last year when her kid was in this course. The book looked so good I decided I needed my own copy so Ed and Christopher could use one copy while I used the other. So I went to Barnes & Noble to buy one after picking Jimmy & Andrew up from their program at the Y. That was the only time I could go, so they had to go, too. Normally I don't go to B&N with Andrew. If I do go, I don't try to buy anything, aside from whatever I'm buying for him. But yesterday I had to look at books and I had to buy books and I had to take Andrew with me because I had to teach to crammery because my school isn't responsible for individual student learning. Parents are responsible. So I had no choice. At B&N Andrew got so obsessed with the Arthur books that he refused to leave and I had to drag him - literally drag him, by the collar of his jean jacket - from the back of the store to the front & then through the check-out line. The lady who helped me carry my stuff said, "This is the worst I've ever seen him." So today my neck and shoulder are a mess, but we all know quite a lot about probability. Which we'll forget in the next couple of days, after the test.
it's official No child without math-brain or math-career parents could get through the Irvington "accelerated" track. Which, as we know, is the average, non-accelerated track in the rest of the developed world. I suppose if you hired your own private math teacher, as some parents have done, you might be able to do it. But that's the only way. If I hadn't been studying math for nearly two years I could never have taught myself probability to crammery the way I did this weekend; nor could I have taught probability to crammery to Christopher (and Ed). No way.
if you thought that was bad — If you thought spiraling in K-5 was bad, wait'll you get a load of it in middle school. Christopher's class has been studying probability for maybe two weeks. The chapter covered at least 18 different topics, so we had to teach all 18 to crammery, instead of teaching 4 or 5 to mastery as you would if you cared about the kids actually learning something. If you want to see what I mean, take a look at the TOC to Probability Demystified:
The book has twelve chapters. The contents of five of them are covered in one chapter of Christopher's math book. (Chapters 1, 2, 3, 4 & 6)
Does a spiraling curriculum lead to negative learning? I'm thinking it does. I'm thinking the effects of a spiraling curriculum are worse than a simple FWOT. When you teach 18 brand-new topics in 2 weeks, you may actually be degrading knowledge.
UPDATE 11-20-2006: Christopher got a 77! Class average 80 or 81. This test wasn't loaded with "Honors" level questions (turns out that's what the tests have been - Honors level tests given to a merely accelerated class in which no Honors level material has been taught). But it had a couple, and it was long. Christopher messed up some minor computations, misread the "spinner" on the spinner problem....and one of the word problems is all wrong. (More later) He could easily have earned a grade in the 80s. He picks up new math concepts much faster than he used to. This started last spring, and has continued this fall. It's cool.
Demystified series
gap anarchy
Engelmann on reteaching material learned incorrectly
teachtocrammery
degradingknowledge
negativelearning
-- CatherineJohnson - 14 Nov 2006 Back to main page.
Please consider registering as a regular user.
Look here for syntax help.
Catherine, All those late night trips to B&N. Too bad you don't qualify for a home educator's discount (20%). Perhaps you can plead your case with the store management. Surely, you deserve it! -- NicksMama - 14 Nov 2006
hey! How do you get a Home Educator's discount? I need one. -- CatherineJohnson - 14 Nov 2006
I REALLY need one. You should see my office. There are practically no books relating to my actual JOB. -- CatherineJohnson - 14 Nov 2006
Well, except for that stack of neuroanatomy coloring books over there against the wall.... -- CatherineJohnson - 14 Nov 2006
I find probability to be the most difficult topic in mathematics. It is tightly coupled with real world phenomena (e.g. Las Vegas) but is difficult to grasp since the information is conditional on all sorts of factors. It is the farthest from intuitive how to go from a description of rolling dice to a mathematical statement accounting for all possible behaviours. Good luck with the tour through mathland. Hopefully there is some time to pick up a skill now and then. -- SeanPrice - 14 Nov 2006
I'll mention the virtues of role-playing games again. The provide exercises in practical probability with incentives to get things right. Is it better to roll 2d6 or 1d12 damage? 2d6 has a higher mean, but a lower standard deviation. How important is it to increase my chance of a higher number at the cost of increasing my chance of a lower number? What are the tradeoffs in taking a penalty in hit probability to gain a bonus to damage when you do hit? Do I need to defeat the monster before he can attack again, or do I just want to maximize damage over time? (Mainchance or Minimax strategies.) (This is in addition to the reading advantages we talked about before.) -- DougSundseth - 14 Nov 2006
heh. if you're going to take the test on probability, ask the teacher this very, very, simple problem (wink, wink***): You're on The Price is Right. You stand in front of three doors, A, B, and C. "There's a prize behind one of the doors!" says the announcer. "Can you find it?" You point at the door of your choice. The announcer says "Well, we'll give you some help. We'll never tell you anything about YOUR choice, and we'll never show you where the prize IS, but we can show you one place where it ISN'T!!" With that, the attendant opens one of the doors you did not pick. It holds no prize. "Would you like to keep your original choice, or switch doors?" says the announcer. What should you do? * An enormous number of teachers and math professionals get this one wrong. But anyone who doesn't understand it has no business teaching statistics. -- ErikHammarlund - 15 Nov 2006
Heh. You might want to take a look at ProbabilityQuestionSaxon87, MontyHallPart3, DougSundsethOnMontyHall, and others in that post thread. We've been here before. ps. By which I mean that I agree that it's interesting, not that you should stop talking about the subject. -- DougSundseth - 15 Nov 2006
I find probability to be the most difficult topic in mathematics. hi, you guys! I think it's damn hard myself. A Commenter sent me a fantastic probability test today - wonderful! I'll get it posted. -- CatherineJohnson - 17 Nov 2006
Erik hey! Great idea! Actually, she may know the answer. I've been talking to the Math Teacher - the guy people have been hiring to reteach the course. He says that all middle school teachers in NY state have been required to have B.A.s in math for years. Her math knowledge is fine, he says. The problem is entirely teaching. That's kind of distressing, I have to say. I didn't know whether her math knowledge might be problematic (really can't tell from this distance).....but somehow I'd been assuming that if you really knew a subject you'd have some idea how to teach it..... Which, of course, now that I "say it out loud," sounds stupid. He said the problem is "presentation" and test construction. (More on the latter later on - very interesting.) -- CatherineJohnson - 17 Nov 2006
I'd forgotten about all the math professors who got that wrong! -- CatherineJohnson - 17 Nov 2006
Now that I know some "starter" probability, I'm going to do the Monty hall problem "from scratch." It was actually a fun weekend (kind of fun). I've always wanted to know probability, and to find myself being able to grasp the material in the chapter pretty rapidly was great. -- CatherineJohnson - 17 Nov 2006
more teaching to crammery
Coming to the end of our 4-day weekend here... Friday I learned from Christopher that on Tuesday (tomorrow) he would be taking a chapter test on probability. Seeing as how I don't know any probability, that was bad news. So I spent the weekend teaching to crammery, big-time. First I had to teach myself to crammery; then I had to teach Christopher to crammery; then I had to make Christopher learn how to draw tree diagrams; & after that I had to make him do a bunch of problems for practice & to see if he got them right. (He did.) By Sunday night Ed was in on the act, too, so 3 people in this household have spent a good portion of Veteran's day weekend teaching probability to crammery. You can make that 4 if you count my neighbor, the statistician. She spent the weekend on stand-by, fielding phone calls Saturday night and drawing tree diagrams Sunday afternoon. She loaned me her copy of Probability Demystified, which she used to teach probability to crammery last year when her kid was in this course. The book looked so good I decided I needed my own copy so Ed and Christopher could use one copy while I used the other. So I went to Barnes & Noble to buy one after picking Jimmy & Andrew up from their program at the Y. That was the only time I could go, so they had to go, too. Normally I don't go to B&N with Andrew. If I do go, I don't try to buy anything, aside from whatever I'm buying for him. But yesterday I had to look at books and I had to buy books and I had to take Andrew with me because I had to teach to crammery because my school isn't responsible for individual student learning. Parents are responsible. So I had no choice. At B&N Andrew got so obsessed with the Arthur books that he refused to leave and I had to drag him - literally drag him, by the collar of his jean jacket - from the back of the store to the front & then through the check-out line. The lady who helped me carry my stuff said, "This is the worst I've ever seen him." So today my neck and shoulder are a mess, but we all know quite a lot about probability. Which we'll forget in the next couple of days, after the test.
it's official No child without math-brain or math-career parents could get through the Irvington "accelerated" track. Which, as we know, is the average, non-accelerated track in the rest of the developed world. I suppose if you hired your own private math teacher, as some parents have done, you might be able to do it. But that's the only way. If I hadn't been studying math for nearly two years I could never have taught myself probability to crammery the way I did this weekend; nor could I have taught probability to crammery to Christopher (and Ed). No way.
if you thought that was bad — If you thought spiraling in K-5 was bad, wait'll you get a load of it in middle school. Christopher's class has been studying probability for maybe two weeks. The chapter covered at least 18 different topics, so we had to teach all 18 to crammery, instead of teaching 4 or 5 to mastery as you would if you cared about the kids actually learning something. If you want to see what I mean, take a look at the TOC to Probability Demystified:
Chapter 1 – Basic Concepts of Probability Chapter 2 – Sample Spaces Chapter 3 – The Addition Rules Chapter 4 – The Multiplication Rules Chapter 5 – Odds and Expectation Chapter 6 – The Counting Rules Chapter 7 – The Binomial Distribution Chapter 8 – Other Probability Distributions Chapter 9 – The Normal Distribution Chapter 10– Simulation Final Exam Answers to Final Exam Appendix: Bayes'Theorem Index
The book has twelve chapters. The contents of five of them are covered in one chapter of Christopher's math book. (Chapters 1, 2, 3, 4 & 6)
Does a spiraling curriculum lead to negative learning? I'm thinking it does. I'm thinking the effects of a spiraling curriculum are worse than a simple FWOT. When you teach 18 brand-new topics in 2 weeks, you may actually be degrading knowledge.
UPDATE 11-20-2006: Christopher got a 77! Class average 80 or 81. This test wasn't loaded with "Honors" level questions (turns out that's what the tests have been - Honors level tests given to a merely accelerated class in which no Honors level material has been taught). But it had a couple, and it was long. Christopher messed up some minor computations, misread the "spinner" on the spinner problem....and one of the word problems is all wrong. (More later) He could easily have earned a grade in the 80s. He picks up new math concepts much faster than he used to. This started last spring, and has continued this fall. It's cool.
Demystified series
gap anarchy
Engelmann on reteaching material learned incorrectly
teachtocrammery
degradingknowledge
negativelearning
-- CatherineJohnson - 14 Nov 2006 Back to main page.
Comments
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Look here for syntax help.
Catherine, All those late night trips to B&N. Too bad you don't qualify for a home educator's discount (20%). Perhaps you can plead your case with the store management. Surely, you deserve it! -- NicksMama - 14 Nov 2006
hey! How do you get a Home Educator's discount? I need one. -- CatherineJohnson - 14 Nov 2006
I REALLY need one. You should see my office. There are practically no books relating to my actual JOB. -- CatherineJohnson - 14 Nov 2006
Well, except for that stack of neuroanatomy coloring books over there against the wall.... -- CatherineJohnson - 14 Nov 2006
I find probability to be the most difficult topic in mathematics. It is tightly coupled with real world phenomena (e.g. Las Vegas) but is difficult to grasp since the information is conditional on all sorts of factors. It is the farthest from intuitive how to go from a description of rolling dice to a mathematical statement accounting for all possible behaviours. Good luck with the tour through mathland. Hopefully there is some time to pick up a skill now and then. -- SeanPrice - 14 Nov 2006
I'll mention the virtues of role-playing games again. The provide exercises in practical probability with incentives to get things right. Is it better to roll 2d6 or 1d12 damage? 2d6 has a higher mean, but a lower standard deviation. How important is it to increase my chance of a higher number at the cost of increasing my chance of a lower number? What are the tradeoffs in taking a penalty in hit probability to gain a bonus to damage when you do hit? Do I need to defeat the monster before he can attack again, or do I just want to maximize damage over time? (Mainchance or Minimax strategies.) (This is in addition to the reading advantages we talked about before.) -- DougSundseth - 14 Nov 2006
heh. if you're going to take the test on probability, ask the teacher this very, very, simple problem (wink, wink***): You're on The Price is Right. You stand in front of three doors, A, B, and C. "There's a prize behind one of the doors!" says the announcer. "Can you find it?" You point at the door of your choice. The announcer says "Well, we'll give you some help. We'll never tell you anything about YOUR choice, and we'll never show you where the prize IS, but we can show you one place where it ISN'T!!" With that, the attendant opens one of the doors you did not pick. It holds no prize. "Would you like to keep your original choice, or switch doors?" says the announcer. What should you do? * An enormous number of teachers and math professionals get this one wrong. But anyone who doesn't understand it has no business teaching statistics. -- ErikHammarlund - 15 Nov 2006
Heh. You might want to take a look at ProbabilityQuestionSaxon87, MontyHallPart3, DougSundsethOnMontyHall, and others in that post thread. We've been here before. ps. By which I mean that I agree that it's interesting, not that you should stop talking about the subject. -- DougSundseth - 15 Nov 2006
I find probability to be the most difficult topic in mathematics. hi, you guys! I think it's damn hard myself. A Commenter sent me a fantastic probability test today - wonderful! I'll get it posted. -- CatherineJohnson - 17 Nov 2006
Erik hey! Great idea! Actually, she may know the answer. I've been talking to the Math Teacher - the guy people have been hiring to reteach the course. He says that all middle school teachers in NY state have been required to have B.A.s in math for years. Her math knowledge is fine, he says. The problem is entirely teaching. That's kind of distressing, I have to say. I didn't know whether her math knowledge might be problematic (really can't tell from this distance).....but somehow I'd been assuming that if you really knew a subject you'd have some idea how to teach it..... Which, of course, now that I "say it out loud," sounds stupid. He said the problem is "presentation" and test construction. (More on the latter later on - very interesting.) -- CatherineJohnson - 17 Nov 2006
I'd forgotten about all the math professors who got that wrong! -- CatherineJohnson - 17 Nov 2006
Now that I know some "starter" probability, I'm going to do the Monty hall problem "from scratch." It was actually a fun weekend (kind of fun). I've always wanted to know probability, and to find myself being able to grasp the material in the chapter pretty rapidly was great. -- CatherineJohnson - 17 Nov 2006
| WebLogForm | |
|---|---|
| Title: | more teaching to crammery |
| TopicType: | WebLog |
| SubjectArea: | AboutBooks, MiddleSchoolMath, ParentsTeachingKids |
| LogDate: | 200611132053 |