Myrtle
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Posts posted by Myrtle
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It looks like the one skill one would want to focus on in arithmetic before hitting algebra is fractions. Be able to add them, divide them, and do word problems with them in your sleep. The skill that seems to help most with fractions that is acquired 2,3,4th grade for operations on fractions is the to have multiplication and division down cold. To know what a common multiple is, to know what a common factor is, etc, be able to compare them (greater than, less than), order them, be able to find the missing denominator or numerator in equivalent fractions.
The bigger picture with algebra is that it's needed for trig, and trig is needed for calculus, and calculus is ultimately needed for physics and engineering.
If you are are interested in the role of math in a Classical education then you might be interested in a course in synthetic geometry in high school which amounts to Euclidean geometry with proofs. This isn't really "needed" if you are headed down the utilitarian math path in which case geometry will include lots of graphing.
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For these schools AP test will not substitute.
Fordham has a report out questioning if AP exams deserve the "Gold Star" status that they seem to have with parents of highs school students and their teachers. They had academicians from each of the fields evaluate the exams. David Klein, the mathematician reviewing the Calculus exam, gave it a relatively low score. A squabble ensued as Fordham tried to coerce him to raise his final grade and he refused to back down. (See Washington Post's article "Secret Gripes of Professor Klein")Ultimately he requested that his name be removed from their report and they raised the score.
The Washington Post has a forum dedicated to the discussion of AP exams and other entrance exams. Lots of fun politics and public disputes over there where the journalist hash it out with admissions and parents over these issues.
If elite colleges don't believe that AP exams represent high standards it would explain why they are looking for alternative proof of mastery of a subject area other than the AP exam.
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We are in Houston.
I think there is a WTM yahoo group for the folks in Dallas.
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My son had this problem but it wasn't due to my faulty teaching or lack of familiarity with the procedure, he is eleven and still hasn't "grown out of it." Slopping his way through procedures of any sort (putting away the laundry, cleaning off the table, math) is part and parcel of his temperament.
Rather than have him memorize steps to the point where they become a neural reflex like playing a sport or the piano, I required him to start doing a "check" after these kinds of problems. So, if he misses long division problems then he check is to multiply the divisor and quotient and make sure that he comes up with a number that matches the dividend,
In the case of sloppy addition, he would have to subtract in order to check. This, I believe, teaches several things:
1. Inverse operations
2. You CAN find your own mistakes.
3. You take responsibility for your work, rather than mom.
4. Math is about thinking and working through problems, it's not a "problem" if you instantly know how to solve whatever is thrown out at you.
5. A math problem isn't correct because an authority arbitrarily says so, it's correct because it is so.
I have seen other posters use a carrot and stick approach: "If you solve the odd problems correctly, you do not have to do the even problems."
When they get tired of the extra work they will concentrate more.
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I don't know all specialists so there may be something that I have missed. A teacher friend of mine gave me all the materials from a special training seminar she had attended and it amounted to huge binders of instruction on how to teach phonics! Another useful resource for me was Earobics which is software. It was designed by speech therapists (so they say) and our school system does actually include it as official therapy with some of their spec ed kids according to my neighbor with one in the system.
It involves no reading at all, colors or shapes represent sounds and the child has to remember, reorder or classify the sounds in the words depending on the activity. It automatically adjusts to the level that the child is performing at. Two mistakes in a row and you are moved down to the lower level, three correct answers in a row and it moves the child up a level. The differences between the levels are tiny, tiny and hard to even notice sometimes so it's very gentle.
It really, really helped my son with spelling and I'm about to get the adult version for him since he's starting to revert back to making many more mistakes than he should. He still is dyslexic. He was never "cured" of that. He never grew out of that. Not only does he still mess up on simple short words but he's still reversing b/dand reversing digits when writing or saying double digit numbers! However, he is literate and I'd say that he can read at grade level. He's eleven and is coming pretty darn close to being able to read adult-level books.
It will sound hackneyed, yet it's true, that the single biggest improvement to his reading skill happened within the past 12 months when he found books that he liked to read that he picked out for himself (knock knock joke books, transformers, fluff) rather than me picking out didicatic, educational books (DK science readers) for him to read. He is definitely over the hump.
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I've been advised to hold off on doing any "school" work with her until next year
Liz in NC
I have a child that has some serious language issues. I was advised by "the" leading expert in his particular disorder, a researcher, to hold off doing school with my child in K and 1st grade and to absolutely hold off teaching him how to read. I had absolute and complete faith in this expert. Within a few weeks of that my son walked up to me with a book open and read it to me. How did he learn these words? I have no idea. Against the expert advice I began formal reading instruction although I did it only with the complete cooperation (he was begging for it by this time) of my child. The lesson I learned was that the expert was an expert with the disorder but not with my child!
I think a lot of people advise to delay seatwork and workbooks unfil 1st grade or even later because they imagine that you will push an unwilling child into something that she's not ready to do, and perhaps that is true for some people, but if your child is an eager learner and happens to enjoy workbooks I don't see how it hurts anything at all. Also, there are folks out there that if you question them carefully turn out to be completely against any sort of seatwork. They think that all of education should be one long series of hands on projects and would extend the crayola curriculum into high school if given the chance. They too will reap what they sow.
By the end of K I was doing 2nd grade arithmetic with my oldest son; we still called it K.
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Does anyone have any advise on how to teach story problems? My son is in the second grade and can solve very simple math story problems, but not ones with multiple steps, he just doesn't get how to solve those. We use Horizons math 2 and they just do not have much practice with these. Anyone have any ideas on what might help? Thanks!
A good math program would teach these by explicitly breaking down the various steps. (Foerster's algebra program does this in algebra for example)
Here's one example of how one of these proto-multistep word problems might be worded.
Mrs. Tan bought 125 fishballs. She kept 110 fishballs for a party and divided the remainder among her 5 children.A) How many fishballs did she give away altogether?
B) How many fishballs did each child get?
After solving a multitude of such problems the intermediate question would be eliminated in the hopes that the kid would have intutively learned how to do an intermediate step. The word problem would then look like this,
Mrs. Tan bought 125 fishballs. She kept 110 fishballs for a party and divided the remainder among her 5 children. How many fishballs did each child get?In the Singapore math program there is a device called a "bar diagram" that is a visual organizer that the kids use which is very, very helpful once you get the hang of it (So helpful that I resort to using one for myself to solve hairy algebra word problems that are linear equations in one variable It helps me to figure out how to set up the equation)
I have a seven year old son with a bad language delay, and I would have thought that his weak point would have been word problems, however, after demonstrating how to organize the information with bar diagrams he has dramatically improved his ability to recognize when a problem needs an intermediate step and what that step is.
Here is a blog post about multi-step word problems which is a very important pre-algebraic skill to develop. There are sample problems and bar diagrams. While you wont' be able to figure out with only one or two bar diagrams how an what to do with each of your word problems, the Singapore math program systematically teaches these for each class of problem that the kid comes across.
With my first son I believed that he personally needed to demonstrate every single problem with a bar diagram whether he needed to or not. Now with my second son I'm only using them to demonstrate the thinking behind a new class of problems that I know he'll be coming across and then if and only if he misses the problem will I have him go back and fill in the info on the bar diagram.
I wish I could give a bar diagram 101 course! My printer is broken right now and maybe one of these days I'll get arounding this, so for right now, be assured that indeed there is a math program that does explicitly teach this step-by-step.
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I have been homeschooling for 11+ years and have never read The Well Trained Mind[/i
In wondering why teaching Latin is so important, when my 5th grade son's schedule is dreadfully full already,
Well Trained Mind doesn't really explain extensively why Latin and Greek are important, it's more of a "how to" book with resources once you've decided that you do indeed want to do Latin and Greek. An extended discussion of why Latin and Greek are important in education would be Tracy Lee Simmons Climbing Parnassus and for a discussion for the educational thinking that resulted in the demise of Classical Education see Diane Ravitch's A Century of Failed School Reform. Both of these are probably available through your public library.
While the Ravitch book is about American public schools it's close to the top of my list of books which have helped me understand the myriad of curricula out there and quickly identify the underlying educational philosophy of them in order to consider them or reject them when making choices. It was useful to me to see why Classical Education was important after seeing why it is that the alternatives failed and what those alternatives were.
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Hi Holly,
That any number added to zero is still the number you began with is not a "concept" in math. It's an axiom. (It's one of the field axioms) It's not that one can't illustrate it with objects, but that doesn't provide an explanation since there isn't a mathematical explanation.
A kid simply has to memorize this as a rule.
I have found that my third child is impervious to attempts to teach her using manipulatives and a "conceptual" approach. Ultimately, after she has been exposed to a landslide of drill she realizes the utility of the "trick" that I tried to explain to her (counting on by 1 for +1, for example) It's as if the method she uses, while conceptual in nature, must be her idea and not mine for it to stick. When I give up and do just plain drill work, making sure to only give her a very few problems, say 3 number facts randomly repeated 10 times) the concept itself will click with her with time.
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We directly taught our ADHD 11yo son symbolic logic from an old 1960s algebra book.
The modern (as in still in publication) logic books for students that we have seen have the kid study logic as an academic subject rather than training them to think logically. In addition, many of these were simply asking to much of a younger child or one that can't focus very well. There seems to be a complete absence of good logic programs for middle school students. Also other programs which are age appropriate, while providing entertaining opportunities for students to use logic in activities, never explicitly teach the student how to go about doing this.
The areas that helped our son the most, and me as well, was learning what the converse was, why not to assume the converse, what the contrapositive is and why one can use it to arrive at a conclusion. He also learned how to negate expressions with "or" and "and" in them--both natural language, and mathematical expressions. In the end he was able to prove mathematical theorems using proof by contradiction and proof using the contrapositive "Prove that the additive identity is unique." He was also able to follow adult conversations that were political or philsophical in nature a little better than before. Let me emphasize, this is an eleven year old ADHD dyslexic kid with a tested IQ of only slightly above average.
The other program that we used with him that teaches how to apply logic was Mathew Lipman's Philosophy for Kids series. This is still being sold by the publisher and is quite expensive. The child reads a short novel and the teacher's manual (which is several inches thick) then provides activities and topics for discussion. While there is much more going on in the novel than logic, here is a short passage from Harry Stottlemeier which is the 5th/6th grade level.
Now, sitting at his desk, Harry turned over in his mind the conversation between Tony and TImmy. "If ther are many ways of forming a number, " he said to himself, couldn't there be lots of different words all equal t the same word? Like 'father' cold aslo be experessed as 'daddy' or 'dad' or 'pop'." Then, in a flash, he had an idea. "Coul it be that words like 'all' and "no' are really like the number ten that Tony was explaning to Timmy? Because if that were so, then all sorts of other setences could be changed into sentences begining with either the word 'all' or the word 'no'!But when he tried to figure out some other setnences that he could change around the way he wanted to, he couldn't think of a single one...
It is unfortunate that logic was removed from the curriculum in the 1970s. Sometimes I joke that we are heading back into the Middle Ages when it comes to education, but even in the Middle Ages logic was taught.
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Can anyone confirm that there is no typing involved in any of the activities?
It's just pointing and clicking, right?
If anyone has access to the full program I'd love to hear them confirm this. I see that it's clicking for the sample activities, I just wanted to make sure it was that way for all of them. I don't want my 2nd or 3rd grader having to hunt and peck to do phonics.
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The ability to rep someone else is called "rep power" and it looks like that admin determines this. It's possible to not have any rep power at all in theory. Nonetheless, seems like a nice way to let someone to know privately that you appreciated their post.
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Amy,
The idea is that when folks see a particularly outstanding post that they "rep" the poster. Those posters with the most outstanding posts will eventually accumulate little squares by their names. Looks like everyone so far has only a single little green square. I don't know exactly how the algorithm works for this board but other boards have a formula by which those when someone with a high rep reps someone else it's worth more points to the receiver than if someone of low rep, or few posts, reps them. I've also seen boards where you can negative rep a person if you don't like their post but I haven't seen it here.
It's not clear how this will play out on these boards. If the board culture is such that folks rep those with informational posts then you'll see the super helpful people with the highest reps. If they rep those that are witty and funny then the rep would indicate the political popularity of the poster.
Another function that it might serve is a private way of giving someone a "thumbs up" for something they have said without doing so publically (Remember the old "ITA" posts??)
When you rep someone you are given the opportunity to make a comment and you can explain to them why you repped them. When someone reps you, there will be a note of it in your user account. ('ll rep you so that you can see) It will tell you the particular message that you were repped on. The poster repping you is not revealed.
If you go to list of users an click at the top of the column which is titled "reputation" it will show those with the highest reps at the top. Right now those are the board administrators and this will give you an idea of what a high rep would look like.
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I ordered some books and was unintentionally mailed someone else's order. The company told me that it wasn't worth it for them to pay for return shipping since the value of the item that they accidentally shipped me was to low. They told me to keep it.
Had they wanted their item back I would have gladly shipped it back at their expense. They can offer to pay the bill to FedEx for you, and in fact, if they do any amount of shipping at all they will have an account set up in advance for the purposes of returns, you show up to mail the shipment and that code is placed on the item by the clerk and you walk away without paying a thing. In some instances I've known of companies who send a courier to pick up the item (if it has a high enough value) so that you don't even have to leave your house.
Ultimately, it doesn't matter if their mistake was intentional or not, it's their mistake, not yours. Contact the company, explain the return postage situation and ask them what other arrangements they can make. They may offer to pick up the cost in some other way, or they may decide that it's not worth the item. What they can not do is require you to pay for an item for which you did not request, and no reputable business would! If you'd feel better talk to your postmaster. There is a whole body of law about these very issues.
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Pronouce "Thee" if the next word begins with a vowel-sound (this would include words like hour that don't technically begin with a vowel)
Pronouce "thuh" if the next word begins with a consonant sound
At least that's what I learned years ago -hth
Yes, and in slow spoken English glottal stops are unconsciously inserted before words that being with vowels which ends up making all the words begin with consonants. :-p
You say tomah-to, I say ?apple.
I'll have to listen to whoever is reading the news on the radio this afternoon to pay attention to what they do with "the". (NPR-speak is what I think of when I think standard English. )
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Mine are nonfiction:
Just finished Fastnet, Force Ten (The deadliest storm in the history of modern sailing). This book wasn't nearly as good as Tall Ship Down though. I'm about to start either,
Once is Enough by Miles Smeeton which is about a British couple who sailed around the Southern Ocean in their 40 foot sailboat during the 1950s and it got somersaulted in the ocean. This was evidentally the first time that anyone had heard of this happening to a small sailing vessel. Don't know why they say that once was enough for them because after bobbing aimlessly around for some weeks while making repairs, they sailed into Chile, fixed the boat and headed back into the Southern Ocean only to get somersaulted a second time in aother storm. I guess "Twice is Enough" wouldn't sound as ominous? Oh yeah, the guy's wife is interesting in her own right because she also made headlines in an attempt to climb Everest.
The other one that I'm tempted to launch into is The Floating Prison which is of the experiences of a French prisoner of war (Napoleanic Wars) in a British prison hulk from 1806-1814. Against all odds the guy survived and wrote long book about it which is available in translation.
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Or is it pretty much set/determined that if a child passes 8/7 they are definitely ready for Algebra, even if they still have a few weak spots here and there?
Hey Robin!
Remember me?! ;-p
I have a copy of Saxon 8/7 and I'm familiar with what's in it. You'll have covered a good chunk of standard American algebra programs by using Saxon 8/7. As for whether the gaps are significant, it seems like it depends on what the gaps are in. For example, mine made horrendous idiotic mistakes when adding fractions, but you get fractions in spades once in algebra and that alone forces him to pay more attention to his arithemetic (which has improved simply because of his acquired skill in algebra)
Also factoring polynomials has forced him to focus on things that he didn't focus on before simply because he didn't need to and he's much better at doing thing like factoring integers in arithmetic. On the other hand, if the gaps is something like, "Well I can't remember how to add to fractions with unlike denominators" and the kid is still adding the denominators then they need some more work before heading into agebra.
Another useful skill is having experience working with multi-step word problems and being able to "show your work" by writing down a single equation which results in the answer. This would involve the student using parenthesis to indicate order of operations. A student who has facility with this in arithmetic would have a huge load taken off of them once they hit the word problems in algebra.
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Easy Grammar has a supplement called "Daily Grams" which offers daily review of prior topics. Think: Saxon Grammar.
I had no problem at all with my fifth grader not knowing the difference between a subject and a verb since he was studying Latin.
I'm supposing after the 7th grade I'll have to go revisit Susan Wise Bauer's grammar recommendation for high school since I doubt a fourteen year old would be ready for Radford's Transformational Syntax.
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He's getting faster... but really its just faster at counting not actually adding and subtracting or even memorization of the facts.
I stopped this in my daughter by explicitly telling her, "Hey, if you can remember what you said the last time you saw this card you don't have to count it up, you can just say it." It was as if she thought that the whole point of arithmetic was to go through the procedure each and every time whether you need to or not. And how are they supposed to know otherwise?
I reduced her problem set down to three addition problems. She would count on only if she couldn't remember the answer. When she had rapid recall of those three I'd add one more. We did "concepts", we did manipulatives, we did coins, beads, ducks, blocks, legos, we did number bonds, we did every drill sheet in Christian Liberty Press, and then went back and did it again because it didn't stick. We did Rod and Staff drill booklet twice. We did Flashmaster.
When she started learning addition with sums 11-18 the same thing happened. She ran out of worksheets before she had automatic recall. I got a Saxon 2nd grade student book and ripped out all the drill sheets and use those. Don't know how the Saxon kids can memorize it so fast but with mine I have to let her work a single row of problems, cover up the answers, have her repeat the problems and their answers to me orally and she can't do it. We go through the same row of problems five or ten times before she can "remember" the answers for those five problems. Then I add on another row. Then when it's all done I program the Flashmaster to give her only those problems that she did on the Saxon drill sheet. The next day I have her review the Saxon drill sheet, redo the problems in Flashmaster, preview the new problems, and then we repeat the same long slow process with the second drill sheet.
She has no problem with "concept." She makes a group of ten by subtracting from one digit and adding to the other. Its just that she needs, tons and tons or practice to get this to be automatic. She is finally learning that her conceptual approach is a tool that one uses when one's memory fails them but that she should try to remember it without going through all the steps.
I am planning on keeping her in Singapore math. Considering her approach to math of all people she is most in need of being exposed to multiple approaches to problems. I think, with mine at least, that it's going to take longer in the short run but in the long run it will pay off.
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acquaintancedesterousQUOTE]
Niiiiiice
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Look at the final Explode the Code books and guestimate if your daughter knows the phonics rules listed for those particular books.
Explode the Code 8:
-ness, -less
-ous, -or (as in generous, humorous, inspector)
-ist, -ity
-ture, -ment
-able, -ible
-sion, tion
-ance, -ence
-tive -sive
-ify, -ize (as in qualify, motorize)
-ti-, -ci- (as in delicious, essential)
Other words in ETC 8 with these phonographs: acquainted, acquaintancedesterous, fortify, defective, defection, investigator, hazardous, dexterity, collective, recollection, dependent, patience, indestructible.
If you can remember your daughter just cruising over these phonographs while reading whatever it is she reads aloud to you then she probably doesn't have much to gain in Explode the Code and would be ready instead to study words with Greek and Latin roots. On the other hand, if she stumbles over multisyllabic words with these endings she might benefit from a systematic study of these phonographs in ETC 8.
ETC 7 covers soft c and g and ei, eigh.
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Or do you just say "we need to get such and such done in this amount of time"?
Sometimes the kids are on their own schedule and I can't impose my ideal schedule on them. If I did that I'd either have to dumb down the material or skip material when the kid isn't getting it, or switch to a watered down book. Better to do part of the skill in depth than to skim across it and get all of it done superficially.
I doubt I'm going to finish algebra this academic year, for example. I've got another kid with serious spelling issues. He'll just have to keep working on it before he gets to the next stage/grade.
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Can't remember the name but my neighbor showed me.
It isn't as bad as some of the ones that you all have been listing. It does teach standard algorithms, however, the topics are not sequential and there is not nearly enough practice.
While I wouldn't instantly gouge my eyes out if my child came home with this textbook I probably do so within a day or two since in this textbook's alternate universe plumbers do number theory on their jobs (aka perform operations on fractions) and mathematicians have been using decimal expansions for centuries in an attempt to understand PI.
Never is an opportunity passed up in which math is not treated like an experimental subject and fallacious reasoning is encouraged whenever possible. Want to know more about PI? Grab a measuring tape and a calculator.
The kids are frequently denied recess all day long and I've been told that the playground is as much fun as the math classes.
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Some suppliers are not reliable about having items in stock and I want to start early in case there is some unanticipated wait. There have been two years where I couldn't start school when I wanted due to late shipments.
I'm waiting for the new Singapore science textbooks. Once they get here I'll have to figure out what lab supplies to order and then hunt around for the best place to get those things. Meanwhile, I have to wait for them to get 3rd grade MPH Science tests back in stock. I also need to get the Explode the Code phonics early from my homeschool bookstore. Last time I discovered that they only ordered that twice a year and they were out of stock when I wanted them. One year Rainbow Resources had me on back order for MONTHS, etc.
Need some free resources...
in K-8 Curriculum Board
Posted
Arizone Geographic Alliance has some nice ones