vito
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Posts posted by vito
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About prerequisites:
Sorry for not being clear. I mostly meant not formal prerequisites, i.e. courses “Algebraâ€/ “Precalculusâ€, but specific material in very detail.
Precalculus is a very general term. MIT needs precalculus too.
For example, if this ATA degree program has math classes in the first year, then what are they in detail? what specific math knowledge does your son need to succeed in them?
Since you mentioned the program does not have math classes at all then you can look into the syllabi of electronics classes of that program. For example, Electric Circuits courses would require thorough knowledge of fractions, proportions, elementary algebraic manipulations etc.
You can visit the school, find instructors from that program, visit their office, and ask, find students on campus from that program, chat and ask.
Try to get assignments/tests from specific courses in that program. Elicit the kind of math that those assignments require.
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If your child is already well into high school and he is struggling with word problems then:Don’t focus on being different when someone lacks “conceptual understandingâ€. Everything is plug and chug, including high school material. Google language phrases that translate into math expressions/ equations. Also in a particular topic of any textbook try to elicit how language phrases translate into math expressions/ equations discussed in that topic.Many people think they have “conceptual understandingâ€. In reality they just practiced properly, and now they subconsciously translate word problems into known plug and chug patterns.Visit the school your child wants to get his electronics degree from. Find out in detail what math prerequisites are. Also, get the syllabi of the courses that your child will take first year and retrieve math material that is used there.About Foerster, MUS, etc. There are many books. Some harder, some easier. Find the one that is easy. Let him do it fast. Find another that is somewhat harder and do it fast. And so on.Long = hard.In any given one book some topics (or some problems in a topic) could be harder, some easier. Skip the hard ones for now, do fast the easy ones (no repetitions). Come back to the hard ones later.
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Nan in Mass said (Posted 20 March 2011 - 09:34 AM):
A recent thread made me realize that if I could do one thing over again homeschooling (other than sending my oldest to community college instead of public high school) it would be to do more of TWTM language arts skills - copywork, dictation, narration, outlining, grammar, spelling, vocabulary, memory work, and logic. I didn't know why these were important (guess I didn't read TWTM carefully enough - sigh) so I tended to skip the ones that were hard for us, when in fact, those were the very ones we needed to work more on. I thought I'd just post this as a separate thread in case it helps even one person from making the same mistake I made.
Caution: This might not have been true if I had had a child with strong learning style differences or slownesses, but mine were just engineering-bright/language-arts-dim or wired just a bit differently, not drastically different. Aquiring academic skills so they can learn something by academic means is more difficult than for most children, but not an unreasonable goal. TWTM is the key to that for us. It specifically teaches the skills that the more academically gifted children are just naturally good at. And that means that we needed to work on the ones that my children are not good at. I wish I had known this earlier.
You may need to back way, way up to work on these. Follow the progression laid out in TWTM, and work through the progression. Don't just give up on the skill because your child is so far behind. And if your child is good at a skill, good enough that you decide you don't need to practise it, it is really important to keep checking every year and make sure that your child can still do that skill at the new, higher level. That is the mistake I made with one of mine with narration.
The whys of doing TWTM skills even though they are hard, boring, and miserable:
I think the key to being able to write well is to read tons of well-written material (like great books), to have the physical part down so you don't have to think about it (handwriting and typing), to have something to write about (good knowledge base and good research skills), to have a system of taking the mishmash of thought and putting them together in an organized way (find a method of putting them down in an unorganized way, organize them into a linear structure (outlining), and then rewrite - word processor is nice for this). You need to work on narration and logic for organization, vocabulary and grammar for style. Copywork and dictation deal with the mechanics of spelling and punctuation in a whole-to-parts way and spelling books and grammar books deal with it in a parts-to-whole way. You need to do the narration and the dicatation in order to put the pieces together and apply them.
I think the key to being able to read well (once the phonics part is out of the way) is grammar (so you can understand non-standard word order - think Shakespeare and poetry) and vocabulary. That is the parts-to-whole part. And then I think you need to do tons of reading and narrating and discussing. That is the whole-to-parts, applying what you learned, part.
I think the key to being able to learn the content subjects is study skills, and those depend on dictation (think note-taking), outlining (picking out the main points from the details), narration (summarizing), being able to read well at a variety of speeds from skimming to sentence-by-sentence reinterpreting, and being able to memorize (memory work).
I think the key to being able to teach yourself things as an adult or the key to being able to survive college is reading well, writing well, test taking skills, some sort of knowledge base, good study skills, and good organizational skills - keeping an assignment book, keeping track of one's materials, efficiency (resisiting the temptation of the internet, games, cell phones, and whatever else one does for escape and socializing), prioritizing (skimp on this because that is more important), and dividing large projects into little ones. One also needs to understand the system, how to pay attention to what this particular prof wants, and how to get help if you don't understand something. That last is more important and harder than one might think so I recommend finding opportunities to practise approaching strangers and asking for help. Truly - this is one of those things that seem obvious and easy to grownups but turns out to be a practically insurmountable obsticle to young adults, one that causes them to flunk courses. Sigh.
The advantage of this system is that if you get these academic skills down, high school content subjects are hard work but straight forward. For any subject, you pick a spine (doesn't have to be a textbook - it can be any sort of overview), study it (read, outline, summarize it), figure out what skills are involved and learn them (laboratory skills if it is a science), figure out which bits need to be memorized and memorize them, and then pick areas that are particularly interesting to you and investigate them further by doing research - reading and writing about them about them, and doing experiments. This is the pattern that adults follow when they learn anything using an academic way.
It is scary to concentrate so much on skills at the expense of content when you are homeschooling. What worked for us when the children were small was to do skills Mon-Thurs (along with reading aloud) and history and science on Friday (along with math and foreign languages, skills+content subjects that we couldn't skip or we forgot everything, and piano). It is important to apply the skills to the content areas, once you can do them a little, in order to improve and speed up, and in order to make the skills truly useful rather than just separate skills.
I hope this helps someone,
-Nan
(My credentials GRIN: two sons in college, one 16yo still homeschooling at home and taking community college classes for two and a half more years before going (hopefully) off to 4-year college)
PS - I did do some of these WTM skills. I just can see now, as I have two older children struggling their way through college, that they would have an easier time if their study skills were better, so I am trying to teach the youngest one better study skills and finding that those study skills depend on being able to narrate, outline, take dictation, etc.. Sigh.
PPS - I am editing this to add that a lot of the credit for figuring this out should go to Colleen in NS. If you do a search for posts by her with the word "outline" in them, you should be able to find some more information.
PPPS - Now that I see how many people have read this thread, I am having nightmares thinking that I have doomed some children to long boring days of drill. TWTM has lots of good ideas for making things less dry. TWTM says that what content you do should be allowed to go down bunny trails following your children's interests. TWTM recommends heavily illustrated spines, ones that my family, at least, found interesting even when we thought we weren't interested in the material. All the reading-to-oneself is a pleasant chore once one has learned to escape into a book, and TWTM has lots of reading time built into it, both reading aloud and reading silently and listening to audio books. Reading is still one of those foundation skills. Those fairy tales and folk tales and myths lighten the load. The grammar and logic stage science recs are hands-on and active. Your day should have lots of nice parts, too. TWTM says the skills should be attacked in a "nibbled to death by ducks" manner, a little bit consistently over time. If you do something like Kalmia suggested and establish some sort of routine for working on the skills, then you can just plug through your routine and everyone will know that it isn't forever until a nicer part of the day comes, and nobody has to think about it except when they are actually doing it. School is hard work, but it doesn't have all have to be hour upon hour of unpleasant drudgery at one thing. Think nibble nibble nibble, once the initial explanation is gone through. Cut the task down until it is taking too long. Yllek says not more, but more consistently. That is a good thing to keep in mind. And Lisa (swimmermom) says to emphasize working hard, not being good at something. That is a good thing to keep in mind, too. : ) -
I remember I was a kid. 12-13.In school we had a boy who was seen by teachers and everybody as having real difficulties with remembering and understanding even simple straightforward material.It was accepted by teachers, students, and eventually parents and him himself that he was this way, and nobody bothered him much with homework, questions, etc. He was a quiet outsider. I remember I felt sorry specifically for that he was being already “assigned†a place in life.One day a group of city kids played outside after school. We started naming soccer players that we liked, also their positions, jersey numbers, age, birth place etc.I was astonished to hear the boy I knew from classes easily and happily named 30-40 players, tons of stats about each, and also he genuinely analysed their tactics, techniques, etc.Something wrong here I thought, with perception. Find your way.
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I think high school years are critical for intelligence.Until 13-14 you can unschool: paint sunset, collect butterflies, read Jules Verne, wake up early morning and walk to the river.You could party or coast in college after 18.In between I believe it is time to work hard.
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There is an alternative view on how prestige is earned at the top schools.Watch the last 30 min. of "Inside job" documentary.It argues that corruption in prestigious universities is deeply entrenched.First I was reluctant to watch that film. Nothing new it could offer I thought. Yet it did.Now, a neighbourhood college with humble teachers looks not bad at all.
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IMO, Jacobs geometry (we saw and used only second edition) is important.
You can hold off for now, then come back in a year or two.
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...struggling with the concept of regrouping and with adding or subtracting three or more numbers.
Any ideas on something that might help him grasp the concept. Thanks
If you imply he can regroup two numbers then teach him to insert parentheses and remember to do only two numbers in parentheses first and ignore everything outside of the two numbers in parentheses.
Do it visually, in writing.
Example:
39+19+25=(39+19)+25=58+25
You can even cover "+25" with paper, or do 39+19 on a separate page.
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I sort of disagree ... Button could do 2-digit addition quickly in his head, and forcing him to break it down to regrouping actually completely stalled his mental matth.
There is no academic value in doing calculations mentally and not being able to explain. Analogy: read aloud with no comprehension.
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He can do it in his head, but I have no idea how he gets it.
Bad sign.
He's not using pencil/paper and is getting frustrated when I ask him to write it out.Another bad sign.
Someone said: think clearly, express clearly.
As for Singapore, there is no a separate Singapore "method" that it's OK not to understand and at the same time to understand another way, at least not for two digit addition. All roads lead to Rome.
Take a different book for the same topic if it's still no go. It's better to have at least four five books. Then come back to SM 3A.
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But I also don't want to "ruin" AOPS for her by giving her too many algebraic strategies in her toolbox, so to speak.
Any advice from those who have been there?
The more books you use the better.
Doing a harder book then coming back to an easier book is a good practice for clarity.
I think the true "discovery" approach is a luxury and ultimitely a myth as it requires tons of time, a gifted student and a genius teacher, a rare combination in real life.
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Yes, we homeschooled our older son for one year with great success. He was in grade 7.
He is in college now majoring in math.
We afterschooling now with other kids.
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But where'd you get the idea we were "cosy" homeschoolers?
That was hyperbolic to emphasize the point.
;)
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No. If you understand trig, it will be very easy to derive the trig identities when you need them.
Have you ever participated in a math contest?
It's different to cosy homeschooling.
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Don't you need to memorize trig.identities or something?
If you come to a test having memorized just multiplication tables it will be someone else's turn to smile.
:)
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How do you require a child to divide large numbers before he can recall his multiplication tables?
"Memorizing = bad" is just trendy these days, possibly in light of problems with teaching in schools.
IMO, memorizing and understanding are equally important.
Where are those days when kids were memorizing poems, and it was considered one of the key points in education?
There is no way to do long division without strong multiplication skills including quick estimations of say 2-digit number multiplying by 1-digit number.
Example: do long division 234/27.
You will need to estimate 27*8. For this you will need to do some of 27*7 and 27*9 and 27*6 depending on your skill.
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So given these responses, I think I need to modify my question. I have not seen the pre-algebra book or beast academy, so I guess I am only really asking about Intro Algebra, which I get the impression is a step up from pre-algebra beyond the obvious increased level of the material. The material in Intro Algebra ramps up in difficulty, so I am interested in hearing from people who have done more than half of the book.
Has anyone used Intro Algebra as written (meaning as the primary/ sole curriculum) with a non-mathy kid? If so, I would like to hear how that went.
Alternatively, I would also like to know if anyone who has used Intro Algebra would recommend it to a non-mathy kid, and if so under what circumstances.
It sounds like the people who have responded so far have used the pre algebra text, or used AoPS for supplement, or have considered AoPS but not used it.
Thanks, Ruth
I would suggest try not using AOPS algebra prior the age of 13-14.
The whole idea of seeing someone mathy/ non-mathy, gifted/not gifted before the age of 14 is moot.
Until ~14 focus more on memorizing techniques (example: steps to find LCM), and focus less on trying to elicit how mathy/ gifted your child is.
AOPS by publishing pre-algebra book enters new waters. Their target market is gifted high-school students.
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Well, my kid was confused and asked for help.
We bought SM three weeks ago, and this is actually the first time I looked into the book closer.
The problem #5 has a lot of irrelevant given including this 100 vs. 280.
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Hi all,
Singapore math 6A St.Ed. p.88 #5 says:
<<<
The results of a survey of 100 households ... showed that of 280 households ... 71 reported buying ...
>>>
280 is less than 100. How is it possible?
:001_unsure:
Thanks.
Help me "differentiate" instruction in Foerester Algebra
in High School and Self-Education Board
Posted