Is there no room for contemplative types?

[Jean in Newcastle]

One of my biggest frustrations in university (and somewhat in high school) was that there was no time to really learn material, to think over it and to let it soak in. One of the reasons I wanted to homeschool was so that once we hit the high school years we could learn at a calmer more contemplative pace. That doesn't seem to be the reality. Or when it is, we have to pretend it isn't and still cram other stuff in. What I mean by the last statement is that we've taken longer to do certain courses - we took a year each for Traditional Logic 1 and then Traditional Logic 2 because despite working every single day, it took us that long to really delve into the material, to look up other information on the syllogisms and to really understand it. But each class will only count for a semester credit. I'm stressed out looking at all the requirements we need to have for the transcript (we're on track but there is no slack there.) Is there really no room for a more rambling learning speed - esp. if you want to go on to university?

[regentrude]

As a student, I personally have not made the experience that there is too little time to digest the material in university. We covered a lot more in a semester than my students do here (I will refrain from going on a rant about this). We did work hard and had 60+ hour weeks and supplemented with many additional books outside of the class, but it never felt hurried.

Material and concepts settle, even when the course is over, and learning does not stop at the end of the course. There are concepts students will truly understand a year after they have taken the class, when they encounter the topic in a different context - things will click and make sense on an entirely different level. I think this is the nature of all learning.

 

I do not feel any time pressure in high school and feel we have enough time to digest. We do, however, focus heavily on the five core subjects (4 years of each) and limit the number of electives.

What are all the requirements of which you speak?

[Jane in NC]

I discovered T.S. Eliot's Four Quartets while following a rabbit trail as a college student. In later decades, I have continued to read, digest and contemplate this work. Even if I did not study Calculus, Shakespeare, Meteorology or German, I would never had had time in college to say that I have grasped these poems.

 

Some things take a lifetime to study. Some things that I thought I understood I saw with new eyes when I taught them. I agree with Regentrude: the learning does not stop at the end of the course, especially since we may learn even more connections the following semester or in years to come.

[Lori D.]

Jean, I think it is possible, but it will mean some careful planning and scheduling on your part. It's always the the balancing act between breadth and depth. (Remember the "Depth vs. breadth question" mega thread?! Also check out the "Broad vs. Focused Study in high school and how to find balance" thread ;)). As with all things in life, there is only so much time and energy to go around, so we have to choose carefully how we want "spend" those resources.

 

To go more slowly and more deeply means a bit of a compromise. There are 2 ways I see that happening, and you could decide to make it a combination of the two:

 

1.) It may mean limiting the scope (breadth) of a class so that the fewer science topics you cover or the fewer books you read for literature can be done at a slower, deeper pace.

 

2.) It may mean limiting how many credits/classes you do in a year so you have the time to go slower/deeper for each.

 

What does that look like?

- It may mean dropping or scaling back some outside activities and interests.

- And/or dropping or scaling back other classes -- i.e., not go so deeply in some classes, just make them "get 'er done" classes" esp. if they are not of high interest to you and DC

- And/or reading or doing some school in the evenings or on weekends.

- And/or working through the summer.

- And/or scheduling only 5-6 credits per year, which would accrue 22-24 credits (a solid amount for university entrance), rather than the faster-paced 26-28 or more credits.

 

(Check out the thread: "S/O: how many credits to graduate. Is less more?".)

 

More ideas:

Are there areas you can outsource and be fine with? Say, learning a foreign language? You can get a credit's worth done at someone else's pace pretty easily and it's probably NOT an area you'd *want* to slow down and go more deeply... (If you did, going and living short-term in a country that speaks the language would be the most efficient way of going deep both in the language and the culture. And that could be done as a short-term mission, a summer-long vacation, a study/travel year, or other options...)

 

In other words, each year, consider picking just TWO subjects of most interest to you and DC (OR, the subjects that will NEED the most time to absorb), to go deep on and take the extra time. For example, History and Science. And, you could still go deep with Literature, just do fewer works to be able to go slower and deeper. Then your other 2-3 classes, decide you don't need/want to go slower/deeper, but just accomplish them (for example, Math, an Elective, and Foreign Language).

 

Also, it's important to be able to learn how to say "when" -- in other words, when to move on to the next book for literature, or the next topic in history. Deep discussion is great, but you can also get caught in the trap of thinking you have to cover every little detail, and you'll spend 4 years covering Ancient History. Which is great if that is your DC's interest and passion. But you can't also expect to cover the rest of World History during high school going at that pace. Remember, you want to encourage life-long learners; you and DC can continue to cover more literature and more history as adults together for fun and interest! We've done a little of that, as have friends of ours with 3 grown/college DSs.

 

Perhaps schedule yourselves by time; literally, set a timer, and when it goes off, you're done with that subject, or with school for the day. Use the rest of the day for letting what you learned sink in, and discuss over the dinner table. The next day, move on to the next topic or chapter. Let the dinner discussions be your time for processing and depth. Or bring up previous discussions/chapters as you cover the new ones, and discuss how the topics fit together while learning the new material...

 

I like this past thread (probably because I got to rant in it -- LOL!): Are we all crazy?! How can a kid get everything done in high school homeschool?!

 

BEST of luck as you work to balance the breadth and deep of high school for your family! Warmest regards, Lori D.

[RootAnn]

What I mean by the last statement is that we've taken longer to do certain courses - we took a year each for Traditional Logic 1 and then Traditional Logic 2 because despite working every single day, it took us that long to really delve into the material, to look up other information on the syllogisms and to really understand it. But each class will only count for a semester credit.

 

Forgive my not-to-high-school, don't-know-much question, but if you worked every day (req. # hours for a full credit), added more information (your look-ups), etc., why can't it count for a year-long course?

[elegantlion]

I contemplating this as I'm planning today. It seems like we start at the lingering soaking pace and end in a frenzy. I'm trying to eliminate that next year. Add to that he'd be quite happy to drop English and Writing and focus solely on his interests, which are academic but fall into the elective category. Also adding he's going to have to be more independent next year.

 

My weakness is planning at my reading pace, not his. He's just a slower reader. And he likes to discuss things that interest him. I just lined out one textbook for next year, he'll be reading at breakneck speed for most of the year if I schedule all of the chapters I want to cover (not even all the chapters in the book). So now I'm going back through the book to see what I can eliminate (it's a college text, so I could safely eliminate a few sections from some chapters). I want to have time to hear his "I wonder if..." as he reads.

 

I also decided to try a block schedule for next year, rotating A and B days. Odd weeks will have 3 A days, 2 B days, even weeks 2 A days, 3 B days. That will give us a little daily time to linger. It will also affect my scheduling, but at least I won't overschedule - hopefully.

 

I don't know, I'm unsure about a lot of things lately. I do know ds isn't shooting for a top tier school, he can't be pushed to do more or faster - he has an even pace. I also know our lives outside of school are changing drastically and I don't want to lose the "magic" that adds value to our school, the discussions and time to linger. We spent 10 weeks reading The Iliad this year. It was a perfect pace for us. We read it all aloud, we listened to the Vandiver lectures, we joked about Achilleus' whining, we fully experienced the book.

 

I also try to go back and revisit my goals and requirements for our school. I spent a lot of time last year sorting though how I felt about the whole homeschooling high school experience. I was in a good place. I need to get there again, in my head at least.

 

I also know that he'll grow and change even over the summer. I try to leave that window open to modify plans as necessary, jump into a different section of a subject, loosen up a bit on another. I remind myself of those words written here so many time, he won't finish high school at 15, He'll grow so much between now and then.

 

I want to ds to call me from college, excited about learning something new. I want him to continue learning as an adult. I don't want to burn him out between now and then. For now I'm going to be cutting out part of his text readings for next year and schedule some discussions instead.

 

Great question, Jean.

[HollyDay]

I've been contemplating this all year. One wonderful advantage of homeschool is the pacing. If you are able and want to move faster, you can. No need for busy work. If you want to slow down and take more time, then you can do that too.

 

Until reality hit in my daughter's junior year. Speed reading, timed math questions, check off the box, etc., etc. When prepping for the SAT, dd had to learn to read the questions first then quickly skim the text to find the answer and move on. She kept asking what was the "point" of that type learning. She wanted to digest the info. But, there isn't time for that on the test and the prep instructors kept reiterating that there would be no time for that in college. Dd asked them what the point of going to college would be if not to learn and digest the info.....to own it, not just be able to answer the question on the test.

 

Taking the SAT prep test untimed, dd could get a fabulous score. There were several sections she got a perfect score. But, timed, the score comes down because there isn't enough time. I guess that is the point. They want to see who can work fast and who can't. But, what does that say about higher education? I've heard kids who have come back this summer from their first and second years of college say that you don't have to worry about retaining the info, just get the work done the way the profs want it done and move on.

 

I'm not sure what to make of it all at this point. Learning is life long. It doesn't stop with high school or college. In fact, much of the learning is just beginning at that point IMHO.

[Jean in Newcastle]

A couple of responses.

 

Yes, I think I'm asking about depth vs. breadth. I had read some of those threads when they happened, Lori, but it will be good to read through them again. Thank you!

 

I think part of it is my own awareness of how much I don't know even of subjects where I was getting top marks in University. But as a couple of you pointed out, it is a lifelong endeavor.

 

Some of it is coming up to a realization that the dreams I had of homeschool high school (more individualized cross-disciplinary studies just aren't happening because we are crossing our t's and dotting our i's.

[Jane in NC]

At the end of the day, Jean, I think that homeschooling allows us to choose certain subjects in which we can go into greater depth. Yet our students themselves may not wish to pursue depth in all disciplines. Unfortunately there are things that I wanted to do--like political philosophy as part of an American Government course. I laid the foundation earlier in high school but by senior year we had simply to "get 'er done".

 

But that does not mean every course went like this! My son has revisited his extensive reading from high school as a college student and enjoys what professors who have made a lifetime study of some of these works have had to say. Build a strong foundation from which your students can grow!

[Lori D.]

I do know ds isn't shooting for a top tier school, he can't be pushed to do more or faster - he has an even pace. I also know our lives outside of school are changing drastically and I don't want to lose the "magic" that adds value to our school, the discussions and time to linger. We spent 10 weeks reading The Iliad this year. It was a perfect pace for us. We read it all aloud, we listened to the Vandiver lectures, we joked about Achilleus' whining, we fully experienced the book.

 

I want to ds to call me from college, excited about learning something new. I want him to continue learning as an adult. I don't want to burn him out between now and then. For now I'm going to be cutting out part of his text readings for next year and schedule some discussions instead.

 

 

 

Totally agree!

 

And just wanted to say, we were slower paced workers, too. We spread out 3 credits of science over 4 years of high school. One DS took 1.5 years *each* for Algebra 1 and then Algebra 2. We, too, took a good 10 weeks at least on the Iliad to do it at our pace and really absorb it and often reference it. All of our Lit. was done at a much slower pace than what others on this Board schedule -- and that's great that they know they need to go faster through their Literature or they go nuts. And others can knock out a science or math in .5 year, and that's great, too! But, it wasn't the right pace for us.

 

So, we got through less... A LOT less when I compare to some on this Board. But, we thoroughly enjoyed and understood what we *could* cover. We managed to accomplish -- and accomplish it well -- a basic classical education, even though we were missing a number of traditional elements of classical ed (like Latin). But in looking back, I feel it was a solid accomplishment with 2 average students, neither of which had clear career plans or were ever thrilled with the idea of any kind of schooling. (lol)

 

And our slower pace allowed DSs to participate in several extracurriculars that were pivotal for helping DSs mature in faith, maturity, leadership, generosity, and responsibility. And for that I'm profoundly grateful -- if I'd been pushing harder for more volume and/or breadth of academics, we would have missed out on the very things that have helped DSs become the young adults they are. Going slower has been part of allowing our DSs to mature at *their* pace and to not hate learning.

 

So far, with DSs 1 and 2 years into Community College and looking towards transferring to state universities, continuing to take life at the slower pace, and refusing to get swept up in the college / future career / job availability panic, is allowing DSs to move into the opportunities, the learning, and the life experiences as they open up in the right timing for DSs...

[regentrude]

At the end of the day, Jean, I think that homeschooling allows us to choose certain subjects in which we can go into greater depth. Yet our students themselves may not wish to pursue depth in all disciplines. Unfortunately there are things that I wanted to do--like political philosophy as part of an American Government course. I laid the foundation earlier in high school but by senior year we had simply to "get 'er done".

 

But that does not mean every course went like this! My son has revisited his extensive reading from high school as a college student and enjoys what professors who have made a lifetime study of some of these works have had to say. Build a strong foundation from which your students can grow!

 

 

I completely agree. We certainly have no time to dwell on every.single.subject and go above and beyond, but my students don't have that interest in every single subject. Some we just get done and check the box. Others, we go broad and spend a lot of time.

I see the revisiting already with DD in high school. We studied Shakespeare for a few weeks in Renaissance, nowhere near enough time to get into all of it in depth. But since then, she has read and re-read many plays, watched plays, discussed staging, wrote about plays, read about Shakespeare - in her free time, because she is interested. She has read Hamlet seven times now and gets something new out of it every time. She'll take another class this fall, and I imagine she will continue to go see and read and listen to plays for fun.

DS is interested in politics and government. outside his coursework, he watches podcasts and reads magazines and debates political topics online. I do not have to squeeze everything into a "credit".

 

I do not believe one can ever achieve comprehensive knowledge. There are scholars who spend their entire life on Homeric epics! Anything I do in high school has to fall short of their depth. But by at least touching it in highschool, my kids know it is there, waiting to be revisited if they so choose. And by reading literature, they develop the skill to read the literature we could not cover on their own, later. We can not be truly comprehensive in any subject, we always select.

[elegantlion]

 

I do not believe one can ever achieve comprehensive knowledge. There are scholars who spend their entire life on Homeric epics! Anything I do in high school has to fall short of their depth. But by at least touching it in highschool, my kids know it is there, waiting to be revisited if they so choose. And by reading literature, they develop the skill to read the literature we could not cover on their own, later. We can not be truly comprehensive in any subject, we always select.

 

 

I agree. I hope I didn't come across as we've gotten everything out of Homer we will ever get, I know better (can't seem to write clearly lately). However, because we took the slower pace he's more apt to return to Homer later (hopefully). I goofed with another book. I tried to schedule it in for the last few weeks of the year. The quick scheduling didn't work, he has no interest in finishing the book now.

 

I do struggle with what subjects can be git-r-done and what needs better coverage. Many previous posts about building skills vs. content have found their way to my "guidance counselor" notebook, should dig those out today.

 

It doesn't help his interests lie in totally different subjects than mine. So what I originally thought we might cover less in-depth have been subjects he was to study more in-depth. I could simply say this is what we're doing and this is how we're doing it, but that's not why we homeschool. Outside of the basics, he does get a lot of input into what he studies.

 

Lori, thanks for your comments. It's nice to know it works in the end. There are so many of you I am grateful to for sharing over the years. I'd feel so lost trying to homeschool high school with this board.

[Kareni]

 

Forgive my not-to-high-school, don't-know-much question, but if you worked every day (req. # hours for a full credit), added more information (your look-ups), etc., why can't it count for a year-long course?

 

 

Your question is a valid one. Sometimes courses count as one credit no matter how long they take to complete. So, for example, the body of material typically known as Algebra 1 is generally considered to be worthy of one credit whether a student completes it in three months, one year or two years. Jean, in her initial post, is implying (I infer) that Traditional Logic 1 is considered a half credit course even though she and her child went deep and took a year to cover the material.

 

Regards,

Kareni

[HollyDay]

 

 

Totally agree!

 

And just wanted to say, we were slower paced workers, too. We spread out 3 credits of science over 4 years of high school. One DS took 1.5 years *each* for Algebra 1 and then Algebra 2. We, too, took a good 10 weeks at least on the Iliad to do it at our pace and really absorb it and often reference it. All of our Lit. was done at a much slower pace than what others on this Board schedule -- and that's great that they know they need to go faster through their Literature or they go nuts. And others can knock out a science or math in .5 year, and that's great, too! But, it wasn't the right pace for us.

 

So, we got through less... A LOT less when I compare to some on this Board. But, we thoroughly enjoyed and understood what we *could* cover. We managed to accomplish -- and accomplish it well -- a basic classical education, even though we were missing a number of traditional elements of classical ed (like Latin). But in looking back, I feel it was a solid accomplishment with 2 average students, neither of which had clear career plans or were ever thrilled with the idea of any kind of schooling. (lol)

 

And our slower pace allowed DSs to participate in several extracurriculars that were pivotal for helping DSs mature in faith, maturity, leadership, generosity, and responsibility. And for that I'm profoundly grateful -- if I'd been pushing harder for more volume and/or breadth of academics, we would have missed out on the very things that have helped DSs become the young adults they are. Going slower has been part of allowing our DSs to mature at *their* pace and to not hate learning.

 

So far, with DSs 1 and 2 years into Community College and looking towards transferring to state universities, continuing to take life at the slower pace, and refusing to get swept up in the college / future career / job availability panic, is allowing DSs to move into the opportunities, the learning, and the life experiences as they open up in the right timing for DSs...

 

 

well said

[katilac]

I think that everything in life has a price. If one wants to maximize their chances at getting into a competitive university, the price is often a hectic schedule, a lack of free time, and less choice in what or how one wants to study. Conversely, if one wants to blaze their own educational path, the price is often a reduced chance at getting into a competitive university. We just have to look at the price honestly and decide if we are willing to pay it.

 

Of course, many students with off-kilter high school careers do wind up at competitive universities, but it's important to acknowledge that it is likely reducing your chances. Where is your comfort level? (you meaning both parent and student)

 

If you keep along the same track, what schools are you likely to get into to? Are you okay with that list of schools? Are you locking yourself out of certain majors?

 

We are on a pretty non-competitive path. Sometimes, it's hard to not hit the panic button (or, more honestly, the competitive mom button), but we've done the research, and we're confident that there are schools that will suit them when the time comes. None of us thrive on hectic schedules, and the trade-off of (possibly) fewer schools to choose from is worth it to us.

 

My parents and I had no idea what we were doing when I applied to college, and my choice was pretty random and limited. I actually only applied to the one school! I would like my kids to have more choice than I did, but you know what? I'm leading a pretty happy life after attending my random and utterly non-competitive college! And, while I haven't set the world on fire career-wise, others from my school have.

 

There are lots of good and happy people who do strive for and attend competitive schools, and lots of good and happy people who don't. Decide what's important to you, decide what you're willing to pay, and then live your life.

[PeterPan]

Lori gave you lots of practical ideas. Two things that I'm not sure got mentioned. First, you can mark *units* on your transcript instead of credits. Units = time spent, credits = material covered. While I'm with you that TL1 is probably more of a semester than a year course, it also really depends on what you were doing in that extra time. If you actually spent 5 sessions a week or 120+ hours on it, then you EARNED the full unit. You were probably bringing in literature or something else there. So maybe some of that time goes toward your lit credit or whatever. Think through that. Tally time and then clump times spent on things into units to put on the transcript. You can divide up one book like that if you're actually hitting multiple angles. (writing, lit, etc.)

 

Thing two, several people mentioned time on testing. There is such a thing as having a low processing speed that is a disability. Those people get accommodations on testing. For some people this makes a huge difference, and it's always worth considering evals when you're seeing indications that things like this are going on. PS or a private psych can do it. And you know that's information that helps not only on testing but also when they get to college. Those kids may be advised to take lighter loads, etc. to have time to process what they're covering. It has nothing to do with IQ or how smart they are. Some people have processing speed issues.

[Jean in Newcastle]

Your question is a valid one. Sometimes courses count as one credit no matter how long they take to complete. So, for example, the body of material typically known as Algebra 1 is generally considered to be worthy of one credit whether a student completes it in three months, one year or two years. Jean, in her initial post, is implying (I infer) that Traditional Logic 1 is considered a half credit course even though she and her child went deep and took a year to cover the material.

 

Regards,

Kareni

 

You infer correctly. At least according to what I've been told.

[JanetC]

When you go beyond the textbook and add extra research and study, it is OK to give credit where credit is due. I would give one semester each for "Logic 1" and "Logic 2", but add a semester or two of "Special Topics in Logic" or whatever you want to call the additional work.

[Ellie]

There's absolutely room for ambling.

 

There may come a time when you've ambled enough and decide to move like a laser beam towards the goal...whatever the goal is. At that point, your dc will probably be more than ready.

[Nan in Mass]

We ambled and zoomed, as Ellie put it, and thought deeply and thought lightly. In general, I tried to pick one subject each year to be the subject during which I worked on teaching them to think, one that we did more in less depth (usually a textbook one), and the rest I tried to have them do in such a way that they had to use the thinking skills they had learned or were learning, but were not necessarily a huge step up. You can definately amble, but you might need to think more out-of-the-box, enough that you are out of your comfort zone.

 

I would also like to point out that there are many situations in which skimming is a good thing. It all depends on one's goal. It isn't a bad idea to teach your student how to skim through something picking out just the bits of information or skills that he needs; or doing a quick survey, taking note of the things he wants to come back to later. Keeping up with the current research on a subject or current events in the world are examples. Mine fought learning this until they needed the skill for their own uses lol.

 

Nan

[mathwonk]

One of the things that sometimes worries me, is that some of us seem to feel obliged to follow a traditional set of curricular norms when homeschooling our children. I am especially concerned that we are being taken advantage of by a whole industry devoted to selling expensive materials, at around $40 per quarter/per course, for each topic.

 

All the while there are free and possibly better materials online (at least in math) which I worry that I apparently have difficulty enticing people to try. [ I realize of course that the wise principle of consensus is being followed rather than "what does the flaky professor like best?"]

 

In the present context I personally see another troublesome result of this tendency of teaching from the books that are generally approved for all home schoolers, namely the problem of "covering the syllabus". If we use the same books dictated by the publishers, we are stuck in the same bind as teachers in public school, i.e. trying to cover the same number of pages as the school system, with the same problem of too many pages, too little understanding.

 

It is certainly not easy, but the only solution to this I can see is to design our own programs, from our own materials, with our own goals for each subject. If we just accept that we need to cover the same curricula as the public schools, aren't we just replicating their program without their resources?

 

As a small beginning on this problem, I suggest that the goals should include learning to:

 

i) read and analyze literature,

 

ii) understand and render into symbols, and solve, numerical problems stated in words, and

 

iii) learning to be curious about, and design experiments to investigate, questions of science.

 

There is also a basic library of respected sources to become familiar with, including standard history, fiction, poetry, art, and practical skills.

 

All else is detail. And the details are in our hands. I can advise books for the math part of this, and have done. Have faith in yourself, and take all advice such as mine for what it is worth to you. I myself have great faith in each parent's ability, as evidenced by all I have read from members here.

 

Let's go for it! (My biological children are grown but I am currently striving to help my epsilion campers.) and let's give thanks that we have the support of this community.

[Jean in Newcastle]

Mathwonk, you make some good points. I'm hampered though by my own limitations in the maths and sciences. In the humanities I can and do branch off the beaten path and feel confident doing so and putting the result on a transcript along with proof that my son has received a superior education in those subjects. But because I don't have that confidence or ability in the maths and sciences, I feel like I have to follow the beaten path even though I think my son would really really profit from deviating some - esp. in science. I hired tutors hoping they could go off the beaten path somewhat but the first tutor went on rabbit trails that never touched the basics that were needed first and the second tutor had to remediate some of that.

[elegantlion]

nm - changed my mind

[regentrude]

It is certainly not easy, but the only solution to this I can see is to design our own programs, from our own materials, with our own goals for each subject.

 

Mathwonk, I am sorry that I have to strongly disagree with you on this.

Starting out homeschooling in middle school, I tried designing my own math program because I had no book and thought, hey, with a doctorate in theoretical physics, I should be able to teach prealgebra without problem. I had not realized how insanely time consuming it is to design a math program from scratch, to construct practice problems that precisely illustrate the one aspect I am intending to teach, and that progress in the logical sequence of how material needs to be taught from easier to more complex concepts. I found quickly that even a mediocre math text is better than reinventing the wheel .... and when I found AoPS, it was heaven sent and exactly the right fit for my kids.

 

I would never recommend to anybody they should design their own math program; most people do not have the necessary insight to know what to teach when and how, and even for those they do, creating their own math curriculum is a full time job.

 

Now, I completely agree that we can pull together resources form different books - but I would not want to make my own program, from my own materials. Not for math. And not for science either.

[PeterPan]

I am especially concerned that we are being taken advantage of by a whole industry devoted to selling expensive materials, at around $40 per quarter/per course, for each topic.

 

All the while there are free and possibly better materials online (at least in math) which I worry that I apparently have difficulty enticing people to try. [ I realize of course that the wise principle of consensus is being followed rather than "what does the flaky professor like best?"]

 

(My biological children are grown but I am currently striving to help my epsilion campers.) and let's give thanks that we have the support of this community.

 

 

You know I love diversity on the boards, so I'm all for all types of people pursuing things all types of ways. However I'm not sure why you're making this personal. If I want to spend $600 to outsource math because I'm tired and DO have more kids and DO have SN issues going on and DON'T find anything online for free that is at all comparable to what I can get when I outsource or plunk out, then that's totally MY BUSINESS.

 

I don't think any mom should be made to feel like she's doing less than what she needs to for her child simply because she doesn't chose to create from scratch every single thing her kid does. Kid sister of that is that people shouldn't be slammed simply because they happen to say that college texts don't fit their high schooler. So something works for your situation, that's nice. I'm tired, I want a life, I want to think about something BESIDES homeschooling once in a while. And if I chose to outsource, pay, or anything else to get that relief and keep my life practical and do what I deem is a good job by my kid, that's MY BUSINESS.

 

You say be thankful for the boards. I am, and I'm super glad SWB decides to pay for them out of her pocket. But I also recognize that they create peer pressure that makes us turn from looking at our kids and think we have to keep up, keep up. Now what that "keep up with" is varies with the flavor, whoever's voice is dominant, blah blah.

 

My kid is not a theory, and I no longer dwell the land of theory. I tried to watch Perrin's talk on classical education someone linked to, and it was vomitous to me, because it was totally theory. I've done theory for years and years. Now I have reality in front of me, and I really have to fit HER, the ONE.

 

You can also have a voice that is the lone voice and still be right for your situation. You have to remember that people are going to read these archives years from now and see your posts, follow your threads (if they were inspiring or applicable to their situation) and learn. We're not merely posting here for the immediate.

[mathwonk]

Unfortunately my naive suggestion seems to have derailed the thread. My apologies. Perhaps also I misunderstood the problem facing Jean in Newcastle. Re - reading her post, it may be that the detail on the transcript she is trying to fulfill in order to obtain credit is the problem, rather than the detail in the text she is using.

 

I.e. my suggestion, even if workable in some cases, did not account for convincing anyone else that my course contained all they asked for. Except of course that I would be happy to have my pupils take an accreditation test after the course. I.e. perhaps there are two ways to establish credit, i) cover a text which lists all the required topics, or ii) take a test afterwards that demonstrates competence in the required topics.

 

I apologize for my ignorance. Jean in Newcastle, could you help me understand what it is that needs to go on a transcript to prove ones child has an excellent grasp of a subject? I.e. do schools ask that one has mastered a topic as measured by a competency test, or that one has actually spent as much time as is usually done on a subject, or covered as many pages? Some of these methods of measurement would of course make it very hard to teach in more depth than usual.

 

My suggestions are based partially on my own frustration of teaching for decades in a public school where I was forced to use standard texts that had far too much material, yet still failed to emphasize the most important points. Our list of required topics often consisted simply of a list of chapter headings and subheadings in our chosen text. Many teachers expressed the same concern as here that we were not allowing time for material to sink in.

 

Many of us felt that a slower pace that allowed better understanding of fewer topics would be beneficial, but we did not have that freedom.

 

In my own experience, these lengthy lists of topics are compiled by people outside the classroom who apparently want to give the impression that all these things are being learned, when in fact they usually are not. At one point I was asked to evaluate the materials being used by the state to test aspiring public school teachers on their competence in various math topics. They were required to pass a test whose questions were prepared by currently accredited teachers, and we were evaluating the preparation booklet used to assist them in studying for the test.

 

It quickly became clear that the large majority of the topics listed on the official curriculum for each course were greatly over ambitious and were seldom if ever covered. I.e. not only was it unfeasible to cover all the topics listed, but the teachers preparing the test questions knew this and indeed only tested on a small basic core of material.

 

In fact the questions on the preparation test also revealed that many of the accredited teachers who were preparing the tests were unqualified to teach or test even the basic topics, e.g. the questions sometimes failed to test the appropriate material, and even when they did, the "answers" in the answer booklet were too often incorrect.

 

The lesson I carried away was that both teacher preparation and teacher testing were in trouble, and that part of the problem was a tendency toward illusory completeness in lists of required topics, i.e. trying to cover too much.

 

I conclude that it would be very hard to demonstrate full competence on all the topics that were listed at least on the curricula I was reviewing, but it would be much easier to demonstrate mastery comparable or superior to that of actual public school students. Thus I would hope that what home school parents are required to do would be the latter rather than the former.

[mathwonk]

regentrude, I myself would be challenged to choose a science curriculum. Are there materials you would recommend for learning physics? Preferably aimed at beginners, but which in the spirit of this thread would repay thoughtful and unhurried contemplation.

[regentrude]

regentrude, I myself would be challenged to choose a science curriculum. Are there materials you would recommend for learning physics? Preferably aimed at beginners, but which in the spirit of this thread would repay thoughtful and unhurried contemplation.

 

 

Beginner with what kind of a math background?

[PeterPan]

... could you help me understand what it is that needs to go on a transcript to prove ones child has an excellent grasp of a subject? I.e. do schools ask that one has mastered a topic as measured by a competency test, or that one has actually spent as much time as is usually done on a subject, or covered as many pages? Some of these methods of measurement would of course make it very hard to teach in more depth than usual.

 

 

 

Transcripts typically show carnegie units (time spent) or credits (material covered). In a traditional school, those are going to be one in the same. In a homeschool setting, a parent can use that difference and flexibility to create a transcript for a non-traditional, out of the box student who may have covered material in very non-traditional ways. If they spent the time, they get the 1 on the transcript.

 

There are some common sense limitations to this. You don't get to mark double just because your kid is pokey or struggles at math. There are more situations, but you get that there are caveats and lots of common sense.

 

The assumption is that your standardized test scores will validate your transcript claims. Schools (universities, colleges) tend to take the transcript at face value, unless something looks amiss.

[Jean in Newcastle]

 

Transcripts typically show carnegie units (time spent) or credits (material covered). In a traditional school, those are going to be one in the same. In a homeschool setting, a parent can use that difference and flexibility to create a transcript for a non-traditional, out of the box student who may have covered material in very non-traditional ways. If they spent the time, they get the 1 on the transcript.

 

There are some common sense limitations to this. You don't get to mark double just because your kid is pokey or struggles at math. There are more situations, but you get that there are caveats and lots of common sense.

 

The assumption is that your standardized test scores will validate your transcript claims. Schools (universities, colleges) tend to take the transcript at face value, unless something looks amiss.

 

I'm going to quote Elizabeth, to answer Mathwonk. How's that for multi-tasking? My original question was partly due to frustration for my son's pokeyness. So Elizabeth's point that credits need to be fair to accommodate both the rabbits and the turtles is a valid one. But it was also due to a frustration with the "throw facts into the brain and then regurgitate it for the test" form of education that also seems to be a by-product of the credit system. What Lori upthread pointed to in the breadth vs. depth discussions deals with that by saying that if you go more in depth, you should be able to get as much credit as if you went more superficially but covered more breadth of facts on the subject. My problem is that I'm not always sure what is pokeyness, what is legitimate depth (when he gets distracted by rabbit trails) and when to say "we've done enough". I'm better at judging the answers to those questions when it comes to the humanities for the same reasons that it is easier for me to write my own humanities curriculum because I have more experience with which to make those judgments and can back myself up with "proof" if I need to. But despite that confidence, the system of testing etc. is geared more for the brain dump kind of learning because tests cover a certain amount of material - an amount of material that seems destined to frustrate those of us who like to chew things in a bit more depth.

[mathwonk]

Thank you. I was hoping there was a test based credit system so that those who take longer and understand fewer things better could demonstrate their competence without spending as much time or pages on each topic. My own feeling is that deep understanding of key facts translates into as much or more competence as broad based but shallow acquaintance with a lot of stuff. Of course that belief requires justification in practice. But as an old mathematician, I tend to forget a lot of math facts and cling to a few deep principles that I use over and over. Then I tend to re-derive the formulas when I need them.

 

E.g. in my opinion, a kid who knows that a quadratic equation asks us to find two numbers whose sum and product are known, is miles ahead of one who knows the formula says X = (1/[2a])(-b ± sqrt(b^2-4ac)), without grasping where that came from, (and I even got it wrong the first time). That's why I advocate books like the classic from Euler which emphasize these principles over just formulas. Of course after understanding the principles I hope the formulas are easier both to remember and to use.

[Lori D.]

My problem is that I'm not always sure what is pokeyness, what is legitimate depth (when he gets distracted by rabbit trails) and when to say "we've done enough".

 

 

 

Don't know if it would work for you, Jean, but I would google search and look at the table of contents of several textbooks, plus look at a good half dozen public/private (regular and rigorous) school syllabi for a specific kind of course to help get a feel for how long to hang out on a topic, and to esp. get an overview idea of the general types of topics to attempt to cover over the course of a year.

 

Of course, you have to give yourself leeway for your DC's particular interests, and your own educational philosophy, but I found that when I blended together the syllabi and table of contents, I would come up with a plan that was comfortable for me, that we were covering what was "standard", but with elbow room for us to bunny trail and go deep where we wanted to. And, I could put an asterick beside some topics to indicate to myself that if needed, we could drop that topic if we needed more time for going deep/bunny trailing.

 

The school syllabi often give you a good feel for how much time to schedule, or how much work is reasonable to expect from your student, to help you gauge if your student is taking a reasonable amount of time or is being pokey. Again, you do have to adjust that depending on how much work you've decided to require and your specific student's abilities. But at least it gives you a starting point. :)

[katilac]

<snip>

E.g. in my opinion, a kid who knows that a quadratic equation asks us to find two numbers whose sum and product are known, is miles ahead of one who knows the formula says X = (1/[2a])(-b ± sqrt(b^2-4ac)), without grasping where that came from, (and I even got it wrong the first time). which emphasize these principles over just formulas. Of course after understanding the principles I hope the formulas aThat's why I advocate books like the classic from Euler re easier both to remember and to use.

 

Can you give specific titles you would recommend for algebra and geometry? Any books that give definitions of this sort would be so helpful to me and dd14. Her algebra book is full of 'definitions' like, "A quadratic equation is one that can be expressed in the following form . . ." and this makes our heads want to explode.

 

We do have other books to refer to, and we hop online all the time, but every resource we find seems to share this mania for not actually explaining things.

[regentrude]

Can you give specific titles you would recommend for algebra and geometry? Any books that give definitions of this sort would be so helpful to me and dd14. Her algebra book is full of 'definitions' like, "A quadratic equation is one that can be expressed in the following form . . ." and this makes our heads want to explode.

 

We do have other books to refer to, and we hop online all the time, but every resource we find seems to share this mania for not actually explaining things.

 

 

If you want curriculum that explains every single concept thoroughly, I recommend AoPS.

[Jean in Newcastle]

Very good advice. Thank you, Lori.

 

 

 

Don't know if it would work for you, Jean, but I would google search and look at the table of contents of several textbooks, plus look at a good half dozen public/private (regular and rigorous) school syllabi for a specific kind of course to help get a feel for how long to hang out on a topic, and to esp. get an overview idea of the general types of topics to attempt to cover over the course of a year.

 

Of course, you have to give yourself leeway for your DC's particular interests, and your own educational philosophy, but I found that when I blended together the syllabi and table of contents, I would come up with a plan that was comfortable for me, that we were covering what was "standard", but with elbow room for us to bunny trail and go deep where we wanted to. And, I could put an asterick beside some topics to indicate to myself that if needed, we could drop that topic if we needed more time for going deep/bunny trailing.

 

The school syllabi often give you a good feel for how much time to schedule, or how much work is reasonable to expect from your student, to help you gauge if your student is taking a reasonable amount of time or is being pokey. Again, you do have to adjust that depending on how much work you've decided to require and your specific student's abilities. But at least it gives you a starting point. :)

[mathwonk]

@regentrude: as to the math background for learning physics, I would leave that flexible.

 

I.e. I would hope that there is a basic core of physics that does not require much math,

 

but if you recommend one should know a certain amount of math first, I would like to know that as well.

 

 

Are there basic concepts of physics one can understand without much math? If so, I would want to start there.

 

Or if not, which physics concepts really require which math methods to grasp?

 

 

 

Here is an example:

 

In teaching calculus in school I struggled to teach its applications to concepts like "work" for which I had little intuitive grasp.

 

I wanted to "see" or "feel" work somehow. It helped to think of it as change in potential energy, or the damage that a big rock would do

 

if dropped after being lifted a certain height.

 

 

I finally got help from connecting it with volume, i.e. linking physics with geometry helps me.

 

 

E.g. in physics I believe there is the principle that the work done by moving a wire or plate of uniform density

 

is proportional to the mass times the distance traveled by the center of mass. This parallels an ancient principle

 

in geometry (Pappus' theorem) that area or volume generated by revolving that figure is proportional to the

 

distance traveled by the center of mass.

 

 

It finally dawned on me that since physicists also understand the work done by moving a solid,

 

so too one could think of the 4 dimensional volume generated by revolving a solid, (around a plane in 4 space I guess),

 

as proportional to the work done by raising that solid against gravity. I wrote this up in the epsilon camp notes, showing how

 

Archimedes could have calculated the volume of a 4 dimensional ball, just by computing the work done by moving

 

a half ball a certain distance against gravity and multiplying by 2Ï€.

 

 

So the physicists' concepts seemed to me more comprehensive than the mathematicians', since their concepts

 

involving motion and time allow one to contemplate 4 dimensions.

 

 

Thus even Archimedes knew enough physics to compute 4 dimensional volumes,

 

if those had made sense to him. Until I realized this, I had struggled with the trig identities needed to do this volume integral.

 

So as a mathematician I am very envious of the intuition physicists have that

 

gives them a leg up in understanding both the world and the math we use to study it.

[mathwonk]

katilac, my lengthy answer to recommended books just got lost. I will try again. Basically, it is Euler's Elements of Algebra, and Euclid's Elements (for geometry), but there were lots of useful examples and some caveats included.

[mathwonk]

Here is a free version of Euler:

 

http://archive.org/details/elementsalgebra00lagrgoog

 

 

One can see on pages 244-245 a clear explanation of the meaning of quadratic equations. It is very simple.

 

 

There is one basic fact, that a quadratic equation factors into a product of two factors, each determined by one root:

 

X^2 -bC +c = (X-r)(X-s) where r,s are the two riots of X^2 -bX + c = 0. there are two immediate consequences:

 

1) the equation X^2 -bX + c = 0 can be true only if the equation (X-r)(X-s) = 0 is true, which happens if and only if

 

at least one factor in the product is zero, i.e. if and only if X=r or X=s. Thus such an equation can have only two solutions.

 

2) Multiplying out, gives X^2 -bX + c = (X-r)(X-s) = X^2 -rX-sX+rs = X^2 -(r+s)X + rs.

 

Hence by comparing coefficients, we must have b = r+s and c = rs; i.e. the coefficients of the equation itself always determine

 

both the sum and the product of the two solutions sought for.

 

 

There are also many clever worked examples and sample word problems. Still it is not cheap, my Cambridge Univ Press edition is about $50. And it is in old style English from 1822 or so, and may require adult assistance for even a bright child.

The advantage is that it is was written by an absolute master of the subject, with a view to instructing complete beginners. It is said that Euler aimed it at his butler, an intelligent man innocent of mathematics. It is essentially unheard of today for great mathematicians to write elementary books, not even calculus books, much less high school algebra.

 

 

But please just take a look at the explanation on pages 244-245, and maybe the absolute begining introduction on pages 1-2, as to what "quantities are:" and how to introduce numbers into measurement of arbitrary quantities, to see how this book differs from all others. If this appeals, I suggest further preview of it before investing any significant sum of money. And the Amazon reviews warn against some editions such as that from Tarquin.

 

It may be that Euler is not practical as a standalone book for home school. But I hope it could be useful as a supplement for child or parent, since it does explain what the material means. In this role the free versions online may suffice.

 

 

I think I can guarantee that a child who masters the version in Euler will understand much more than one taught from traditional modern texts. E./g. Euler teaches how to use ones knowledge of solving quadratics to also solve cubics, a few pages later. This is not taught in any modern high school algebra books that I know of, but Euler makes it look relatively easy.

 

E.g. If u^3+v^3 = q and 3uv = p, then X = u+v solves X^3 = pX+q. (You can "easily" check this by multiplication.)

 

E.g. since 1^3 + 3^3 = 28, and 3(1)(3) = 9, then X = 1+3 = 4 solves X^3 = 9X + 28.

 

 

Moreover, given the coefficients p and q, to find u,v, that satisfy u^3+v^3 = q and 3uv = p, is easy, since we only need

 

u^3+v^3 = q and uv = p/3, or u^3v^3 = p^3/27. Then since we know both the sum and product of u^3,v^3, we can find them

 

by solving a quadratic! Namely just solve t^2 - qt + p^3/27, for t = u^3, v^3, and take cube roots.

 

 

In the example above, p=9 and q = 28, so we solve t^2 -28t + 27 = 0, for t=1,27, and take cube roots to get u,v = 1,3.

[mathwonk]

If Euler does not suit, then for modern day books, written by a pedagogical masters, and very child friendly, I suggest the two books by Harold Jacobs, Elementary Algebra, and Geometry (preferably first edition). These books make math fun, and still teach solid material.

 

There are used copies available on abebooks.com for $15.50 for geometry and about $32 for algebra.

[mathwonk]

The recommended version of Euclid is the beautiful Green Lion edition. at about $15 paper. A recommended companion volume is Hartshorne's Geometry: Euclid and Beyond, about $50, or my much less useful but free epsilon camp notes on my web site at the UGA math dept, under retired faculty. Hartshorne's book is also chock full of advanced material that will last for years and years. Chapter one alone suffices for a first course from Euclid.

 

 

I do not believe at all that my recommendations of Euler and Euclid will work for every particular case, and I welcome advice from those with more experience as to what uses they may have. They have worked with the epsilon camp kids, in an intense 2 week setting, with highly motivated and "gifted" math types.

 

I am just trying to throw them out there and get more content choices in the mix, for what that may be worth. These suggestions are aimed at long range value of the material learned, as being of high quality, but the everyday crux is what works in the real world of teaching it.

 

Even if these sources are better as second courses, for those already knowing the material, they need to be known for that to be possible. It may be that in practice the usual suspects are the most workable, but maybe these could be useful as review and a test of how well the main ideas have been grasped.

 

for those interested in trying Euclid, there is an excellent essay on Teaching according to Euclid, by Robin Hartshorne, available on the website of the Notices of the AMS.

[katilac]

Wow, lots of great books to check out! Thanks, guys.

 

I like to have supplements/second resources hanging around, and some of those look affordable enough to buy even if I use a different text.

[mathwonk]

Here is a link (hopefully) for the beautiful Hartshorne essay:

 

http://www.ams.org/n...-hartshorne.pdf

 

 

One basic point is that Euclid does not assume one understands "real numbers" before doing geometry as do almost all other modern geometry books. That allows him to first build a familiarity with the geometric concepts of lines and triangles and planes and areas, before introducing numbers to measure them.

 

This is the historic development of the subject. Real numbers grew out of a need to quantify the geometric notion of similarity in Euclid, which appears there (Book VI) using a sequence of rational approximations.

 

In fact the notions of similarity and area are equivalent, but that is not made clear in some modern treatments. E.g. in the excellent book on geometry by AOPS, area of a triangle is defined to be (1/2) the product of the length of the base by the height. Unfortunately a triangle has three potential sides to be considered as the base and there is no way to prefer one over the others, so one needs to know that every choice leads to the same result.

 

To prove this fact uses the principle of similarity. That principle however is proved in AOPS later in the book, as Euclid did, and relies in turn on the concept of area. So the reasoning there seems to be circular. Euclid had given a different more geometric development of area.

 

I.e. in AOPS, two triangles with the same base and "in the same parallel lines" (hence same height) have the same area by definition, but Euclid shows instead that they can be decomposed into congruent pieces.

 

This does not mean AOPS is not a wonderful book. But what it is attempting to do I think, is build problem solving skills, and convey good mastery of geometric facts, rather than give a completely theoretically sound logical development of the subject.

 

It does a wonderful job at achieving its goals, but it helps i think to know what those goals are. Not only is writing ones own materials from scratch mostly unfeasible, as regentrude said, but even choosing from among the available sources seems challenging to me.

 

I would like to comment on some of the different books out there, since there is not just

"geometry", but many flavors of that topic and many presentations and focal points for it.

 

I would suggest that the primary goal of AOPS is as its name implies, learning to solve problems. So it teaches creative thinking and it also imparts a lot of sound information. I believe the series was conceived and executed by someone who enjoyed math contests and tries to prepare students for them..

 

I would say the strength of Harold Jacobs' books is that they teach that math can be fun, they explain the concepts clearly, and the concepts are related to everyday situations with cartons and humor. This may be a book many kids will "take a shine to" and agree to read alone.

 

As the Jacobs geometry book progressed from first to third edition, it became less reasoning oriented, with less logic content, and more factual. I.e. more facts were taken for granted and fewer were deduced by reasoning from prior material.

 

The Saxon books seem to have as strong point good retention of what is taught, and lots of repetitive drill on fundamental manipulative skills. They are said to raise scores on standardized tests. Deep explanations and fun may be lacking.

 

The book of Euclid provides a foundation for geometry via logical reasoning, the historical development of real numbers, the combination of ideas from geometry and algebra, and the beginnings of reasoning by limiting processes, which leads to calculus. Even the deeper results of geometry in Euclid, like constructing a pentagon, were omitted from my high school book.

 

I hope this helps choose ones own sources. Of course they should always be previewed oneself, preferably at leisure in a library, for free.

[justamouse]

One of my biggest frustrations in university (and somewhat in high school) was that there was no time to really learn material, to think over it and to let it soak in. One of the reasons I wanted to homeschool was so that once we hit the high school years we could learn at a calmer more contemplative pace. That doesn't seem to be the reality. Or when it is, we have to pretend it isn't and still cram other stuff in. What I mean by the last statement is that we've taken longer to do certain courses - we took a year each for Traditional Logic 1 and then Traditional Logic 2 because despite working every single day, it took us that long to really delve into the material, to look up other information on the syllogisms and to really understand it. But each class will only count for a semester credit. I'm stressed out looking at all the requirements we need to have for the transcript (we're on track but there is no slack there.) Is there really no room for a more rambling learning speed - esp. if you want to go on to university?

 

 

In Dr Senior's book, The Death of Christian Culture, he makes the argument that the advanced student needs to go slower. That 'on pace' is for the average.

 

Pg 91

 

"A Chinese once criticized American education by saying, "You are always pulling on the flower to make it grow faster." We need, rather, in the words of T. S. Eliot, a "life of significant soil". If a student has greater capacity to learn, all the more reason for him to complete the full four years of his college life so that he actually realizes his potential. Slow him down. At Princeton, under Dean Root, the students in the four-year college normally took five courses per year; the exceptionally bright ones were permitted to take four, on the grounds that for them it was really worthwhile to go slow. An education is not an annoying impediment to research or business, but a good in itself, indispensable to the development of the qualified person."

 

Take a step to the left and let the rushing river pass you by.

 

My son could have easily skipped 8th grade. And, we hovered there for a few months, until HE decided that he didn't want to skip, that he wanted to do 'high school' until he was 18, instead taking his time.

 

Can they learn the rest of their lives? We hope so, but they only have this precious time once. I hate rushing them through it.

[mathwonk]

a very interesting and thought provoking post.

[kiana]

I would agree that for most students, skipping grades in homeschool just to get done more quickly isn't a good idea. Honestly, if a student is not prepared to excel -- not just to succeed, but to excel -- in their new grade, I don't think it should be done. A possible exception could be a 15 year old who has a vocational goal and is chomping at the bit to get started.

 

But I would NOT argue the same about doing algebra early, or reading excellent books early, as long as the child is enthused about doing so. I *would* agree that it applies if the student is doing algebra early with a non-challenging program, planning solely on racing through the material and getting to a weak calculus at 11. But if the student is doing well in good and challenging courses, such as AOPS or some of the other good texts, and still flying through them, let them fly! For many students, moving slowly through non-challenging material, rather than teaching thoughtfulness and deep understanding, teaches them that they don't have to study to learn, and if they do have to study, it must be because they're stupid/not good at that subject. An ex was a perfect example of this -- he was actually quite talented at mathematics, but because it was the only subject he had ever had to work at before A levels, he believed he was stupid at it.

 

tl;dr summary -- Skipping grades, honestly, is more for unusual circumstances, but accelerating *subjects* to an appropriate level of challenge is usually a good idea.

[Beth in Mint Hill]

One of my biggest frustrations in university (and somewhat in high school) was that there was no time to really learn material, to think over it and to let it soak in. One of the reasons I wanted to homeschool was so that once we hit the high school years we could learn at a calmer more contemplative pace. ... Is there really no room for a more rambling learning speed - esp. if you want to go on to university?

 

Dear Jean,

This was exactly my experience, too! I went to Wheaton College (and this was over 40 years ago!) and loved the professors and atmosphere, but the full load of courses was so frustrating. I remember starting a paper and wanting to delve into the research, but alas! I had biology, old testament, history, and something else to do stacks of reading for, etc. Since they wouldn't allow a student to be part time, after 2 years I finally left and went home to Orlando, where I studied 2 courses at a time while working as a waitress. I loved the balance. Took me 7 years to get a BA that way, but I really dug deep into the subject and wrote the kind of papers that I could be proud of.

 

So in homeschooling we simply ignored the so-called requirements for a transcript. I got to thinking of all the successful people who didn't go to "ivy league" colleges, or who came from alternative schools where they simply did "projects" rather than subjects. All of these people had had no problem going to college--or succeeding without college, so I decided this was the way for us.

 

Our transcripts were very non-standard, but I thought what the guys will have in creativity and language skills might make up for that. Perhaps their thinking skills will help them do well on the standardized tests and this can make up a little for the weakness of the transcript. Anyway, I felt so strongly that freedom was important in this area, that I dared to thumb my nose at what the educrats say needs to be "covered." I prayed that God would take care of us in that daring journey!

 

But in my weak faith, I still feared that I would have crippled them for any good college. But now my early reader and philosophy guy is in law school (for which he received a large scholarship)--and my dyslexic guy is loving advanced economics courses, even doing fine with the calculus and statistics, making As on all of these! THe 3rd one is rejecting college at this point. THe first son is great at tests and get high scores, and my dyslexic son performs abysmally on them.

 

So, I just tell this little story to show that the highschool transcript does not need to be a taskmaster! You should *see* the weak transcript that my law school student had! I didn't fib on it, just cobbled something together. And some of the grades were pretty low, because I just asked myself "what would he have scored in a regular classroom if he had done the kind of work he did for me?"

 

I'm telling you, it is really freeing to realize that the transcript is a small factor in your child's future! Break free--be happy in studying what is important to you!

[Jean in Newcastle]

Beth - thank you so much for writing that. I can see that you really, really understand! I haven't been that courageous on ignoring the requirements but I'm hoping that for our last two years of high school (which is all that ds has left) we can unloose the shackles and really delve into things. I also have a daughter who is starting the logic stage who is vehemently opposed to doing anything in lock-step fashion so I think her experience will be looser for that reason.

[justamouse]

Beth, it's so wonderful to hear stories like that from a mom who's done it, while you're just trying to have the faith to!

[swellmomma]

katilac, my lengthy answer to recommended books just got lost. I will try again. Basically, it is Euler's Elements of Algebra, and Euclid's Elements (for geometry), but there were lots of useful examples and some caveats included.

 

 

I have never heard of Euler's elements of algebra. My homeschool board offers 3 classes of euclid's geometry that I hope to have my kids take when they are ready. I will need to look further into Euler's algebra

[mathwonk]

swellmomma: Did you see the link for a free online copy of euler in post 38? I had never heard of it either, and I was a professional mathematician and math professor for 35 years. In retirement I get to read stuff I like and not just run in the rat race of publishing more papers on obscure topics.

 

As a high school student I thought quadratic equations was about remembering that x = (1/2a)(-b ± sqrt(b^2-4ac)) and had trouble understanding where that came from. As an old man I read euler and learned that all we need to find the roots r,s of a quadratic is to know their sum (r+s) and their difference (r-s), and then we can add and subtract these and get 2r = (r+s)+(r-s), and 2s = (r+s) - (r-s). Then we divide by two to get r and s.

 

So that last part is where the (1/2) comes from in the formula, and also the ± sign in the formula. In fact in the formula, -b/a = (r+s), and sqrt(b^2-4ac)/a = (r-s)

 

I.e. in a simplified equation like X^2 -bX + c = 0, the sum r+s is just b, and the product rs is c.

 

So since we know that (r+s)^2 - 4rs = (r-s)^2, we can compute the square of the difference as (r-s)^2 = b^2-4c, and that's where the 4 came from! So now all the numbers in the formula make sense. the 1/2, the 4, the sqrt...

 

Why didn't anyone ever tell me this as a child? Well, maybe it's because I read Welchons and Krickenberger instead of Euler. (And Welchons et al is a lot better than most choices out there today.) In fact I learned by reading another great elementary algebra book, by LaGrange, that this clear conceptual explanation of solving quadratics is in the book of Diophantus, written almost 2,000 years ago!

 

And this may not appeal to everyone but I love the charming problems in Euler, like: "Two country girls took their cheeses to market and sold them. Afterwards one said to the other, if I had sold yours at my price I should have received 10 shillings more,...."

 

 

This might seem odd, but after 35 years as a mathematics researcher with a PhD, I am now relearning high school algebra by reading Euler and LaGrange. Why? Because I want to understand it. For the same reason I am still interested in learning physics from scratch. It has dawned on me I should probably red Newton. I still sigh at the folly of lightening my load 35 years ago by selling my unread copy of the Principia for ten cents! to a used book buyer.

 

I am also learning that things that high school students used to learn, like how to solve cubic equations, was dropped out of the curriculum many years ago, but i don't know why, since euler makes it look so easy.

 

One reason was the move toward universal high school education. For that to work, the curriculum had to be dumbed down a lot. Before 1900, when at most maybe 10% of people went to high school, the level was much higher. Remember those PBS shows about Abigail Adams and her husband the president and their accomplishments with a high school education or less?

 

Now that we have more universal college education, the same thing has happened there. College is now high school, graduate school is college.......