Regrets - Page 6

[newcastlemama]

Thank you Tigeresse and others for sharing your struggles on this thread. I am friends with a former unschooler IRL who has also struggled and is now doing things differently with her younger children. I do agree that unschooling does get promoted by a vocal some as the self-actualized way of homeschooling and that we should always be trying to get ourselves there.  (I can aslo see how it could work out in some families so this post is not to say it is never a good choice).

My oldest is only 7 and I thought we would unschool but we have settled into a moderate daily rountine that works well for us. Yes, there is resistance at times, but he sure feels good about being able to write and read with the schooled children he goes to other activities with. We are still very gentle parents even though we require a certain amount of school work everyday, along with brushing his teeth, bedtimes ect.  I guess what I have learned this year since having my 3rd child is that something does not have to be at the extreme end of the spectrum to be good and well. I can breastfeed for 2 years instead of child-led wean, cook many things from scratch instead of everything, we can do a moderate amount of homeschool work with plenty of time to pursue interests instead of unschooling or public schooling.

The fact is that most of the nation is being formally schooled and there is a level of knowledge that is expected to do certain things at certain times in your life in this complex society. Even my dh who did not need a university degree still needed to study a lot and a pass test to get into his profession. I am looking for the balance to have children who have a good amount of freedom but are not hindered by choices they made as children and could not see the future consequences of. (I am really glad my parents did not let me do what I thought was best growing up.) I don't see why I can't have daily school work requirements for my children and have a deeply loving relationship with them at the same time.

Try not to beat yourself up too much Tigeresse.

[beckington]

Originally Posted by SweetSilver 

And if I divide the pie in half, lets see, that's 1 divided by 1/2, right?

Ah, but no - it's 1 pie divided by 2, not by 1/2. You divide the pie *in* half, but you divide *by* 2 to do that. Just like if you have 10 pies and you want to find out what 1/2 is, you divide by 2 to get that. Does that make sense? I'm getting confused, lol!

ETA: Dividing the pie in half is dividing the pie into two pieces, which is where the dividing by 2 comes from.

OK shutting up now because my brain hurts!

[4evermom]

Originally Posted by beckington 

Ah, but no - it's 1 pie divided by 2, not by 1/2. You divide the pie *in* half, but you divide *by* 2 to do that. Just like if you have 10 pies and you want to find out what 1/2 is, you divide by 2 to get that. Does that make sense? I'm getting confused, lol!

ETA: Dividing the pie in half is dividing the pie into two pieces, which is where the dividing by 2 comes from.

OK shutting up now because my brain hurts!

Lol.  Sweetsilver, just remember the little line in a fraction is the same exact thing as a division symbol.  So 1/2=1 divided by 2.   10 pies divided by 2 is 10/2 but that is a crazy top heavy fraction and we are supposed to simplify it to 5.  (The division symbol isn't even on this keyboard, just the slash symbol in it's place.)  

I feel like I mostly got through math by being good at figuring out what to plug where into whatever the equation du jour was...  Percentages didn't click for me until I was well out of college.  I don't know why.  I guess I didn't shop enough:-)

[SweetSilver]

Originally Posted by moominmamma 

SweetSilver, have you considered Miquon Math at all as mathematical learning fodder in your home? I ask because it helped me sort out some basic mathematical concepts in more depth in a way that delighted me as I explored it alongside my kids ... and it seems like you have the same kind of desire to understand this stuff!

Miranda

I almost considered bringing it home for the girls, but they are making such good progress on their own, I wanted to wait for a while.  But then I remembered the book you mentioned and the Miquon math mentioned and I did think, wow!  I would really love to go over this stuff myself.  I would have no problem starting from counting on my fingers!  
 

Quote:

Originally Posted by beckington 

Ah, but no - it's 1 pie divided by 2, not by 1/2. You divide the pie *in* half, but you divide *by* 2 to do that. Just like if you have 10 pies and you want to find out what 1/2 is, you divide by 2 to get that. Does that make sense? I'm getting confused, lol!

ETA: Dividing the pie in half is dividing the pie into two pieces, which is where the dividing by 2 comes from.

OK shutting up now because my brain hurts!

Join the club!  I did eventually have that revelation for myself, but it took a lot of clunking around of grey matter to finally make the connection.  This is why I had such trouble with the story problems in school.  I could follow the abstract math well enough, but had trouble when it came to needing to devise the proper equation. 

So, two questions came up.  One is about those blocks of your son's, and squares, and how his blocks illustrated the idea.  I came up with nada.  Too much noise and confusion from all that pie. (And I didn't get a single bite!)

The second is about all those tricks with fractions.  I mean, really.  To *add* fractions you invert and multiply them um.... diagonally?  (OK, I have totally forgotten the terminology.)  Who thought that one up?  My inner 7th grader is protesting.  (You also notice that I don't really remember when I got taught all this stuff.)  Not one teacher told us why, as far as I can remember (I can be amazing oblivious, though.  And to think I got straight A's in math.....)

Edited to add:  the best introduction to fractions was actually my years in piano lessons.  If not for that, I think I might not have done so well in math at that point.

Luckily I have a few years ahead me before I get a turn explaining it to my befuddled daughters.  Or perhaps like beckington's son they will be explaining it to me!

BTW the connection between fractions less than one and negatives came from my husband.  He cocked his head for five seconds, screwed up his face just so and told me that.  He can figure that out first thing in the morning, yet after 15 years of correction, he still can't remember to spell "cereal" correctly!  I guess I'm glad we make a good team.  Between the two of us, I think we might have all the bases covered!

[beckington]

Originally Posted by 4evermom 

Lol.  Sweetsilver, just remember the little line in a fraction is the same exact thing as a division symbol.  So 1/2=1 divided by 2.   10 pies divided by 2 is 10/2 but that is a crazy top heavy fraction and we are supposed to simplify it to 5.  (The division symbol isn't even on this keyboard, just the slash symbol in it's place.) 

My dh pointed out to me that in higher level maths they don't use the division symbol (the one with the dot above and below the line) at all. It's a slash or the fraction bar.

[beckington]

Originally Posted by SweetSilver 

I almost considered bringing it home for the girls, but they are making such good progress on their own, I wanted to wait for a while.  But then I remembered the book you mentioned and the Miquon math mentioned and I did think, wow!  I would really love to go over this stuff myself.  I would have no problem starting from counting on my fingers!  
 

Quote:

Join the club!  I did eventually have that revelation for myself, but it took a lot of clunking around of grey matter to finally make the connection.  This is why I had such trouble with the story problems in school.  I could follow the abstract math well enough, but had trouble when it came to needing to devise the proper equation. 

So, two questions came up.  One is about those blocks of your son's, and squares, and how his blocks illustrated the idea.  I came up with nada.  Too much noise and confusion from all that pie. (And I didn't get a single bite!)

The second is about all those tricks with fractions.  I mean, really.  To *add* fractions you invert and multiply them um.... diagonally?  (OK, I have totally forgotten the terminology.)  Who thought that one up?  My inner 7th grader is protesting.  (You also notice that I don't really remember when I got taught all this stuff.)  Not one teacher told us why, as far as I can remember (I can be amazing oblivious, though.  And to think I got straight A's in math.....)

I am looking at Miquon for my son - it looks good. I am also wary of introducing a curriculum but he seems to be looking for something like that (and of course it would not ever be required of him, but I might do some gentle persuasion). We are actually having a little meeting/date today to discuss it along with his 'learning goals' for the next little while (which will probably include 'learn how to play Mario Brothers better'!).

As for your question about the squares, square numbers 4, 9, 16, 25 etc. If you have 9 square blocks you can put them together to make a square. If you have 10 square blocks you cannot. That's it!

As for your comment about fractions, to add fractions you don't invert, you just find the lowest common denominator and add. I don't really understand the 'why' behind that, just that it works! :)

[Dar]

But the why matters, IMO. You find the lowest common denominator and convert and add because when you're adding you need to add pieces of the same size in order to know how many you have.

[beckington]

Oh I agree the why matters - I just didn't know why! Though I could have given the explanation you did but I guess I still don't understand that as 'why'. It just makes sense. Comparing like with like and all that. So is that really all there is to it? Maybe this math stuff is easier than I thought! ;)

[SweetSilver]

beckington, you are right about the inversion.  So, is it division that I'm thinking of when I'm thinking of the inversion and change of function?  Still screwy.  I get the common denominator/ adding thing then.  Slowly, slowly it's coming back.  

The fact is, in my life I've rarely encountered the need for more than a basic use for fractions, so it all kind of gets lost and muddled.  If I get stuck adding fractions in baking, I simply convert to Tbsps or something like that.  In fact, I had an easier time than my math-major-teacher sister when it came to that.  I was halving a recipe, and was jabbering on the phone and came across 3/4 of a cup.  What's 1/2 of 3/4?  While she was doing it in her head, I quickly converted the amount to Tbsps (12 T, 4 in each 1/4 C) and had a more useful answer (6T) than she had (3/8).  (Then I think I finished mixing the cake and baking it halfway before I realized I left the sugar out-- of my daughter's birthday cake!  She was nearly in tears while I was trying to convince her I could start over again.... this time no jabbering on the phone!)

[onatightrope]

Originally Posted by SweetSilver 

beckington, you are right about the inversion.  So, is it division that I'm thinking of when I'm thinking of the inversion and change of function?  Still screwy.  I get the common denominator/ adding thing then.  Slowly, slowly it's coming back.  

The fact is, in my life I've rarely encountered the need for more than a basic use for fractions, so it all kind of gets lost and muddled.  If I get stuck adding fractions in baking, I simply convert to Tbsps or something like that.  In fact, I had an easier time than my math-major-teacher sister when it came to that.  I was halving a recipe, and was jabbering on the phone and came across 3/4 of a cup.  What's 1/2 of 3/4?  While she was doing it in her head, I quickly converted the amount to Tbsps (12 T, 4 in each 1/4 C) and had a more useful answer (6T) than she had (3/8).  (Then I think I finished mixing the cake and baking it halfway before I realized I left the sugar out-- of my daughter's birthday cake!  She was nearly in tears while I was trying to convince her I could start over again.... this time no jabbering on the phone!)

Division is the inverse function of multiplication, which is another way of saying that dividing is basically un-multiplying.  Anytime you are supposed to divide say A by B, you could instead multiply A by the inverse of B.  And the inverse of B is the number that, when multiplied with B gives you 1 (the identity property of multiplication) which is 1/B, because B*1/B=B/B=1.  And if B is 1/3, you can convert 1/(1/3) into a less cumbersome 3 by multiplying the top and the bottom of the fraction by 3.  Once you've done that a few times, you stop writing the step of multiplying by 3/3, and just flip the fraction.

It's kind of like subtracting a negative number:  2-(-2)=2+ (-(-2))=2+2  The negative signs mean "opposite" as long your adding or subtracting, and two of them cancel each other out. 

Is that any clearer at all?

[SweetSilver]

Originally Posted by onatightrope 

Division is the inverse function of multiplication, which is another way of saying that dividing is basically un-multiplying.  Anytime you are supposed to divide say A by B, you could instead multiply A by the inverse of B.  And the inverse of B is the number that, when multiplied with B gives you 1 (the identity property of multiplication) which is 1/B, because B*1/B=B/B=1.  And if B is 1/3, you can convert 1/(1/3) into a less cumbersome 3 by multiplying the top and the bottom of the fraction by 3.  Once you've done that a few times, you stop writing the step of multiplying by 3/3, and just flip the fraction.

It's kind of like subtracting a negative number:  2-(-2)=2+ (-(-2))=2+2  The negative signs mean "opposite" as long your adding or subtracting, and two of them cancel each other out. 

Is that any clearer at all?

I'll need to work out the second half of your explanation, but it is a bit clearer.  I'll see if I can make it clearer still by plugging in some more numbers.
 

[Roar]

I can understand why someone wouldn't want to engage in forcing a kid to sit at a table and methodically work through a curriculum, but I don't understand of gently introducing something like Miquon. We really enjoyed it and I think it can be a very helpful tool for developing number sense and mathematical thinking. What is the worry about having a tool like Miquon available?

[SweetSilver]

Originally Posted by Roar 

I can understand why someone wouldn't want to engage in forcing a kid to sit at a table and methodically work through a curriculum, but I don't understand of gently introducing something like Miquon. We really enjoyed it and I think it can be a very helpful tool for developing number sense and mathematical thinking. What is the worry about having a tool like Miquon available?

Who mentioned worry?
 

[purslaine]

Originally Posted by Roar 

I can understand why someone wouldn't want to engage in forcing a kid to sit at a table and methodically work through a curriculum, but I don't understand of gently introducing something like Miquon. We really enjoyed it and I think it can be a very helpful tool for developing number sense and mathematical thinking. What is the worry about having a tool like Miquon available?

Many USers believe in creating a resource rich environment, from which their children can learn and explore. Curriculum can play a part in this.  I suppose some USer eschew textbook like things - but so do some more traditional HSers.  It often comes down to the parents feeling they can create better custom made resources.  I used to feel like this, lol, but the reality of time management made it better for me to buy a few already put together things.  

[Roar]

Originally Posted by SweetSilver 

Who mentioned worry?
 

Maybe not worry? Beckington mentioned being wary of curriculum. You mentioned feeling confused by math. I was just trying to process when feeling confused with math why not offer the possibility of other resources?

And, Kathy I certainly get the idea of believing you can create better resources - I certain feel that is true with a lot of what passes for curriculum. Having spent time with it though I'm not at all deluding myself that I could come up with something better than Miquon. It isn't for everyone, but there can be some wonderful discovery in the process. I wish it had been my start in math. 

[beckington]

Originally Posted by Roar 

Maybe not worry? Beckington mentioned being wary of curriculum. You mentioned feeling confused by math. I was just trying to process when feeling confused with math why not offer the possibility of other resources?

Only because of my experience and understanding of my son, and my own concern that *I'll* feel once we have a curriculum that we *must* use it. I should have been more clear, sorry. A full-fledged curriculum on something he has expressed an interest in is likely to send him running the other way if not introduced carefully. I've seen it happen before when I've gotten heaps of library books on a subject out for him. It's too much, too soon, and not allowing him to control the process. Lesson learned. FWIW, we've decided to have a go with Singapore for math. Gently!

[SweetSilver]

Miquon Math continually gets very good recommendations.  I have a notebook, and inside goes all kinds of ideas (orienteering!), books, games, curriculums (for specific subjects), websites, fairs, festivals, local crafts groups (knapping anyone?), parks all over this state and Oregon, etc. etc. etc.  Miquon is already in there under "math".  It is just one of a bazillion things I could use to enrich our homeschooling.

One of the ideas in that notebook, which came from the girls, is to build birdhouses.  We gathered the information we needed to build species-specific birdhouses, they received child-size handtools for Christmas, and we are going to build birdhouses (right after we build toolboxes!).  So, being one of a bazillion things, why did I choose this project to put my resources into?  The enthusiasm was there, as simple as that.  Not worry, or wariness, not out of a *need* to learn specific skills, or to avoid learning other ones out of fear of some such thing.  Just because that seems to be where the joy is.  (And having those handtools out and available to use seems like a lot of fun, especially since we have lots of wood scraps from our house being built.)  

Well, why not get Miquon Math now and have it around the house?  That's a good idea, and I do need work on my own math skills up into fractions, squares and the like, but maybe I want a children's encyclopedia instead, get the girls geared up for riding lessons, get more guidebooks because they are well-loved (I have my eye on the Smithsonian Rocks and Minerals), maybe a microscope, maybe some map puzzles or more art supplies.  

Like I said, it is one of a bazillion things.

It should come as no surprise to unschooling parents on an unschooling forum that some parents are not using curriculums or other learning programs (I'm not quite sure how to classify Miquon).  

My not using these (for now) is not a criticism of other parents (USing, HSing, or somewhere in between) who do use these.

And, again, I'm glad to hear so many good recommendations about Miquon Math.  It is worth investigating.

[moominmamma]

Originally Posted by beckington 

Only because of my experience and understanding of my son, and my own concern that *I'll* feel once we have a curriculum that we *must* use it. I should have been more clear, sorry. A full-fledged curriculum on something he has expressed an interest in is likely to send him running the other way if not introduced carefully. I've seen it happen before when I've gotten heaps of library books on a subject out for him. It's too much, too soon, and not allowing him to control the process. Lesson learned. FWIW, we've decided to have a go with Singapore for math. Gently!

We've found both Singapore Primary Math and Miquon to be excellent at various different stages. I just wanted to point out, though, since you mention your concern about your own potentially overzealous use of curriculum and your ds's control of his learning, that Singapore is much more a "full-fledged curriculum" in the traditional sense. It's designed to be taught in a sequential way and is workbook-focused. The Miquon approach as explained in the First-Grade Diary and Lab Annotations Manual is much more like a set of resources and ideas with a framework that provides some guidance, but is designed to be implemented in whatever order appeals to your child, with the discovery and exploration facilitated by the parent but largely led by the child. In other words, to me it seems to be about as close to unschooling as you can get in a curriculum. Yes there are workbooks, but they're not the heart of the program, they're mostly a way to learn to translate the discovery-based activities into symbolic form, and to engage in exploration of other pictorial, geometric and pattern-based explorations.

Miranda

[onatightrope]

If you wanted to just have some fun math resources around, and you're ok with computer games, Singapore Math has cd-roms that do a very good job of illustrating things like multiplication and borrowing.http://www.singaporemath.com/CD_ROMs_s/26.htm

[beckington]

Originally Posted by moominmamma 

We've found both Singapore Primary Math and Miquon to be excellent at various different stages. I just wanted to point out, though, since you mention your concern about your own potentially overzealous use of curriculum and your ds's control of his learning, that Singapore is much more a "full-fledged curriculum" in the traditional sense. It's designed to be taught in a sequential way and is workbook-focused. The Miquon approach as explained in the First-Grade Diary and Lab Annotations Manual is much more like a set of resources and ideas with a framework that provides some guidance, but is designed to be implemented in whatever order appeals to your child, with the discovery and exploration facilitated by the parent but largely led by the child. In other words, to me it seems to be about as close to unschooling as you can get in a curriculum. Yes there are workbooks, but they're not the heart of the program, they're mostly a way to learn to translate the discovery-based activities into symbolic form, and to engage in exploration of other pictorial, geometric and pattern-based explorations.

Miranda

I did consider Miquon and was all set to get it, for all the reasons you mentioned. But ds pulled out an old Singapore 1a that we had kicking around and has started working in it and seems to like it so far, so he's made the decision himself! :) I'm just going to go with it for now and if he loses interest or finds it boring or frustrating then I'll suggest Miquon to him.