Better-Late-Than-Early Folks, Advise me on Math, Please!

[lewelma]

Bill, I would be interested in knowing what your ideal math education would look like for younger kids. When do you start?  How does this vary depending on readiness?  What materials would you use? How do you adjust your expectations and your program given the skill of the student?  How would you adapt to frustrations in young children?  

 

I'm honestly curious.  I have worked with the full range of students from dyscalculia (scoring in the 0.1 percentile) to a highly gifted student (competing internationally in mathematics), and everything in between.  I work with older students, so get the results of the primary school education system and have to clean up the messes. I have a number of unschooly friends whose kids didn't do maths in k-4, but unlike bsdmama, they never got onto it in grade 5 and convinced themselves that it was not worth doing if their child was not interested.  I have seen these kids launched as dancers, hair dressers, makeup artists, outdoor education, etc.  No university for them, but yet they seem quite happy and have jobs at 18. So their education definitely limited their options, but I'm not sure did harm, which leaves me somewhat conflicted.  So I do know what you are saying, that there is a subset of parents who delay and then fail to follow up.  But I also know that there are people like me, who did delay formal math education, not to the extent of blsdmama, but with my older I delayed until he was 7.  This doesn't sound very late, but by 7 he was ready for algebra, so in some ways I delayed even longer than blsdmama. Before that all we did was play shop sometimes and make up silly word problems for each other occasionally. So this gets me wondering about the confluence of age, ability, and emotional readiness on the ideal math program for each student and the age of starting. I'm not convinced it's straightforward to untangle, and I would be very interested in your opinions.  If you think it would be appropriate, we could start a new thread as it seems that there are some who would prefer that this thread kept to the request for advice of the OP. 

 

Ruth in NZ

[Rosie_0801]

Ironically, there's an eye therapy for PTSD that actually works.  But that's just a total rabbit trail.  Apparently it's something about getting them to use both sides of their brain while they process the trauma, to get all the disparate pieces to reconnect.  

 

Interesting. I wonder whether it works on all kinds of ptsd. Actually, I wonder if there are officially different kinds of ptsd or if that's something I'm making up.

 

Anyway, rabbit trail.

[Rosie_0801]

So can we talk about what IS taught in K-4?  Please add yours, but I know simple addition, subtraction, intro to multiplication, place value, clocks/time telling, money, skip counting.   And I definitely don't want to dismiss anyone's hard work, but kids pick up the concepts of addition and subtraction pretty much as easy as breathing.  Money, telling time, and skip counting at age 9/10 can be taught readily in a week.  I'm open to hearing what I'm missing and why it's so vital, but I am just *not* seeing it. 

 

For dd, adding fractions with the same common denominator had to come before multiplication and division.

[ktgrok]

Of course it is, because of the attempted character assassination of one questioning the model.

 

 

 

Not what I asked. Are you seeing educational neglect or parental neglect in any of the people participating in this thread? It's a yes or no answer. 

[ktgrok]

Art Robinson says young children can teach themselves math, and he's a homeschooling "guru" who has a tremendously negative influence on home education.

 

Why do you (all) attempt to personalize every issue by suggesting (falsely) that it's some sort criticism of someone on this thread ? That is a strange phenomenon. 

 

 

 

But no one has brought up Art Robinson in this thread! And we assume you are referring to someone or something in this thread, because otherwise, hello, why bring it up??

 

I don't bring up coffee in a thread about milk. 

[ktgrok]

Interesting. I wonder whether it works on all kinds of ptsd. Actually, I wonder if there are officially different kinds of ptsd or if that's something I'm making up.

 

Anyway, rabbit trail.

 

My good friend swears EMDR saved her life when she was suicidal after PTSD from a traumatic birth. 

[PeterPan]

Our goats are amazing. I grudgingly admit I wasn't sold on the idea of goats when we got them. But they are fabulously fun. 

 

Are chickens a gateway to goats?  I have a friend who got chickens, then BOOM she had goats, multiple goats, goats even on her FACEBOOK page.  You're really far gone with your farming when you're putting your goat videos on FB.   :lol:  I was hoping for chickens once we get past homeschooling, but if chickens are a gateway to goats, I'm gonna be careful!   :D

[PeterPan]

My good friend swears EMDR saved her life when she was suicidal after PTSD from a traumatic birth. 

 

Yeah, the story I was personally told was SO amazing, I wouldn't hesitate to pursue EMDR or recommend it for someone I loved.  And this was someone who had dealt with a different kind of PTSD from what has been listed.  I think they're also using it on soldiers.  I think the reason it works is because of the *way* it works.  It gets the two sides of the brain reconnecting, so the fragments can come together so the person can finally process them in a safe place, with a trusted person.  I don't think it's something you would do by yourself, if that makes sense.  

 

I was just blown away by the increased joy and peace of the person after so many years of attempting to process and deal with their PTSD.  Amazing and so happy for them.

[Rosie_0801]

Yeah, the story I was personally told was SO amazing, I wouldn't hesitate to pursue EMDR or recommend it for someone I loved.  And this was someone who had dealt with a different kind of PTSD from what has been listed.  I think they're also using it on soldiers.  I think the reason it works is because of the *way* it works.  It gets the two sides of the brain reconnecting, so the fragments can come together so the person can finally process them in a safe place, with a trusted person.  I don't think it's something you would do by yourself, if that makes sense.  

 

I was just blown away by the increased joy and peace of the person after so many years of attempting to process and deal with their PTSD.  Amazing and so happy for them.

 

So is there PTSD that is a lack of processing and PTSD that isn't?

 

Or something (that deserves its own thread :p )

[PeterPan]

I don't bring up coffee in a thread about milk. 

 

Trader Joes has really good coffee candy.  I don't drink coffee, but I like their coffee candy (a little too much!) and coffee milkshakes.  But the one breaks the diet and the other doesn't.  Hmm.

 

Besides, what are we supposed to devolve into?  We're going to debate whether uneducated people, dumb people, and lemmings exist?  I mean, dude, all we have to do is turn on the tv.  Life isn't fair, and not all kids get equal access to everything.  I've given up trying to understand the nature of all of it.  I try to work in my own little corner.  There are pro-active ways to harness your passions.  Teach online classes, tutor pro-bono, change the world.  Get on your school board.  Actually do something to effect change.  I have this idea (that I haven't had time to completely research yet), that we ought to bring OG tutoring to our public libraries.  This is change we can actually make happen!  I live in an area where 70% of the kids live below the poverty level and will never have access to the high quality tutoring 10 minutes away.  So why should our libraries NOT provide this kind of service to give access to their kids?  I found that San Francisco has a similar program.  I'm just looking for programs and how we actually make it HAPPEN.  

 

Don't just talk change.  Make change.  

 

Adding: If anybody actually knows how to do that or has a library that offers reading tutors, I'd welcome the info.  

Edited November 4, 2016 by OhElizabeth

[PeterPan]

So is there PTSD that is a lack of processing and PTSD that isn't?

 

Or something (that deserves its own thread :p )

 

I haven't had PTSD, so I don't know.  What you might want to do is talk with EMDR practitioners and see when they've found it useful.

[lanalouwho]

Trader Joes has really good coffee candy. I don't drink coffee, but I like their coffee candy (a little too much!) and coffee milkshakes. But the one breaks the diet and the other doesn't. Hmm.

 

Besides, what are we supposed to devolve into? We're going to debate whether uneducated people, dumb people, and lemmings exist? I mean, dude, all we have to do is turn on the tv. Life isn't fair, and not all kids get equal access to everything. I've given up trying to understand the nature of all of it. I try to work in my own little corner. There are pro-active ways to harness your passions. Teach online classes, tutor pro-bono, change the world. Get on your school board. Actually do something to effect change. I have this idea (that I haven't had time to completely research yet), that we ought to bring OG tutoring to our public libraries. This is change we can actually make happen! I live in an area where 70% of the kids live below the poverty level and will never have access to the high quality tutoring 10 minutes away. So why should our libraries NOT provide this kind of service to give access to their kids? I found that San Francisco has a similar program. I'm just looking for programs and how we actually make it HAPPEN.

 

Don't just talk change. Make change.

 

Adding: If anybody actually knows how to do that or has a library that offers reading tutors, I'd welcome the info.

I have no advice on how to make that happen, but I think it is a wonderful idea!

Does your library have a programs director you could talk to?

 

Sent from my HTCD200LVW using Tapatalk

[Rosie_0801]

Local government grants, OhE?

[Spy Car]

Are chickens a gateway to goats?  I have a friend who got chickens, then BOOM she had goats, multiple goats, goats even on her FACEBOOK page.  You're really far gone with your farming when you're putting your goat videos on FB.   :lol:  I was hoping for chickens once we get past homeschooling, but if chickens are a gateway to goats, I'm gonna be careful!   :D

 

All I know is that after we got chickens all I heard about from Mrs. Spy Car was how she wanted goats. No matter that we live in a leafy suburb of Los Angeles where I don't think goat-keeping would really work.

 

I'd say more, but far be it from me to take a thread off course :D

 

Bill

[maize]

All I know is that after we got chickens all I heard about from Mrs. Spy Car was how she wanted goats. No matter that we live in a leafy suburb of Los Angeles where I don't think goat-keeping would really work.

 

I'd say more, but far be it from me to take a thread off course :D

 

Bill

I'm pretty sure goats are an acceptable side trail to any thread.

 

We're not allowed goats, don't have the acreage our city ordinances require. They say we can have a chicken. Just one.

[ktgrok]

I like chickens, and want that mini donkey, but no goats. They pool everywhere, and they don't like me. Seriously, they hate me. I don't know why. I get along great with most other creatures, but sheep and goats don't like me. 

[Spy Car]

Bill, I would be interested in knowing what your ideal math education would look like for younger kids. When do you start?  How does this vary depending on readiness?  What materials would you use? How do you adjust your expectations and your program given the skill of the student?  How would you adapt to frustrations in young children?  

 

I'm honestly curious.  I have worked with the full range of students from dyscalculia (scoring in the 0.1 percentile) to a highly gifted student (competing internationally in mathematics), and everything in between.  I work with older students, so get the results of the primary school education system and have to clean up the messes. I have a number of unschooly friends whose kids didn't do maths in k-4, but unlike bsdmama, they never got onto it in grade 5 and convinced themselves that it was not worth doing if their child was not interested.  I have seen these kids launched as dancers, hair dressers, makeup artists, outdoor education, etc.  No university for them, but yet they seem quite happy and have jobs at 18. So their education definitely limited their options, but I'm not sure did harm, which leaves me somewhat conflicted.  So I do know what you are saying, that there is a subset of parents who delay and then fail to follow up.  But I also know that there are people like me, who did delay formal math education, not to the extent of blsdmama, but with my older I delayed until he was 7.  This doesn't sound very late, but by 7 he was ready for algebra, so in some ways I delayed even longer than blsdmama. Before that all we did was play shop sometimes and make up silly word problems for each other occasionally. So this gets me wondering about the confluence of age, ability, and emotional readiness on the ideal math program for each student and the age of starting. I'm not convinced it's straightforward to untangle, and I would be very interested in your opinions.  If you think it would be appropriate, we could start a new thread as it seems that there are some who would prefer that this thread kept to the request for advice of the OP. 

 

Ruth in NZ

 

Ruth, I can't think of anyone I'd enjoy conversing with on this subject that you.

 

Early math education remains an area of great interest to me. I'm convinced there is an alternative to either delay or the premature use of a traditional workbook approach. For lack of a better term, it could be called a "Math Lab" approach.

 

Goals would be to teach (or to create situations where the child "discovered" for him or herself) concepts in ways that promote real understanding and numeracy. By necessity, this approach does require meeting a child where they are in terms of understanding and building from there. Many times I'd think about topics I'd wish to cover in the medium term, but would always ask myself what my child needed to grasp before tackling those things. There is no timetable or rushed agenda. Developing real understanding being the primary goal. To aid understanding I generally tried having activities, games, manipulatives, and other aids that hit concepts using very different looking activities.

 

Another hallmark was using materials that required reasoning and logical thinking. I believe (and medical science appear to validate it) that the neural network of the mind hardwires permanent connections when given appropriate stimulus. And creative math play in the early years IMO helps build a stronger brain. Math-play is (obviously) not the only way to stimulate young minds, but there are still plenty of hours to play in drainage ditches  (inside joke :D) before and after a nurturing Math Lab.

 

I'll leave it there. Deeply incomplete. 

 

Bill

[PeterPan]

I have no advice on how to make that happen, but I think it is a wonderful idea!

Does your library have a programs director you could talk to?

 

Sent from my HTCD200LVW using Tapatalk

 

 

Local government grants, OhE?

 

I have the in at the library.  What I need is the information on how places actually make this HAPPEN.  It seems complex to me.  You have to get some lead people trained.  You have volunteers who need background checks.  Lots of levels of things to happen.  There's a gap between my vision and what I'm actually making happen.  I wouldn't actually have to make it happen.  I just want to get enough info gathered (when I get over this pneumonia and asthma) that it can be proposed.  Innovation, moving forward.  It's not enough to TELL kids to use the library if they can't actually READ.  

[PeterPan]

All I know is that after we got chickens all I heard about from Mrs. Spy Car was how she wanted goats. No matter that we live in a leafy suburb of Los Angeles where I don't think goat-keeping would really work.

 

I'd say more, but far be it from me to take a thread off course :D

 

Bill

 

You're in LA?  You're back on-topic!  That library I found was in San Francisco!  Do your LA libraries offer reading services for young people or adults? 

 

I'm imagining goats on astro-turf, and I can't decide if that's sanitary or not.  People in CA often do artificial grass, yes?  So this could really work.  Miniature goats.  With collars.  They'd be kinda like chihuahas, only not.  :D

[Jean in Newcastle]

I had dd price out how much it would cost for us to utilize one of the renta-goat services they have here for yard "mowing" and clean-up.  One of our neighbors actually did it.  But alas, they are much more expensive than you would think.  So living math and goats.  How progressive is that?!  (This was a couple of years ago.  We also did the Simply Charlotte Mason "Business Math" curricula where you run a pet store or sports store or toy store and have to keep up inventory, balance the books, figure out sales tax and offer sales once in awhile along with the attendant math.  I added onto the store idea and had her figure out how much it would cost to recarpet the store (area), and how much for new paneling (perimeter plus area of the walls) and we had raffles for our business and fund-raisers with free cupcakes, all which required math to figure out.  This was in upper elementary but dd still had a good time and learned a lot.  (I said in another spin off thread that she was my highly concrete thinker longer than is the norm and doing this kind of goat and store math was good stuff for her. 

[PeterPan]

...Early math education remains an area of great interest to me. I'm convinced there is an alternative to either delay or the premature use of a traditional workbook approach. For lack of a better term, it could be called a "Math Lab" approach.

 

Goals would be to teach (or to create situations where the child "discovered" for him or herself) concepts in ways that promote real understanding and numeracy. By necessity, this approach does require meeting a child where they are in terms of understanding and building from there. Many times I'd think about topics I'd wish to cover in the medium term, but would always ask myself what my child needed to grasp before tackling those things. There is no timetable or rushed agenda. Developing real understanding being the primary goal. To aid understanding I generally tried having activities, games, manipulatives, and other aids that hit concepts using very different looking activities.

 

Another hallmark was using materials that required reasoning and logical thinking. I believe (and medical science appear to validate it) that the neural network of the mind hardwires permanent connections when given appropriate stimulus. And creative math play in the early years IMO helps build a stronger brain. Math-play is (obviously) not the only way to stimulate young minds, but there are still plenty of hours to play in drainage ditches  (inside joke :D) before and after a nurturing Math Lab...

 

Extended math lab (or what I think you mean by that) *is* the best way to handle dyscalculia, or it's at least how I'm handling it.  What you're calling "reasoning and logical thinking" is probably much like what we're doing with our worksheets.  I pick things focused on problem solving, not computation. They usually need a little computation, but they're more focused on thought, language, noticing details, reasoning.  I suppose they could go wittier and farther, but for a boy who a year ago was still struggling with what came before 5 (I kid you not, with a gifted IQ!), we're doing pretty well.  And they're something where I can easily keep him 1-2 grades above grade level, allowing him to scratch his itch to THINK in spite of his delays.  So like today one problem asked which could get to the other side of the chess board sooner with just their moves (assuming no opposition, obviously, just the moves), a knight or a pawn.  He could visualize it in my mind, but I had to get out the board and check. That was kind of fun!  I love seeing how actually AMAZING his mind is at THINKING, even if really basic things like 6+ 7 are hard.

 

Adding: For us much as the way we work now seems obvious and good, we're only doing it because it's *necessary*.  I can totally see why someone whose dc didn't absolutely positive have to have that to comprehend things would move on.

Edited November 5, 2016 by OhElizabeth

[PeterPan]

Jean, you are JOKING.  You can RENT-A-GOAT???   :lol:  :lol:  :lol:   The things we learn here!!!   :smilielol5:  :smilielol5:  :smilielol5:

[Spy Car]

You're in LA?  You're back on-topic!  That library I found was in San Francisco!  Do your LA libraries offer reading services for young people or adults? 

 

I'm imagining goats on astro-turf, and I can't decide if that's sanitary or not.  People in CA often do artificial grass, yes?  So this could really work.  Miniature goats.  With collars.  They'd be kinda like chihuahas, only not.   :D

 

What do you mean by "reading services?" There are often nice (usually elderly female) volunteers that will read to children if that's what you mean.

 

I wouldn't say that artificial grass is common around here; however, there is one very expensive home on our block where they put in turf.

 

The drought has really put pressure on homeowners to cut back on water, and the once luxuriant lawns that were standard in earlier decades may go the way of the dodo. 

 

I imagine goats might eat plastic grass. But what do I know? :D

 

Bill

[Jean in Newcastle]

Jean, you are JOKING.  You can RENT-A-GOAT???   :lol:  :lol:  :lol:   The things we learn here!!!   :smilielol5:  :smilielol5:  :smilielol5:

 

http://rentagoat.com/  This one looks like it is Bill's territory, not mine.  But yes, there are goat rental places around here.  Maybe it is more West Coast? 

[PeterPan]

Spy-Tutoring for dyslexia.  In San Francisco, from what I could tell online, they have an OG-based program (good!) that kids can come in and do once a week with a tutor.  That's as far as I got.  My mind swirls with the possibilities and the logistics.  At our library people are more likely to check out a pile of videos and games than books.  And while I'm ALL FOR  multi-media and usefulness at the library, I think there's more we can do with making sure the kids coming in actually can READ. 

 

Just as an aside, what would I be looking for in the category of "make them think" that doesn't get limited by computation and the dyscalculia?  Right now, I'm doing pretty well with materials from TCR, because they're short and fine-tuned.  So I can get a product like https://cdn.teachercreated.com/samples/3578s.pdf, use it a couple grades above his age grade, and give him a fun chance to think without really having him held back by the computation.  I usually just jiggle him through.  I just know there's FARTHER we could go.  

 

Right now it's just this idea in my mind (explore math in more directions that aren't limited by his computation), and I haven't actually quite figured out what I'm looking for.  I think Llewelma did some of this yes?  He's not profoundly gifted either, so just more run of the mill gifted level would be adequate.  Like fun without expecting him to think through one problem for an hour.  I don't know if he would sit through a problem for an hour.  

[PeterPan]

Jean, you have BLOWN MY MIND.  That's all I'm saying.  :D

[maize]

Spy-Tutoring for dyslexia. In San Francisco, from what I could tell online, they have an OG-based program (good!) that kids can come in and do once a week with a tutor. That's as far as I got. My mind swirls with the possibilities and the logistics. At our library people are more likely to check out a pile of videos and games than books. And while I'm ALL FOR multi-media and usefulness at the library, I think there's more we can do with making sure the kids coming in actually can READ.

 

Just as an aside, what would I be looking for in the category of "make them think" that doesn't get limited by computation and the dyscalculia? Right now, I'm doing pretty well with materials from TCR, because they're short and fine-tuned. So I can get a product like https://cdn.teachercreated.com/samples/3578s.pdf, use it a couple grades above his age grade, and give him a fun chance to think without really having him held back by the computation. I usually just jiggle him through. I just know there's FARTHER we could go.

 

Right now it's just this idea in my mind (explore math in more directions that aren't limited by his computation), and I haven't actually quite figured out what I'm looking for. I think Llewelma did some of this yes? He's not profoundly gifted either, so just more run of the mill gifted level would be adequate. Like fun without expecting him to think through one problem for an hour. I don't know if he would sit through a problem for an hour.

Some of the Beast Academy stuff does not involve computation.

[PeterPan]

https://cdn.teachercreated.com/samples/2563s.pdf  Ok, for a 2nd example, this is a 3rd gr target age book that I got to intersperse between reading pages for him.  At this level they're candy for him, just fun and fast.  He did 4 pages interspersed between a whole bunch of other (more challenging) reading comprehension worksheets.  But when we get into puzzles that use spelling and language too much, he has to suck it up as it's a disability for him.  I'd love to go more in the direction of more math-y brain candy.  Even just one page a day.

 

https://cdn.teachercreated.com/samples/2493s.pdf  I ordered him this today, and I think it will be more interesting.  It will actually be hard for him, because for some reason holding a ruler and connecting points to draw a straight line is hard!  But the idea is cool.  I just wish it were nifty pictures or fractals or something, not QUILTS.  :(

[PeterPan]

Some of the Beast Academy stuff does not involve computation.

 

When I looked at the books, they seemed like they were intending to be math instruction.  Are there components I don't realize?  He might think the cartoons were funny, but I'm not sure he'd actually understand math presented that way.

[Spy Car]

Extended math lab (or what I think you mean by that) *is* the best way to handle dyscalculia, or it's at least how I'm handling it.  What you're calling "reasoning and logical thinking" is probably much like what we're doing with our worksheets.  I pick things focused on problem solving, not computation. They usually need a little computation, but they're more focused on thought, language, noticing details, reasoning.  I suppose they could go wittier and farther, but for a boy who a year ago was still struggling with what came before 5 (I kid you not, with a gifted IQ!), we're doing pretty well.  And they're something where I can easily keep him 1-2 grades above grade level, allowing him to scratch his itch to THINK in spite of his delays.  So like today one problem asked which could get to the other side of the chess board sooner with just their moves (assuming no opposition, obviously, just the moves), a knight or a pawn.  He could visualize it in my mind, but I had to get out the board and check. That was kind of fun!  I love seeing how actually AMAZING his mind is at THINKING, even if really basic things like 6+ 7 are hard.

 

Adding: For us much as the way we work now seems obvious and good, we're only doing it because it's *necessary*.  I can totally see why someone whose dc didn't absolutely positive have to have that to comprehend things would move on.

 

I savored finding "problems" that would make my boy's mind whirl. As you say, not computations, but problem-solving. Questions that hit just the right spot so he had to think. To me, that's the magic part. It drives both intellectual growth ((literally and figuratively) and give a student a reason to want to learn the math necessary to do the fun stuff. The things that excite you (like the chess problem) also excite me.

 

Before "adding" or computing using algorithms much time was spent seeing groupings of different pairs to make a value. These included using C Rods, and cards with red dots (two rows of five to make ten), tally marks, dice style (to five), RS-style (5 blue dots and 5 yellow dots on a line), an actual RS abacus, and the like. So the child got used to seeing groups and pairs visually (and holding them as manipulatives) well before moving on to pencil work.

 

And before pencil work happened, and addition had to be explained in terms of re-grouping (particularly when the sums were over 10). Memorized answers earned no credit here.

 

The 7+6 problem you mentioned would involve seeing the 7 needs 3 to become a Ten, and if the 6 gave up 3 to make that happen. it would become a 3. So then, you'd have 1-Ten and 3-Units.

 

When 1-Ten and 3-Units is clear, then we'd talk about the silly names English has for such numbers, like "thirteen." 

 

Using "math names" (instead of common English names)of numbers  in the early years is very (very) helpful in my estimation.

 

Bill

[ktgrok]

http://rentagoat.com/  This one looks like it is Bill's territory, not mine.  But yes, there are goat rental places around here.  Maybe it is more West Coast? 

 

We have them in Florida. I looked into it as well. They are also used by the city in Tallahassee to clear Kudzu vine. 

[Dmmetler]

https://cdn.teachercreated.com/samples/2563s.pdf Ok, for a 2nd example, this is a 3rd gr target age book that I got to intersperse between reading pages for him. At this level they're candy for him, just fun and fast. He did 4 pages interspersed between a whole bunch of other (more challenging) reading comprehension worksheets. But when we get into puzzles that use spelling and language too much, he has to suck it up as it's a disability for him. I'd love to go more in the direction of more math-y brain candy. Even just one page a day.

 

https://cdn.teachercreated.com/samples/2493s.pdf I ordered him this today, and I think it will be more interesting. It will actually be hard for him, because for some reason holding a ruler and connecting points to draw a straight line is hard! But the idea is cool. I just wish it were nifty pictures or fractals or something, not QUILTS. :(

Does he like graphing? There are lots of "graph coordinate points to make a cute picture"

[Spy Car]

http://rentagoat.com/  This one looks like it is Bill's territory, not mine.  But yes, there are goat rental places around here.  Maybe it is more West Coast? 

 

There are absolutely people bringing in flocks of goats to clear (especially hillsides) in the high fire-danger areas where it is mandated by law, instead of using laborers. While not "super common" I have seen goat crews at work in the hills above our home. 

 

They are not replacing gardeners in well-tended gardens, because goats eat everything.

 

Bill

[wapiti]

Right now it's just this idea in my mind (explore math in more directions that aren't limited by his computation), and I haven't actually quite figured out what I'm looking for.

 

Yes!  This is sort of what I mean by teaching through strengths.  I have no idea how to teach computation from the big picture, but I do strongly feel that you are on the right track here in general.  People over on the accelerated board might have ideas for you.

 

As far as computation, I haven't kept up with your latest and I don't know the programs, but in my fuzzy mind I'm thinking you eventually move to miquon, or something with the rods.  ETA, as Bill discusses above and can probably describe in even more detail.

 

Like maize mentioned, I did also think of Beast, though not necessarily yet.  But eventually.  And later aops.

 

Ultimately, with the problem solving skills (and spatial strength development?) you are providing a much richer learning experience than he might otherwise have had.  I think it's awesome.  The computation can come eventually, but loving the puzzle thinking can be a hard fire to light and you're doing a great job.

[maize]

When I looked at the books, they seemed like they were intending to be math instruction. Are there components I don't realize? He might think the cartoons were funny, but I'm not sure he'd actually understand math presented that way.

3A has puzzle stuff that is not computation. Tangrams are one type (can't quite remember if those were in 3A or not), there are others. My impression is that is was meant to get kids problem solving; it is not arithmetic.

[Jean in Newcastle]

There are absolutely people bringing in flocks of goats to clear (especially hillsides) in the high fire-danger areas where it is mandated by law, instead of using laborers. While not "super common" I have seen goat crews at work in the hills above our home. 

 

They are not replacing gardeners in well-tended gardens, because goats eat everything.

 

Bill

 

Yes.  My neighbor had them in a fenced area of tall grass and weeds that needed to be cleared.  The goat rental people came first to make sure there were nothing toxic to goats in the area. 

[maize]

There are printables here:

https://www.beastacademy.com/resources/printables.php

[....]

For lack of a better term, it could be called a "Math Lab" approach.

 

Goals would be to teach (or to create situations where the child "discovered" for him or herself) concepts in ways that promote real understanding and numeracy. By necessity, this approach does require meeting a child where they are in terms of understanding and building from there. Many times I'd think about topics I'd wish to cover in the medium term, but would always ask myself what my child needed to grasp before tackling those things. There is no timetable or rushed agenda. Developing real understanding being the primary goal. To aid understanding I generally tried having activities, games, manipulatives, and other aids that hit concepts using very different looking activities.

 

 

I think your "Math Lab" is similar to what we call Living Math, except I try to include math readers (there's a ton of them at our library) and it's not always discovery math.  Math Lab is actually a better term for it, come to think of it...maybe I should start calling it that instead.  

[Rosie_0801]

https://cdn.teachercreated.com/samples/2563s.pdf  Ok, for a 2nd example, this is a 3rd gr target age book that I got to intersperse between reading pages for him.  At this level they're candy for him, just fun and fast.  He did 4 pages interspersed between a whole bunch of other (more challenging) reading comprehension worksheets.  But when we get into puzzles that use spelling and language too much, he has to suck it up as it's a disability for him.  I'd love to go more in the direction of more math-y brain candy.  Even just one page a day.

 

https://cdn.teachercreated.com/samples/2493s.pdf  I ordered him this today, and I think it will be more interesting.  It will actually be hard for him, because for some reason holding a ruler and connecting points to draw a straight line is hard!  But the idea is cool.  I just wish it were nifty pictures or fractals or something, not QUILTS.   :(

 

I've just finished the fractions lessons in here with dd: https://www.amazon.com/Geometry-Fractions-Geoboards-Problem-Solving-Activities/dp/B000R91AV2/ref=sr_1_4?s=books&ie=UTF8&qid=1478307605&sr=1-4&keywords=geoboard+maths

 

No pencils required.

[barnwife]

Are chickens a gateway to goats?  I have a friend who got chickens, then BOOM she had goats, multiple goats, goats even on her FACEBOOK page.  You're really far gone with your farming when you're putting your goat videos on FB.   :lol:  I was hoping for chickens once we get past homeschooling, but if chickens are a gateway to goats, I'm gonna be careful!   :D

Well, in our case, yes. First came the chickens, then came the goats. Once upon a time, we had a couple pigs. The pigs were before the goats. I can't remember if they came before the chickens.

 

If we had FB, I'd be shocked if we didn't have goat things on there!

 

Do it...get the chickens. 

[PeterPan]

I savored finding "problems" that would make my boy's mind whirl. As you say, not computations, but problem-solving. Questions that hit just the right spot so he had to think. To me, that's the magic part. It drives both intellectual growth ((literally and figuratively) and give a student a reason to want to learn the math necessary to do the fun stuff. The things that excite you (like the chess problem) also excite me.

 

Before "adding" or computing using algorithms much time was spent seeing groupings of different pairs to make a value. These included using C Rods, and cards with red dots (two rows of five to make ten), tally marks, dice style (to five), RS-style (5 blue dots and 5 yellow dots on a line), an actual RS abacus, and the like. So the child got used to seeing groups and pairs visually (and holding them as manipulatives) well before moving on to pencil work.

 

And before pencil work happened, and addition had to be explained in terms of re-grouping (particularly when the sums were over 10). Memorized answers earned no credit here.

 

The 7+6 problem you mentioned would involve seeing the 7 needs 3 to become a Ten, and if the 6 gave up 3 to make that happen. it would become a 3. So then, you'd have 1-Ten and 3-Units.

 

When 1-Ten and 3-Units is clear, then we'd talk about the silly names English has for such numbers, like "thirteen." 

 

Using "math names" (instead of common English names)of numbers  in the early years is very (very) helpful in my estimation.

 

Bill

 

Oh don't worry, we've done the latter kind of stuff you're describing OUT THE WAZOO.  He has SLD math (and reading and writing) but also ASD.  So the names mean nothing, things don't generalize to new situations, etc.  So he can learn a number or scenario with one manipulative or in one setting and not know it in another.  Like literally he just won't know it.  It didn't "generalize".  So we spent a month, a literal MONTH on this is the number 5.  When he was 5.  With a gifted IQ.  And it was as tedious as "this is 5 (dots).  Can you see a ONE inside the 5?" and we did this every with day, with games (yes, games to practice seeing 1 dot inside of 5 dots, 2 dots inside of 5 dots, etc.) for a month, and then he could understand 5 dots.  But we had to generalize it to 5 EVERYWHERE, not just 5 dots.  So 5 turtles, 5 m&ms, 5 when we're at gymnastics, 5 in the car, that all the 5s are the same.  

 

And that was age 5.  While my dd (with a lower IQ, mind you!) was, at that age, discovering for herself subtraction and multiplication.  And my ds, with dyscalculia, was trying to understand the number 5.

 

We have more we can do with bridging and quantities, sure.  It gets tedious.  I diverged and have done other things, like measuring.  I taught him fractions.  I'm trying to teach him decimals and how fractions and decimals relate.  When I show him written addition, I include decimal places.  He's conversant with negative numbers and has been for a year.  He'd actually find it easier to answer 6-7 than 6+7.   :lol:  We did a Ronit Bird game with ante poker cards, and the idea of negative numbers just totally clicked in his mind.  

 

So essentially I'm saying I feel free to do any math, through about 6th grade, conceptually with him, and I take anything he CAN access that far. And that's all good.  That's that math lab stuff.  But I think there's something MORE we could be doing.  I just don't know what it is.  TCR has a pre-geometry  Math In Action: Pre-Geometry - TCR3531 « Products | Teacher Created Resources that is sort of what I'm looking for.  It's just too light.  It's aimed at gr 1-2, and I'm not sure it's worth the money for ds, if only a little is useful.  I can't really tell.  I'm ok with things that make him feel like a rock star or that build confidence so he can go into the NEXT book and be confident, sure.  I just thought this was a pretty low starting point for him.  Their gr3-5 How to Succeed in Geometry is kind of dry.  

 

Badabing!  I missed their Practice Makes Perfect Geometry book!  Well bummer.  The gr 3 book is on the easy side, rock star level for him.  Gr 4 turns into just tons of computation, no wit at all, and it loses the multiple choice.  With his dysgraphia, multiple choice is really helpful.  Wow, I must be really hard to please!  But I *am* picky.  I don't think it's fun to do pages and pages of computation.  I like things that make him think, with just enough practice. Later we can do Patty Paper Geometry.

 

But really, there has to be more than that.  There have to be other types of math he could explore. I guess I could get brilliant and answer my own question, duh.  I'll bet NCTM or one of those places has books they sell, lol.  And Family Math is cool.  Have that.  You can keep endlessly busy.  It's easy to find stuff at the middle level and instructional level.  What's tricky is to keep up with that "really make you scratch your head" level, the ones that are most satisfying.  That's where you just do ONE but it made you feel SO GOOD.  Those we leave as his ultimate reward pages, the ones he works toward.  So it's actually really important we have them.  

[PeterPan]

There are printables here:

https://www.beastacademy.com/resources/printables.php

You are SO my new bestie!  :D  This is just the kind of thing I wanted!  And, you know, I looked at BA two years ago, when my ds couldn't even identify 5 of something.  He's a real oddity to work with, and I just kind of gave up and shuffled it into the long way off, Star Wars kind of file.  Might be time to re-examine that.  :)

 

I've just finished the fractions lessons in here with dd: https://www.amazon.com/Geometry-Fractions-Geoboards-Problem-Solving-Activities/dp/B000R91AV2/ref=sr_1_4?s=books&ie=UTF8&qid=1478307605&sr=1-4&keywords=geoboard+maths

 

No pencils required.

 

I'll go check it out!  We have geoboards, and anything hands-on is good!  :)

[maize]

You are SO my new bestie!   :D  This is just the kind of thing I wanted!  And, you know, I looked at BA two years ago, when my ds couldn't even identify 5 of something.  He's a real oddity to work with, and I just kind of gave up and shuffled it into the long way off, Star Wars kind of file.  Might be time to re-examine that.   :)

 

 

I'll go check it out!  We have geoboards, and anything hands-on is good!   :)

 

Art of Problem Solving is interesting; the pre-algebra book is one of my favorites precisely because it does not emphasize complex computation but rather deep thinking about the problems themselves and possible solutions. When my dd was working in it I sometimes had to remind her "this is AOPS, if you find yourself doing long involved computations you're probably going about it the hard way. Look for the easy way." Because that was frequently how the problems were set up--they wanted the kids to really think about what  they were doing and find the simple solutions to seemingly complicated problems.

[idnib]

http://rentagoat.com/  This one looks like it is Bill's territory, not mine.  But yes, there are goat rental places around here.  Maybe it is more West Coast? 

 

 

We have those in the hillsides of the bay area. It's an eco-friendly way to keep everything trimmed back, especially in the Oakland Hills, after the firestorm  of '91.

 

Lawrence Berkeley Lab's "Goats Gone Wild" video.

 

Goats at Google

Edited November 5, 2016 by idnib

[maize]

I think I owe Bill an apology. I was irritated with the way he entered this thread without apparent  consideration for the question and discussion at hand. I still think that jumping in the way he did was not an appropriate response to a poster asking a legitimate question of which he was definitely not the target audience.

 

I went on however to make and express assumptions about his motivations and character that were uncalled for. 

 

I am sorry, Bill, and will delete my comments if you would like.

[Sahamamama2]

All I know is that after we got chickens all I heard about from Mrs. Spy Car was how she wanted goats. No matter that we live in a leafy suburb of Los Angeles where I don't think goat-keeping would really work.

 

I'd say more, but far be it from me to take a thread off course :D

 

Bill

 

Actually... these people may be your neighbors! ;) Even without goats, homesteading in LA is a possibility.

 

http://inhabitat.com/this-family-produces-6000-pounds-of-food-per-year-on-4000-square-feet-of-land/

[Sahamamama2]

I'm pretty sure goats are an acceptable side trail to any thread.

 

We're not allowed goats, don't have the acreage our city ordinances require. They say we can have a chicken. Just one.

 

No, that would be cruel. Chickens need friends. Seriously, one chicken? So lonely! :crying:

[Sahamamama2]

Jean, you are JOKING.  You can RENT-A-GOAT???   :lol:  :lol:  :lol:   The things we learn here!!!   :smilielol5:  :smilielol5:  :smilielol5:

 

Our neighbor does this with his goats. They eat poison ivy, weeds, just about anything. They really clear out the brush, better than a lawn mower or weed whacker. But, yes, goat rental is expensive. I'm trying to barter with him -- I'll take care of his goats when he goes on vacation, and he'll bring his goats over in the spring and fall to clean up our poison ivy patches. Alas, his son still lives at home, so I am not needed. For now....

[BlsdMama]

Are chickens a gateway to goats?  I have a friend who got chickens, then BOOM she had goats, multiple goats, goats even on her FACEBOOK page.  You're really far gone with your farming when you're putting your goat videos on FB.   :lol:  I was hoping for chickens once we get past homeschooling, but if chickens are a gateway to goats, I'm gonna be careful!   :D

 

 

Chickens ARE a gateway animal... to many things.  Goats are just the natural progression of what any normal human being who lives on at least a half acre would want.  Just sayin'.  ;)

[lanalouwho]

Chickens freak me out. DH likes to joke that in my head I see a bunch if tiny raptors running around.

 

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