Questions about little kids doing big math

[Just1More]

Dd is almost 7, and is pretty mathematical.  She's not crazy gifted in this area, but does seem to have a head for numbers.  We have done very little bookwork, but she can figure out an amazing amount mentally.

She, fairly easily, does addition, subtraction, multiplication, division, percentages, fractions, and some very basic algebra.  Not really hard equations, but she does frequently surprise me with her rapidity and understanding.  She seems to group things off, and figure it out from there.  We haven't taught her that.

She can't, however, do very well if she is asked directly, or if she feels any pressure about the answer.  If SHE wants to know, she figures most things out quickly.  If I ask her, she seems overwhelmed by the question, and stumbles over the most obvious of base 10 queries.

So, my question is, do you wait until they are really solid in writing down mathematics before introducing much in the way of geometry and algebra?  Or do you just keep throwing out whatever concepts they are wanting/needing at the moment and let it sort itself out later?

How much bookwork should I worry about at this stage?  (We do homeschool.)  If not now, when?  (And what would I use?)  If I wait until later, should I start her at the beginning and work up to where she really is?  Or just try to guess at her level?

[ollyoxenfree]

I'll leave it to the homeschoolers to answer your questions and make suggestions about bookwork etc. I just wanted to mention that at that age, my dc loved making graphs and charts about everyday stuff and figuring out calculations for their observations.

They were a few years younger when they learned basic geometry concepts like planar shapes and geometric solids. They liked playing with tangrams, origami, pattern-blocks and puzzles and cones and pyramids for hands-on learning. The bathtub is a great place to learn about volumes and shapes (filling up with water, pouring it out into different shaped geometric solids.....).

[moominmamma]

It sounds to me like she has a very mathematical mind and is discovering all sorts of neat relationships between numbers and operations, but doesn't yet have the tools to systematically and reliably tackle problems where the complexity increases or where her anxiety increases. That's perfectly understandable at her age. To my mind she's on a perfect trajectory, developing a fabulous understanding as a foundation, and on that foundation, sometime before she's ready to move into proper pre-algebra and high school studies she'll need to build those systematic tools. Plenty of time!

Personally I would continue to feed her enthusiasm for concepts. I do not believe that memorization of the timestables, for example, needs to come before learning about percents and decimals. Or that the multi-digit subtraction algorithm needs to be learned before learning how to calculate unknown angles in a triangle. 

But at the same time I would make her aware that there are certain tools that she will eventually need to learn to make the tricky stuff easier. I often talked to my kids about how "when the numbers get bigger" and "when the problems get more complicated" they would need to know how to do math on paper using computational tricks, since you can't do those ones in your head. And I would leave it up to them to decide when they wanted to learn/master/practice the algorithms and pencil-and-paper stuff.

They all eventually got around to it. Usually beginning somewhat after age 7, though my youngest was keen on all of it from the get-go. 

I think that K-7 math should be likened to a giant intellectual playground full of delightful things worth exploring. Once curious kids have explored most of it and understand how the different pieces sort of fit together, they're likely to return to areas they rollicked through at a first pass to try to increase their skills and push their limits. I say if she's keen on trying the trapeze but hasn't yet learned to do flips on the horizontal bar, that's just fine. In fact, I find that once my kids have realized that their ability to explore advanced concepts is being held back a bit by their lack of mastery of more basic skills, they're much more motivated to do the practice required for that mastery.

There's a really neat early algebra program called "Hands-On Equations" (www.borenson.com) which helps kids with only basic arithmetic skills explore algebra and negative numbers. If she's ever interested in something slightly more structured, that might be a good resource to keep in mind.

Miranda

[Geofizz]

The two ladies above know what they're talking about.

I'm navigating this myself right now.  We're not homeschoolers, and our focus is generally to have school time be used productively.  At home, we play a lot of games:  Set, Chess (&bug house chess), checkers, Q-Bitz, Qwirkle, connect 4, etc.  DS plays Tinkerbox on my ipad.  We spent a lot of time in December cutting snowflakes and looking at the patterns that result.  He also is self-motivated to figure stuff out, so I spend a lot of time biting my tongue and sitting on my hands.  Yesterday he decided to figure out how tall the house was from the bottom of the basement to the ceiling on the second floor.  He had found a 5 foot measuring tape and was looking for a challenge.  :lol  We ended up talking about accuracy, precision, and  triangles -- he initially was measuring up the stairs, so not getting the true vertical height -- no, we don't have 14' ceilings, child!  We have plotted data on how long it takes a cup of cocoa to cool off when in a metal or plastic mug, and stuff like that.  He's got a compass, and we make treasure maps or set up scavenger hunts using compass directions and paces.

We have Singapore books available for him to use when he chooses.  He will dive into them for a math book orgy every few weeks, plowing through a few sections in a sitting or two every few weeks.

[sunflwrmoonbeam]

My husband was homeschooled from grades 3-8 then went to a boarding school with a heavy math focus, and then went to college for math (got a degree in CS with a math minor, but close enough). The man has VERY strong opinions on how math should be taught and he thinks it's ridiculous that we don't introduce basic algebra until 7th grade. There's no reason to wait to do basic algebra until the kid is writing well, just as there's no reason to wait to do addition until the kid is writing well. 7+x=10 what is x is not much harder or more complicated than 7+3=? If your child wants to do algebra, do it.

[minkin03]

Originally Posted by sunflwrmoonbeam 
 

There's no reason to wait to do basic algebra until the kid is writing well, just as there's no reason to wait to do addition until the kid is writing well. 7+x=10 what is x is not much harder or more complicated than 7+3=? If your child wants to do algebra, do it.

Actually my daughter is in 2nd grade and they do problems like 7 + x = 10. It may depend on the school and the math program.

[Just1More]

Thank you for your replies.  I've been mulling over the earlier ones since last night.

The hands-on casual stuff is daily here.  We talk math just like we talk diptheria, or disco balls, or sea urchins, or whatever other random conversation (a few from yesterday, lol).  She is quite a bit beyond basic concepts, like volume, or measurement, or even the pathagorean theorem, or the find the number games (like 7+x+10).  My concern is that she does it all in her head, and is not necessarily consistent with  what I think/expect she understands.  One second she can't answer the most obvious of questions, the next the uses that same infomation to come up with a much more complex equation.

For example, she wanted to know how long the longest snake was.  We googled it and came up with 10m.  I told her that a meter is roughly 3 feet, so how long was the snake?  She couldn't tell me.  But then, said, "Oh, so Daddy is 2 meters tall."  And then proceeded to list how tall roughly everything else was in meters instead of feet.  Or, same day, we were talking about how much I sold something for.  After hearing that people usually pay about 10% for used items, at the most, and hearing how much I paid for it, said, "So you were only expecting x amount, then?  She gave you twice that, cool."  Or, at a young 4, I said, "We have 15 smarties, and 3 kids, how many do we each get?"  She didn't even hesitate and told me 5.  I was a little surprised, so I started giving her bigger double digits, and then some with remainders.  She got all but one or two of them without any effort.  (Oh, and I'm laughing and editing because I remembered why she didn't get them.  She was bothered by the unfairness, and was creating new euqations.  Like, well, if Daddy were, he could eat the two extra, and then we could each have 12.  Or, no, but if we just had x more, than all, of us, even you and Daddy, could have 8.)  If I were to say, even now, "What is 15 divided by 3?" Or show her on paper, she'd be stumped.  Maybe it's just a vocabulary thing?

Anyway, thank for your thoughts.  Also, thank you, Miranda, for encouraging me in my unschooling ways.  Just keep talking, and being patient and having faith in the process....that's what I'll do. :)

[KaliShanti]

Originally Posted by minkin03 

Actually my daughter is in 2nd grade and they do problems like 7 + x = 10. It may depend on the school and the math program.

Yes I'm doing Math U See with my4 yr old son and he s solving for the unknown too.

[moominmamma]

Those pre-algebraic puzzles are part of the Miquon math program's first book as well. KG/1st grade level. 

Miranda