4am fractions

Kiisu (that's Chana's Japanese name, which we have taken to using) took the CAT test this week.  As per homeschool regulations, 7-12 graders in our state have to be tested every year.

In my facebook memories from 2011, there was a post about testing reminding me why I unschool.

This year we were armed with a 504 and extra time.  (I don't know how to make this happen in homeschool.  It is only because she needed it for her 2 classes in yeshiva that she got this accommodation, which gives her extra time for testing, and since last time she took the timed CAT test she was unable to complete it in the alloted time, I applied it).  So when she needed up to double the time for reading comprehension because her preferred method is to read something slowly four times, she had it.

The Math sections drove her nuts a little.  The math was all things she's done and forgotten long ago.  Long division.  Fractions and decimals.  I'm pretty sure she got the required 33rd percentile but she was frustrated to tears.

To "study," we had reviewed some basic fraction-decimal-percentage facts.  She quickly remembered most of how to work with fractions with the reminder.  Some things she remembered the mechanics, but didn't "get."  The next day, she asked her friend (who is a homeschool high school senior and also tutors her in ACT math every week), who explained it to her.  But then the next day on the next section, when she encountered some conversion problems, she again struggled.

Last night I was awake in the middle of the night and Kiisu and I ended up hanging out for a bunch of hours until the sun rose.  (Yay for random insomnia and nocturnal teens.)

We were talking about converting fractions into decimals and she was telling me how her friend told her to do it.  And she didn't remember learning it that way from me.

"Yeah, that's not how I do it," I said.  "I think my way is easier and makes more sense."  I explained how the fraction line means "to divide" (which she's heard me say a million times during algebra) and how you move the decimal place over.

"That's what I don't get," she said.

It was pitch dark, and we were just chatting desultorily about fractions to percents.  There was no purpose, no lesson, no point.  No pressure because we weren't trying to achieve anything.

"You know, maybe you never really wrapped your head around the whole fractions thing," I said.  "You didn't get it in 3rd or 4th grade and while eventually you did understand how to do it, I'm not sure you ever really spent a lot of time thinking about how it all worked conceptually."

But as I said that, I realized that she did understand fractions, pretty much.  "You know what might help you?" I said.  "Maybe you aren't really getting the relationship between fractions, decimals, and percents.  And I think it's because I left something out.  I never taught you this--and I think it will all make sense."

And I told her about something that I did in school in first grade when I was a kid.  And spent many hours on, in many of my elementary school years.  I had never taught it to her because it hadn't really come up.  (Not because I didn't have a cardboard hands-on flip number chart that taught it that she never wanted to play with and that I eventually konmaried, because I did.)  I taught her Place Value of numbers.  Hundreds, tens, and ones I barely had to teach her because they were so intuitive and it was clear exactly how that worked.  (See? We said to each other.  Kids spend hours doing that in school but when you are older it's quite simple and quick to grasp and makes perfect sense.)  Then I introduced her to tenths, hundredths, and thousandths.  And working with 50%, 0.5, and 1/2.  And tenths being actual 1/10ths.  And 0.25 being 25/100ths and also 1/4.  And 1 being a whole and 100%.

We were just playing around.  Talking about it because she was genuinely grappling with trying to understand conversions.

And when she understood it, it was so enjoyable for her.  She was absolutely delighted about how it all fit together and how it all made sense and how they were all talking about the same relationships.

I looked at the clock.  "It's 4:30am," I said.  "We've spent a half hour in the middle of the night learning math for fun."

Then she told me about how her friend was teaching her derivatives and how interesting it was.

Unschooling math looks really different than how I thought math would go.  It's a process of learning to trust and learning to let go.  I thought that since she loves math, she would learn geometry, learn trig.  Instead, she loves fiddling with math.  

I have so many things that I want to teach my children, that I want to share with them, that I want to give them.  But so often trying to do that causes friction, conflict, and stress.
And it's amazing what happens when you make space for what they want to learn and follow their lead.