the non-linear learner

[blondeviolin]

My 8yo has come a long way. She has some fine motor/letter forming issues. I have been on top of her from kindy about letter formation, pencil grip, etc. She turned 8 in July and still mixes orientation of letters. She can't remember which way some letters go (b, d, p) nor can she remember what some letters look like (g, capital y).

 

That being said, she's a very visual, non-linear learner. She didn't have an extraordinarily difficult time learning to read. She's a decent speller (I guess thanks to the visual nature of spelling).

 

Math is completely frustrating to her sometimes. Again, she's non-linear. Explaining regrouping blows her mind. After using c rods, abacuses, and other manipulatives, she learned to add past ten like so: 7+8 = (5 +2) + (5+3) = 10+2+3=15. It's mathematically sound, so okay. When teaching her regrouping with subtraction ("borrowing") she couldn't figure out why we regrouped a ten. After WEEKS hitting the same points in her warm up (while doing clocks and shapes as the main lesson), she finally figured some of it out. But again, the orientation of the minuend and subtrahend tripped her up. FINALLY, she figured a method that works for her: 14-7 = 10 + -3 (basically subtracting the ones first). Listening her trying to explain this was painful until I finally gave her the language of negative numbers.

 

At what point does this difference in learning styles become a problem?

 

She's "behind" in math because she had to find her own paths rather than understanding what I was trying to teach her. Some of it was bullheadedness, but some of it really is just her not understanding. I'm suspecting she is a whole-to-parts learner and there's not a whole ton of math that speaks to her this way. (FWIW, I'm not too worried about her being "behind." Is the beauty of homeschooling.)

Edited September 27, 2017 by blondeviolin

[blondeviolin]

FWIW, she also really struggled with FLL 1 and 2, but between MCT and the strong visual component of diagramming, her grammar is starting to fall into line. She may not be able to remember a verb's definition at all times, but she understands the function of the word in the sentence, if that makes sense.

[Kiara.I]

The way you described 7+8, that's a specifically taught method in some curricula (well, in Righstart at least.)  You *see* the numbers on the abacus, and it's called the "two-fives strategy."  You enter a 7 (5 and 2) and an 8 (5 and 3) and you can clearly see that the dark beads make 5 and 5, so 10, and the remaining yellow beads are then quite easy to see as a group of 5.  So that part doesn't worry me in the slightest.

 

And for the subtraction example, that works too.  

I wonder if she might do better with a math curriculum that strongly encourages visual and non-linear strategies?  I think from your signature that you're using CLE math with her.  Is it pretty traditional?  Some curricula teach as "this is the way to do this problem."  Others teach as "you could do it like this.  Or this.  Or this!  How about this?  Which way do you find easiest?"

 

It sounds to me like she has a fabulous understanding of how to pull numbers apart and put them back together again, which is actually a *super* skill to have, far more intuitive than just relying on an algorithm.  But of course if the curriculum only teaches the algorithm, she may struggle against it.

 

Regrouping, for instance, or "borrowing".  What if it's taught as trading?  You have 10 ones, so you don't have space to write that, so you trade your 10 ones to make 1 ten, and carry on with what you're doing.  I'm familiar with introducing it using base 10 cards, so they can actually do the problems with the cards.  Four cards showing a block of 1000 cubes, three cards showing a flat of 100 cubes, seven cards showing a line of 10 cubes, and 8 cards showing a single cube each...and there you go, 4,378.  If you need to trade to add or subtract it, well that becomes pretty obvious.

[Shoes+Ships+SealingWax]

I would strongly recommend RightStart B (2nd Ed) for her. It really digs deeply into the issues she seems to be struggling with & introduces them in a way I suspect she would find more intuitive.

[Shoes+Ships+SealingWax]

As for finding her own ways to make things "make sense" - I don't think that will be too much of an issue unless it holds her back significantly. It's good that she is coming up with her own strategies.

[Shoes+Ships+SealingWax]

DP

Edited September 27, 2017 by Expat_Mama_Shelli

[HomeAgain]

You describe how ds7 does math.  He thrived with MEP (a lot of mental math going left to right and learning how to 'break'/'steal' to make addition/subtraction easier), he does well with Right Start, and loves Life of Fred, which approaches math in a non-linear way.

 

Traditional right to left math took longer for him to learn because the other way made more sense to him.  As long as his process is sound, he can explain his math, and he is quick at it, I don't care how he gets there.

[blondeviolin]

Right now she's using Math Mammoth. But the curricula that I'm using doesn't matter as much for me because I'm actually sitting down and teaching. I don't care if she follows certain steps as long as she is capable of consistently getting a correct answer. In regards to math, my big concern is that she cannot seem to apply the standard algorithm and it will become a bigger problem because, while she's fantastic at breaking numbers apart, she can only do it in small numbers. Her inability to apply the standard algorithm is causing her anxiety when the numbers get bigger (3-4 digits). And as much as I teach what the algorithm is doing with manipulatives, the fact remains that she doesn't want or can't take the numbers apart in a way that makes sense in her head, notate it in a way that makes sense to her, and arrive at a correct answer. All of the numbers get jumbled in her head.

 

She also doesn't seem to be aware of the way the numbers are oriented. 6s and 4s still are written backward. Because her world has no right, left, up or down, realizing that her subtrahend is smaller than her minuend and subtracting appropriately isn't a guarantee. The order of the numbers matters with subtraction but there's no linear order in her world. She's not logicking an a+b=c pattern. Rather, she logics a+c=b or b+c=a as well. We've gone round and round in circles with part-whole circles and manipulatives and she is getting it, but to still struggle with it at age 8, is beyond what my experience has been. That's a skill acquired at a younger age at my house. Even RS and Singapore hit this in first grade.

Edited September 27, 2017 by blondeviolin

[almondbutterandjelly]

Number lines really helped my visual learner.  In her brain, she tells me, she jumps around on them.  Maybe post up a nice big number line.  It might really help.  Demonstrate moving around on it. 

 

As a for instance, she didn't understand bigger or smaller until I mentioned that the number was smaller if it was on the left of the other number on the number line.  Then she got it.  

 

FWIW, my dd needs her own way to learn stuff, too.  For multiple digit multiplication, she wouldn't do it the regular way.  She had to break all the numbers apart and then distribute.  (By the way, after a year or two of this, she does do it the regular way now.)  (But the regular way is actually a short cut and doesn't make much sense except as an algorithm.)

 

The way I had to teach her to do long division is opposite of what the regular way is (she writes down what we do in our heads and she does in her head what we write down), but it works for her and she still uses it.  (We're in high school.  By the way, Mathusee is your answer for high school math.)

 

We had a fair amount of success with Singapore Math and Mathusee for elementary.  Middle school was eclectic, but the Key to books were pretty good, heavily highlighted (color is really important for visual learners).  Now we use Mathusee for high school (heavily highlighted).

 

Oh, for grammar, you might try The Sentence Family and Grammar Tales and Parts of Speech Tales and Schoolhouse Rock.  Very visual, very fun.  Totally helpful for big picture thinkers.  Once she gets older, we liked Seton (even though we're not Catholic).  It's short and really straightforward.

 

HTH!

 

 

[geodob]

You wrote that:'her world has no right, left, up or down'.

 

Though left and right are how we concieve of quantities.

With each being located in different sides of brain.

Which crucially, enable us to concieve of opposing points.

That extend to infinity in both directions.

With zero and now, located just between our eyes.

 

We use left and right to concieve of 'less than' and 'greater than'.

Also 'before' and 'next'.

 

But crucially, we need to concieve of these as opposing points.

As their cannot be more, until we concieve of less?

Edited September 27, 2017 by geodob

[almondbutterandjelly]

I also wanted to add that you might find it helpful to research "Right brain learner" or "Visual Spatial Learner."  They do seem to be on a different time line than traditional learners, but really in my opinion it's more that they are big picture thinkers and curriculum is not written that way, almost ever.  Dianne Craft has some helpful things to say about them, the gist of which is that color, pictures, stories, and humor are what makes things stick in their heads.  This has helped us tremendously at our house.

[Shoes+Ships+SealingWax]

"...she doesn't want or can't take the numbers apart in a way that makes sense in her head, notate it in a way that makes sense to her, and arrive at a correct answer. All of the numbers get jumbled in her head.

 

She also doesn't seem to be aware of the way the numbers are oriented. 6s and 4s still are written backward. Because her world has no right, left, up or down, realizing that her subtrahend is smaller than her minuend and subtracting appropriately isn't a guarantee. The order of the numbers matters with subtraction but there's no linear order in her world."

Have you had her evaluated for dysgraphia &/or dyscalculia? This sounds like it goes beyond being a visual-spacial learner. Edited September 28, 2017 by Expat_Mama_Shelli