Resources for helping young student with idiosyncratic math issue?
September 12, 2016 4:28 AM   Subscribe

I"m tutoring a 12 year old girl in math and she displays an idiosyncratic learning disability / learning style. (Specific issue was in learning to calculate the area of a rectangle, an example was used of a rectangle with area of 48 and she didn't understand why all rectangles don't have areas of 48.) Could someone offer suggestions for this specific student, or, more generally, a resource where I might be likely to find others who might have run across similar students?
posted by Jon44 to Education (15 answers total) 4 users marked this as a favorite
This is one of those situations that can really be helped with physical tools.

Cut out 100 individual identical little squares out of construction paper or cardstock and let her use those to make rectangles that match her problems.

Need to calculate the area of a 6x8 rectangle? Have her physically build it. Count how many squares it took. Then have her build a 4x12 rectangle right next to it. Looks different, same area. Then have her make other rectangles with different areas and count the individual squares making up those. Once she sees for herself that rectangles don't have a set dimension or area I think things will start to click.

With shape problems (you see the same with things like angles and fractions), some people need to be able to actually see and manipulate a problem before the ideas start falling into place.
posted by phunniemee at 4:50 AM on September 12, 2016 [20 favorites]

Graph paper?

Cuisenaire Rods?
posted by Bruce H. at 5:08 AM on September 12, 2016 [1 favorite]

I like the cut up little squares from above. It would have really helped me when I was younger.

I just wanted to add that she may have gotten mixed up with triangles and the idea that all interior angles add up to 180 degrees (and of course, a similar dynamic with 90 degree angles in squares and rectangles). Maybe articulate the difference to her.
posted by eisforcool at 5:47 AM on September 12, 2016 [4 favorites]

Counting out, and then colouring, rectangles on graph paper.

Building rectangles out of Lego single blocks.

For both these exercise, I'd encourage using lots of colours of pencil crayons or lego, so it's easier to count the tiny squares once they're all stacked together. And if she's at all like me, she'll want the colours to look good together so she'll assemble them in patterns, which might help her passively learn factors while she's at it.
posted by pseudostrabismus at 6:01 AM on September 12, 2016

Are you talking in terms of "units"? Is there any chance she understands the concept of scale independence too well, where it can be 48 cm² or 48 in² or 48 ft² or 48 km², and extrapolated some sort of independence from shape? Another similar thing is how the angles of a triangle remain the same no matter the size of the triangle, and always add up to 180° no matter the shape of the triangle.
posted by XMLicious at 6:03 AM on September 12, 2016 [2 favorites]

I suspect that the student is viewing this as a game where you give some answer that is "right" for arbitrary or mysterious reasons, and hasn't yet really considered what "area" even means. I'd try phunniemee's method first.
posted by thelonius at 6:05 AM on September 12, 2016 [13 favorites]

Does she understand _why_ one would care about the area of a rectangle? Maybe some real-life models, like using little tiles to decorate some things and having to decide how many to make/buy, would make it a lot clearer.
posted by amtho at 6:17 AM on September 12, 2016 [7 favorites]

If you have a lot of legos handy I would do this with standard 2x2 bricks (preferably assorted color) and a baseplate. Phunniemee's idea is great but I would have trouble aligning 48 squares of paper neatly in a grid :) The 2x2 bricks are square, and big enough to assemble a rectangle with quickly and count easily.

In the same vein (not that you have one laying around, but) the Montessori Multiplication Board that my son's school uses to introduce kids to the idea of multiplication results in a pretty visual explanation of why multiplication results in the area of a rectangle.

At any rate, n'thing that you need a physical solution to this problem.
With 48 [units], you could do a great demo of why some rectangles of different shapes have the same area, but not all rectangles.
posted by telepanda at 7:12 AM on September 12, 2016 [1 favorite]

Minecraft is great for this, if she's interested. The blocks in Minecraft are 1 cubic meter. There are flat 1 square meter 'carpet' pieces, too.
posted by Huck500 at 7:54 AM on September 12, 2016

It's also a reading comprehension issue, actually. She needs to understand that _all_ parts of a question are significant: What is the area of this floor. What is the area of the red wall in centimeters. Later, what is the perimeter of this garden (for fencing or whatever).

People often tune into just one word of a sentence, but it's an important life skill to be conscious of all words: please write this letter by Monday morning; Don't take this drug with alcohol and drive; hand wash in cold water; do not dry clean.
posted by amtho at 9:46 AM on September 12, 2016 [2 favorites]

Nthing manipulatives. They got me from addition through to algebra. I found gazillions of tiny squares to be especially helpful for this exact problem type.
posted by SMPA at 9:46 AM on September 12, 2016 [1 favorite]

I suspect that the student is viewing this as a game where you give some answer that is "right" for arbitrary or mysterious reasons, and hasn't yet really considered what "area" even means. I'd try phunniemee's method first.

I agree it’s something along these lines, but probably more to do with math anxiety than thinking it’s a game.

I’m actually pretty decent at math when I’m alone and have all the time I need. But in test situations, or even being tutored, the pressure of performance makes it hard for me to absorb information. Anytime I don’t understand something immediately, I panic and sort of seize on any kind of pattern I can find, even if it makes no sense at all. Again, it’s not that I’m incapable of grasping the concepts (I did, for example, eventually get an A in calculus). It’s just that I’m so afraid of *not* getting it that my mind kind of freezes — it’s very similar to the blankness of stage fright.

I think the triangle project could be useful in this particular case partly because it will slow both of you down, and may help differentiate whether there actually is some form of learning disability here, versus math anxiety that is preventing learning and looks like a learning disability.

The unfortunate thing about math tutoring is that tutors are people who get math easily, and the tutored are people who don’t. I think it can be difficult for even the kindest, most patient tutors to really understand the self-defeating fear that can paralyze someone who is afraid of not understanding something.
posted by pocketfullofrye at 10:31 AM on September 12, 2016 [1 favorite]

Yes, anxiety is _huge_.

I once invented an exercise in which I gave a student a jelly bean for every _wrong_ answer. The point was to emphasize that _trying_ was important and hard. Getting an answer right is usually rewarding in itself.

It did seem to help.
posted by amtho at 10:45 AM on September 12, 2016 [1 favorite]

My oldest son had serious math challenges. Manipulatives may help, but ghis child also may need explanations of basic concepts that they somehow just never got for some reason. This was one of the things that helped my son.

Are you sure the student understands what "area" even means?

My son got through early math by memorizing the right answers with no understanding of any of the meaning. Fortunately, in fouryh grade, he had a teacher that took some time to explain and I also taught him a lot. When you have a student that is not getting it to this degree, ignore their age. Don't assume they have the background other kids their age have. Try to determine if they understand the most basic pieces of the subject. They may not.

This sort of thing also implies this child may be twice exceptional. 2xE kids often look average but are really going nuts at school. Their strengths help hide their weaknesses and their weaknesses help hide their strengths. They often muddle through with a B average but can be just miserable.
posted by Michele in California at 10:58 AM on September 12, 2016

It seems like she hasn't learned to generalize concepts which isn't that unusual.

I would go back to the very basic idea of what area means and most definitely use graph paper or manipulatives to show that area refers to ALL figures, not just that one.

I'll bet money when she begins doing algebra and X can suddenly mean 7 or 51 or whatever, she will be confused as hell.
posted by yes I said yes I will Yes at 12:47 PM on September 12, 2016

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