Some thoughts:
In addition to asking students to begin to think abstractly, algebra also asks them to do multiple calculations while applying concepts. So, perhaps a student can see the big picture but be fuzzy on the details.
When learning to do both of these tasks (calculate while applying abstract concepts) it's easy to get tripped up --- especially if fractions and/or negative numbers are involved. So is it possible that she's having trouble doing both of these tasks at once?
I teach algebra to my kids and am on kid #3 now. I've realized that what looks like a stupid mistake to the adult may really be a valid difficulty for the student. The student may not even be aware of the problem --- I can see it because I've learned how to. As an example, I get my kids to think in terms of numbers having two components: sign and value. Determine the sign first. Write it down. Now worry about the value. This is a very difficult method to apply consistently, because the mind wants to bundle it all (which leads to trouble). Slow it down, do things one step at a time, and you won't have to worry as much about missing the details.
Also, one of my kids might get tripped up in the beginning of a lesson because it was easy to see the answer to 2x + 3 = 13. This led to sloppy work in the first problems in a section because the answer was obvious for all of them. Then, when things got harder, trouble started. He hadn't practiced the technique when the problems were easy and then got lost when they got harder. Maybe she didn't pay attention to the technique because the examples were easy. She could sort-of explain the concept for the easy problem, but I'd realize that she was seeing from the perspective of the arithmetic involved, and not seeing the abstract ideas.
So I'd go over stuff again and force them to write things step by step, in logical order. After that, things got much better.
Remember that kids make oddball excuses to avoid taking responsibility. Is your DD really, truly trying to save paper, or is she having trouble, and using small writing as a strategy for getting partial credit? Is her disorganization perhaps a sign of a fuzzy understanding of details? When an excuse is really lame or nonsensical, I assume that something else is going on.
Finally, math books can make the problem worse. Is your DD using a woeful mainstream modern textbook? If it's full of color pictures and there are random distracting notes all over the margins, the answer is, "yes."
Last edited by Val; 09/30/16 11:09 AM.
