Math and Abstract Thinking


Our state requires all homeschoolers to test each year. My daughter scored well for reading, spelling and language arts but not so well on her math. On abstract thinking and estimation, she scored under 1 percent! Math has been really difficult for her—she has a hard time grasping the concept. She is a facts learner. 5 x 5 = 25—that is the fact but when I have her work a problem like 55 x 5, she just sits and stares at the paper. Unless I am right there with her going over step-by-step, she cannot do the problem. She says things to me like . . . “too hard”, “don’t know what you’re even talking about!”. I currently use ABEKA math (have for years) but am wondering if Singapore Math would be better. What do you recommend?


Abstract thinking is a big part of math, for sure, so if she is low on that ability, she will struggle with math.

thumbnailMy advice? Make it much less abstract and much more concrete. I would definitely do Singapore Math and I would buy the Home Instructor’s Guidebook and I’d invest in (or gather around the house) some manipulatives. Teach each lesson beginning with the hands-on example from the Home Instructor’s Guidebook. Singapore has 3 phases: concrete hands-on, then pictorial (showing hands-on in picture form), and then moving to the abstract.

So the lesson might be adding 2 plus 3, just for a simple example. The Home Instructor’s Guidebook might have you take 5 blocks, putting 2 on one side and 3 on the other, then merging them and counting them. If you daughter struggles with math, I’d really put emphasis on this first step—doing the same thing in the textbook and workbook, using pictures to depict the blocks.

Last step, the number “2” would be shown, representing the blocks on one side and the number “3” would represent the blocks on the other side. Now they are using abstract symbols to represent a concept. If you make sure she understands the hands-on, concrete part of learning math, she will be able to more easily grasp the abstract depiction of the hands-on.

Definitely take the Singapore placement test at no charge to find out where she needs to begin. It would be quite discouraging to her if she was put in a level too hard for her to feel success. Better go a bit easier and let her gain confidence.

I think your daughter is very blessed to have a mother who cares enough to help her “get it”. So many girls grow up “math dumb” because no one really bridged the concrete with the abstract for them.


May I recommend:

Messed Up in Math

Hates Math


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