Reviews and Reflections on Math

I am always intrigued by studies that point to the one subject where many American children, homeschooled or not, struggle: mathematics.   I have read that, especially in the case of homeschoolers, the struggle is often not with math concepts, but  computation—in other words, speed.    

 Enter my children.   Funny, given my love for math, I assumed that I’d have at least one child who shared my excitement over solving for x, but as of now, all three seem to be in loathing rather than in love.   (Well, loathing might be strong, but they definitely don’t run for their math studies).

Take my youngest, as one example.   She’s just begun this week learning how to borrow, as in take-one-from-the-tens’-column-and-add-the-ten-to-whatever-is-in-the-ones’-column.

When she saw the page, she immediately noticed that she was being asked to do something that was different.   She is also currently preoccupied with multiplication, or “times,” as she calls it.   Thus, everything in math that is different to her, she thinks it’s “times.”    “They want me to do times,” she wails, then goes into a whine about it would be soooo hard, and woe is my life, etc.    We went through the concept a few times (the curriculum, Horizons, had introduced the concept in pieces for several days), and by the third problem, she had it.   That’s that quick grasp of a concept.   Now comes the part that disturbs me far more than slow understanding: she gets bored, or maybe just tired, and the distractions come.   I’m glad we’re using Horizons, where several concepts are introduced at once.    With most curriculums, children learn one concept to the point of mastery, then the next, then the next…

We once used Making Math Meaningful with the older two children.   It was word problem heavy, which I loved because, well, that makes math meaningful.    It wasn’t drill intensive; I had the revelation with my oldest that drills had taught her the mechanics of how to complete a math problem, but she had no clue of what she was doing or why.    Our first year of homeschool I spent re-teaching much of what she’d been “taught” in school.

Making  Math Meaningful didn’t prepare our kids well for higher level mathematics, however, and I hated the way that particular curriculum taught multiplication.   I learned all of my facts by memorization, up to 12×12; MMM suggested learning the facts of 0-5 and then using those to expand upon all the other facts.    Thus, 7×8 becomes 5×8 + 2×8—not a bad method, but different (read uncomfortable) for me, and seemingly more time-consuming.   Our son still doesn’t have the command of his higher facts that I would like; he adds extremely fast at the higher levels.    We drill on these occasionally, but it occurs to me that he might not ever “get” them as I’d like.   As a bit of an aside, one of the homeschooling groups we participated in would often joke about the “math police,” as we called them—an imaginary phantom that would come to the door and punish us for being poor math teachers.

When we switched the older two to Teaching Textbooks, we had much better success in terms of understanding, and especially in the area of independent learning.   I think, though, that part of the dilemma with building speed is that homeschooling, by its very nature, doesn’t rush a child to complete anything in a given time.    We must create those artificial deadlines.    In our home, we’ve used Calcu-ladder to allow the kids an opportunity to build speed in computation.    But recently, Calcu-ladder went to a CD format, meaning that I have to think ahead of time of when I want the kids to complete drills, determine which drill (a somewhat time-consuming search through the CD), then print the materials so that they’re ready in time.    Another digression, but bear with me: does anyone else think we lost something significant as home educators in all of the e-text information that is now available?   The other day, I needed to print out lapbook materials for my oldest, but I needed a color cartridge.   By the time I bought the cartridge, she’d moved to a new chapter.   So now, do I make her go back so that the lapbook is complete, or do I live with the gap and move forward?    I’ll contemplate that one over our break. 

So we move forward.    I love to think that slow and steady wins the race, but as the oldest takes more of the pre-college exams, I know better.   At least, I should say, slow and steady won’t win that particular race.   I’m curious, though: how are your kids doing with math concepts?   How about speed?

Finally, this is a recent shot of my youngest learning to tie her shoes. 

 

 I love two things about this picture.   The first is the way she looks over her glasses, like a much older woman.  In truth, she’s not learned to keep her fingers off the lens, so her glasses are often smudged such that she sees better not looking through them.    The second thing I love about this picture is her intensity.   She is determined to master tying shoes.   One day I may see that same look with math, or if not, I’ll be okay with the reason why.

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5 thoughts on “Reviews and Reflections on Math

  1. Interesting insights and observations. My children, thus far, enjoy math- although I am noticing less interest in my older child- who is 9 and just beginning multi-digit mutiplication and long division. I was a math major in college. I also was a public school teacher and was a site math rep at the school I taught. Naturally, when I began to homeschool, I presumed math would be easy for me to teach my own children. For the most past, it has been, both conceptually and the computation, especially for my 7 year old son. He can compute in his head with great accuracy and speed- he doesn’t always use traditional alogorithms either. He has this way of manipulating numbers. My children have learned their basic facts through games. I didn’t give them a ton of paper and pencil drills, but we worked on speed and memorization. Once they learned the facts and the concepts behind the operations, they had all they needed to be a problem solver. My daughter prefers doing word problems to pure computation. I think that children in general need to understand that mastery of the facts is like phonics in reading. Mastering phonics helps them decode words and sentences that enable them to extract meaning when they read. When we teach our kids to read, we want the phonics to be automatic and not have the words sounded out each time. It’s the same way with basic math facts. We don’t want our children to be forever counting on their fingers to solve problems. We want the facts to be automatic so that they can be drawn up at any time to work our more complicated or tedious problems. I don’t know how well children would understand this analogy- but if they did, maybe they’d be more motivated to commit those facts to memory.

  2. Belinda, I think you would really enjoy reading The Outliers, by Somebody Gladwell. He explains, among many other things, the effect of culture (and other things) on success in such areas as math, for example, why Asians, even American ones, are stereotypically good at it, and why the rest of us typically aren’t, and etc. Very fascinating book. Forgive the grammatical structure of my second sentence. Too lazy today to fix it.

    When I read here that Making Math Meaningful has lots of word problems, I was excited and thought maybe this was our next series. And then I kept reading… thank you for your input. My sixth grader just finished TT pre-algebra. She is NOT ready for Algebra I, I know, so I’m wondering where to go with her now. Maybe some logic and critical thinking. Math is a puzzle, both literally and figuratively. 🙂

    Love the photo of your youngest. Emily shares her penchant for touching her lenses.

  3. Sally, you might try the “Keys to…” workbooks as an interim program. The books are less than $5, and there are several “keys”: to algebra, to fractions, to geometry, etc. We used the Keys to Measurement one summer after some standardized testing revealed that my kids, much younger then, didn’t know how to distinguish the length of different objects. We had a lot of fun measuring the height of stop signs (which I never realized were so tall!) and all kinds of objects around the house. Most importantly, the kids learned much in a little bit of time. I’ll try to see if I can find a link on the internet, but if you have a local homeschool store, they’re probably sure to carry it.

    Thanks for stopping by. Your visit always blesses me.

  4. Thanks, Belinda. I have considered the Keys to… series. We don’t have a homeschool store nearby, and the one near my parents’ closed. I’ll have to do some sleuthing so I can see those in person. I have to see them before I will buy! Betsy has fractions down, as well as decimals and percents, but I’d love to see what else is available! Especially for that price.
    I had not checked the box to have follow-up comments emailed to me, so I’m glad you followed through all the way and went to my blog. 🙂 It is now checked, just in case.

  5. Hello friend. Long time no see, huh?

    Now, you know I HAD to comment on a math-related post, right? *LOL* I love math and can’t imagine why anyone wouldn’t! Fortunately, at least one of my girls enjoy math. It’s too soon to tell with the Kindergartener. I love your comments on the various math curriculum. I’ve only used two – Saxon and Math-U-See. I like the mastery concept, however, I have learned that “mastery” at one point in time does not necessary mean “mastery” at a later point in time. It’s true that “if you don’t use it, you lose it”, so review is vital. I agree that we MUST enforce time restrictions – especially on exams. I have seen my kids crash and burn on standardized tests because they weren’t used to working quickly.

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