Math

August 2, 2012 in Homeschooling | 5 comments

Continuing my series of posts on subjects we are studying in homeschool, today I want to talk about math.

Sam’s Montessori teacher assured me when she graduated that Sam had a good grasp of place value, addition, and subtraction, that she was beginning to understand multiplication, and that she was also beginning the process of memorizing her math facts. I had my doubts based on what I had seen at home and unfortunately, I think I was right.

I started Sam off in homeschool exactly as my Montessori curriculum guide for “first grade” suggested, because it lined up with what Sam’s teacher had told me. All of the exercises we have been doing are things Sam did in her class at Montessori – I didn’t introduce anything new. But it was the material at the edge of what I thought was her ability: the addition and subtraction “snake games,” where you add and/or subtract a series of single-digit numbers, the “finger charts” which are just tools for memorizing math facts, and the multiplication “bead board” which is the first concrete work with multiplication.

But it looks to me like Sam still does not understand that addition, or “plus,” means AND, that subtraction or “minus” means TAKE AWAY and that multiplication means adding things a certain number of TIMES. I also do not see any clear understanding of place value. She loves the memorization, though, and is pretty good at it. Maybe she is like her father and has an excellent memory and has gotten by without having to really understand anything. This is not an insult to either of them. It’s a wonderful thing to have a great memory! But I think it is natural to try to accomplish any task with the minimum effort necessary, and I know Adam’s memory is so good that he was able to do very well in math as pure memorization until he got to algebra, when it all fell apart.

I think moving forward too early would be a huge mistake. One of the best things about homeschooling is that I can spend as long as it takes for Sam to master whatever it is that she is working on. We will not move on with math until I can see that she is at least beginning to grasp these concepts.

So, I have to take a few steps back and put together more basic activities. Luckily, most of the materials I purchased can still be used, and other things I might need are easy to make. I’m going all the way back to the “bring me” game, where I give Sam a number and ask her to bring me the beads (units, ten-bars, hundred-squares) that represent it. (Well, really, the number that I give her is a level more abstract than the beads, so I shouldn’t say “the beads that represent it,” but I think you get my idea.) I’ll see how she does with that. We’ll also do the reverse: I’ll give her a bunch of beads and ask her to write the number. Then we will do some kind of work with exchanging – there is something called the Game of Nines which I have to look up, and we might use dice, too.  I can also just give her a huge pile of beads to exchange into the proper number of hundreds, tens, and units and then she can write it down. I’ll have to see how she takes to each of these games. We have an abacus but I have no idea how to use it so I have to look that up and see if it might help. Also, I have some iPad games that are excellent, and I’m not afraid to use them! One of them is the Stamp Game, which is something I know she did almost daily during her second year of Montessori, and yet I don’t think she really gets it, even a year later. In fact, I don’t think she is ready for the Stamp Game yet!

What all of this says about her Montessori education, I can’t say for sure. If Sam really does have an exceptional memory like her dad, then it might be understandable that her teacher did not catch this. Or, I could be totally off-track and she does understand these things as well as any five-year-old. Sam does tend to hide her true abilities and “play dumb” sometimes. I don’t understand what’s going on with that and I don’t know if it is happening here. I have no knowledge of other five-year-olds, so maybe I’m just off-base in my expectations–meaning, maybe she really does “understand” as well as is necessary to move on. I thing those things will be more clear once I see firsthand how she does with the earlier material. But it is also possible that her teacher was just not observing her well enough. That would be a disappointment, and I need to know because we plan to put either Leo or Zoe into that teacher’s class in two years.

The only way to find out more is to keep experimenting and to keep observing. I don’t mind that we have to go back. I don’t think Sam is in any kind of trouble, educationally. It doesn’t feel like any kind of failure or shameful. I know Sam is capable of learning, and I know I am capable of teaching her. Going back like this is precisely why one-on-one education is so great. It’s a real challenge to figure out what she will need to help her along – it’s like a little mystery. I love doing all of it! I love homeschooling!

  1. Kelly Elmore on August 2, 2012 at 1:31 pm

    One thing that Livy really loved when working on place value was bundling sticks. We used popsicle sticks, and we would count, say 46 sticks, then bundle 40 of them into groups of 10. It made the concept really visual. I don’t know if Sam is dealing with stuff like that yet, but it was kind of fun until we got to hundreds and then it was just annoying. :)

  2. Kelly Elmore on August 2, 2012 at 1:33 pm

    Also, we play a lot of Yatzee, which turned out to be amazing for multiplication. At first, she just added up her score by saying 6 + 6 + 6 + 6, but once she learned the concept of multiplication, it helped her solidify it by looking at groups of 6 as another way to do the adding she had been doing. It showed her both ways and helped her make the connection, I think.

  3. Amy on August 3, 2012 at 11:49 am

    Kelly, bundling popsicle sticks is exactly the kind of thing we are doing now. We just happen to have the Montessori beads, which come in bundles of “ten bars” and “hundred squares” and “thousand cubes.” (Although I haven’t purchased a thousand cube yet because they cost like $35 or something outrageous like that….still thinking of how to make my own.) Anyway, we started with this today, and I’m finding that this is exactly what Sam needs to be doing. If I tell her “bring me 54,” she has no idea that it means five tens and four units. I don’t know how her teacher could not have realized this. The only other possibility is that Sam is playing dumb with me, which is not impossible. More evidence: at first she liked the “bring me” game but then she didn’t easily know the answers, so she got frustrated and wanted to stop. This is an indication that she really does not get it.

    I like the Yatzee idea since we love board games. I’ll have to see if we have it and if she is ready for it. Thanks!

  4. Cornelia on August 18, 2012 at 12:19 am

    Amy, it may be that Sammy is unclear about her tens. See, every ten has 2 names: e.g. 54 = “fifty-four” but also “five tens and four units”. It can take a lot of repetition for students to grasp the idea that tens can be named in two ways. In Montessori, when counting quantities of beads, we’d count something like this while pointing to them: “1, 2, 3, 4, 5 — we have five tens — and 1, 2, 3, 4, — four units. Five tens and four units. That’s fifty-four.” It’s important to say it in both ways so the child starts to grasp the connection. And, yes, it’s possible that Sammy didn’t get enough practice with the golden beads to be able to retain the meaning of each operation. A lot of teachers also don’t require students to verbalize the process of each operation, which of course is vital to their retention of it. …If you want inexpensive thousand cubes, try http://www.montessorioutlet.com — you can get the wooden ones.

  5. Amy on August 24, 2012 at 2:17 pm

    Thanks, Cornelia. I’ve started doing exactly what you suggest and I can see that Sam definitely does not yet have the connection between “fifty” and “five tens.” But now that I’m being explicit about it, I see some wheels turning. Also, I got those exact thousand cubes. I still think it is so expensive, but it was worth it – when I opened the box, Sam yelled, “THOUSANDS!” and was so excited.