Just had my first class tonight on Montessori Elementary Math. I have to say, other than the cost factor, Montessori Math really is the way to go for a homeschool math curriculum. I did a mapping of Common Core vs Montessori Math presentations and for most of the presentations Montessori does math about 2-3 years before Common Core. Now it doesn’t mean it’s forced on the children, it’s just that since the curriculum is already there for the 3-6 year olds, it kind of naturally progresses faster. Of course, not all children progress at this level either. But you do get introduced to a lot of abstract concepts early due to the concrete materials. I need to do a brain dump before I forget all the answers I got tonight to my pesky homeschooling problems I’ve been having the last few months. Some of the answers made me go “D’oh! I knew that! <sigh>”
- How come the kid(s) just work on a material for a bit, or none at all after my presentation? Apparently very normal for elementary kids. The 3-6 child likes repetition in work. The 6-9 gets a concept and then is ready to move on. You want to really invoke their interest in anything you present and tweak it in different ways in order for them to work on it. I can ask the child to work with the materials but I don’t need to have any written equations, goals for them to explore, etc. I now feel so much better that when I presented the Least Common Denominator it took 10 minutes and then we were kind of done.
- My trainer really advocated for the child to NOT do writing if they don’t want to or need to. To have the child really work on concrete materials as is. This explains so much why I did not see any written paper work in my presentations and yet I keep seeing it online in blogs. And she’s talking about this even for the early elementary kids (1st graders). If the child’s hand isn’t ready to do a lot of writing, as evidenced by all the wriggly writings, then there’s no reason to have them write. The emphasis is really on the concrete materials. And I’m reminded of the recent arithmetic book I read from the Life of Fred guy about how you really need the child to work in the concrete level as deeply as possible before moving on to abstract. He says abstraction doesn’t start till 12. I don’t know if it’s true but he’s basing this on Piaget’s theories. But the take away is just really concrete, manipulative materials as much as possible and it’ll translate so much easier to abstract when it’s time. Otherwise it shows up 3-4 years down the line when the child is working in the abstract and now doesn’t get it. I’ve heard that for sure from public school teachers.
- Going back to point #1. Tonight I saw a lot of 10-15 minute presentations on multiplication. My question when I saw these presentations was, that’s it? It appears that the beginning presentations (we haven’t gotten to the abstract parts yet) contains ideas that the child would have worked on in 3-6 but now they’re formal presentation. So I can totally try this out with Thumper this week!
- I also learned that I want to make sure to have introduced the concept of multiples before fraction. Oops. Thank goodness we stopped at equivalence.
- Lastly, I was all set to poo poo the multiplication presentations (common multiples, commutative and distributive laws) at the beginning of my album, thinking “Why does Thumper need it if she already is learning her multiplication table?” But apparently a lot of these presentations contain a lot of indirect preparation for geometry!
- Continuing with point #2 and #5, it was pointed out to me that you don’t want to give the child hints. For example, you could point out to the child that 3 x 5 is the same as 5 x 3. Basically telling them what a commutative law is. But once you do, then the child doesn’t want to do your concrete material work. And now you’ve missed the chance for them to play with math so to speak. Oops!
- For the Great Lesson on Story of Numbers, apparently you don’t need to present them all at once. You can just do 1 poster at a time every few days. And most importantly, this Great Lesson doesn’t contain a lot of information precisely because it’s only there to arouse the child’s interest. You can do the whole sequence maybe in 3rd grade. That’s why it doesn’t have the whole history of numbers and the charts are a bit limited in information.
- I also learned that you might need 2 decanomial boxes instead of 1 because in the common multiplier layouts it doesn’t have enough otherwise.
- When I asked about the Fraction Charts, I was asked, “Why not have the children make it?” It’s always so weird to ask questions that have been confounding me for awhile because the answer always takes me in another direction and suddenly the question itself, and my obsession with the right answer, seems so unimportant
There is also the thing against timed math. But that is one area I disagree with because I feel it kind of depends on how you do it. We can just give them a stack of multiplication flash cards and have them practice and why do we need to know our facts fast? I think with me learning math in Chinese I see this in a philosophy difference. One focuses on understanding math concepts and the other is a bit more on memorization. One helps when you want to do advance work, the other helps in day to day life. I advocate both because you need both. And for me I see multiplication table being much easier to memorize in Chinese to begin with so why not?
