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Cheryl Floyd

Building up Math Ideas

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I have heard talk lately in Classical circles about the lack of mathematical understanding as opposed to mastery of processes. In this Schole` article, https://www.scholeacademy.com/guiding-principles-for-math-education/ an interesting suggestion is made at the end about including a writing assignment along with the math lesson. A student could give a summary of the process for solving certain problems, or a summary of the lesson. I really like this idea. Having to explain how you go about doing something is beneficial to the student and the teacher. Each can start to see what they are getting right and what they need to work on. 

For younger students I think copying vocabulary and simple sentences of the laws that govern the processes they are learning could be a great start to a math journal. What a great way to incorporate beginning writing and handwriting with math concepts. 

What are some ways you help your students comprehend math ideas? Or where do you struggle or they struggle? 

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11 hours ago, Cheryl Floyd said:

What are some ways you help your students comprehend math ideas? Or where do you struggle or they struggle? 

One thing that I learned pretty late in the game (too late to be of use to any of mine except my youngest) is that slowing down makes a huge difference in a child's attitude toward math. Early computation is so simple, we are quick to move on the next thing, and we have a tendency to assume that if a child can add 7+2, he is fully ready to understand 7-5, or 17+2. We also associate computational ability with understanding. What I learned to do, with my youngest, is slow down. In the not-so-distant past, it was not assumed that every student needed algebra, and whatever high school students did for math, only some of them did algebra. Now, we expect algebra to be done in grade 8, not 9 (when I was in those grades, advanced students did algebra in grade 8, all others in grade 9), so that the student has time to get to calculus while still in high school.  I saw an article not long ago, in which college professors were asking high schools to stop teaching calculus, and to do a better job with with algebra and geometry, so that their students really understood those things and were ready for calculus, which they would prefer to teach themselves. The current STEM trend has us urging "more" instead of "better" on our students--not a classical approach, I don't think.

Now, I never went that far in math myself, and it was a long time ago. But what I found, by slowing down so that my student never moved on until she found problems at the current level *easy* and *intuitive* (not just "doable"), was that she was already more than ready for the next level, and grasped it quickly. But more importantly, to me, was this: she is the first of all my students to ever say the words, "I love math." And if you believe, as I do, that education is the science of relations, of learning to love and care about knowledge, then this was more than a win--it was the only success I ever had.

We are still in the midst--she's in 9th grade--but I decided to have the courage of my convictions. This year, we're finishing up arithmetic, and we going to start geometry with Euclid, and just begin pre-algebra. Next year, we'll work on geometry and algebra simultaneously, with geometry getting the lion's share of attention (I'm following the suggestion in A Liberal Arts Education by Clark and Jain, to let geometry come first). I'm pretty sure we'll finish (by the end of high school) geometry, and algebra I and II, and I'll probably have her do at least 1/2 of a consumer math course for practical knowledge. It's plenty for a high-school transcript, and if she finishes with her love of math intact, that matters to me more than credits on her transcript. She'll be well prepared for whatever higher math she wants to pursue, and there will be plenty of time for it. "Slow down" is now my biggest suggestion for math. :)

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OH this is so good. Thank you for "confessing" where you are in math with your daughter. I agree with all your shared, but agreeing isn't the same as action! When my son turned 15 I became so anxious because he hadn't crossed into algebra yet. But you know what, he isn't having a hard, frustrated time working on it! I still have my younger children doing their basic operations time-drills, but making the jump to preparing them for algebra and geometry seems to be a trouble spot for me. I so agree about the ability to do the process doesn't mean perception is present.

When you exemplified 7 + 2 doesn't mean the readiness for 9-2 or 17+2 it made me think of Common Core. As a 47 year-old adult, I love the idea of breaking down 17 into: 10 and 7, in order to mentally add the 7 to the 2, because I already know 7 + 2 = 9. But I've been playing with arithmetic for forty years! I really began to notice my comprehension of "numberness" only in the last ten years! No one was really brining it to my attention before then, so I am not saying students couldn't be awakened to it sooner, but not as soon as it being pushed now, nor in the way it's being pushed.

I feel like there is this idea that we are to be competing in these "subjects" with other cultures and nations. We can't compete with Japan or Singapore when their whole culture is arranged and focused differently than ours. We'd have to transform more than our curriculum to get their "results". Which, what even does that mean when we are referring to human beings?

I read that Leigh Bortins, the founder of Classical Conversations, had one son out of four who just couldn't seem to get past algebra. And she wouldn't let him either. He made a "C" all three years. She wouldn't move past it till he mastered it. But he apparently didn't hate math because he applied to an engineering college. They called Leigh to say he received a full ride scholarship! She thought they had made a mistake in the names or something :) . But they said because of his WRITING and his reading list, they wanted him. When she asked about his math, they said they would improve his math. Apparenlty he's done fine too! Amazing! Really goes along with what you shared. Colleges aren't just looking for "scores" or credits. You have to have actually comprehended what you were supposed to have learned, and you have to have a work ethic and the ability to submit to learning. 

I don't want my children to hate learning. I love how you showed the link between your daughter loving math and therefore loving learning. The love of learning is certainly disunited when we harm one area of learning. - Lord have mercy, I don't want to do that to my kids, or myself as the teacher-learner. 

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