How do I take control of math-teaching?

[Colleen in NS]

OK, that is a weird question, so hopefully this will explain it.

 

I feel like I have an alright handle on teaching writing skills to my kids, with some knowledge gained from various sources such as WTM/SWB's writing lectures/R&S writing lessons. I feel like I have an alright handle on teaching Latin skills, even though I don't know Latin any more than my oldest child - but I've figured out a few things about the language and was able to set up a study pattern to follow. I know how to teach spelling and reading; I'm doing alright with teaching English grammar (using R&S and applying that knowledge to writing and reading/analysis); I even have a sort of handle on teaching art skills here and there, with the help of some books, when we can get to it.

 

But I've been reading those threads about conceptual vs. rote math, and am nervous. Not really, but just slightly. We have been using R&S and I intend to stick with it til we switch to the old Dolcianis for high school. I *have* found that, like 8FilltheHeart said somewhere in one of those threads, that this traditional program *does* teach concepts - and I know this because I have read explanations in it that helped ME understand elementary things that I never understood before. The TM would tell me to make some little chart or manipulative or something, to illustrate what it was talking about, or it would tell me what to say to the child to help him understand the concept. Sometimes, if my dd10 didn't understand, I was able to figure out a way to explain, that she would understand. Or I was able to figure out how to use something to illustrate it. Even now, when she's going through division flashcards, sometimes I will still say to her: 24 divided by 6? (dd hesitates for too long) OK, 24 cookies divided among 6 people? Oh, 4.

 

BUT. Even before reading those threads, I still usually have this uneasy feeling that *I* don't understand concepts really well, and so I wonder if she does. (ds "gets" math very easily - he is one of those who figures out different ways to solve problems, like I read on another thread) So today I asked her some questions to get her to articulate what she understands so far about numbers, addition, subtraction, mult, and div. - so far so good. (she's in R&S 5)

 

But I find that math is the one subject where I can follow the book to teach my kids, but I never feel like *I* have absorbed and understood the concept well enough. Yet because R&S has so many lessons in it, I always feel this pressure to make sure we get our lesson-a-day in, so we can finish in June. I wish I could take the book, take a step back from it, look at it with a bigger picture, and KNOW which lessons are important, which parts of the lesson are important for them to do, and leave out other parts. I've already dropped doing the tests because the review lessons are way longer than the tests and the tests just repeat what they reviewed the day before.

 

Does anyone else do this? Actually take control of the book and pick out from it what is important? I already do stuff like odds or evens, letting my kids answer many things orally, etc. to make it shorter, but I still feel driven by the book, and I somehow feel like I should be driving the book but I don't know how because math is not my strength and yet I WANT to "see the beauty of math" that Jane in NC is always talking about. I also get math activity books from the library, but even with these I feel like I'm skipping through them in random order. I guess I don't see yet the bigger picture of how to build arithmetic skills - this first, this next, etc.. The only thing I'm sure of is memorizing math facts - yes, that is important to me and I'm glad we did it.

 

I'm not really looking for advice on "how to cut down time in R&S" - more in general, how do I teach math while using R&S and assorted library books? I've looked into buying LoF books, but I don't really want to use another program alongside R&S, but I don't mind creating my own "supplementary games/activities/list of skills" type of thing, as long as I see a pattern and purpose and progression in it, and know what to include and why.

 

So, any thoughts? Who's able to do this, and how do you do it?

[Guest Alte Veste Academy]

big-time :bigear:

 

I did find this thread somewhat helpful.

[JennW in SoCal]

I was just talking about this today with another homeschool mom. I "got" basic math and was able to teach it, though had to get creative a few times to help my kids overcome a few hurdles in fractions or long division. I felt comfortable to pick and choose from the main book -- but I was generally picking and choosing *how* to teach a topic. I covered everthing presented in a given text. But as we got deeper into algebra I was blindly following the text book. While I would get things well enough for myself, I couldn't find other ways to explain things to my child if he was stuck. Sometimes I'd search on the internet or look for other books to do a better job of explaining, but we were both frustrated that I couldn't always answer questions.

 

To shorten a potentially long story, my youngest ds, a science and math guy, is taking the rest of his math starting with Algebra II at the community college, and he LOVES it. Loves having a teacher who knows his stuff and can explain things clearly and can answer questions and challenge him. I keep joking with friends that I was "fired" as his homeschool math and science teacher.

[regentrude]

It has been my experience that, in order to effectively teach math, a teacher should have knowledge way beyond the material that is being taught. If the math teacher is just one step ahead of the student, she simply can not see the big picture to the extent it is necessary to teach the concepts well and go beyond simply drilling procedures by assigning and grading worksheets.

So in order to "take control" (I like the way you phrased this), you should work ahead and get a thorough understanding of the math material that lies ahead, not just the material you are currently teaching.

This is, IMO, one of the factors that contribute to poor math teaching in schools: the teacher's inabilities to do math that is harder than what they teach.

I think for math it is not sufficient to follow the book and be just where the student is - you need to math-educate yourself first, and then you can go back and teach math that is below your highest level of math expertise. That way, you will be comfortable teaching and you will be able to judge materials, procedures, assignments instead of blindly following some prescription.

 

If you feel you are unwilling or unable to do that, I would recommend to "outsource" math by using a curriculum that is designed so the student can work without you as a teacher.

[Carol in Cal.]

I look ahead and emphasize things that are coming in science or math.

I have mostly used Saxon, which has tons of practice, and my feeling has been that my particular non-mathy kid needed it.

But I would add in descriptions of why unit analysis works, or practice aspects of the equation of a line, slope, etc. in the car, or practice the quadratic formula in the car, verbally, in addition to the regular Saxon assignments. Also, I often explained the general case in addition to Saxon's specific ones, when I knew that down the road DD would need to know that.

 

She is a kid who benefits from a lot of review, so this extra material being introduced early and repeated often was helpful when she got to it in Saxon.

 

My expectation is that she will have a much easier time with chemistry because of these extra explanations in pre-algebra and algebra.

 

Earlier, whenever we started to talk about changing fractions to decimals or percentages or working with them, I would start by saying, "What is a fraction again?" DD learned to say (and think about the fact that), "A fraction is fundamentally a division problem," and to think of it that way.

 

I should add that DD is really not 'mathy' at all, and other kids probably wouldn't need nearly as much scaffolding.

[Colleen in NS]

Some really helpful replies and links here! Thank you! I can't do justice with replies to you all tonight (national holiday here in Canada, and birthday celebration tomorrow), but I will get back to this in a day or two. Meanwhile, wouldn't mind hearing from more people.....

[onaclairadeluna]

Good questions. I love the reading lists on this site:

http://livingmath.net/

 

She has lists for kids and adults.

 

My favorite-see the beauty in math-adult resource is "The Joy of Thinking" from the teaching company.

[scrapbabe]

Good questions. I love the reading lists on this site:

http://livingmath.net/

 

She has lists for kids and adults.

 

My favorite-see the beauty in math-adult resource is "The Joy of Thinking" from the teaching company.

 

 

:iagree:

 

Ignore the smileys below...my 5 yr old added these.

 

Smiles,

Shalynn

 

 

:svengo::drool5::party::cheers2::willy_nilly:

[Colleen in NS]

big-time :bigear:

 

I did find this thread somewhat helpful.

 

Yes, that WAS an interesting thread that I had never seen - thanks for linking it!

 

I "got" basic math and was able to teach it, though had to get creative a few times to help my kids overcome a few hurdles in fractions or long division. I felt comfortable to pick and choose from the main book -- but I was generally picking and choosing *how* to teach a topic. I covered everthing presented in a given text.

 

This is pretty much what I'm doing, and then trying to get creative if something isn't understood (more the case with dd). I go on a math book binge at the library every few months and try out a few things here and there.

 

So in order to "take control" (I like the way you phrased this), you should work ahead and get a thorough understanding of the math material that lies ahead, not just the material you are currently teaching.....That way, you will be comfortable teaching and you will be able to judge materials, procedures, assignments instead of blindly following some prescription.

 

I think you're right. Although, with going through it with my second child, it is a lot easier to pick through and decide what to have her do. In some ways, ds is coasting this year - he is in the last year of R&S before Algebra, and it has mostly been review and reinforcement. He's getting sort of bored, but I'm not ready to move him on to algebra yet. Guess I should take advantage of this year for figuring things out myself.

 

I look ahead and emphasize things that are coming in science or math.

 

But I would add in descriptions of why unit analysis works, or practice aspects of the equation of a line, slope, etc. in the car, or practice the quadratic formula in the car, verbally, in addition to the regular Saxon assignments. Also, I often explained the general case in addition to Saxon's specific ones, when I knew that down the road DD would need to know that.

 

I do this now with Latin with dd10. I struggled so much with getting ds through LC 1 and 2 because I'd never studied Latin, and I still think those books are very confusing at times; but at least now I can confidently explain things to her and ignore some of what the book is telling me or telling her. I guess I need to learn and incorporate some more math thinking into our lives. I have done this in spurts in the past, when I get math-ish books from the library.

 

Good questions. I love the reading lists on this site:

http://livingmath.net/

 

She has lists for kids and adults.

 

My favorite-see the beauty in math-adult resource is "The Joy of Thinking" from the teaching company.

 

Thanks for linking those lists, too! Another good source with which to reserve library books.

 

Can you tell me more about this TTC DVD? I didn't know it had to do with math; I thought it was more about logic/critical thinking.

[Colleen in NS]

I spend time practicing math on my own and I do the math problems with my kids. I don't rely on the answer key. I actually sit down and do the math.

 

This is just what I'm going to have to do, even if it's just a lesson or two ahead.

[Colleen in NS]

We have been using R&S and I intend to stick with it til we switch to the old Dolcianis for high school. I *have* found that, like 8FilltheHeart said somewhere in one of those threads, that this traditional program *does* teach concepts - and I know this because I have read explanations in it that helped ME understand elementary things that I never understood before. The TM would tell me to make some little chart or manipulative or something, to illustrate what it was talking about, or it would tell me what to say to the child to help him understand the concept. Sometimes, if my dd10 didn't understand, I was able to figure out a way to explain, that she would understand.

 

I think I figured out something. I looked closely at my R&S book 8 that ds is going through, and found that the "introduction" section in some of the lessons actually has questions/discussion that either reinforce previous concept learning, or introduces the current lesson's concept. You see, because ds has taken to math so easily, I would sometimes tend to gloss over that part and get right to the lesson. He understood, we'd talk a bit about it, and I'd assign him his written work. But this is the section where concepts are talked about from different angles, and where questions are asked (similar to how R&S grammar has oral review questions in the TM, that I do religiously go over each day with both kids) that get kids thinking about the ideas from different angles. I checked my other TMs, and this "introduction" section starts in book 6. Good thing dd is not up to that yet, or we'd have had more trouble. It made me resolve to be more faithful even with her oral drills in book 5, even if she complains. Even these will drill things from past lessons, that might not be included in the current lesson. Anyway, I'm going to have a closer look at the intro sections in book 7, to compare to the intro sections in book 8, to make sure I know what ds understands for concepts. I'm pretty sure he's up to snuff in them, but I need to reassure myself. I did go through most of the intro. sections with him today in book 8, up to his current lesson. He understood most things, but I did find a little snag which we untangled, in BOTH of our understandings of the commutative, associative, and distributive laws. Nice!

 

I feel a bit better about all this, and resolved to just stick with the TM a little more closely now. I guess if I do this for my oldest, even though he "gets" math more easily, I will have more confidence myself and be able to teach my younger more easily.