Methods of teaching math

[Annie Mac]

First off, my LO is too young for any sort of schooling, but HS will definitely be in the mix when she reaches the age where I need to make a decision. I just read this article:

http://www.npr.org/2011/03/05/134277079/the-way-you-learned-math-is-so-old-school

and found it fascinating! The idea that you need to build an algebraic way of thinking so that the kids will be able to function in a sophisticated manner in our computerized world. Just wondering how you all teach elementary math? And in general, are you teaching things the way you learned them or another method? 

[Wild Iris]

I think you will find most contemporary math curriculum teach elementary algebra concepts, and the concepts are presented in an age appropriate manner. I wrote a review of math curriculum you may find helpful, or at least a place to begin looking at the different types of curriculum on the market.

Homeschool Reviews and Resources: A Review of Homeschool Math Curriculum

(Sorry this is kind of a double link to my blog then it links through to HubPages, an article writing site.)

Not every curriculum includes math drill on basic math facts. I've found having my kids know their math fact quickly encourages their enjoyment of math. I just wrote about this at my blog too. Figuring out how you want to homeschool before your kids reach school age is an excellent idea. Post back if you have any questions.

Iris

[lach]

The "new math" that article is talking about (which really can't be called new anymore: it's been popular for at least a decade) is one of the primary reasons I want to homeschool.  It's been an unmitigated disaster.

http://d-edreckoning.blogspot.com/2006/09/its-official-everyday-math-sucks.html

(the other main one is TERC math.  If you google "TERC criticism" or "everyday math sucks" or something like that, you'll find a ton of articles)

I don't know what I'll use yet: probably Saxon or Singapore.

[luv my 2 sweeties]

I'm not sure the npr piece is specifically referring to "Everyday Math" -- the curriculum in the article Lach linked to.  I use RightStart with my kids, and from talking to some of my school mom friends, it sounds like many schools are using a similar "understanding" based approach.  Singapore also emphasizes this kind of approach and is an excellent curriculum.  I have to say that using RightStart, my kids are *way* ahead of where I was at their age in their understanding of basic mathmatical concepts and how to manipulate numbers.  I may have memorized my multiplication and division facts a little earlier, but if they don't know a given fact, they have about 3 or 4 methods of figuring it out that DO NOT involve counting on their fingers, which is what I always had to resort to!  They do have to memorize them, and they do, but I'll take depth of mental resources over rote speed any day.

The multiplication example in the NPR link is a good example of what I mean.  When I was in 3rd grade, I would not have understood why the second example works.  (I didn't understand why the top example works either, but I could execute the algorithm.)  My son is 8 (3rd grade age) and is just now learning multi-digit multiplication.  RightStart teaches a way that is in between the 2 examples, but my son would be able to look at that second NPR example and understand why it works.  In fact, we "discovered" that that method works while doing an exercise in finding area in a previous lesson.  It was a real "ah-ha" moment for him.  (And kinda for me too!)

So I think it depends on what "new math" you are talking about.  I have a friend whose children's school is using Singapore! 

[Annie Mac]

I wrote a well-thought out response, but the Internet Gods decided I shouldn't post it. Grr! I'm trying again.

Can the math methods be distilled into 3 basic camps? As in

1) Old School (Singapore?): reliance on rote memorization of tables and formulae. This is how I was taught, and it served me very well until junior high when they started throwing more complex calculations and formulae at me. Once I fell behind a little bit, there was no regaining ground for me and I went on to fail just about every math course until I was finished high school. Interestingly, I took a first year college math course about 8 years ago and I aced it -- during the coursework, when I could look up the formulae I needed. I very nearly failed the final though because I couldn't remember the steps on my own.

2) Terc: math using manipulatives. Focus on understanding the basic underlying pattern of numbers vs memorizing tables and algorithms. 

3) The math the NPR article talks about: focus on the algebraic principles. I don't much else about it. Except that, judging from the example in the article, it's kind of how I do math in my head. Despite being pretty horrid in school in the subject, I ended up in a job that required quick numerical calculations all the time. Yes, I had a calculator, but eventually I taught myself a way of quickly doing the math in my head. It was actually easier sometimes than figuring out how to ask the calculator to give me the right number. 

Do those represent the main pedagogical methods these days? What am I missing here? 

Right Start sounds like a good program, kind of marrying several concepts together. I do like the idea of teaching the underlying concepts to the kids. Memorization is helpful, but to have the tools that will get you there even on your own...I like that!

[moominmamma]

Originally Posted by Annie Mac 

Can the math methods be distilled into 3 basic camps? As in

1) Old School (Singapore?): reliance on rote memorization of tables and formulae. This is how I was taught, and it served me very well until junior high when they started throwing more complex calculations and formulae at me. Once I fell behind a little bit, there was no regaining ground for me and I went on to fail just about every math course until I was finished high school. Interestingly, I took a first year college math course about 8 years ago and I aced it -- during the coursework, when I could look up the formulae I needed. I very nearly failed the final though because I couldn't remember the steps on my own.

2) Terc: math using manipulatives. Focus on understanding the basic underlying pattern of numbers vs memorizing tables and algorithms. 

3) The math the NPR article talks about: focus on the algebraic principles. I don't much else about it. Except that, judging from the example in the article, it's kind of how I do math in my head. Despite being pretty horrid in school in the subject, I ended up in a job that required quick numerical calculations all the time. Yes, I had a calculator, but eventually I taught myself a way of quickly doing the math in my head. It was actually easier sometimes than figuring out how to ask the calculator to give me the right number. 

Do those represent the main pedagogical methods these days? What am I missing here? 

I don't think many math programs fit into any one of these categories. For instance, I would never portray Singapore as "old school:" in fact it's very far from that, IMO. There's no speed drill and next to no repetitive practice of "facts," algorithms are taught very conceptually, talking from the earliest stages about "creating [place value] units of higher value" and such, mental math exploits commutative and associative properties, and so on. Although not required, manipulatives are used quite extensively with it in the classroom and the home instructor's guides encourage their use, and the explanations use symbols in place of manipulatives and numbers, very much a manipulative-friendly and para-algebraic approach. And their system of bar diagram solving of complex problems introduces algebraic type math at the early 3rd grade level. And Miquon Math, which I'm also very familiar with, is deeply into both your #2 and your #3 -- and it's been around since the 1960's.

My own feeling is that focusing too heavily on any one type of approach will become problematic. The best programs have a melding of all three elements, emphasizing manipulatives heavily at first but incorporating logical problem-solving and various algebraic-type approaches to arithmetic along the way, gradually bringing in some rote learning and drill near the tail end of the K-5 years if children have not already naturally gained speed and fluidity through repeated use of their arithmetical skills.

Miranda

[emski4379]

Originally Posted by moominmamma 

My own feeling is that focusing too heavily on any one type of approach will become problematic. The best programs have a melding of all three elements, emphasizing manipulatives heavily at first but incorporating logical problem-solving and various algebraic-type approaches to arithmetic along the way, gradually bringing in some rote learning and drill near the tail end of the K-5 years if children have not already naturally gained speed and fluidity through repeated use of their arithmetical skills.

Miranda

Any suggestions on which you consider the best?

[moominmamma]

Originally Posted by emski4379 

Any suggestions on which you consider the best?

Well, not sure about "the best," but I can say that we've been very happy with quite unstructured, mostly lab-discovery-based use of Miquon Math, then gradually transitioning into more structured use of Singapore Primary Math at about the 3rd grade level (2B / 3A). Augmented by lots of mathematical explorations through daily life, literature, games, conversation, etc.

Although I haven't used it, RightStart seems to have a reputation of being a good balance of approaches too. We stayed away from it because it doesn't integrate the operations early on, which my kids were already doing by age 4 or 5, and that made placement a problem as a result. (It's also a lot more expensive.)

Miranda

[luv my 2 sweeties]

Originally Posted by emski4379 

Any suggestions on which you consider the best?

The best math program is the one that works for your child!  I've only used RightStart and have found it well worth the expense.  Even if I had to re-buy everything today, I would do it -- that's how much I love it!  Plus, if you have several children, you get to use it more than once; if you only have one, the resale value of the manuals is high.  RightStart pretty much does just what Miranda describes in the paragraph you quoted above.  While they do have transition lessons for children moving to RS from another curriculum, and I know people do have success switching into it, it strikes me as a program best done from the beginning or near the beginning. (Level A or B)  I am just so impressed with the depth of my kids' math sense thanks to RS.  I've had one child complete the program all the way through Level E, and another who will finish Level D this spring, so I'm pretty experienced with it by now.  Another thing I like about it is that it incorporates methods that appeal to visual, auditory, and kinesthetic learners.  The methods that appeal to your child will get used the most, while others will get tossed aside, but at least you go over them all to reinforce learning and to help the child find a way that works best for them. 

I've also heard great things generally about Singapore, Miquon, and Math-U-See.  I would suggest trying to get to see each one and pick the one *you* feel most comfortable with, at least to start.  There was one curriculum I looked at early on (maybe Miquon, but I'm not sure) that just made my eyes swim when I opened it up.  It was highly visual, and I just don't do well with that -- I'm better with a written description *followed* by a simple diagram or picture.  I'm sure I could have figured it out, but why struggle?  Pick one that speaks your language!

Finally, some children will thrive best with less "conventional" math curricula.  My daughter has a friend that struggled mightily in math until they tried a Waldorf math curric.  It was the oddest way of teaching math I've ever seen -- very circuitous and imaginative (and a lot of work for mom!) -- but this girl just embraced it and took off!  I don't think I'd recommend it generally, but clearly it worked for her.