The "Perfect" Math Curriculum - Does It Exist?
Julie Brennan, June 11, 2008, in response to question, "What is the best conceptual currriculum":
People have been asking for recommendations on a one-stop conceptual curriculum, and I've not answered completely. I always have trouble answering this question.
The only perfect conceptual curriculum I've found for my children is myself. I've made myself a better and better resource to my kids by using a variety of resources that make me a better teacher over a number of years. But ultimately I've not found any resource to globally address everything I'd want my children to learn in and of itself, outside of a snapshot period of their development.
Now, this isn't as bad news as it sounds for people who consider themselves not to be math people. Ironically, one of the most revolutionary ideas I learned in homeschooling is that experts are often NOT great teachers. The fact I was good at math did not make me a good teacher when I started homeschooling, it was in fact a liability! I could not easily bridge what I could do and how I did it to my child's level. I had learned a lot on my own, I now realize, through *using* math in context, and not a lot of what made me good at math was taught in classrooms, so I hadn't a clue how to teach it. I had to learn.
There are excellent curriculum resources out there, and the LivingMathForum list has been a great place to evaluate why something is good, why it worked for a learner and/or parent, and for what ages / developmental learning stages certain resources work for. I recall years ago getting many recommendations for Miquon, Math U See and Making Math Meaningful when we were having a terrible time with highly recommended but very traditional and procedural workbook programs. After trying all three, Math U See worked best for our family for the elementary years,
I learned as much as my children, because for the first time I thought about *why* 8 plus 4 is 12, beyond my ability to think it's the same as 10 plus 2 . . . But Mr. Demme on the tapes gave us the rather silly but effective "8 wants to be 10, so it vacuums 2 away from what is added to it . . " I've adapted this for all my kids to understand adding 8's and 9's. There were many other things I learned from those teaching tapes I use again and again. I felt it was a very good conceptual series.
Imagine my dismay when I realized somewhere in the latter elementary years that it wasn't working the same way for us. I thought I'd found the perfect curriculum, even if it was a bit dry at times and we'd already learned to supplement with living math literature. I have no idea if the program has changed, but for us, it stopped being a good conceptual resource. This doesn't mean Math U See isn't a good curriculum; but the format no longer worked and after a time, I felt strongly that continuing to use it was doing more harm than good to my children's attitudes and confidence in math learning. We began looking for other materials to learn upper elementary / middle school concepts for. And the materials we found that addressed our needs in these stages would not have worked well for us in the earlier elementary years.
Even now it seems there is a common theme of this kind of strength / weakness pattern in many curricula, because curricula is not designed for our specific children in mind. Such and such worked well for a certain stage, and then failed to deliver when a child moved into another stage of development. RightStart, for example, generates a ton of fans for early elementary; many people seem to be looking for something else in upper elem. Now, a parent can adapt how they use a curriculum resource if they have the confidence and ability to do so, but it may not be that easy to identify what has changed.
Add into the mix factors of the child's learning style, preferences for independent or interactive learning, and the parent's proclivities, and it becomes nearly impossible to make any kind of global recommendation. I found Ray's Arithmetic pretty recently, and I found it to be something my daughter really likes, and I like, for all the reasons I posted in my review. It does not require a great financial investment, and is resellable if you don't like it. So it goes on my list of things to recommend, but with with qualifications, I see a shift in usability between the 4th grade level and beyond. I still like and hear good things about Math U See for elementary - but it requires more of a financial investment, so you would want to do more due diligence before investing unless money is no object (not the case for most hs families unfortunately). Others love Math On The Level which has excellent features that were brought up in reviews, but a large financial investment is required, which makes it either unfeasible or more of a risk for others. Singapore Math has excellent features that justify its extensive reputation, but the character of their workbooks changes over different levels that causes them to be less attractive to my children, and some parents find it hard to teach even with the teaching guides.
I haven't tried everything out there, but we certainly have managed to cover a lot of territory over the past 11 years! And of course, being a homeschool parent myself, I cannot try out every single product out there, and I don't feel comfortable giving glowing reviews of anything just based on how it looks, personal experience with anything trumps an overview anyday. That's why personal reviews of products I haven't used, either because we didn't run across them, or because they didn't appeal to us due to some feature, are very important to me, the LivingMathForum is a resource made up of members, not just my personal opinions, I know many members who have children with very different needs / strengths than mine who find different resources helpful than I would.
One of the projects I have had on the back burner that I will finish over the next month is a matrix of curricula and resources that have been discussed here, taking into account feedback from members, organized by strengths, weakness and target users. As often as these questions come up, this resource is needed, I know. It will likely generate more questions, but they will be narrowed down.
Anyone can pick up the conversation from here!
I love what Julie wrote here. What really resonated with me is the part about learning how to be a good teacher. I learned all math by rote-got straight A's and never understood a thing! RightStart Levels A and B taught me how to teach the basics in a conceptual way and gave me confidence to branch out and become more eclectic in our math approach. I still lack some confidence, but I'm reading and researching in order to improve my own math skills, and find the most effective way to explore math with my dc so they develop a love for and understanding of it.
I am also just discovering what she finds to be true-that different things will work in different stages even with the same child! One program probably won't do it for most children. That's why you see SO many homeschoolers doing two concurrent math programs (or pieces of two programs.) There is an element of flexibility we need to have in order to accomodate this fact. I am finding that keeping abreast of what is available, even though it may not appeal to me at the time, is important because the need may arise for just such a program or resource later on! (I like the idea of a matrix too.)
I wholeheartedly agree, that the teacher makes all the difference. Knowing this though, seems to lead to the next logical question..how does a hs parent grow as a teacher? The parents I know want some tools to help them and save time for them. As I get to more advanced math, I can see how piecing everything together will not be feasible (am I right about that?) so I am thinking that I will have to "commit" to using one (ok, maybe 2 or 3) resources for a subject.
My question is not meant to short-circuit the learning process for the teacher - but to help steer them to good resources to help them grow as teachers. That is the difference between Homeschool and public school teacher..most hs teachers rely on a curriculum to show them HOW to teach math, but PS teachers do not use curriculum to do that. Well, that has been my experience. And I think, this is as it should be since most of us never give thought to how to teach something until we are faced with doing it. A hs parent is not going to go get a degree in education or even have time for extensive self-study (well, except those of us who love math), so their growth will likely occur as they glean ideas from the math programs they use with their children.
Thanks for all the discussion and ideas. I really want to make it "doable" for folks. What have you (by this I mean anyone on this loop) done to grow as a teacher? Where do you find ideas on teaching math? Maybe these are better questions.
Vicki, I wonder if you read this article? http://libertylyceum.org/articles/mathteaching.shtml
It might address your remaining questions as well as it has specific how-to comments in it.
This ties into thoughts that I have had recently, now that I have the first 3 years of math under my belt for my oldest.
First, I want to again mention MEP, a complete FREE and excellent math curriculum (Julie, you are so right about the cost for some of these programs, and I'd rather spend my money on books and enrichments!) http://www.cimt.plymouth.ac.uk/projects/mep/default.htm
Just starting it, my kids have really liked it because it has a wide variety of short activities in each lesson, some in the workbook, some on the board, some in their heads. I like it because it gently introduces advanced concepts early on and throughout the program. By the end of year 2 kids are starting concepts of multiplication and division. But this is not about the merits of MEP!!!
Second, after 2 years of MUS, which my kids also liked, I realized that Alpha basically teaches adding and subtracting without regrouping, Beta teaches regrouping, Gamma teaches multiplication, Delta teaches division, Epsilon (which was slated for next year) teaches fractions--not even sure if it does decimals and percentages. When I asked moms using other curricula, they say that basically those programs follow the same scheme of things. Would people here generally agree with this?
When I realized this, I had an "aha" moment. I always felt elementary math teaching was mysterious, learning special knowledge in order to perform these mathematical operations, LOL. I guess it all became demystified for me after watching Mr. Demme and reading the experiences here. Now I don't think I really need a curriculum to teach fractions to my child (the recent discussions regarding fraction division was wonderful!) Nor do I need to use MUS strictly to teach the younger two.
I think this is why I am currently drawn to MEP. My kids are not learning just one little concept and drilling on it each day. Instead, they are learning the little concepts through a variety of different activities, and putting them in the context of more advanced ones. More importantly, I see that I do not have to follow it strictly, but rather use it as a "spine" (to put in Charlotte Mason terms) or core resource that I then enrich with readers, manipulatives, and activities. Other people will be drawn to other "spines" based on their needs, like Ray's, or Right Start, or MUS, etc. I guess I no longer have the fear that I will leave something important out that without it their math success will be hindered down the line. Yep, that's what I thought! And it took me being on this list how long to finally "get it?" I guess I had to hear it several different ways and try to apply it before it clicked for me, LOL!
This is a big departure for me, and I'm a bit nervous about it. We'll see if ds#1 ends up learning anything about fractions at the end of next year! Any comments on pitfalls would be greatly appreciated!
Kris wrote: < When I asked moms using other curricula, they say that basically those programs follow the same scheme of things. Would people here generally agree with this? >
Julie: Generally, yes, for elementary concepts, but one thing MUS does differently than many (or at least it did, we used the "classic" version years ago), is delay long division for when a child has a complete grasp on all these ideas. Demme also teaches long division in the context of the presentation of multiplication as the dimensions of a rectangular grid, which I recall thinking at the time was utterly ingenious, because from early on in the course he has you thinking of multiplication in this format, so it tied it altogether. Having come from the first curriculums we tried (ACE and Abeka provided to us by an ISP) which had my son trying to learn the long division algorithm at the end of 2nd grade, I was so happy with this. So was he when he finally revisited it again and was so surprised to find it was easy rather than that utterly confusing procedure he tried to learn when he was 8.
It's been a long time, but I recall MUS also had a clearer way of moving a child into larger number than I see Singapore presenting. But then, Singapore has great word problems and presentation of ratios/proportions that MUS lacked. Nice to know what your tool is best designed to accomplish ;o).
Kris: > When I realized this, I had an "aha" moment. . . . I guess it all became demystified for me after watching Mr. Demme and reading the experiences here. Now I don't think I really need a curriculum to teach fractions to my child (the recent discussions regarding fraction division was wonderful!) Nor do I need to use MUS strictly to teach the younger two. >
Julie: This is exactly what happened to me. I felt I was the winner when we went through those videos with my oldest son. I was equipped with the basics of teaching, and everything I learned from that point on was just added tools to my toolkit.
Kris: > My kids are not learning just one little concept and drilling on it each day. Instead, they are learning the little concepts through a variety of different activities, and putting them in the context of more advanced ones. More importantly, I see that I do not have to follow it strictly, but rather use it as a "spine" (to put in Charlotte Mason terms) or core resource that I then enrich with readers, manipulatives, and activities. Other people will be drawn to other "spines" based on their needs, like Ray's, or Right Start, or MUS, etc. I guess I no longer have the fear that I will leave something important out that without it their math success will be hindered down the line. >
Julie: EXACTLY. I couldn't have said it better myself ;o) Over the years it seemed that if anyone mentioned they "supplemented" a curriculum that meant it was inadequate, incomplete. I have tried to point out that no curriculum was written with *your* child in mind, it was written for mass production, for a general population, and we are in the wonderful position of allowing our children to use the best tools for them.
You may not have any pitfalls with fractions, btw, if this is you how are going about it. I recall thinking fractions were so hard with my oldest. And then when I relaxed and took this approach, keeping in mind the ideas in Patricia Kenschaft's book, Math Power, that some "meadows" require more time than others to master, I haven't considered them a "problem" ever since.