Rebekahy has a point. For a complete math curriculum, not only do you need to have the ideas down, but you need plenty of practice (the amount will differ kid by kid, but most would have a problem with only 10 problems per concept!) and also plenty of practice with different types of problems, different ways of coming at the concept. I glanced quickly at some of the LOF books yesterday at my conference, and was actually impressed with the size and scope of the upper level books I looked at, but they often had a number of problems of all one type, and then moved on. That is going to be insufficient for a lot of kids. The only section I read closely in the manual was Bayes Law, but even so, there was not enough number and variety of practice for a student to be able to apply it wherever he will be meeting it. Just talking about math is probably not going to get you there, either, unless you are really familiar with Bayes Law and its uses in real life and you really, truly do discuss it (AND stop what you are doing, work out the problems, etc. right then and there to show how it's done!) I like the idea of the problem sets you work as narration :-) The act of knowing. You don't KNOW math unless you can really apply it, and apply it even in situations that are not exactly like the one type in the book. I don't know that a direct comparison to history, say, and living book use in history is exactly apt. I think it more likely to consider math as a foreign language. Which it is--it's a symbolic language with its own rules. Reading stories ABOUT Spanish isn't going to get you to speak Spanish. Speaking Spanish will get you to speak Spanish. Lots and lots of speaking Spanish. A small handful of words you repeated once wouldn't do it. :-)
Math: What to do next?(27 posts) (16 voices)
@pslively - I respect your opinion that LOF is fine as a stand alone curriculum. All kids and families are different. LOF is not enough for my family nor the families of several friends who use it successfully as a supplement. We each must choose what works with our own families.
The fact is that math is different than science and history. Living books are a great addition to any math program and may be enough for some children, but the fact remains that many children require more practice to get those mathematical concepts down. The amount of work a child needs is highly individual.
There are also families for whom a more complete program, for lack of a better term, is useful and beneficial. Some families may be great at "thinking math, talking math..." while others simply need to get the job done efficiently and well. There are many ways of doing this. My way may not be the way you would choose, but that does not make it less valid.
@Rachel - We're working through the elementary series right now. DD11 started at Apples a couple of weeks ago and is in Edgewood now. It has really clicked for her. It's helping her to see why we need to know all of this math stuff. DS8 is currently working through Butterflies. I intend to use the whole series at this point. However the elementary series will simply be a supplement for our family. I own the Fractions and Decimals books, but haven't looked at them closely just yet. DD11 is quickly going through MUS Gamma right now and then quickly through the Delta, too.
Rebekahy & Bookworm - I couldn't agree more with your assessments.
I can see what Pslively is getting at, BUT, again, you have to be intentional as to looking for those everyday opportunities to use math. I'm not saying you MUST have a dozen work sheets on each topic, or even one if you are working with your child orally on a regular basis. What I'm saying is it is going to take effort from you, the parent, to see that those facts get mastered. The book offers a lesson, and you have to take it beyond that and encourage them to apply the concepts in other ways. There is no direction for you as a parent on how to proceed beyond the end of the chapter. I agree that you could use it as the "spine" for your math program and use other things to suppliment it, rather than the other way around.
I actually agree with everything you all are saying. I am not there yet with the "thinking math-y" and stopping right then to figure out a problem that has come up in real life. Like I said, we are still doing our Strayer Upton, our pet shop, and our Miquon. But I would like to look at math more as a living subject, like we do with History or Science. And I would like to quit relying so much on the textbooks, worksheets, etc. There is a reason why all the kids seem to love Fred. I would like to work towards that being our primary method of doing math.
pslively, you might want to consider looking at Math on the Level. It is VERY living in nature and definitely NOT a textbook. http://mathonthelevel.com/
I do have to agree that LOF is fun and appealing (we have Fractions and Decimals/Percents and Pre-Algebra I). Our boys love Fred as wel. I think it goes deeper than one might think, and it does have some spiral review built-in over time. The Fractions and Decimal/Percent books have 30 or so lessons though.
If you order from the publisher's site, Polka Dot Publishing, they have a money-back guarantee. It is hard to find LOF used b/c everyone keeps it and it is priced at less than $20 a book, and is totally non-consumable which makes it super family-friendly.
I also agree with others that LOF by itself might not be enough for most students (for 1 of mine who is math-y it could be enough but we still use the MOTL 5-A-Day review problem concept in addition to using LOF).
The way I use LOF is use it for a time frame (maybe 3 weeks) and then take a break and teach new concepts and then we go back to LOF. This works for us as it allows some independence for our older sons and also time for me to spend one-on-one reassessing where they are and teaching new concepts in depth.
I will say LOF and MOTL work well together.
Hmm. Well, in a way I see what you mean, pslively, but Textbooks Are Not Evil. Textbooks are a tool. In a great many situations, textbooks are not the best available tool. In many cases, living books are. But textbooks ARE sometimes the very best option. In fact, in some areas, there really ISN'T a sensible other option and there is nothing wrong with using them. I really hate to see the attitude that textbooks are always bad, because you are eventually going to find out that you will need them. One can study a "living" subject and still use texts. It's OK. CHARLOTTE USED TEXTBOOKS. Not all the time, assuredly, and it depended greatly on the age of the students and upon the subject being studied, but she did not believe all textbooks were The Devil. There are just some subjects that lend themselves poorly to any other sort of thing, since the subjects are fact-dense. We were talking here this weekend--it's really the case. You just CAN'T put all the data, facts and concepts needed to study an upper-level lab science course in a "story". You can try to find the best-written materials you can, you can use various other options as aids and as high-interest assistance and try to use imaginative ways to explain ideas, but at the very, very bottom, you just are not going to have a "living book" that teaches you all of, say, laboratory calculus-based physics. It'd have to be six thousand pages long to get everything into some kind of story. And it'd most likely be ridiculous. You need the facts, clearly explained. I actually have lots of what I do consider living physics books--we love them! But they do not convey everything we need to know.
All kids might very well NOT love Fred. My oldest kid would have HATED it. Why put math in a story? He did math to get AWAY from stories. This is a kid who, when asked to do a nature notebook entry on the wildflowers by the side of our road, painstakingly measured all the petals, leaves, and stems and made a table. This would not be a kid who wanted to learn fractions by a story. :-) All our options in materials are just tools. Textbooks are tools, sometimes very useful ones. Living books are tools, lovely ones which bring delight to us all (or most of us, anyway.) We should know when to use each tool. There is no shame nor harm nor foul in using a text for a subject that works well as a text. We should all be looking at our kids, their learning styles and ages, the subject matter, and take a "long view" of the entire educational process, and then select the best tools and materials. Six year old learning about butterflies? Find a living book. Nine year old learning about George Washington? Find a living book. Fourteen year old doing proofs? Maybe a text, maybe a combination of text and story-line book or other methods of explaining. Sixteen year old doing differential equations? Have a hard time seeing how that's going to happen without a text of some sort, or something based on a text (lecture, etc.) and it's going to take some practice. Probably a lot of practice. Supplementing with different ideas to explain when necessary is GREAT. Depending only on story-like explanations? Maybe not always a good idea.
Very few of the parents on my college-bound email group use ONLY LoF. Although a good number use it to supplement. For many kids there it's been just what they needed to understand. I've heard of many others who really just want a nice text. :-) I enjoyed my look at the LoF statistics book, but I did not buy it. We'll be getting a text, possibly supplemented by video instruction somewhere. It's the most sensible option for my sixteen year old who is headed for college soon, where he will NOT be receiving all his instruction via living books.
We don't need to fear textbooks or avoid them completely or replace them utterly. We simply need practical knowledge of when they are most appropriate and when they are not. And using them at times does not make the subject we are studying dead. It's still a living subject. It's OK.
In regards to what to do between now and September to fill in - Math Mammoth has some really neat worksheets that we have used during the summer before. The Golden series is by grade and the Green series is ordered by topic. Both are the same worksheets. They do not have teaching in them but are just worksheets to reinforce concepts needing more practice.
There are also plenty of sample pages available on the Math Mammoth website.
Wow! What a great bunch of thoughts! I am learning so much. So from what I can tell the biggest issue w/LOF is not enough practice.
My plans for this year were to do LOF with Math Facts Now! online and math games in order to really strengthen skill in the +,-,x./ area. I am imagining my 5th & 6th graders will complete through LOF decimals this year as we did quite a bit of that in their curriculum last year. My question if we go this route is will my 6th grader have a big jump from there to jr high curr?
What things do those of you that have taught upper levels see him needing? What weaknesses do you see in doing this for one year?
Bookworm, I completely agree with what you said. I think I have been misunderstood. I'm not sure what I said to give you the impression that I think textbooks are evil. In fact, I cringe when I hear someone who refuses to use them. Sometimes they are the best option. And there are many very good textbooks out there. Believe me, in my 14 years of homeschooling, I have used many, many textbooks and I am very comfortable with them. My oldest thrived on textbooks for every subject. She was just a textbook and worksheet kind of kid. I did not mean to give the impression that I am anti-textbook. I certainly didn't mean to start any kind of argument, merely a dialogue about how we can better teach math. Math is almost universally dreaded by children, and that bothers me. It should not be so. I will be more careful with my words next time. I certainly did not mean to offend you or anyone else.
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