Better-Late-Than-Early Folks, Advise me on Math, Please!

[LostintheCosmos]

If you delay starting a formal math program, when you do start and what do you use? Do you do anything in particular to prepare your students for the transition? 

 

Saxon 54 seems to be the traditional choice for families starting formal math a bit later, but I'm hesitant because of childhood Saxon trauma.  :laugh: Also, it seems like Saxon has changed a bit since the good old days. Any other options people have had success with? Or can someone persuade me that my anti-Saxon prejudice is unjust? 

[maize]

My oldest started with Math Mammoth 2B when she was 8.5. She took about two years to get through the next several levels--I think through 5B? Then we moved on to other things.

 

Math Mammoth was a good fit for her. We didn't do every problem, I assigned them based on how much practice she seemed to need with each topic. Also, I didn't just move through the books in order--I would assign two or three pages a day but often from different parts of the worktext, so maybe two from multiplication and one from geometry. I cut off the corners of finished pages to make it easy to see what had been completed and what had not.

[Farrar]

Not that late, but one of my ds didn't really start a math program until near the end of first grade. He started with Miquon. It worked really well for him.

 

ETA: I do think Miquon (because of the threads system) is potentially a good program to use to bring a late learner up to speed or just to have a gentle start to math. If you want something more traditional, I would guess that Ray's or Strayer-Upton would be good Saxon alternatives.

Edited October 26, 2016 by Farrar

[birchbark]

I start in third grade with Strayer-Upton's first book, which just happens to begin at the third grade level. It begins with addition, and no previous knowledge is necessary.

 

I do some oral story problems with the kids in 1st and 2nd grade, using the first half of Ray's Primary with some chocolate chips for counters. But it is mainly for providing a fun association with numbers. Very hit and miss. Totally unnecessary for beginning in SU.

 

I am loving SU. It covers grades 3-8.

 

[PeterPan]

Just as a sort of aside, if there's a *reason* your Saxon experience was so bad (like you have dyscalculia or vision problems or ADHD or...) then your dc might have it too.  And the problems might make you more prone to WANT a delayed math approach or make the dc seem more "not ready" when in fact there's an actual issue they're bumping against.  

 

It would just be something to think through.  My ds has SLD math (among other things), and I use very alternative methods with him.  We do Ronit Bird games, lots of living math around the house, games that use math, and some Daily Warm-Up worksheets from Teacher Created Resources.  I can't fathom doing NO math, and I think even delayed math people advocate some form of contextualized, life-based math, yes?  Like they're not saying do NOTHING.  Family Math is another good one with terrific, terrific games.  It's just that little things (what is bigger, recognizing coins, etc.) are very hard for my ds, meaning rote math is way less important to me than just being able to do it in LIFE.  But really, most of your grade-leveled math can be done just with life for several years.  

[Ellie]

I didn't get to delay older dd, because I sent her to school when she was five, but I certainly delayed younger dd. We counted things, and learned to read a calendar (because I bought calendars for the dc each Christmas) and tell time (because we bought analog watches for them). She was curious about money, so I put a bunch of coins in a jar and she played with them and learned their values and counted them. We did some math when she was eight (because long story), but she hated the text we were using and so we put it away around October, maybe November, and I didn't replace it. I did eventually pick up a couple of cute workbooks at ToysRUs or somewhere. :-)

 

She did some of Math 87 when she was about 14. She took the placement test at the community college when she was 14 and placed into pre-algebra (not a college-level course); she took it the first time and dropped it because she didn't like the teacher; took it again and aced it, then took algebra 1, algebra 2, and statistics and aced them. That was all the math she needed.

[LostintheCosmos]

Thank you all for the suggestions so far. Two clarifications: first, we use and practice math every day.

 

Second, my experience with Saxon was that it left me thinking I was very good at math until I met people who were actually good at math. Now, apparently people do come out of Saxon with good conceptual understanding, so it could be that the real weakness in my math education was the prior foundational work, and on that, my children will be ahead of me. 

[Spy Car]

Start at 4 (or so) with Cuisenaire rod play, and don't miss out on the critical window of early learning (in a fun way) due to some misguided ideology.

 

Bill

[maize]

Start at 4 (or so) with Cuisenaire rod play, and don't miss out on the critical window of early learning (in a fun way) due to some misguided ideology.

 

Bill

OP was asking about formal math instruction Bill, not about avoiding developmentally appropriate activities with young children. There is no critical early childhood window in which texbooks and workbooks are required.

[maize]

Thank you all for the suggestions so far. Two clarifications: first, we use and practice math every day.

 

Second, my experience with Saxon was that it left me thinking I was very good at math until I met people who were actually good at math. Now, apparently people do come out of Saxon with good conceptual understanding, so it could be that the real weakness in my math education was the prior foundational work, and on that, my children will be ahead of me.

Math Mammoth worked well for me as a conceptually strong program that could be accelerated as needed. Other good options for conceptual understanding would be Singapore Math or Math in Focus, also Beast Academy though I prefer to use that more as a supplement. For pre-algebra, we like Jousting Armadillos and Art of Problem Solving; there are lots of good options at the high school level.

[wapiti]

Thank you all for the suggestions so far. Two clarifications: first, we use and practice math every day.

 

Second, my experience with Saxon was that it left me thinking I was very good at math until I met people who were actually good at math. Now, apparently people do come out of Saxon with good conceptual understanding, so it could be that the real weakness in my math education was the prior foundational work, and on that, my children will be ahead of me.

So you're not a Saxon person. (Join the club!) There are many other excellent choices that you may find are a better fit for your family if conceptual understanding is important to you. Some kids presumably intuit concepts along the way in saxon's learn-via-repetition philosophy while other students may get further and deeper with an entirely different approach. There are loads of options that are not saxon. Edited October 26, 2016 by wapiti

[Spy Car]

OP was asking about formal math instruction Bill, not about avoiding developmentally appropriate activities with young children. There is no critical early childhood window in which texbooks and workbooks are required.

 

Delay it too often the road-to-ruin and an excuse for educational neglect. Those are bad paths. not being real about this is a shame in the home education community.

 

"Formal" (in the learning context) means intentional and methodical, which are great ideals in early math education.

 

"Formal" does not mean using developmentally inappropriate means, despite the assault on early education by zealots who'd lead parents down a bad path.

 

There is a critical window for learning, and children should get deep enrichment from a young age using developmentally appropriate means in a deliberate fashion. Neglect is injurious to young children.

 

Bill

[Epicurean]

The only reason I can think of for Bill's posts on this thread is that his high horse is so high that the atmosphere is thinner up there where he sits.

[maize]

The only reason I can think of for Bill's posts on this thread is that his high horse is so high that the atmosphere is thinner up there where he sits.

Ah well, we all know that Bill is THE expert on all things educational. I'm sure he has decades of serious research experience and many published studies under his belt :D on top of that, he has surely homeschooled several dozen children. We must bow to his superior wisdom and experience (especially when he entirely ignored the question asked).

Edited October 26, 2016 by maize

[Spy Car]

The only reason I can think of for Bill's posts on this thread is that his high horse is so high that the atmosphere is thinner up there where he sits.

 

Nah, it is due to a decade of reading this forum and seeing too many threads from parents who "delayed" math now desperate because their little Johnny or Jane is 9 or 10 years old and horribly behind doing basic figures. And it is hard to read about the panic of parents who bought into the siren-song.

 

The negative repercussions of "delay" are a persistent theme on this forum. Especially when post-delay, parents then turn to the driest, shallowest, and most "procedural" math education programs possible. It is a recipe for disaster.

 

Better to start early with fun, effective, and appropriate means that turn a developing child mind onto math.

 

Bill

[PeterPan]

Thank you all for the suggestions so far. Two clarifications: first, we use and practice math every day.

 

Second, my experience with Saxon was that it left me thinking I was very good at math until I met people who were actually good at math. Now, apparently people do come out of Saxon with good conceptual understanding, so it could be that the real weakness in my math education was the prior foundational work, and on that, my children will be ahead of me. 

 

 

Start at 4 (or so) with Cuisenaire rod play, and don't miss out on the critical window of early learning (in a fun way) due to some misguided ideology.

 

Bill

 

Not to perpetuate debate (because I have no clue about SpyCar's horse and don't care), but I agree with him that it's really ironic that you'd swing from one extreme that didn't work (Saxon all the way, little emphasis on conceptual, which obviously wasn't your fault!) to the other direction of waiting on formal math.

 

There *is* an alternative camp that says do living math till later and then come in with formal math, and it *is* a strong, reasoned approach.  You can read about it on the AOPS website.  They recommend Family Math, one of the books I suggested to you.  As I said, I am using an alternative path like this with my ds (for now!), because he is gifted with SLDs.  With his dyscalculia, basics like what a dime is or number sense are very hard, but complex things (geometry, spatial problem solving, etc.) are a snap.  He's considered math gifted with a math disability.  

[PeterPan]

Fwiw, you might like to read some books on conceptual math instruction to bring you up to speed on things you missed with Saxon.  There's a book by Sousa on how the brain learns math, etc.  Ronit Bird has an extremely helpful website and inexpensive ebooks.  They're less than $10 each, and if you read through the ones she offers you'd have learned much of the equivalent of the conceptual instruction in MUS, along with getting lots of great games, etc.  LOVE Ronit Bird.

[maize]

Not to perpetuate debate (because I have no clue about SpyCar's horse and don't care), but I agree with him that it's really ironic that you'd swing from one extreme that didn't work (Saxon all the way, little emphasis on conceptual, which obviously wasn't your fault!) to the other direction of waiting on formal math.

 

There *is* an alternative camp that says do living math till later and then come in with formal math, and it *is* a strong, reasoned approach. You can read about it on the AOPS website. They recommend Family Math, one of the books I suggested to you. As I said, I am using an alternative path like this with my ds (for now!), because he is gifted with SLDs. With his dyscalculia, basics like what a dime is or number sense are very hard, but complex things (geometry, spatial problem solving, etc.) are a snap. He's considered math gifted with a math disability.

But what makes you think that OP is not taking exactly the approach you recommend? She says her kids use math on a daily basis--it sounds to me like the living math approach is precisely what she has been doing, and now she is ready to add in a more formal component.

[maize]

I had a delayed formal math education--nothing really structured until age eight when I started public school in third grade.

 

What I did have was tons of math manipulatives (I thought cuisinaire rods and pattern blocks were normal sorts of toys) a mom who engaged with us in various activities such as cooking, and involvement in a family business where I took cash and figured changed. Conceptually, I was leaps and bounds ahead of my classmates once I started school; for many of them, math meant correctly manipulating symbols on a page to get the answer the teacher wanted. I had a much better understanding of quantities and relationships.

Edited October 26, 2016 by maize

[wapiti]

LostCove, you might get more precise suggestions if we can be a little more concrete about the particular situation in question.  Is this for the 8 y.o.?  Do you have an idea of what the student already knows?  For example, does the student already know place value, addition and subtraction of multi-digit numbers, etc.?  Or do you need to start at an earlier point?  Is there anything else about how your student learns best that might be taken into account?

[Another Lynn]

It's possible the title of her thread is throwing some of us off.  Or maybe it's not.  I'm not sure if her question is about delaying some aspect of math education or about Saxon particularly.  But I am a little sleep deprived today, so the fault is probably mine.  

[Spy Car]

Ah well, we all know that Bill is THE expert on all things educational. I'm sure he has decades of serious research experience and many published studies under his belt :D on top of that, he has surely homeschooled several dozen children. We must bow to his superior wisdom and experience (especially when he entirely ignored the question asked).

 

Wow, that's snarky (hate to have read the unedited version).

 

As it happens I'm very pleased that an enriched early math experience led to my son being accepted into the most advanced Middle School mathematics academy in our school district (of 640,000 students) where he is excelling in a very demanding program that's both accelerated and deep.

 

I'd take that over the incessant failures we read about on this forum where delay followed by low-quality math education leads to total failure. Those threads are heartbreaking.

 

Bill

[LostintheCosmos]

Hmmmm, I guess addressing my thread to the better-late-than-early crowd wasn't signaling what I was hoping to signal. Well, this has been an interesting Rorschach test if nothing else.  :laugh:

 

I am not worried about "catching up" any of my children who have been keep in ignorance of mathematical concepts - that is not our situation. I'm trying to figure out the best way to transition my students from what other folks would probably call "living math" (I don't particularly like that language because it seems to me to still take school math as the standard, but whatever) to studying from textbooks - both the when and the what. By "formal math program" I simply mean "according to established form, custom, or rule." My goal is for them to be able to work independently on a day-to-day basis, but of course, always with my overall guidance and special assistance whenever it is needed. 

 

Maize, your experience confirms my wondering about whether a child grasping concepts or not really has much to do with whether they use a "conceptual" or "procedural" program as much as the real-life experiences they bring to it. I can see how a conceptual program might be able to remediate a lack of concrete experiences to a certain degree and is probably a generally good idea for that reason, but I wonder if it's strictly necessary. I'm not planning on using Saxon, but I'm also not sure that was truly the weak link in my math education - I did place into Honors Calc in college, so I probably shouldn't badmouth it too much. But maybe if Beast Academy had existed back then, I wouldn't have dropped out into the lower track... 

Edited October 26, 2016 by LostCove

[Slache]

I believe most of the curricula available have placement tests so I would pick what looks best and just take the placement test. For independence I would go for a work text like Math Mammoth, Saxon or CLE. I'm a better late than never but my son's not, so while I've thought about this I certainly haven't been there. Beast Academy, Saxon and Strayer Upton all have later starting points, but I don't feel that that's necessary at all.

 

Many that have started later are frustrated by a lack of math fact mastery and Xtra Math is highly recommended in those cases, so I wanted to mention it just in case.

[maize]

Wow, that's snarky (hate to have read the unedited version).

 

As it happens I'm very pleased that an enriched early math experience led to my son being accepted into the most advanced Middle School mathematics academy in our school district (of 640,000 students) where he is excelling in a very demanding program that's both accelerated and deep.

 

I'd take that over the incessant failures we read about on this forum where delay followed by low-quality math education leads to total failure. Those threads are heartbreaking.

 

Bill

I have no doubt that your son is also very gifted. I don't question whether you have provided an excellent education that fits him well.

 

I also don't doubt that the OP of this thread is providing an excellent education for her children. She asked a valid question that deserved thoughtful and relevant responses.

 

Yours, full of assumptions that are in no way supported by her posts, and completely ignoring the question she asked, does not qualify.

[wapiti]

On the independence, that will vary by child and age.  For many kids, math is not a great subject for lots of day-to-day independence.  Perhaps part of the day's math work might be more independent, the exercises, but that'll depend on the attention of the child and the grasp of the topic.  For some, your teaching of the lesson followed by a hovering-nearby approach may work best, regardless of program.  Still other children will be most efficient when you sit with them throughout math time.  Some can handle increasing independence by 4th-5th gr, but others may be more successful with hand-holding up through middle school - very individual.

 

MM has a curriculum option organized by topic rather than by grade level, which can be helpful for starting a topic at a point in time that differs from most sequences and also for filling in random holes.

 

If you are considering Beast, look at the prerequisite skills and fill them in as needed beforehand.

[maize]

I haven't had any that could work independently on math at age 8. One could do MM mostly independently at age 9, but needed me there for BA.

 

Independence may not be the best thing to prioritize for math learning.

 

For independent practice my kids do like the Prodigy math game, I've been surprised at how long it has continued to hold there interest and I like being able to personalize their assignments.

[Spy Car]

I have no doubt that your son is also very gifted. I don't question whether you have provided an excellent education that fits him well.

 

I also don't doubt that the OP of this thread is providing an excellent education for her children. She asked a valid question that deserved thoughtful and relevant responses.

 

Yours, full of assumptions that are in no way supported by her posts, and completely ignoring the question she asked, does not qualify.

 

I'm still at a loss as to what question is being asked.

 

Best I can tell it is how to move from some unknown base to independent study. That's a leap that is potentially fraught with complications.

 

Semantics are an issue in the discussion as well.

 

I'd reject the definition myself, but if "formal" is to mean "according to established form, custom, or rule," then (depending on whose "custom" one is talking about) I'd likely pass. I don't think "formal" is a synonym for "conventional." Otherwise, I'd try to negotiate a common term for teaching (encouraging learning) with intention and with a method in mind.

 

Some of the best ways of teaching early math might fly in the face of "convention" (depending on whose standards we're talking about).

 

I suspected we'd have common ground in the importance of introducing math concepts to children using means that makes it easy for them to grasp the point, that promotes deep understanding, builds autonomy & competence, and offers the appropriate amount of cognitive challenge that will help their minds grow and will make learning fun.

 

Being methodical, intentional, and scaffolding the learning in a way that makes sense for young minds is critical. Better this sort of learning happens as a natural part of life from a young age IMO. 

 

My kid isn't stupid, but he wasn't born fully-formed with some unusual math genius. His gifts were cultivated with intent, with the underlying question if someone born to a gene-pool of Liberal Arts-types could be raised to think like a young mathematician?

 

As to the open question of the OP's, where to go next depends both on where her children are now and what the goals are for the future. The desire for "independent" learning both complicates the matter and IMO diminishes the probability of success. But "living math" could potentially cover a huge range of conceptual understanding, from very deep knowledge to how to measure flour for a cake.

 

Who knows?

 

Bill

Edited October 26, 2016 by Spy Car

[Spy Car]

I haven't had any that could work independently on math at age 8. One could do MM mostly independently at age 9, but needed me there for BA.

 

Independence may not be the best thing to prioritize for math learning.

 

 

Exactly. Especially if they are building on little (or no) foundation. Unfortunately, the "better late than early" model is largely predicated on this sort of double-neglect. Delay, followed by low-quality "procedural-only" independent study.

 

And that's a tragic choice in my estimation.

 

Bill

[maize]

I understood the OP to be asking what would be a good introduction to formal curriculum-style math for kids who have previously been learning in a more organic, hands on, and unscripted manner. Specifically wanting to know what other parents had used in similar circumstances other than Saxon, with which she was already familiar and not exceptionally impressed by.

 

Parents can be quite intentional about exposing their children to mathematical concepts and ideas without ever cracking open a book or following a formal program. I have a six year old who enjoys playing with math, likes to make up multiplication problems to quiz me on, but hasn't yet been introduced to workbooks or indeed any systematic instruction unless you count his big brother reading Beast Academy guidebooks to him as bedtime stories.

 

There will be time enough to learn to put problems in standard form all written down and official.

[wapiti]

Part of the difficulty is not having any idea where the student is at with the early skills, so I'm not sure what the needs are, e.g. has anything at all been done on paper and if so, what.

 

My big kids mostly went from montessori math (very hands-on) to MM grade-level curriculum (gr 4-5 math, at school and/or at home, depending on the kid) to AoPS Prealgebra to secondary math at school.

 

Without knowing more, I'd suggest using either Miquon from roughly the beginning (I'm not sure how quickly this can be accelerated for the older student?) or MM topic books to shore up the K-2 skills.  If the student already has those skills, then there's nothing to worry about.  After that, if you are so inclined, go to Beast or whatever other program around the gr 3 level.

 

Getting a handle on the sequence of elementary topics, which is similar for grade levels across many programs, and comparing that to what you know your child can do, will go a long way toward figuring out what is the best fit and what bits and pieces to use if you'd like to fill in holes before jumping into something at a particular grade level.  Knowledge is power.

 

ETA, should you start a program at a level and it turns out that the student isn't quite ready for the topic, there's nothing wrong with pausing to fill in the prerequisite hole.  No need to fear.

Edited October 26, 2016 by wapiti

[Rosie_0801]

CSMP is gentle, but has some great stuff in it. The minicomputers are even better than sliced bread.

[Spy Car]

I understood the OP to be asking what would be a good introduction to formal curriculum-style math for kids who have previously been learning in a more organic, hands on, and unscripted manner. Specifically wanting to know what other parents had used in similar circumstances other than Saxon, with which she was already familiar and not exceptionally impressed by.

 

Parents can be quite intentional about exposing their children to mathematical concepts and ideas without ever cracking open a book or following a formal program. I have a six year old who enjoys playing with math, likes to make up multiplication problems to quiz me on, but hasn't yet been introduced to workbooks or indeed any systematic instruction unless you count his big brother reading Beast Academy guidebooks to him as bedtime stories.

 

There will be time enough to learn to put problems in standard form all written down and official.

 

And, as I said, I would call any education that is intentional and methodical "formal education." That's true if a textbook or workbook is cracked, or not.

 

My belief is that organic and hands-on math education is invaluable. But I'm skeptical that this sort of rich "math lab" type of learning is what's typical in the "better-late-than-early" model, as the years of reading about the failures and the double-neglect have left a very bad impression.

 

Bill

Edited October 26, 2016 by Spy Car

[chiguirre]

LostCove, BA is an excellent choice. We used Singapore Math and my dd loved it. She's now doing algebra 2 at the WTMA and loves math. We used some Math Mammoth too but dd preferred the layout of SM and they are similar choices. Another possiblity that's free for download is MEP, a British program:

 

http://www.cimt.org.uk/projects/mep

[Spy Car]

Miquon, MEP, Primary Mathematics, CSMP, and the like are all good "conceptual" math programs. But hands-off, teacher-free, independent study-type math programs? Nope.

 

Bill

[Rosie_0801]

Miquon, MEP, Primary Mathematics, CSMP, and the like are all good "conceptual" math programs. But hands-off, teacher-free, independent study-type math programs? Nope.

 

Bill

 

I had a disagreement with Ronit Bird over the mini-computers recently. She thinks they are mere computational devices! :svengo:

[Spy Car]

I had a disagreement with Ronit Bird over the mini-computers recently. She thinks they are mere computational devices! :svengo:

 

Oh dear! :D

 

Bill

[PeterPan]

But what makes you think that OP is not taking exactly the approach you recommend? She says her kids use math on a daily basis--it sounds to me like the living math approach is precisely what she has been doing, and now she is ready to add in a more formal component.

 

That's what I was trying to figure out.  And if that's the direction she's wanting to go, finding more resources is always good.  :)  

 

Sometimes talking things out clarifies your thinking.  Like sometimes you're SO CLOSE and you don't realize the extra little thing that will get you where you're trying to go.

[PeterPan]

And, as I said, I would call any education that is intentional and methodical "formal education." That's true if a textbook or workbook is cracked, or not.

 

My belief is that organic and hands-on math education is invaluable. But I'm skeptical that this sort of rich "math lab" type of learning is what's typical in the "better-late-than-early" model, as the years of reading about the failures and the double-neglect have left a very bad impression.

 

Bill

 

That's why I came back with my point suggesting she do more reading, because, frankly, my ability to feel pretty comfortable doing things in alternative ways is predicated on the idea that I've DONE all this before.  I've taught through all the grades, know where it's going, and I can flex.  I can pull ideas from up and down grade levels and actually TEACH using whatever is in front of me that he's into.  If he's into measuring on a given day, with his autism I can't just say Oh no darling, we're doing money!  Nope, if he's stuck on measuring, measuring is what we'll be doing.  But I know where I'm going and am constantly expanding it.  (measuring leading to fractions leading to decimals leading back to the money I wanted to work on, hehe)  It's called chaining.

 

But you can't chain and you can't do that when you don't know where things are going.  If the person's background is VERY ROTE, they don't even realize what they're missing and what they're not doing when they try to do things on their own.  They're just going to recreate the same, narrow thinking that they were taught with.  To bust out, the op needs help of some kind.  There are lots of great resources, so it's just a matter of trying things.

 

On a side note, I don't underestimate the risk in what I'm doing, sigh.  It's not like I'm going dude, you're awesome woman.  I'm just kinda plastered in the corner because of the SLDs and ASD.  We work with what we've got.  But when I was teaching a dc with only ADHD (people hate that, oh well), I used just a happy, normal concept-driven curriculum (RightStart, later BJU), and it worked great.  I think, in general, most people are better of with curriculum, because their own backgrounds are so shallow that they're likely to learn a LOT with good curriculum.  Good curriculum, conceptually-based curriculum.  But that wasn't what the op wanted, lol.

[PeterPan]

I understood the OP to be asking what would be a good introduction to formal curriculum-style math for kids who have previously been learning in a more organic, hands on, and unscripted manner. Specifically wanting to know what other parents had used in similar circumstances other than Saxon, with which she was already familiar and not exceptionally impressed by.

 

 

If that's what she's wanting, anything would work.  I like BJU, MUS, just normal kinds of things.  When we were doing our math hopping, the most helpful thing I did was buy a dab each from a bunch of different curricula.  That way I could get a feel for them and see how my dd reacted to them without laying out a lot of money.  Also the placement tests for curricula will give you a good sense of how they approach things.  You'd think they wouldn't, but they really do.  You start to see what they emphasize, even for the same topics.

[letsplaymath]

Hmmmm, I guess addressing my thread to the better-late-than-early crowd wasn't signaling what I was hoping to signal. Well, this has been an interesting Rorschach test if nothing else.  :laugh:

 

I am not worried about "catching up" any of my children who have been keep in ignorance of mathematical concepts - that is not our situation. I'm trying to figure out the best way to transition my students from what other folks would probably call "living math" (I don't particularly like that language because it seems to me to still take school math as the standard, but whatever) to studying from textbooks - both the when and the what. By "formal math program" I simply mean "according to established form, custom, or rule."

 

I'm not sure if this is what you had in mind, but I posted a series of blog articles about the original "Better Late Than Early" math educator, L. P. Benezet. It contains a summary of the math his students did each year of school. The transition seemed to consist primarily of measurement (all types) and mental-math word problems.

• Delayed Arithmetic series

[Spy Car]

While L. P. Benezet would have had students delay learning basic arithmetic until 7th Grade, the 7th Grader I live with is graphing trigonometric functions.

 

I don't care how quickly he believed students might have caught up, by time they closed the gap the other kids would be in graduate school.

 

Empowering creative math education is a very positive endeavor. Encouraging delay and neglect on the assumption kids can catch up later, not so much.

 

Bill

[OneStepAtATime]

1.  OP, as I understand it from what you ACTUALLY posted, not the assumptions of some others posting here, you actually do work consistently with all of your children on math (despite some odd posts from someone else to the contrary).  You just haven't started a more formal program yet and wanted to know your options for a good solid conceptual understanding. There are many out there.  Hopefully the suggestions on this thread will help you.  Personally, I found that my kids did better with combining several.  We used CLE/Beast Academy/CTC Math/AoPS Pre-Algebra for Elementary/Middle School.  At one point we also used Math In Focus.  All were good programs and helped in various ways.

 

2.  I think it is unrealistic to look for a math program for a young elementary age student that can be done independently with only overall guidance and periodic supervision.  It is too easy for a child to misunderstand what they are doing and get that misunderstanding ingrained.  Unlearning then relearning material is very inefficient and can really muck a child up.  I would absolutely still be working with a young child daily to introduce concepts, work together through examples, THEN let them try some problems on their own.  After they finish trying some problems on their own, review what they did DAILY to make sure there are no misunderstandings.  Slow down when they need to slow down and pick up the pace when they need to move faster.  If you need your oldest to work independently upon occasion then maybe get something like CTC or Prodigy for practice on the computer but not as the primary program.

 

Good luck in your search.  :)

[vonbon]

2.  I think it is unrealistic to look for a math program for a young elementary age student that can be done independently with only overall guidance and periodic supervision.  It is too easy for a child to misunderstand what they are doing and get that misunderstanding ingrained.  Unlearning then relearning material is very inefficient and can really muck a child up.  I would absolutely still be working with a young child daily to introduce concepts, work together through examples, THEN let them try some problems on their own.  After they finish trying some problems on their own, review what they did DAILY to make sure there are no misunderstandings.  Slow down when they need to slow down and pick up the pace when they need to move faster.  If you need your oldest to work independently upon occasion then maybe get something like CTC or Prodigy for practice on the computer but not as the primary program.

 

This is helpful--thanks.  I'd been a little frustrated lately that DD8 does not seem to be motivated to work as independently on math as I'd hoped.  I've been following the steps you wrote out here (introduce, work together through examples, then some independent work...never thought about reviewing at the end), but hoped the independent work might come a little easier and faster.  (This is partly because I don't think the math DD is doing is particularly difficult for her--just right.  Trying to ferret out if it's an attitude thing, an "I'd-rather-work-with-someone-else-than-alone thing, or...???)

 

This thread lets me know it is normal for an 8yo to be unsure/reluctant about completing all of the independent work alone.  

 

Gathering that the independent part comes along later down the road--

 

More thoughts?  (Not to derail--)

[OneStepAtATime]

This is helpful--thanks.  I'd been a little frustrated lately that DD8 does not seem to be motivated to work as independently on math as I'd hoped.  I've been following the steps you wrote out here (introduce, work together through examples, then some independent work...never thought about reviewing at the end), but hoped the independent work might come a little easier and faster.  (This is partly because I don't think the math DD is doing is particularly difficult for her--just right.  Trying to ferret out if it's an attitude thing, an "I'd-rather-work-with-someone-else-than-alone thing, or...???)

 

This thread lets me know it is normal for an 8yo to be unsure/reluctant about completing all of the independent work alone.  

 

Gathering that the independent part comes along later down the road--

 

More thoughts?  (Not to derail--)

Yeah, perfectly normal.  Lots of kids are not terribly independent at that age.  And in fact, depending on personality, you may have a child that NEEDS that interaction to learn.  My DD does not.  She prefers to function as independently as possible and is not into lots of collaboration and discussion.   DS is the opposite.  He actually retains better, stays more focused, stays more interested if he has someone to bounce things off of, discuss with and generally share.  He does not learn well in a vacuum.  

[....]

If you delay starting a formal math program, when you do start and what do you use? Do you do anything in particular to prepare your students for the transition? 

 

Saxon 54 seems to be the traditional choice for families starting formal math a bit later, but I'm hesitant because of childhood Saxon trauma.  :laugh: Also, it seems like Saxon has changed a bit since the good old days. Any other options people have had success with? Or can someone persuade me that my anti-Saxon prejudice is unjust? 

 

Two of my kids do not use a formal math curriculum (they are also doing living math).  I plan to start using a formal curriculum at Prealgebra - I think around 7th grade.  My daughter is actually ready for pre algebra now (she's 11), but I'm going to wait until next year.  She's enjoying all the math books from the library right now, so I don't see a reason to push it.   I'm also planning to work through Hands on Equations with her before we start pre algebra and I'm really trying to get ahold of the Horrible Maths series (for fun).  She's kinda in her own little world right now, so she's not interested in doing trig next year.   :tongue_smilie:  (Both of my living math girls are planning to major in Fine Arts in college.)

 

I will probably use AOPS Prealgebra, because I already have it and that's what my oldest daughter used (and we enjoyed it).  We plan to take 2 years for the pre algebra book (that's how long my oldest took - it's a huge book).

 

About Saxon...After teaching math 3 or 4 times a day for 8 years, I've come to the conclusion that it's the teacher and NOT the curriculum (sorry, I know that's controversial on this forum).  Two of mine are using the older Saxon high school series and doing really well with it.  I chose it, because it was one of the few programs I could find that has EVERY problem completely worked out in the Answer Book (and was in my budget).  With the geometry especially, I need the problems worked out, so I can see what went wrong if they miss a question.  I don't like the lower levels, because it doesn't look like much fun.  I'm sure it's a good fit for some kids, though.  But, look around - there are a gazillion programs out there for pre algebra and below (it's just high school math doesn't seem to have a lot out there).  

 

Sorry that was long...hope that helps, OP.

[....]

And, as I said, I would call any education that is intentional and methodical "formal education." That's true if a textbook or workbook is cracked, or not.

 

My belief is that organic and hands-on math education is invaluable. But I'm skeptical that this sort of rich "math lab" type of learning is what's typical in the "better-late-than-early" model, as the years of reading about the failures and the double-neglect have left a very bad impression.

 

Bill

 

A lot of homeschoolers use the term formal to mean more of a school-at-home approach or using a formal curriculum (like Singapore, for example).  This is how I always use that term.  My 11 year-old isn't using a formal math curriculum, but she worked on word problems for about 40 minutes yesterday from a book we checked out from the library (about word problem strategies).  Mine are still required to do math every day, even though we don't use a math program.  So, maybe we are all picturing different things.

 

About what's typical...I'm around homeschoolers all week and honestly, 99% of the ones I've met are very rigid school-at-home/co-op-going/Classical Conversations homeschoolers (I'm in Texas).  I've actually never met anyone IRL who homeschools like we do.  Over the years, I have met maybe 2 families like you describe (not saying they're not out there).

 

I don't think this forum is a typical representation of the homeschooling population (based on what I've seen in real life).

[lllll]

nm 

 

Edited October 29, 2016 by 1' n'ye

[maize]

This is helpful--thanks. I'd been a little frustrated lately that DD8 does not seem to be motivated to work as independently on math as I'd hoped. I've been following the steps you wrote out here (introduce, work together through examples, then some independent work...never thought about reviewing at the end), but hoped the independent work might come a little easier and faster. (This is partly because I don't think the math DD is doing is particularly difficult for her--just right. Trying to ferret out if it's an attitude thing, an "I'd-rather-work-with-someone-else-than-alone thing, or...???)

 

This thread lets me know it is normal for an 8yo to be unsure/reluctant about completing all of the independent work alone.

 

Gathering that the independent part comes along later down the road--

 

More thoughts? (Not to derail--)

Down the road, yes. For some kids, far down the road.

 

And it can come and go. One of mine has gone through phases of being able to work fairly independently, then reverting to needing more hand holding.

 

Most kids certainly reach a point where they can do regular assignments by themselves. Some reach a point where they work almost entirely independently with a textbook for a teacher. In the whole, however, humans learn best from other humans. And immature humans work best with someone at their side.

 

Some of this may depend on introvert/extrovert nature--- an introvert may be most comfortable working on their own much of the time, while an extrovert will crave companionship and struggle to focus if it is withdrawn. In that case it may be enough for the teacher/mom/dad to sit nearby working on something of their own.

[BlsdMama]

If you delay starting a formal math program, when you do start and what do you use? Do you do anything in particular to prepare your students for the transition? 

 

Saxon 54 seems to be the traditional choice for families starting formal math a bit later, but I'm hesitant because of childhood Saxon trauma.  :laugh: Also, it seems like Saxon has changed a bit since the good old days. Any other options people have had success with? Or can someone persuade me that my anti-Saxon prejudice is unjust? 

 

 

I can weigh in.  I was an early math mama.  I was diligent.  I ended up with a kiddo that seriously struggled in high school math - Algebra I and II and I felt pretty confident teaching it.  She used Rod & Staff and Saxon.  For high school we had to branch out and try different things.  Life of Fred finally got her through Algebra I and then we just used TT Alg I and II.  

 

Second child, slightly delayed math until 2nd grade - has always loved math, used Foeresters and then transititioned to math at the CC.

 

Third child - I decided to intentionally delay formal math instruction until after age 10.  So she would have been about 6th grade when we picked up TT 6.  Explanations were needed along the way, but essentially, she had no issues.  She's 14 and doing Algebra now with absolutely zero hiccups and I wouldn't say she's mathy.

 

Fourth child - really WANTED to keep her out of formal math but she loves the stuff.  By 4th grade she'd want workbooks for fun. She's doing Saxon right now.  I expect her to get through Saxon's 8/7 this year and then we'll go to Algebra next year.

 

Fifth child - Has learning challenges.  He is using Rod & Staff Math and is 11.

 

Sixth child - 10 and she started formal math this year with Saxon though she did do a little TT the last half of the year.  She's in 6/5.  Had absolutely no problem at all picking it up from scratch.

 

 

All that to say, kids don't live in a vacuum.  They just absorb the concepts of math like addition, subtraction, etc.  My kids play in the kitchen a lot with baking so fractions come readily.  This year we started using XtraMath for "drill and kill" and it's been fun for them because they just haven't had years of tedious math and they are READY to absorb it all.  I've used Times Tales for one particular kiddo as well.  We own a lot of boardgames and Prime Climb and they can play card games like cribbage, Pepper, rummy, etc.  Recently my grandpa taught the 8yo, 10yo, 12yo, and 14yo pinochle. :)  By age 10 they can easily count money without formal math.  It was really quite easy to pick up a 5th grade book, with no formal curriculum prior, and go.  And they have SUCH a good attitude about it.

 

Obviously my experience is anecdotal based on my kiddos.  It's not scientific and it proves diddly-squat.  However, you might find this link useful:

http://www.triviumpursuit.com/articles/research_on_teaching_math.php

 

And there are some other interesting articles over there.

 

 

Saxon

 

My oldest daughter would tell you Saxon was the bane of her existence.  So much so that my other children were scared of it.

Now, my second daughter, who did not have Saxon, played with a few different choices for Algebra I this year before she settled on.....  Saxon. :)

We're about 1/4 of the way through the book this year and she loves it.  

 

I love that they are thorough and consistently teach through skills with repetition.  I think, at some point, I must have owned every math book ever published. ;)  Okay, probably not, but I have owned a LOT of math curriculum and, currently, Saxon is my favorite.  Keep in mind I'm extraordinarly fickle and my attitude tends to change based on test scores. :P   A great place to talk about curriculum is the high school board.  Look at what they are using and with what kind of kiddos (for example their mathy student may not be the best example for your non-mathy student to follow) and then trace the line backwards to fifth grade, kwim?