Our shorter summer break here in Australia is not without its problems. The kids get between 6-9 weeks off oer Christmas in that time I see almost every child in grades k-4 drop 2 whole reading levels. They forget their math facts and forget h to tell the time too.
When working with Saxon with my daughter I can see if she has one week off she starts finding things harder for a while until she is back in the swing of it ( usually 2-3 sections later) even small breaks count, clearly not as much as losing 2 months of learning but our shorter holidays don’t work either.
Throughout the year Aussie kids get 3 other holidays of 2-3 weeks each. I don’t notice any loss of ability from these breaks other than in the very early stages of learning to read. What we do see though is it takes the kids a full week to settle back into classroom rhythm and stop disturbing everyone else in the room. So for a 2 week break we loose 3 weeks of effective teaching plus the last day before the break ( when the kids can’t focus cause tomorrow is a holiday!) at a minimum Aussie kids loose 12 weeks to holidays private schools loose 15 or more as they have more holidays. Plus the extra 5 weeks of unproductive schooling days.
Yep even we have problems! lol
When I calculated out what David did I decided it wasn’t for us. I do want to accelerate my kids but I decided I didn’t really need a kid doing calculus at age 9. What I needed was a child constantly working above grade level enough that they couldn’t be taught wrongly. I also wanted them done with math by about age 14… I don’t really want them in collage by 12 but at 14 I think it would be great. I have a nearly 10 year old now and the idea of her doing university in 2 years is far too scary for me to consider. She isn’t ready at all and has some growing to do first. I know its possible but its isn’t what I want for my kids. S I calculated out the pace we need to work at to get there and we work at that pace. It’s just a book and a half a year. It is so easy to achieve that we will be ahead of schedule by the time the hard books hit and she will have time to slow down for the harder ones.
She is zipping through lessons in 20 minutes at the moment so we arnt so time pressed as before when it was taking her 2 hours, 90% of that time spend staring out the window daydreaming! :ohmy:
Robert,
I have been following this thread and pondering heavily…
We also live in Texas, and the more I read and research, are going to have great difficulty in finding a suitable solution for my daughter as far as schooling. I have already decided that homeschooling is the ONLY option for us. We do have a few things working in our favor, which I will mention.
Alex is now 3.5, and she lives and breathes math. Part of this is contrived via EL, and part of it seems to be her idea of fun. We are hitting some stumbling blocks now as her ability to sit still/write are light years behind her knowledge/understanding. For this reason, we have a wide range of skills to work on…she can find the perimeter and area of many polygons for example, yet is just as thrilled to play math games aimed at speeding up her addition/subtraction fact recall. We are working on Soroban at home, although she will have a weekly tutor come fall. She thinks Hands-on-Equations algebra work is a reward for tidying her room in the evening, and literally BEGS for a card game called Multiplication War, where the greater product wins the hand.
So far, this is perfectly acceptable. We are working our way through Life of Fred math books, have done a unit on fractions, decimals, and percents, and she thinks that the Art of Problem Soving books, Beast Academy (Level 3A-D) are for three-year-olds rather than third-graders.
Great, She is having fun, we are having fun. Most of our work is total play. There is no way she could sit down and do an hour of independent work, so there is very little chance of skipping grades later…Not to mention the fact that her December birthday has her scheduled to start Kindy just prior to her sixth bday…
So. Is there such a thing as too much? You intentionally slowed David down, but would you have chosen to do this if your were able to primary homeschool him? Or would you have simply expanded the scope, as we plan to do/are doing? We include living math books daily in our reading, her favorite of which is the Penrose the Cat series. This introduces much more advanced concepts in a ‘survey’ fashion…say, binary numbers one day, Mobius strips another, and math with different bases yet another.
To add to the mix, we are based at a private central Texas uni (you can probably guess by my discription of abysmal elementary school options and general location!), and as hubby teaches there will have general access to free uni-level courses as she is ready…even if only on an auditing level.
How would this have altered your plans with David, if at all? What do you think he would have chosen to do, assuming he was old enough to actually have an opinion in the matter:)? I cannot imagine slowing down drastically, although her writing skills are seemingly a natural roadblock, but can envision greatly increasing the scope of learing and hopping a bit to things that are less writing intensive:)
What say you and the collective wisdom of the forum?
Just wanted to let you know those blasted writing skills are James’ current roadblock too! So I completely understand that. 
Mandabplus3,
“When I calculated out what David did I decided it wasn’t for us. I do want to accelerate my kids but I decided I didn’t really need a kid doing calculus at age 9.”
No argument from me. Unless you, as a parent, have some need to have a kid being that advanced, there’s really no reason for the kid to be there (and if you have that need, I feel sorry for the kid). In our case, as I mentioned, we backed off a bit, so he was 11 when he started Calculus. Still, of course, very young, but at that point we were getting nothing out of the Christian school, our attempt to home school had failed, so we figured why not try college full time. He went to a day school (2-year college) about 10 miles from us, so my wife could drive him to classes and drive him home. Not much chance to get in trouble. But a key thing for him was that he absolutely loved being in college, relative to the Christian school, and no one bothered him, ever at the college, whereas he was having some trouble towards the end at the Christian school. He also loved the idea of not having to deal with a police state (the way our schools are now) - if he didn’t feel well, he packed some Advils and took them when he was supposed to - no nurses or shrinks to deal with at the college. Little stuff like that meant a lot to him, as heard plenty of stories from his church friends who were in the public schools. He then went to his 4-year school, which was 20 miles away, but again he was driven there every day, until the happiest day of his mom’s life, when he got his driver’s license. But still no issues there.
So that’s the good side. The bad side we avoided, which would have been sending him away on his own, in any form, to college. He simply would not have studied (and proved that, as I mentioned earlier). So, we played it careful, but it was easy when you had one kid, and one parent available full time for that kid. I realize that most people have/want more than one kid, and that would have greatly complicated things in our case, possibly making the logistics impossible - so delaying would definitely help there.
Overall, you got my message. It’s not how advanced you can get the kid, it’s whether you are the one in charge of how they get their early education, because, in my opinion (and opinion is putting it very gently, I consider it a fact in this country), the education system we have, especially at those ages, is designed to fail, or at least hinder, the kids. I base that on my understanding of the people that run the system and what their overall goals are for this country (and likely most of the West), and having well-educated kids is simply not in their interest.
Kerileanne99,
Tough questions, but I’ll get through them.
“There is no way she could sit down and do an hour of independent work, so there is very little chance of skipping grades later.”
I don’t agree with the above. Getting any kid to sit down and work independently at age 3.5 is a losing battle, but she seems already ready for Saxon 54, which is meant for 9 year olds, and which David started right when he turned 7. So you definitely have time for her to settle down a bit, and still be ahead, and that’s only when you start Saxon 54. From there she’ll be able to whip through the books and get further ahead. You didn’t mention reading, but I assume that she also reads well by now too. If that’s the case, she will be bored to death if she stays at her grade level, based on age.
For me and David, the hypotheticals are tough as I have to go back to my mindframe back then. I do remember vividly thinking: “wow, this kid is so far ahead, what on earth is his future going to be like”, rather than planning anything out and knowing what apartment he will be living in when he goes to MIT. I do remember asking myself what to do next with a kid who has gotten as far as he had gotten. I didn’t actually expect him to end up in college that early, as I didn’t think he would be accepted, based on his age. So I would have basically kept trying to advance him in my area, which is engineering, by having him do higher and higher level math, and then engineering work (from text books) - with the idea being that when he finally did make it to college, it would have been a breeze for him, and with that, he may have been able to really learn the material well. If I wasn’t an engineer, but I wanted him learning engineering, I probably would found an engineer to use as a guide/tutor (and it probably would have been much cheaper than an early-learning tutor, LOL). But that was how I saw it. In college, he would have been able to take a large load of classes and maybe finish up to a year earlier than others his age. He would have had a high GPA, which is critical when getting a first job or going to grad school, and doesn’t hurt for later jobs.
Sorry, but I know nothing of the books/texts that you’re referring to. My background is limited to Saxon, and prior to that, looking at other stuff and not being able to see how it would have helped David (I did try some, but don’t remember anything about them). The other stuff looked intended to keep the kid happy and smiling, but not having to learn. Obviously your child is much different, and those materials seem to work great for you.
I agree with your assessment of your public school options. The advantage you have is that you already understand your schools are junk, instead of having to learn it the hard way (i.e., after it’s too late for the kid to recover), like 90% of the well-intended parents learn. So you do have the right mindframe going in. But also keep in mind the spillover effect into private schools - that was something that I wasn’t ready for and could have hurt David. I figured private schools would be fine, but they are not so hot either. It’s great having the hook into college, and if she stays ahead, just slowly wean her into that school when you think she’s ready. We started by keeping David enrolled in his Christian school, but going to the community college for one class (Calculus). The next semester, he stayed enrolled, but then 2 college classes. After that we tried at our failed home school attempt and I think he was also taking 2 college classes. Finally, we just dumped him full-time into the college, and that worked fine.
As to what David would have done if he had been left to his own devices is a great question. It would have been great if he had a clone, so we could have done a study, but that’s life. Considering that he showed absolutely no motivation to learn prior to me force-feeding him reading starting at 3.5, and then only liking to read after he had learned it, and never showing any motivation to learn math, I would say he would have ended up pretty much like the kids of nearly all of my non-immigrant co-workers (and even some immigrant co-workers). They’re essentially spending most of the 20s now, living at home (mostly), trying to figure out what to do for the rest of their lives. They generally have basic jobs (service industry type), and they dabble in college, but often find they don’t like their path, so they double-back and try again. David’s love for video games would have made even finishing high school difficult, and college impossible - so he would have just been another statistic, maybe finding something that he liked, much later in life than necessary. I also base it on my past, where I just barely able to get the distractions out of my way long enough to get my college degrees (I essentially moved 2 miles from campus my junior year, and lived in housing that was dominated by senior citizens, with no TV or stereo). In today’s Internet/Gaming world, there would be simply no way I would have gotten to where I am, not even close.
That’s why I say it’s the job of parents to steer the kids and straighten them out each time they veer off course, even slightly. Facebook, video games, and other stuff out there is focus-group tested and proven to take kids away from studying. For most kids (maybe not yours, yet, LOL), studying is about one step up from torture. In the past, it wasn’t as bad, as you had schools that actually wanted the kids to succeed, and you had much fewer distractions. But today, if the kid is self-motivated to learn, he still does fine. If not, either parents step in and make the kid learn, or it’s game over.
Alex might not be ready for an hour of sit down study but I don’t see that as too much of a barrier to her starting Saxon. She is ready ( or very close to) so I was thinking how it could be done with our younger el kids…whose parents are happy to do calculus with 9 year olds lol I have a 9 year old and I am struggling to get my brain around that kind of thinking from that age bracket. :blink:
Anyway, if I was doing ti with a 4 or 5 year old I would break up the lessons into chunks. First thing in the morning teach the new concept and work together on the questions for the new concept.
Later in the morning do 10-15 of the 30 practice questions. If 10 is too many then do less. Have a break and finish the rest later in the day. Even doing 5 questions at a time will get you to the end of the book eventually! Starting early gives you plenty of time.
I do think it will be important to questions every day. If you work too slowly there will be too long a time period between when you learn a new concept and when you next practice that concept. If you think you are working too slowly then just revive the recently introduced concept quickly before you start each day. If you could finish a lesson in either 1 or 2 days you probably won’t need review. ( unless you take a break)
If I sat with my then 6 year old she could easily do all the questions but wasn’t able to work independently on it. I decided that since I am time poor, and we have plenty of time, to hold her off Saxon for a while. If you are home schooling then there is no reason to hold them back, or to make them work independently through it so starting early is a valid option. :yes:
If you get to a point where you are finished math at age 12 then worry about that then. Opportunities will present themselves to you when you need them. I only recently started looking for options for advancing high school and found many distance education college/university options that would be safe for kids.
Personally I want my kids to be more well rounded when they start university courses. We aim to achieve that by having them read more quality literature and gradually introducing media. starting with National Geographics magazine and readers digest I was thinking. Your thoughts? My kids are very sheltered at their private school and home life. . I also considered introducing my eldest to regular movie viewing to broaden her horizons…
Robert,
I’m finding that most of the things you say are being confirmed elsewhere. You gave great insights on vacations, and you also said that it was important for an accelerated child to remain level-headed and humble. I was re-reading Alexandra Swann’s book titled ``No Regrets: How Homeschooling Earned me a Master’s Degree at Age Sixteen.‘’ She made comments about vacations, and about level-headedness and humility.
This is what she said about vacations:
While we were not obsessed with our studies we were, and are, conscientious about them. Mother taught us to set high standards for ourselves. The result was that we became our own toughest critics, working diligently on a project until we felt satisfied with it. This attitude not only improved the quality of our work, it also helped us emotionally. Good grades earned through hard work gave us a tremendous sense of achievement and inspired us to work still harder.....Within two and a half months I had completed the first grade. It was now early April, and I could have settled into an extended summer vacation. However, Mother believed that the time away from my studies would ultimately be harmful to me, since I would have a tendency to forget much of what I had already learned. Therefore, she promptly enrolled me in the second grade. I, thus, embarked upon a twelve-month school year, another tradition which continues in our home. I was not required to study on Saturdays or Sundays, and I was given the day off on Christmas, Easter, Thanksgiving, and most federal holidays. In addition, any time I was ill, which was seldom, I had the day off. The rule concerning sick leave was that if I were too ill to go to school I could stay in bed. When I became well enough to get up and play, I was well enough to return to my studies. These were my only vacations. I did not receive two weeks off for Christmas, or spring break, or summer vacation. In fact, I was quite old before I learned that these holidays are observed by most school children.
Though this routine may seem strict, in reality it provided me with an enormous sense of comfort and security. If my routine had been disorganized and haphazard, I might have felt that my life had no direction. Children need constants in their lives, and for many, school is a constant. Whether the school is public or private, they know that they must arrive at a certain time, remain for a certain number of hours, and leave at a certain time. The presence of the studies per se, along with the familiar faces of friends and teachers, can be depended upon.
And this is what she said about her mom (Joyce Swann) teaching her level-headedness and humility towards peers:
Because my emotional development was as important to my parents as my intellectual development, they worked hard to teach me respect for other people for their accomplishments, talents and abilities. They were aware that if I continued to progress at the accelerated rate at which I was working, I would find myself far ahead academically of other children my age, and that this might produce feelings of estrangement. [b]Therefore, they always assured me that while it is true that most five year olds are not in the second grade, basically all people are very much alike, and I was really no different from anyone else. “With proper training, any child with average intelligence could accomplish exactly the same thing,†Mother has often said. [/b]The older I grow, the more I find this to be true, but even then I realized that while my experiences might be different, I, personally, was very much like all other five year olds.(emphasis mine)
By the way, Alexandra Swann is the oldest of the 10 Swann children. All 10 Swann children got their Masters degrees by age 16. PokerDad started a review thread on the Swann children here - http://forum.brillkids.com/teaching-your-older-child/swann-family-10-children-with-ma-at-age-16!-book-review-and-discussion-thread/.
Joyce Swann (their mom and educator) authored a series of education-related articles here - http://www.home-school.com/Articles/columnists/joyce-swann.php
I know we keep moving back and forth on topics here, but I’m currently working through the short book Homeschooling for Excellence by David & Micki Colfax. It’s an older book, but so far cogent none the less. On page 46 under the heading “Efficiency,” David Colfax makes the argument that school, public in particular, is woefully inefficient. This speaks to Robert’s curiosity of what in the world all that time is being spent on…
... there is no question that homeschooling is dramatically more efficient than public schooling.The numbers are straight forward and irrefutable. The child that attends public school typically spends 1,100 hours a year there, but only twenty percent of these - 220 - are spent, as the educators say, “on task.” Nearly 900 hours, or eighty percent, are squandered on what are essentially organizational matters.
In contrast, the homeschooled child who only spends two hours per day , seven days per week, year-round, on basics alone, logs over three times as many hours “on-task” in a given year than does his public school counterpart.
Colfax goes onto say that this leaves a substantial amount of time for other interests.
I’m not sure if it’s been pointed out or not, but school suffers from constant distraction. Anyone that has studied efficiency can tell you that distractions are a large percentage of waste because it takes time to get back focused. In a typical classroom, the class might be distracted several times per hour - and therefore, Colfax’s 220 hours might be overstated.
Article on Lee Binz’s website with interesting insights from a University professor on the importance of Math. (I also noticed the mention of Saxon Math in the professor’s bio.). Link - http://www.thehomescholar.com/blog/homeschooling-curriculum-why-is-math-important/
Kerri, I know this is a late reply, but I just read what you said about Alex. I love reading about her math progress! I think it’s wonderful, and honestly, I don’t think you need to worry about slowing her down. Not that I have any experience in the subject :-). But look at the Robinson Curriculum: when you finish Calculus, you start physics and chemistry, which both keep the math coming. Life of Fred goes through Linear Algebra, and then she can do professional-level computer programming. OK, yes, she’ll be doing all of this at, what, age 7? But then she can decide which one(s) spark her interest and start going into depth in that. With your access to university professors, she can meet mentors who can help her go deeper into whichever one(s) she picks. It’s not like she’ll be unable to have a fun time playing with other kids just because, when they’re doing their multiplication tables, she’s programming AIs. And once you’re into that professional level, there is no upper limit to math. (Assuming, of course, that you have those mentors available.) I mean, people out there make a living doing math all day, so there must be more left to do!
Thought I’d bump one of the all-time great BrillKids threads to point out how constructivist math has hit the news this week in a BIG way (constructivist math is the arch enemy of Robert Levy).
I saw the problem on Facebook many days ago and immediately recognized it as a constructivist approach, while the ignorant parents (on facebook) could only blame “Common Core”. I’m not here to defend Common Core, but to point out just how frustrating constructivist math is for parents. They rightly see it as confusing and adding steps.
My wife is a big constructivist believer and yet even she admitted to me the other night (when I told her this was a big problem with constructivist math) that low IQ kids have a really difficult time with the approach. She says “true.”
If the approach is inferior for someone with lower capabilities, you can ask yourself why. The reason is because it builds artificial complexity that is both superfluous and harder to grasp. Additionally, those with lower working memory can quickly exhaust their stores and get lost (the same problem happens when trying to do traditional algorithms in one’s head). The problem with the lower capable student is simply that the approach surpasses their mental ability. I would argue that this presents an inefficiency in the teaching method.
When working with our kids, we should be looking for the most efficient ways to teach - not the most complex.
This is not to say that learning place value isn’t important (that’s the primary purpose of this anfractuous method), only that there is likely far more streamlined methods. Heck, I never had to do this convoluted “Every Day Math” style learning and I get place value quite well.
Anyway, I post this to show that the pendulum is still swinging in the wrong direction in math education today. If you’re looking for your child to gain an advantage in math, my guess is that this will get easier in the years to come but that remains to be seen.
Hmm…I have to say I disagree on this one, I do not feel the problem is constructivist maths - rather the problem lies with the book publishers interpretation of contructivism. I believe experiential learning is crucial and even more essential for children with lower ability, especially those who are kinaesthetic learners. Most people learn best when they get some hands-on experience the phenomenon they are studying. I feel that the constructivist V rote learning debate in maths is a little like the phonics V sight word debate in reading. Both approaches have their merits and I believe a combination of the two leads to deeper understanding.
BTW The math question in that article is not experiential learning, it is simply complete nonsense.
That’s an interesting view (the parallel with reading). I think it’s insightful and likely right on.
For clarity’s sake, I’m talking more about grades 4+ and especially 9+. I’m not diminishing the value of using manipulatives with our EL and younger kids. My post was more about the “Everyday Math” style approaches to solving problems, which would mirror the viral math problem.
I’m also not for dogmatic approaches on any side. I’ll give you an example. A few years ago, my wife had a learning challenged student with “normal IQ” but low working memory and (can’t recall the exact learning in-proficiency) and this young girl could not gain any ground at all in math. None. My wife went against the norm of the school and just taught her the more traditional methods and the girl was able to make progress. The math specialist at the school couldn’t believe it (because his dogmatic mind wouldn’t accept it). In the end though, they had to dismiss the student from the school (it’s a private school) because they lacked the resources to help her (she had issues in pretty much every subject)… my wife was in tears over the whole thing… and I have to remind myself that “normal” IQ probably means within 1 standard deviation and she was likely below the norm but within that range, which could mean an IQ as low as say 87.
There are other examples where the approach has colossally failed. In Ravitch’s Left Back, I read about a school in inner-city Philadelphia a few years back that had to completely abort the constructivist approach at the school. The school went from child-driven to military style within 8 years. The change had to be made because the students just couldn’t do it. It’s easy to forget sometimes that not everyone has the background, home environment, or genetics to make the learning experience what it can be. Some teachers have overcome (Rafe Esquith, Marva Collins) but neither of them use a constructivist approach and both stress(ed) systematic logical style reasoning to problem solving.
With that said, I can agree that the different methods can co-exist. Math is math. :yes:
This really is an interesting area worthy of discussion. I have been mulling this over since this thread was started way back when.
Over the years, I have worked with many children with Average to Above Average IQ scores struggling with basic maths. In almost all cases, using more constructivist approaches was the key to remediation. I feel that they were moved on to abstract maths too soon without having sufficient time to explore and experience concepts hands-on. I ran a maths club last year and it was incredible to see the kids learn concepts they had been struggling with through playing games. I know if I had tried the drill-and-kill method with them, they would never have grasped what I was teaching as it would have been more of the same. But, through playing games, they became interested by and excited about maths.
I also believe that experiential learning is very valuable even at advanced levels. A watered-down version of it is drawing a picture to break down a difficult problem - I was still doing this when I was studying maths at uni!
Sophie started Singapore Maths recently and I am very interested in the way they lessons are laid out going from concrete to pictorial to abstract for each task. I do not know if they continue this throughout the levels but it is certainly there in the early levels. This is constructivist teaching at its best.
Constructivist approaches are also crucial in science. For example, many people with understand a concept simply by reading it, most people will understand it better by also doing a hands-on experiment, and a few people will ONLY understand it once they have done the experiment.
Here in Ireland, constructivist math has been around for a while but I don’t feel it was ever TRULY adopted, to the children’s detriment. Children still learn maths facts off-by-heart, which I believe is a good thing; however, some kids, especially those with working memory difficulties, cannot hold this information in their minds long enough to successfully manipulate the problem in their heads. I feel that if they were following the concrete-pictorial-abstract format of SM, they would be able to overcome this deficit.
I haven’t read the book Left Back. However, I do have some thoughts on the area. Some authors confuse teaching methodology with school philosophy. Constructivism/discovery learning does not mean child-led, it simply means to explore the world in a scientific manner, testing hypotheses rather than accepting what you are told as dogma. It does not mean loose discipline. In fact the opposite is true as it takes discipline to operate as a scientist, working methodically, thinking creatively etc.
The story about the math specialist in your wife’s school is very sad. It shows the danger and arrogance of believing there is one right way as it blinds you to other possibilities. It’s like the anti-EL people, they believe so strongly that kids are damaged by EL that they cannot take in any evidence to the contrary. In a similar vein, I was reading an old thread on the WTM forum discussing the Robinson curriculum. It quickly descended into a heated debate re whether using the RC constituted neglect simply because the child was expected to work autonomously. I found the whole thing bizarre as the posters minds were so fixed on their own position it meant there was no possibility for them to learn from one another’s viewpoint. Thankfully, it is the opposite here on BK and I feel I learn most from those who hold different viewpoints to my own as it helps me to think critically about my own position and to see the merits in other ideas and methods.
ROAR!!! Did I hear “constructivism” somewhere?
Nice to see this thread light up a bit, it’s been a lot of fun. As always, I have to qualify my comments by stating that my sample size is one person for math (and basically one person for reading). In David’s case, I tried and tried to teach him addition using drawings and objects to allow him to visualize the very basic number facts. I’d ask him if there were 2 apples here, and 3 apples there - how many total applies are there? SEVEN! (of course). I even have a video of us at a Miniature Horse farm counting the horses. He says “one”, “two”, “three”, “four”. I ask him how many total - he says TWO! Hopeless.
I gave up on that approach and then hit him with the raw numbers. No dice there either. Finally, I used a number line - so he could count his way on the line to help him get to the answer. That actually worked. Then I started deleting numbers from the line and leaving tick marks - he adjusted. Eventually I told him to use the “number line in your head” - he did, and then slowly he learned the addition facts without having to count. Multiplication tables, for whatever reason, was a breeze for him. Anyway, that’s my little story.
By the way David’s doing fine. He’s living in New York City, working for a large company as a computer programmer (about the only skill I didn’t teach him, at all). Without getting too specific, they are paying him well, as he has his own 0.5 bedroom apartment (kind of a cross between a studio and one bedroom) in a really nice neighborhood in Manhattan (although it is a 4-storey walk-up), and a 5 minute walk to work - he’s also saving up a bunch of money. And he (finally) gets to see his grandma in New Jersey a lot.
He’s visiting us (here in Texas) this week to work on our cars and do some plumbing repairs (my back’s a bit messed up, so we put him to work). But he is having a great time here and it’s really nice to have a 19 year old come home to visit without asking for money (LOL).
it’s great to have you back Robert - I was wondering if constructivism would be enough to bring you back!
Congratulations to David on his job, you must all be very proud. He really is a shining example of what is possible with dedication and planning.
So, back to the controversial topic at hand…I am in no way saying that experiential learning is the only or even the best way, simply that for some children it helps them to solidify concepts. I can say this with confidence as my informal sample size is in the hundreds. I fully appreciate and respect the fact that it did not work for David and I feel his case is a good example of how you need to explore different methods before finding the best way for each child. My daughter is just beginning her formal maths journey and, at this stage, she benefits from using her fingers or draw pictures to aid her computation. She is quite motivated to drop these aids so she sometimes needs a little prodding to use them if she is stuck. At some point in the near future, I expect that she will progress to visualisation along with automaticity in maths facts.
BTW, I would consider your approach with the physical numberline moving towards the visualised numberline a little constructivist as it involves experiential learning to grasp an abstract concept! (Now I really will hear you roar)
Naa…valid point. Using a number line is a manipulative, at least based upon my understanding.
One thing I meant to mention was that I worried that he would not understand the meaning of what he was learning…be it math or reading. Sure, he might be able to add 2 and 3 - but what does that mean? Likewise, maybe he could read big words - but he might have no clue as to what they mean.
Then I figured his school and social activities would fill in the gaps that I was leaving - and that did work. In fact, it becomes a lot easier to expand vocabulary if you’re not struggling to be able to simply read the word (similarly in math).
I have an old saying, “Do whatever works”
That’s the message I take from the discussion. Thank you seastar & Robert. I didn’t realize you were able to transition to a mental number line - that’s great! I know that Pete Weatherall incorporates the number line on one of his DVDs.
Last I had from you Robert, it sounded like David was pondering the big move to the Big Apple. I’m glad he did and it’s all working out; I especially liked the part about him saving money. Just think of it this way, at 19 years old most of his peers would be going into debt and foregoing wages to do it. David gets to live independently, enjoy a nice stroll to the office, gain work experience, and make connections where they count: in the real world!
I’m currently working on the phonics with my (he’s now 21 months!) little boy and he’s doing well - though lately he’s needed a bit more work to get the patterns down than he did earlier. I think it’s just because he had a lot of exposure to the easier stuff for many months but now it’s getting real… words like “boast” and “grind” which are fairly complicated ideas for a kid still one year old. I mention this only to say that I’m already looking forward to the day we read Hamlet! I’ll make sure to take a video and put it in this thread for you (but give me a year or two to do it)
Poker dad! Shame on you! Two year to hamlet! you are short changing your son lol lol lol
So my two cents…
Well I think math needs to be a bit of both. The way I see it kids need to be given a good solid dose of just do these sums. The purpose being to build memory, speed, resiliency and to continue the march forward. This is where Saxon shines. It is constantly moving forward. Still reviewing but my kids get to learn something new each day as well as consolidate and improve depth in learnt skills. It is endless math questions building mathematical thinking and giving solid practice in copious amounts.
Now constructivist math is real world math. It’s the type of math we face in our everyday lives. I believe that’s what it’s supposed to be anyway. We can see the apples we bag, we can hold the milk and cream and determine their weight. It has merit in the real world. It has less merit in the classrooms of the bigger kids. Usually because the questions are so far removed from the children’s realities they could never actually experience them. It is valuable for the first couple of years of school. But shouldn’t be all that is on offer. Constructivist math takes too long to do enough problems to ever become fluent in numbers. It can help a child learn to think mathematically, so they might be able to tell you how to get the answer but perhaps they don’t have the skills to get there in a reasonable time. This is of course assuming it is even being taught properly…which sadly rarely happens as the kids have always got the manipulatives and step by step procedures that TELL them how to get the answer. Rather than giving them the manipulatives and having them figure it out themselves. ( which clearly has more value)
It’s interesting that as soon as you mentioned the number line I realised that at is how I always did my math facts, on a number line in my head. Learning math facts by rote was never in my school curriculum so I never learnt them. I figured them out on a number line in my head until my first child was born and my brain went very soggy and I started playing math computer games to get it working again ( brain training really works on baby brain, lol ) now they are automatic I see the value in my kids learning them, so we do
Now as for working memory deficiencies, well unless it is a specific brain injury ( and then only in some cases) it is a developable skill. If it’s working memory holding kids back then teach them that skill first! Spend the time working to increase their memory, then teach the math. It’s bound to be quicker.
Interesting. I do math facts with my fingers when I am doing it mentally. I tap my fingers where no one can see. And I use dot formations, like those on a dice, if I am writing them. I just lightly tap my pen down, not marking, on my paper in the dot formation. Number lines are awkward for me as they are a relatively new technique, but I see the merit. I used to have really automatic recall but over the years my brain is sloppy. Honestly, I seldom ever use math. Pretty much only when I am shopping and I round up prices so much as it is easier and if I forget something I am not too far under. I always underestimate the final price. It feels like winning the lottery at the check out.